From Leibniz to Kant 3957431549, 9783957431547

Citation preview

Editors: Uwe Meixner · Albert Newen Managing Editors: Philipp Steinkrüger · Pieter Sjoerd Hasper Logical Analysis and History of Philosophy Philosophiegeschichte und logische Analyse

Editors

Uwe Meixner · Albert Newen Managing Editors

Philipp Steinkrüger Pieter Sjoerd Hasper

Logical Analysis and History of Philosophy Philosophiegeschichte und logische Analyse

21

From Leibniz to Kant

Guest Editors / Gastherausgeber

Katherine Dunlop · Samuel Levey

mentis

Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar. © 2018 mentis Verlag, ein Imprint der Brill-Gruppe (Koninklijke Brill NV, Leiden, Niederlande; Brill USA Inc., Boston MA, USA; Brill Asia Pte Ltd, Singapore; Brill Deutschland GmbH, Paderborn, Deutschland) Internet: www.mentis.de Alle Rechte vorbehalten. Dieses Werk sowie einzelne Teile desselben sind urheberrechtlich geschützt. Jede Verwertung in anderen als den gesetzlich zulässigen Fällen ist ohne vorherige Zustimmung des Verlages nicht zulässig. Printed in Germany Einbandgestaltung: Anna Braungart, Tübingen Wissenschaftlicher Satz: satz&sonders GmbH, Dülmen Herstellung: Brill Deutschland GmbH, Paderborn ISBN 978-3-95743-154-7

LOGICAL ANALYSIS AND HISTORY OF PHILOSOPHY PHILOSOPHIEGESCHICHTE UND LOGISCHE ANALYSE

Managing Editors Philipp Steinkrüger, Ruhr-Universität Bochum Pieter Sjoerd Hasper, Universität Tübingen Editorial Assistant: Maja Griem, Ruhr-Universität Bochum Review Editor Markus Schrenk, Heinrich-Heine-Universität Düsseldorf Editors Uwe Meixner, Universität Augsburg Albert Newen, Ruhr-Universität Bochum

Editorial Board Karl Ameriks Jonathan Barnes Kit Fine Paul Guyer Andreas Kemmerling Wolfgang Künne Franz von Kutschera Wolfgang Lenzen Edgar Morscher Kevin Mulligan Ulrich Nortmann Christopher Peacocke Dominik Perler

Notre Dame Paris-Sorbonne New York University Brown University Universität Heidelberg Universität Hamburg Universität Regensburg Universität Osnabrück Universität Salzburg Université de Genève Universität des Saarlandes Columbia University HU Berlin

Christof Rapp LMU München Nicholas Rescher University of Pittsburgh Edmund Runggaldier Universität Innsbruck Mark Sainsbury University of Texas at Austin Alexandrine Schniewind Université de Lausanne Oliver Scholz Universität Münster Peter Simons Trinity College Dublin Barry Smith State University of New York Gisela Striker Harvard University Rainer Stuhlmann-Laeisz Universität Bonn Paul Thom The University of Sydney Michael Wolff Universität Bielefeld James Wilberding HU Berlin

Call for papers The journal is published annually. Deadlines for papers and reviews is annually announced. The languages of publication are English and German. Further information can be obtained by email or from our website. Submission of Papers Please use the editorial system at rub.de / philosophy /pla and in addition send papers to [email protected]

Send Reviews to [email protected]

Orders Individual copies – Einzelbezug: EUR 58,– / Subscription – Abo: EUR 48,– mentis Verlag, Jühenplatz 1-3, 33098 Paderborn, Germany · www.mentis.de

Table of Contents

From Leibniz to Kant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

Katherine Dunlop & Samuel Levey: Foreword . . . . . . . . . . . . . . . . . . . . . . .

11

Legend of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

Jeffrey McDonough & Zeynep Soysal: Leibniz’s Formal Theory of Contingency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

Julia Borcherding: Reflection, Intelligibility, and Leibniz’s Case Against Materialism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

Paul Lodge: Leibniz’s Justification of the Principle of Sufficient Reason (Mainly) in the Correspondence with Clarke . . . . . . . . . . . . . . . . . . . . . . . . . .

69

Gastón Robert: Simples, Representational Activity, and the Communication among Substances: Leibniz and Wolff on pre-established Harmony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

Patrick R. Leland: Wolff, Baumgarten, and the Technical Idiom of PostLeibnizian Philosophy of Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

Katherine Dunlop: Definitions and Empirical Justification in Christian Wolff’s Theory of Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

149

Huaping Lu-Adler: Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy: A Study of Their Responses to the vis viva Controversy . . . . .

177

Gonzalo Rodriguez-Pereyra: Kant on the Existence and Uniqueness of the Best Possible World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

195

Timothy Rosenkoetter: The Canon Problem and the Explanatory Priority of Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

216

Stephen Engstrom: The Category of Substance . . . . . . . . . . . . . . . . . . . . . . .

235

Book Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

261

Martin Nitsch: Surfing Uncertainty: Prediction, Action and the Embodied Mind (Andy Clark) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

261

Joseph Tarquin Foulkes Roberts: Persons and Things (Roberto Esposito) . . . . .

267

List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

272

From Leibniz to Kant

Foreword Katherine Dunlop, University of Texas, Austin Samuel Levey, Dartmouth College

G. W. Leibniz’s legacy to philosophy is extraordinary for his vast body of work, for his prescience, and for his influence. Leibniz’s advances in formal methods, almost seeing into the future, paved the way for the logical and analytical style that philosophical inquiry would take on two centuries later in the foundational works of Frege and Russell, as well as those of Cantor and Gödel – works which not only followed themes similar to Leibniz’s but also regarded themselves as responding directly to his efforts. In his own time, Leibniz’s revival and defense of ancient and scholastic ideas in metaphysics and philosophical theology served as a counterweight to the growing orthodoxy of materialism and mechanism in natural philosophy in the modern era – expressed in different forms in Galileo, Descartes, Hobbes, and Newton, inter alia – a counterweight that pressed hard for a deeper explanatory role for philosophical inquiry at the foundations of scientific theory. Here too resonances of Leibniz in the present are easy to detect in the renewal of interest in fundamental metaphysics, explanation, and the question of ontology in science. For better or worse, the ‘analytical’ and ‘metaphysical’ tendencies thriving in philosophy today descend in no small part from Leibniz’s thought. Leibniz’s immediate impact in philosophy was large as well, setting the stage for academic philosophy in Germany and elsewhere in continental Europe for a generation. As scholarship has turned toward the question of Leibniz’s influence on his successors, that history has shed new and often unexpected light on the era connecting them – illuminating actual links, roles of lesser-known players, and unrecognized contours of views that are otherwise lost to modern-day eyes. A case in point is the ‘Leibnizian-Wolffian philosophy’ of the universities; while Wolff and his followers’ work was a main conduit for Leibniz’s influence, the extent to which their views agree with Leibniz’s is a matter of contention. To avoid prejudging this question, for this volume we solicited papers on the influence of ‘Leibnizian’ philosophy. In any case, Leibniz and the philosophers of the Wolffian school could both be seen to pair grandiose optimism, in their claims to rational metaphysical explanation, with discomfortingly slender epistemic credentials. This contrast was certainly evident to Immanuel Kant, the next German titan of philosophy, and invited his critical rethinking of the whole philosophical enterprise. Although Kant’s place in philosophy would eclipse Leibniz’s for the nineteenth and twentieth centuries, his thought cannot be fully understood apart from Leibniz either. In putting together this volume, our aim is to provide a snapshot of state-of-the-art scholarship on Leibniz’s philosophy and its legacy, especially in the period up to Kant. The essays collected here newly examine signature elements of Leibniz’s thought – logical theory, contingent truth, anti-materialism, reflective knowledge, the principle of sufficient reason, his technical idiom in the theory of ideas, his metaphysics of substance, etc. – as well as the influence of predecessors such as Lull, Descartes, and Malebranche, the reckoning of his ideas in the works of Wolff and Kant, and the contributions of Clarke,

12

Katherine Dunlop Samuel Levey

Baumgarten, Meier, Du Châtelet, and others to the content, transmission, and reception of the Leibnizian philosophy. But of course much remains to be explored. Recent scholarship has begun to recognize the expansive role of women in philosophy of the modern era, and Leibniz studies offers a rich array of texts to be considered among his correspondents and early readers. Also, while it is well-observed how Leibniz’s division of nature into ‘two kingdoms’ of mechanical and teleological explanation, his distinction between the phenomena of experience and the true metaphysics of intelligible substance, his distinction between a priori and a posteriori justification, his concept-containment theory of truth, and so on, served to frame celebrated responses in Kant’s philosophy, the significance of his ethical and political thought has received comparatively scant attention – whether for its philosophical merit in its own right or for its influence on his successors including Kant. Those are areas in which we especially hope to see future scholarship flourish.

Legend of Abbreviations

This volume uses the following abbreviations for frequently cited texts in original language and translation editions of Baumgarten, Descartes, Leibniz, Wolff, and Kant. Baumgarten Met.

1739. Metaphysica. Repr. 1982. Hildesheim: Georg Olms.

Descartes AT CSM(K)

1964–1976. Œvres de Descartes. Adam, Ch. /Tannery, P. (eds.). Paris: J. Vrin. Cited by volume and page. 1984–91. The Philosophical Writings of Descartes. Cottingham, J. /Stoothoff, R. / Murdoch, D. /Kenny, A. (trs.). Cambridge: Cambridge University Press. Cited by volume and page. Cited as CSM for volumes 1–2, and as CSMK for volume 3.

Leibniz Editions A

C Dut. GP

GM GLW Grua Jag. LH

1923–. Sämtliche Schriften und Briefe. Deutsche Akademie der Wissenschaften (ed.). Darmstadt /Leipzig /Berlin: Akademie Verlag. Cited by series, volume, and page. 1966. Opuscules et fragments inédits de Leibniz. Couturat, L. (ed.). Paris: Felix Alcan. 1903. Reprint Hildesheim: Georg Olms. 1768. G. W. Leibniz: Opera omnia, nunc primum collecta . . . studio Ludovici Dutens. T. 1–6. Genevae. Cited by volume and page. 1875–1890. Die philosophischen Schriften von Gottfried Wilhelm Leibniz. Gerhardt, C. I. (ed.). 7 vols. Berlin: Weidmannsche Buchhandlung. Repr. 1978. Hildesheim: Georg Olms. Cited by volume and page. 1840–1863. Leibniz’ Mathematische Schriften. Gerhardt. C. I. (ed.). 7 vols. Berlin: A. Asher. Halle: H. W. Schmidt. Cited by volume and page. 1860. Briefwechsel zwischen Leibniz und Christian Wolff. Ed. Gerhardt, C. I. (ed.). Halle. Repr. 1963. Hildesheim: Georg Olms. 1948. G. W. Leibniz: Textes inédits. Grua, G. (ed.). 2 vols. Paris: Presses Universitaires de France. Cited by volume and page. 1913. Leibnitiana, Elementa philosophiae arcanae de Summa rerum. Jagodinski, I. (ed.). Kasan. 1895. Die Leibniz-Handschriften der Königlichen öffentlichen Bibliothek zu Hannover. Bodemann, E. (ed.). Hannover. Repr. 1966. Hildesheim: Olms.

14

Legend of Abbreviations

Translations CP DSR LA LC

LDB LDV LoC Log. NE NS PE PPL PT PW PWL Sel. T

2006. Confessio Philosophi: Papers Concerning the Problem of Evil, 1671–1678. Sleigh, R. C. (tr.). New Haven: Yale University Press. 1992. De Summa Rerum: Metaphysical Papers, 1672–1678. Parkinson, G. H. R. (tr.). New Haven: Yale University Press. 1967 The Leibniz – Arnauld Correspondence. Mason, H. T. (tr.). Manchester: Manchester University Press. 1977. The Leibniz – Clarke Correspondence: With Extracts from Newton’s ‘Principia’ and ‘Optics’. Alexander, H. G. (tr.). Manchester: Manchester University Press. 2007. The Leibniz – Des Bosses Correspondence. Look, B. C. /Rutherford, D. (trs.). New Haven: Yale University Press. 2013. The Leibniz – Des Volder Correspondence. Lodge, P. (trs.). New Haven: Yale University Press. 2001. The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672–1686. Arthur, R. T. W. (tr.). New Haven: Yale University Press. 1966. Leibniz: Logical Papers. Parkinson, G. H. R. (tr.). Oxford: Clarendon Press. 1996. Leibniz: New Essays on Human Understanding. Remnant, P. /Bennett J. (trs.). Cambridge: Cambridge University Press. 1997. Leibniz’s ‘New System’ and Associated Contemporary Texts. Woolhouse, R. S. /Francks, R. (trs.). New York: Oxford University Press. 1989. G. W. Leibniz: Philosophical Essays. Ariew, R. /Garber, D. (trs.) Indianapolis: Hackett Publishing Company. 1976. Gottfried Wilhelm Leibniz: Philosophical Papers and Letters: A Selection. 2nd ed. Loemker, L. E. (tr.). Dordrecht Reidel: Springer. 1998. G. W. Leibniz: Philosophical Texts. Woolhouse, R. S. /Francks, R. (trs.). New York: Oxford University Press. 1973. Leibniz: Philosophical Writings. Morris, M. and Parkinson, G. H. R. (trs.). London: Dent. 1934. The Philosophical Writings of Leibniz. Morris, M. (tr.). London: Dent. 1951. G. W. Leibniz: Selections. Wiener, P. P. (tr.). New York: Scribner’s. 1952. G. W. Leibniz: Theodicy: Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil. Farrer, A. (ed.) and Huggard, E. M. (tr.). La Salle, IL: Open Court.

Wolff Anf. CG Mor. PD

1750. Anfangsgründe aller Mathematischen Wissenschaften, Erster Theil. Repr. 1973. Hildesheim: Olms. 1731. Cosmologia generalis, methodo scientifica pertractata. Repr. 1964. Hildesheim: Olms. 1750–1753. Philosophia moralis sive ethica. Repr. 1973. Hildesheim: Olms. 1728. Preliminary Discourse on Philosophy in General. Blackwell, R. J. (tr.). 1963. Indianapolis: Bobbs-Merrill. (Original: Wolff, C. 1728. Discursus praeliminaris de philosophia in genere. In: Philosophia rationalis sive logica. Frankfurt and Leipzig: Officina Libraria Rengeriana.)

Legend of Abbreviations

PP PR PS VGG VGK

15

1736. Philosophia prima sive ontologia. Repr. 1962. Hildesheim: Olms. 1740. Philosophia rationalis sive logica. Repr. 1983. Hildesheim: Olms. 1740. Psychologia rationalis. Repr. 1972. Hildesheim: Olms. 1751. Vernünftige Gedancken von Gott, der Welt und der Seele des Menschen. Repr. 1983. Hildesheim: Olms. 1754. Vernünftige Gedancken von den Kräften des menschlichen Verstandes. Repr. 1965. Hildesheim: Olms.

Kant Except for the Critique of Pure Reason, works published during Kant’s lifetime are cited according to the following scheme of abbreviation. Volume and page numbers are from the Berlin Academy edition [Ak]. Works not published during Kant’s lifetime are cited without abbreviated titles, according to Ak volume and page numbers. The Critique of Pure Reason [KrV] is cited, following standard practice, according to page numbers of the 1781 (“A”) and 1787 (“B”) editions. Ak ApH DMS EmB GMS GSK

KpV KrV KU L MAN MP

ND NL P TG UDG

1902–. Kants gesammelte Schriften. Königlich Preussischen Akademie der Wissenschaften. Berlin: de Gruyter. 1798. Anthropologie in pragmatischer Hinsicht. 7:117–333. 1770. De mundi sensibilis atque intelligibilis forma et principiis (“Inaugural Dissertation”). 2:385–419. 1763. Der einzig mögliche Beweisgrund zu einer Demonstration des Dasein Gottes. 2:63–163. 1785. Grundlegung zur Metaphysik der Sitten. 4:385–463. 1746–49. Gedanken von der wahren Schätzung der lebendigen Kräften und Beurtheilung der Beweise, deren sich Herr von Leibniz und andere Mechaniker in dieser Streitsache bedient haben, nebst einigen vorhergehenden Betrachtungen, welche die Kraft der Körper überhaupt betreffen. 1:1–181. 1788. Kritik der praktischen Vernunft. 5:1–163. 1781/1787. Kritik der reinen Vernunft. 4:1–252 (A-edition) /3:1–552 (B-edition). 1790. Kritik der Urtheilskraft. 5:165–485. 1800. Logik. Ein Handbuch zu Vorlesungen (“Jäsche Logik”). 9:1–150. 1786. Metaphysische Anfangsgründe der Naturwissenschaft. 4:465–565. 1756. Metaphysice cum geometria iunctae usus in philosophia naturali, cuius specimen I. continet monadologiam physicam (“Physical Monadology”). 1:473– 487. 1755. Principiorum primorum cognitionis metaphysicae nova dilucidatio (“New Elucidation”). 1:385–416. 1758. Neuer Lehrbegriff der Bewegung und Ruhe und der damit verknüpften Folgerungen in den ersten Gründen der Naturwissenschaft. 2:13–25. 1783. Prolegomena zu einer jeden künftigen Metaphysik, die als Wissenschaft wird auftreten können. 4:253–383. 1766. Träume eines Geistersehers, erläutert durch Träume der Metaphysik. 2:315–73. 1764. Untersuchung über die Deutlichkeit der Grundsätze der näturlichen Theologie und der Moral. 2:273–301.

16

UGR ÜE VBnG VBO

Legend of Abbreviations

1768. Von dem ersten Grunde der Unterschiedes der Gegenden im Raume. 2:375– 83. 1790. Über eine Entdeckung, nach der alle neue Kritik der reinen Vernunft durch eine ältere entbehrlich gemacht werden soll. 8:185–251. 1763. Versuch den Begriff der negativen Grössen in die Weltweisheit einzuführen. 2:165–204. 1759. Versuch einiger Betrachtungen über den Optimismus. 2:27–35.

Leibniz’s Formal Theory of Contingency Jeffrey McDonough, Harvard University Zeynep Soysal, University of Rochester

Abstract This essay argues that, with his much-maligned “infinite analysis” theory of contingency, Leibniz is onto something deep and important – a tangle of issues that wouldn’t be sorted out properly for centuries to come, and then only by some of the greatest minds of the twentieth century. The first two sections place Leibniz’s theory in its proper historical context and draw a distinction between Leibniz’s logical and meta-logical discoveries. The third section argues that Leibniz’s logical insights initially make his “infinite analysis” theory of contingency more rather than less perplexing. The last two sections argue that Leibniz’s meta-logical insights, however, point the way towards a better appreciation of (what we should regard as) his formal theory of contingency, and its correlative, his formal theory of necessity.

1. Introduction Leibniz’s views on logic and truth might seem to commit him to the view that all true propositions are necessarily true. Leibniz assumes that every proposition can be cast in subject-predicate form (A 6.1.192 /Log. 3). A sentence such as “Peter is a denier of Christ” wears its logical form on its sleeve, while the logical form of, say, “Adam and Eve love each other” might be more perspicuously expressed by “Adam loves Eve and Eve loves Adam.” Leibniz further maintains that “in all true affirmative propositions, necessary or contingent, universal or singular, the notion of the predicate is always in some way included in that of the subject – praedicato inest subjecto” (GP 2.56 /PT 111– 112; see also A 6.4.223). Thus, the proposition Peter is a denier of Christ seems to be true if and only if the predicate expressed by “is a denier of Christ” is contained in the subject expressed by “Peter.” Finally, Leibniz also maintains that for every genuine subject there is a complete concept containing all and only those predicates that will be true of that subject (A 6. 4. 1540 f. /PE 41). Given these three commitments, it is hard to see how any proposition might be contingent. If the sentence “Peter is a denier of Christ” expresses a true proposition, it seems that there must be a complete concept corresponding to “Peter,” that that complete concept must contain the predicate is a denier of Christ, and that that is sufficient for the proposition Peter is a denier of Christ to be true. How then could the sentence “Peter is a denier of Christ” be contingent? It is a measure of Leibniz’s brilliance – or madness – that he offers not one, but (at least) two theories of contingency. The first theory – his hypothetical necessity theory – is relatively plain sailing. 1 It effectively weakens his theory of truth by suggesting that 1

See, for example, A 6.3.128; GP 7.235. For discussion and further texts see Adams 1994, 10–22, and Sleigh 1990, 80–83.

18

Jeffrey McDonough & Zeynep Soysal

predicate containment is a necessary but not a sufficient condition for a proposition’s being true. For the proposition Peter is a denier of Christ to be true, not only must the complete concept corresponding to Peter contain the predicate is a denier of Christ, but Peter must also be created. Peter is a denier of Christ is thus hypothetically necessary in the sense that it must be the case that if Peter exists, then he denies Christ. But Peter is a denier of Christ is nonetheless contingent because Peter’s existence is itself contingent. There are, of course, well-known objections to Leibniz’s “first” theory of contingency. One might worry, for example, that given Leibniz’s system, Peter’s existence might itself be necessary, and so the proposition Peter is a denier of Christ might turn out to be not just hypothetically, but absolutely necessary after all. Likewise, one might object that Leibniz’s hypothetical necessity theory of contingency won’t meet the demands of his theodicy. If, for example, the only way for Peter not to deny Christ is for Peter not to exist, then it might seem that Peter cannot be responsible for denying Christ. Whatever one thinks of the ultimate merits of Leibniz’s first theory of contingency, however, it at least has the following virtue: it’s easy to see what Leibniz is getting at, to see how he could think that the contingency of contingent propositions might be rooted in the contingent existence of their subjects. Leibniz’s second theory of contingency, his infinite analysis theory, or, as we will call it, his formal theory of contingency, may well seem to lack even the minimal virtue of intelligibility. In developing this “second” theory, Leibniz suggests that the distinction between necessary and contingent propositions may be drawn in purely formal terms, gesturing towards a contrast between propositions that admit of a finite formal analysis to identities and propositions for which the process of formal analysis “proceeds to infinity” (A 6. 4. 1656 /L 265). There is little consensus, however, over how these various hints might be pulled together into a theory of contingency. 2 Indeed, in a characteristically blunt assessment, Jonathan Bennett has suggested that it is high time we simply threw in the towel: Nobody has made respectable sense of what Leibniz says about finite and infinite analysis of subject-concepts. Furthermore, even if he did succeed in that, nobody thinks the result would have anything to do with contingency as we understand it, or, therefore, that it could satisfy Leibniz’s need to defend contingency (in our sense) so that God has real choices to make. We should drop the matter. It is too late in the day to expect the mystery to be cleared up, and I guess that if Leibniz or scholarship did remove the veil, we would conclude that the search had not been worth our trouble. I mean: worth our trouble as philosophers. It is different for antiquarians. (Bennett 2001, 329)

While not unsympathetic with Bennett’s frustration, in what follows we intend to flout his advice. Section 2 places Leibniz’s formal theory of contingency in its proper – if often neglected – context and draws a distinction between his logical and meta-logical insights. Section 3 argues that closer attention to Leibniz’s logical insights should make his formal theory of contingency – at least as it has been standardly interpreted – seem more, rather than less, perplexing. Section 4 argues that Leibniz’s meta-logical insights, however, 2

For recent discussions of Leibniz’s formal theory of contingency, see especially Hawthorne and Cover 2000, Malink and Vasudevan 2016, 719–720, Merlo 2012, Rodriguez-Pereyra and Lodge 2011, and Steward 2014. For classic discussions see also Adams 1994, Blumenfeld 1985, Carriero 1993 and 1995, Curley 1972, Hacking 1973, 1974 and 1978, Ishiguro 1972, 171–203, Maher 1980, and Mates 1986, 105–117.

Leibniz’s Formal Theory of Contingency

19

point the way towards a better understanding of his formal theory of contingency. Very roughly, a proposition is contingent if and only if it is not algorithmically decidable in an ideal language. Section 5 argues the same is true for Leibniz’s correlative formal theory of necessity. Very roughly, a proposition is necessary if and only if it is algorithmically decidable in an ideal language. The essay as whole thus aims to show that, with his formal theories of contingency and necessity, Leibniz was, after all, onto something genuinely complex, puzzling and profound – a tissue of ideas that wouldn’t be sorted out for centuries to come, and then only by some of the greatest minds of the twentieth century. Removing the veil will, we think, prove worth the trouble, not just for antiquarians but for philosophers as well.

2. Language, Logic, and Meta-Logic Leibniz’s formal theory of contingency develops against the backdrop of his often-neglected interest in ideal languages. The dream of creating, or discovering, an ideal language is perhaps as old as the myth of the tower of Babylon. 3 It was given a distinctive shape, however, near the close of the thirteenth century by the Franciscan philosopher Raymond Lull. Lacking a traditional university education, Lull conceived a radically nonAristotelian “art” of reasoning based on primitive principles, symbolic representations, and algorithmic rules. Although initially viewed with suspicion, Lull’s work soon inspired related efforts by Renaissance figures such as Nicholas of Cusa (1401–1464) and Guillaume Postel (1510–1581). It was carried further by famous early modern figures such as Bacon, Descartes, and Spinoza through their work on philosophical method, as well as by lesswell-known figures such as Johann Heinrich Alsted, Johann Heinrich Bisterfeld, Jan Amos Comenius, and Athanasius Kircher through their work on combinatorial arts (for background, see Antognazza 2009, 62, and Arthur 2006, 29). While still a young man, Leibniz himself became enthralled with the search for a perfect language (Sel. 17), writing his Habilitation thesis, Dissertatio de arte combinatoria, on the combinatorial possibilities of fundamental concepts. A steady stream of works on logic, method, and combinatorics followed over the course of his long career. Some fifty years after his initial inspiration, Leibniz was still working out what he saw as the fantastic promise of an ideal language (Antognazza 2009, 64). Leibniz thought that the construction of an ideal language would have to involve at least three essential steps. First, primitive concepts would have to be identified. Leibniz maintains that the primitive concepts represented in a truly ideal language would be absolutely fundamental and unanalyzable into more basic, simpler concepts (A 6.4.590 / PE 26; A 6. 4. 1569 /PE 57). Not insignificantly, however, he also allows for the possibility of a relatively ideal language, a language whose primitive concepts would be only relatively, or provisionally, basic. In any case, primitive concepts are to be contrasted with derivative concepts. Derivative concepts are built up from more basic concepts, and can conversely be resolved or analyzed into those more basic concepts (A 6.4.540 /PPL 230). In an ingenious analogy, Leibniz suggests that primitive concepts might be likened to 3

For a helpful overview of Leibniz’s thinking about language see Rutherford 1995. For an engaging overview of the ideal language tradition, see Eco 1993.

20

Jeffrey McDonough & Zeynep Soysal

prime numbers and derivative concepts to composite numbers. Just as a prime number cannot be divided by any other prime number, so primitive concepts cannot be decomposed into other concepts. And just as composite numbers can be reached by multiplying prime numbers and, conversely, be decomposed into prime numbers by division, so too derivative concepts can be constructed from primitive concepts and can be decomposed, ultimately, back into primitive concepts (A 6.4.289 /Log. 37). Second, the construction of an ideal language would require the formulation of a suitable system of symbols. Leibniz’s success with his infinitesimal calculus had impressed upon him the importance of helpful notation (see, for example, A 6.4.910). He recognized that well-chosen symbols may make conceptual relationships almost self-evident, while poorly-chosen symbols can obscure even the simplest of conceptual connections. Leibniz hoped that someday a wholly new language might be devised that would make the conceptual relations of our everyday discourse utterly transparent. In the nearer term, however, he commended “another less elegant road already open to us” that would not “have to be built completely new” (A 6.4.965 /Sel. 52). Picking up on the analogy mentioned above, Leibniz suggests that the names of prime numbers might be used to denote primitive concepts and the names of composite numbers might be used to denote derivative concepts. Anyone capable of performing multiplication or division could then easily discern the relationships between primitive and derivative concepts. So, for example, Leibniz suggests that we might let “6” stand for the derivative concept man, “3” stand for the primitive concept rational, and “2” stand for the primitive concept animal. Anyone familiar with the relevant symbolism, and capable of performing division, could then recognize immediately that the concept man contains the concepts rational and animal (A 6.4.201 /PPL 238). 4 Third, the construction of an ideal language would require identifying a set of rules that would allow users of the language to formally, mechanically, or “blindly” manipulate symbols in order to make new discoveries and draw conclusions without fear of error (A 6.4.587 /PE 25). A helpful example of the sort of rules Leibniz has in mind is provided by his Addenda to the Specimen of the Universal Calculus (1679–86?) (GP 7.221-227 /Log. 40–46). Allowing italicized lower case letters to stand for concepts, Leibniz suggests that “the transposition of letters in the same term changes nothing: e. g. ab coincides with ba, or ‘rational animal’ and ‘animal rational’.” Likewise, he suggests that “[r]epetition of the same letter in the same term is superfluous, such as b is aa, or bb is a: man is an animal animal, or man man is an animal. For it is enough to say, a is b, or man is an animal.” Given such rules, users of Leibniz’s ideal language would be licensed in asserting ab when given ba and a when given aa. Indeed, they could be confident of such substitutions even without knowing what concepts the terms a and b stand for. A user of Leibniz’s ideal language could thus carry out inferences algorithmically just as a mathematician,

4

Leibniz’s suggestion here anticipates Gödel numbering, the technique used by Kurt Gödel to treat a formal system as a mere system of signs with a specified mapping from signs to numbers in order to mathematically study the syntax of Peano Arithmetic. Although it is known that Gödel checked out the Gerhardt volume containing Leibniz’s Dissertatio de arte combinatoria in 1929 (van Atten and Kennedy 2015, 124, n. 67, see also van Atten 2015), and that Gödel studied Leibniz’s work extensively in the early 1930s, around the time of his incompleteness results, there is no direct evidence that Gödel was inspired in this particular respect by Leibniz (Menger 1994, 210). Special thanks to Mark van Atten for helpful discussion of this point.

Leibniz’s Formal Theory of Contingency

21

following the methods of Leibniz’s infinitesimal calculus, may “blindly” or mechanically find derivatives of (say) even complex polynomial expressions. Leibniz’s aspirations for an ideal language may at first glance seem fanciful and utopian. He suggests, for example, that an ideal language would be “very easy to learn,” “will be quickly accepted by everyone,” and that it “will have the wonderful property of silencing ignorant people” (A 6.4.6-7 /Sel. 16). A closer look, however, reveals a more intriguing, if still optimistic, picture. For, on the one hand, closer scrutiny shows that Leibniz was less starry-eyed about the ideal language tradition and its short-term prospects than is commonly supposed. He takes Lull to task, for example, for his seemingly arbitrary choice of primitive concepts (A 6.1.193 /Sel. 53). He expresses amazement at the logical lacunae in the purported demonstrations of his contemporaries (A 6.4.705 /Sel. 37). He acknowledges that, in practice, the construction of an ideal language may depend essentially on experiments and observations (A 3.1.331-332 /PPL 166; GP 1.193-199 /PPL 187). Thus, although characteristically optimistic, Leibniz is far from naïve either about the uneven work of his predecessors in the ideal language tradition or about the difficulties that would need to be surmounted in order to realize the dream of an ideal language. Furthermore, and on the other hand, a closer scrutiny of Leibniz’s work on ideal languages suggests that he has far better grounds for his optimism – or at least his enthusiasm – than has often been recognized. Most importantly for our purposes, Leibniz’s pursuit of an ideal language put him solidly on the path of three startling advances that would, some 200 years later, come to revolutionize the study of mathematics, logic, and, what we now call, computer science. The first of those advances concerns the nature of demonstration itself. With his syllogistic logic, Aristotle had introduced the notion of a formal demonstration, that is, of a demonstration that is truth-preserving in virtue of its form rather than the meanings or denotations of the terms involved (see, for example, A 3.2.449-452 /PPL 192–194). So profound was Aristotle’s influence that his syllogistic logic was still being taught to students in Leibniz’s day. Many of them evidently hated it (see, for example, Locke 1689, IV.xvii.4). Sensing that not all formal reasoning could be, or had to be, fit into the straightjacket of syllogistic form, efforts were made to articulate new methods of demonstration that are intuitive rather than formal. Descartes’s Rules for the Direction of the Mind (Regulae ad directionem ingenii) and Antoine Arnauld and Pierre Nicole’s Logic, or Art of Thinking (La logique, ou l’art de penser) are perhaps the most famous examples of such efforts. Leibniz too recognized that not all valid reasoning could be, or had to be, fit to the procrustean bed of traditional syllogistic logic. Unlike so many of his contemporaries, however, Leibniz held Aristotle’s logic in high regard, praising it as “one of the most important [discoveries], to have been made by the human mind” (NE 478). Rather than abandoning formal demonstration in favor of intuitive reasoning, Leibniz proposed to expand formal reasoning to include any form that “has been demonstrated in advance so that one is sure of not going wrong with it” (NE 479, see also GP 1.194 /PPL 187). His efforts led him to devise a general system of logic inspired by the rules of algebra (see, for example, A 6.4.739-788 /Log. 47–87 and A 6.4.845-855 /Log. 122–130; for discussion see Malink and Vasudevan 2016). Some 150 years later, George Boole would follow the same inspiration in constructing what is now known as Boolean Logic. When, half a generation later, Gottlob Frege sought to expand the rules of formal reasoning even further, he presented himself as continuing Leibniz’s efforts, explaining that what he “wanted to create was [. . .] a

22

Jeffrey McDonough & Zeynep Soysal

lingua characteristica in Leibniz’s sense” (van Heijenoort 1967, 2; see also Davis 2000, 48– 52, and Kluge 1977). The second advance that can be traced back to Leibniz’s pursuit of an ideal language concerns the notion of decidability. For Leibniz, the pursuit of an ideal language was a matter of not only theoretical but also practical interest. Eager to bridge the religious, political and social rifts of his time, Leibniz hoped that a perfect language might allow disputes to be settled in a foolproof, automatic, algorithmic manner like disputes over simple calculated sums. Indeed, he hoped that, armed with an ideal language – “the greatest instrument of reason” – “when there are disputes among persons, we can simply say: Let us calculate, without further ado, and see who is right” (A 6.4.964 /Sel. 51; see also A 6.4.913). In suggesting that arguments couched in an ideal language might be guaranteed to be resolved, Leibniz anticipated an idea notably not taken up even by Frege. For all its brilliance, Frege’s Begriffsschrift offers no way of knowing – apart from success – whether a conclusion can be derived from a given set of premises (see Goldfarb 2001). Questions concerning decidability came into their own during the late-nineteenth and earlytwentieth centuries with the explicit development of meta-logic and meta-mathematics. Gödel’s incompleteness results, together with the precise mathematical explication of the notion of decidability, led for instance to a proof of the remarkable result that mathematics (as encapsulated in Peano Arithmetic) is undecidable if consistent – that is, informally, that there is no computational procedure for telling, given any formula of Peano Arithmetic, whether or not that formula is derivable in Peano Arithmetic. Fueled by such results, contemporary consensus now holds that no language could possibly guarantee that all disputes – or even just all mathematical disputes – could be solved algorithmically. Remarkably, however, Gödel, an ardent student of Leibniz’s philosophy (see Goldfarb 2011 and Parsons 2010), seems to have himself shared Leibniz’s optimistic outlook, insisting that “Leibniz did not in his writings about the Characteristica universalis speak of a utopian project,” and maintaining that “he [sc. Leibniz] had developed his calculus of reasoning to a large extent, but was waiting with its publication till the seed could fall on fertile ground” (Schilpp 1999, 153). 5 Finally, the third advance that can be traced back to Leibniz’s pursuit of an ideal language concerns the notion of computability. Leibniz recognized that if reasoning could be carried out in a “blind,” algorithmic manner, then even a machine should, in principle, be able to carry out formal inferences. Around 1671, apparently inspired by a mechanistic pedometer, Leibniz resolved to construct just such a machine (LH XLII 5, Bl. 69). Within a couple of years, he had invented the first calculator – now known as the Step

5

In a revision, quoted in van Atten and Kennedy 2003, 433, Gödel remarks that the universal characteristic “if interpreted as a formal system” does not exist. Although difficult to interpret, Gödel may have thought that all of mathematics is decidable provided that formal systems are supplemented by a kind of mathematical intuition or experience (see for instance Parsons 2014). If that is correct, his views may be remarkably in tune with Leibniz’s views as we interpret him. In brief, our Leibniz draws a distinction between propositions that are decidable without ordinary experience and propositions decidable only with the aid of ordinary experience. Gödel’s incompleteness results raise difficulties in connection with the class of propositions that Leibniz thought decidable without the aid of experience. Gödel’s optimism is grounded in the thought that that class of propositions, although not decidable without appeal to experience of any kind, might nonetheless be decidable by appeal to some kind of extra-ordinary, “rational” experience and “extrinsic” justifications. For related discussion, see Parsons 2010, 185.

Leibniz’s Formal Theory of Contingency

23

Reckoner – capable of performing all four arithmetical operations: addition, subtraction, multiplication and division. In doing so, Leibniz’s machine improved upon Blaise Pascal’s calculating machine, the Pascaline, principally in its ability to solve – to mechanistically calculate – problems of multiplication and division. In subsequent studies, Leibniz developed further plans for machines that would be capable of solving even more complex problems, including algebraic equations (Couturat 1901, 115). Leibniz’s work on calculating machines adds a concrete dimension to his intuitive thinking about decidability. In thinking through the design and construction of various calculating machines, Leibniz couldn’t but be confronted with questions we naturally think of as questions of computability: given a certain input, will a particular machine (computer) be guaranteed to yield, or “halt” with, the correct output? Given, for example, a problem of multiplication or division, in the case of the Pascaline, the answer is “no.” In the case of Leibniz’s Step Reckoner, the answer is “yes.” Interestingly, our contemporary understanding of decidability, although slightly different and certainly more precise than Leibniz’s, was similarly refined in part by thinking in terms of idealized machines. Today, we think of the decidability of, say, a formal system, in terms of there being a computational procedure for determining whether any given formula is derivable in that formal system. The relevant notion of “computability,” used at first in an intuitive sense, was made more precise in the 1930s in terms of an abstract model of computing machines generally known today as “Turing Machines.” 6 In seeing an intimate connection between formal logic on the one hand and machines capable of carrying out algorithmic procedures on the other, Leibniz had an early glimpse of the powerful combination that, with time, would come to fuel the computer revolution that surrounds us today. 7 At some risk of whiggishness, we have emphasized the sophistication of Leibniz’s work on ideal languages for two reasons. First, although we think that Leibniz’s formal theories of contingency and necessity are best understood against the backdrop of his interest in ideal languages, that interest itself might be thought a cause for embarrassment, a further reason to be dismissive of Leibniz’s second theory of contingency. But Leibniz has nothing to be embarrassed about here. His work on ideal languages is, to be sure, imperfect, incomplete, and not fully settled. But it is also deep, insightful, and far ahead of its time. A better sense of the difficulty of the issues Leibniz was grappling with, and the considerable advances he made in thinking them through, should clear the way for a more sympathetic assessment of the essential background to his formal theories of contingency and necessity. Second, a sense of what Leibniz was on to with his work on ideal languages is crucial to recognizing a distinction that will be central to our discussion to follow. Some aspects of Leibniz’s thinking about ideal languages concern what we may think of as issues belonging to logic per se. His thinking about primitive concepts, proper symbolism, and above all formal demonstration, for example, belongs to this branch of his work. Other aspects of Leibniz’s thinking about ideal languages concern what we 6

Turing machines were first described by Turing 1937. Though their proposals turned out to be equivalent, Gödel 1986 and Church 1936 also independently offered precise mathematical explications of computability. 7 For an engaging discussion of the path from Leibniz’s thinking about language and logic to Turing’s discoveries, see Davis 2000. Although not noted by Davis, Leibniz and Turing also shared a common interest in mechanical cryptography, Leibniz evidently having quickly realized that his Machina arithmetica could easily be modified to serve as a Machina deciphratoria (A 1.2.125; A 4.4.27; A 4.4.68; A 3.2.449-450 /PPL 192). For discussion of Leibniz’s interest in cryptography, see Rescher 2012 and also Beeley 2014, 111–122.

24

Jeffrey McDonough & Zeynep Soysal

may think of as issues belonging to meta-logic. Leibniz’s thinking about whether or not problems, questions and arguments are resolvable by means of an ideal language, or by the operations of algorithmic machines, belongs to this branch of his thinking. With that rough distinction in mind – the distinction between Leibniz’s logical and meta-logical insights – we will argue, in the next section, that Leibniz’s insights in logic initially make his formal theory of contingency more puzzling. In subsequent sections, we’ll argue that Leibniz’s insights in meta-logic, however, point the way towards a better understanding of his formal theories of contingency and necessity.

3. A Logical Theory of Contingency? Leibniz’s understanding of logic in general, and of formal demonstration in particular, are natural places to start in trying to make sense of his formal theories of necessity and contingency. And, indeed, there are a number of well-known passages in which Leibniz seems to encourage just such an approach. So, for example, in a well-known piece that has been entitled “On Contingency” and dated to the mid-1680s, Leibniz writes: And here is uncovered the secret distinction between Necessary and Contingent Truths [. . .] namely that in necessary propositions one arrives, by an analysis continued to some point, at an identical equation (and this very thing is to demonstrate a truth in geometrical rigor); but in contingent propositions the analysis proceeds to infinity by reasons for reasons, so that indeed one never has a full demonstration, although there is always, underneath, a reason for the truth, even if it is perfectly understood only by God, who alone goes through an infinite series in one act of the mind. (A 6. 4. 1650 /Adams 1994, 26; see also A 6. 4. 1515-1516 /PW 96–98)

Passages such as this suggest a natural interpretation of Leibniz’s formal theories of necessity and contingency. The interpretation’s core thought is that a truth is necessary if and only if it can be demonstrated in a finite number of steps. A truth is contingent if it cannot be demonstrated in a finite number of steps. For ease of exposition, let us call attempts to understand Leibniz’s infinite analysis theories of necessity and contingency along these lines logical interpretations. It is relatively easy to see how, drawing on Leibniz’s logical studies, one might begin to flesh-out a logical interpretation for at least some necessary propositions. We might suppose, for example, that the proposition 5 = 2 + 3 could be demonstrated in a finite number of steps by appealing to definitions and self-evident rules of valid substitution and inference. 8 Beginning with the statement “5 = 2 + 3” we could appeal to the definition of “2” and rules of substitution to arrive at the statement “5 = 1 + 1 + 3.” Appealing to the definition of “3” and rules of substitution we could arrive next at the statement “5 = 1 + 1 + 1 + 1 + 1.” Finally, appealing to the definition of “5” and rules of substitution we could arrive at the identity statement “1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1.” In three formally valid steps, we would thus have moved from a statement expressing the proposition 5 = 2 + 3 to “an

8

See, for example, Leibniz’s Specimen of a Universal Calculus 1679 (A 6.4.280-288 /Log. 33–39) and Addenda to the Specimen of the Universal Calculus 1679–86? (A 6.4.289-296 /Log. 39–46). For helpful discussion, see Rescher 1954 and Levey 2014. Note, on the following reconstruction, Leibniz takes for granted the associativity of addition, a point noted and discussed by Frege in his Foundations of Arithmetic (Frege 1884, 7–8).

Leibniz’s Formal Theory of Contingency

25

identical equation.” And in this case at least, a logical interpretation seems to give us the right result. We think that “5 = 2 + 3” expresses a necessary proposition, and, as we’ve just seen, it is indeed possible to demonstrate that 5 = 2 + 3 in a finite number of formally valid steps. It is harder, but not impossible, to see how a logical interpretation might be similarly developed for at least some putatively contingent propositions. Consider, for example, the proposition Peter is a denier of Christ. Drawing roughly on Leibniz’s own examples, we might represent Peter’s complete concept with the letters “mdy,” letting “m” represent the predicate “is a man,” “d” the predicate “is a denier of Christ,” and “y” the predicate expressing the conjunction of all the other predicates contained in Peter’s complete concept. 9 Substituting definitions, we could rewrite the statement expressing the proposition to be demonstrated as “mdy is d.” 10 Leibniz accepts a transposition rule of the form ab is ba, writing, for example, that “The transposition of letters in the same term changes nothing: e. g. ab coincides with ba, or, ‘rational animal’ and ‘animal rational’” (A 6.4.293 /Log. 43). Applying Leibniz’s transposition rule thus yields “dmy is d.” We may then introduce “z = my” as a definition, and appeal to substitution to get “dz is d.” It is clear that Leibniz would see this as being as good as a reduction to an explicit “primitive truth” or “axiom.” He tells us, for example, that “‘ab is a’ is always true,” (A 6.4.754 /Log. 58) and describes “ab is a,” e. g. “A rational animal is an animal” as belonging to “propositions true in themselves” (A 6.4.292 /Log. 42). 11 We might – indeed, probably should – stop our derivation here. If, however, we wish to push on, Leibniz’s logic does provide resources for showing that “dz is d” is logically equivalent to an explicit identity statement. We may introduce “z is z” as an identity, combine to get “dzz is dz,” 12 and eliminate repetition to get “dz is dz.” 13 Since the inclusion expressed by “dz is dz” is symmetric, we may finally conclude with an

9

10

11

12

13

That a predicate such as the one expressed by “y” should be permissible should be clear both from Leibniz’s general understanding of the relationship between signs and derivative concepts as well as from his explicit statements, e. g.: “one letter can be put which is equal to this conjunction of several (just as for the term ‘rational animal’ we put, for sake of brevity, the one term ‘man’); and for the composite term ab or abc, found in the predicate, there can be substituted the simple term a” (A 6.4.283-284 /Log. 35). “Is” here denotes predication rather than identity (denoted above by “=”). On Leibniz’s intensional approach (see Levey 2014, 112), it would seem that a proof of an identity statement should make the mutual inclusion of both sides of the equation explicit, while a proof of predicative statement should only need to make the inclusion of the predicate in the subject explicit. Intuitively, a proof of an identity statement such as “a = b” should show that a is included in b and that b is included in a, while a proof of a predicative statement such as “a is b” should only need to show that b is included in a (even if a is not included in b). Similarly, in his Addenda to the Specimen of the Universal Calculus 1679–86?, Leibniz writes: “[W]hen I say that the proposition ‘ab is a’ is always true, I understand to be true not only the example ‘A rational animal is an animal (taking ‘animal’ to be signified by a, and ‘rational’ by b), but also the example ‘A rational animal is rational (taking ‘rational’ to be signified by a, and ‘animal’ by b)” (A 6.4.289 /Log. 40). See also General Inquiries about the Analysis of Concepts and Truths 1686, (A 6.4.755 /Log. 58). See Leibniz’s Addenda to the Specimen of the Universal Calculus 1679–86?: “(4) From any number of propositions it is possible to make one proposition, by adding together all the subjects into one subject and all the predicates into one predicate. From a is b, c is d and e is f we get ace is bdf ” (A 6.4.293 /Log. 43). See Leibniz’s Addenda to the Specimen of the Universal Calculus 1679–86?: “(3) Repetition of the same letter in the same term is superfluous, such as b is aa, or bb is a: man is an animal animal, or man man [homo homo] is an animal. For it is enough to say, a is b, or, man is an animal” (A 6.4.293 /Log. 43).

26

Jeffrey McDonough & Zeynep Soysal

explicit identity statement, that is, “dz = dz.” 14 Given Leibniz’s logic, it therefore seems that the proposition expressed by “Peter is a denier of Christ” may similarly be reduced to an identity statement in a manner closely analogous to the way in which “5 = 2 + 3” may be reduced to an identity statement. 15 In contrast to our earlier example, however, in this case our derivation seems to yield the wrong result. We generally think that “Peter is a denier of Christ” expresses a contingent proposition. But, as we’ve just seen, it now seems that it too can be reduced to an identity statement in a finite number of formally valid steps. Although we’ve come at it from a different angle, this is essentially the same difficulty famously identified by Robert Adams as the Problem of the Lucky Proof: Even if infinitely many properties and events are contained in the complete concept of Peter, at least one of them will be proved in the first step of any analysis. Why couldn’t it be Peter’s denial? Why couldn’t we begin to analyze Peter’s concept by saying, ‘Peter is a denier of Jesus and . . .’? (Adams 1994, 34)

The Problem of the Lucky Proof brings out a deep and central difficulty for logical interpretations of Leibniz’s formal theory of contingency. For what the problem shows most centrally is that Leibniz appears to be committed to the existence of finite demonstrations of contingent propositions. And if that is right, then, of course, it cannot be the case that a truth is contingent if and only if it cannot be demonstrated in a finite number of steps. In response to the Problem of the Lucky Proof, many commentators have argued that Leibniz is not, in spite of appearances, committed to there being contingent truths that can be demonstrated in a finite number of steps. In making those arguments, commentators have, for the most part, followed one of two broad strategies. The first and most dominant strategy looks to non-formal considerations in order to, as Robert Adams puts it, place “some sort of restriction on what counts as a step in an analysis of an individual concept” (Adams 1994, 34). The driving idea here is to appeal to non-formal considerations in order to rule out otherwise valid inferences and thereby to block otherwise possible finite proofs of contingent propositions. So, for an example, it has been suggested that the analysis of the subject Caesar in the proposition Caesar crosses the Rubicon should have to follow the causal order of the appetites that lead Caesar to cross the Rubicon. Assuming that there are infinitely many such appetites, a story can be told according to which Caesar crosses the Rubicon cannot be demonstrated in a finite number of steps. 16 14

See Leibniz’s Addenda to the Specimen of the Universal Calculus 1679–86?: “If a is b and b is a, then a and b are said to be ‘the same.’ For example, every pious man is happy, and every happy man is pious, therefore ‘happy man’ and ‘pious man’ are the same” (A 6.4.294 /Log. 43). 15 Notice that the rules of combination and elimination used above could be used to turn even a false statement of the form “a is b” into an identity statement “ab = ab” (we can add “a is a” and “b is b” to “a is b” to get “aab is abb” (see n. 13), then eliminate repetitions to get “ab is ab” (see n. 14) and thereby conclude “ab = ab” (see n. 15). So, it would seem that in order to properly “reduce” a sentence to an identity in Leibniz’s sense, the sentence we “reduce” to an identity should be “logically equivalent” to the identity, and not merely logically imply it. In our example above, our two sentences (“mdy is d” and “dz = dz”) are indeed logically equivalent (for the trivial reason that they are both axioms on Leibniz’s logic). But “a is b” and “ab = ab” are not logically equivalent for any arbitrary a and b. 16 This version of the non-formal strategy is developed in Cover and Hawthorne 2000. For specific discussion and criticism, see Bennett 2001, 327–32, Rodriguez-Pereyra and Lodge 2011, and Stewart 2014, 37–38.

Leibniz’s Formal Theory of Contingency

27

By drawing on non-formal considerations, such as the causal structure of a subject’s appetites, one might thus hope to solve the Problem of the Lucky Proof by showing that there are, after all, no contingent truths that have finite demonstrations. The non-formal strategy represents an enticing and creative approach to addressing the Problem of the Lucky Proof. As a way of saving Leibniz’s formal theory of contingency, however, it seems to us to face a devastating dilemma. For the non-formal considerations appealed to in order to block otherwise permissible finite demonstrations must be understood as placing constraints either (i) on what counts as a valid inference itself or (ii) on what counts as a legitimate analysis. But if, taking the first horn, the non-formal constraints are thought of as constraining what counts as a valid inference, then those constraints would undermine Leibniz’s advanced understanding of logical demonstration itself. For if, for example, the inference from “a is ab” to “a is ba” may be beholden to, say, the order of Caesar’s appetites, or, more generally, what “a” and “b” mean or signify, then Leibniz would be forced to abandon the notion of a formal inference, and with it his advanced understanding of the very notion of formal demonstration. If, however, taking the second horn, the non-formal considerations are understood as additional constraints on what counts as an analysis, then the distinction between contingent and necessary truths is no longer being drawn in terms of Leibniz’s logic after all. For, on this horn, contingent propositions will still admit of finite demonstrations even if they don’t admit of finite analyses in some non-logical sense of analysis. To take the second horn is not to defend a logical interpretation of Leibniz’s second theory of contingency but rather to deny that he has a logical theory of contingency after all. The second, and recently resurgent, strategy for responding to the Problem of the Lucky Proof appeals to additional formal considerations rather than non-formal considerations. Drawing inspiration from Leibniz’s critique of the ontological argument, its core idea is that a complete proof requires, in effect, two phases: first, a reduction of the relevant terms to an identity statement, and, second, a demonstration that the concepts involved are themselves consistent. 17 On this consistency strategy, it can be allowed that even contingent propositions, for Leibniz, may admit of finite reductions to identity statements, that, for example, the statement “Peter is a denier of Christ” might be reduced to an identity statement via a finite number of substitutions and inferences. But, proponents of this strategy will insist, such finite reductions do not show that contingent propositions admit of finite proofs or demonstrations. Rather they maintain that for “Peter is a denier of Christ” to be demonstrated it is necessary to show that the concept of Peter is itself consistent, and given that the concept of Peter is infinitely complex, one might suppose that such a consistency check will itself require infinitely many steps. The consistency strategy thus suggests that Leibniz can allow that in the case of contingent propositions there may be, as it were, lucky finite reductions (first phase) while still denying that there are lucky finite demonstrations (first and second phase). While it resonates nicely with Leibniz’s thinking about the ontological argument, and has been skillfully developed by its proponents, the consistency strategy nonetheless faces

17

This avenue of response is developed by Maher 1980, 238–239, Hawthorne and Cover 2000, 153–156 and especially Rodriguez-Pereyra and Lodge 2011.

28

Jeffrey McDonough & Zeynep Soysal

a number of long-standing, well-discussed difficulties. 18 Most importantly, it implies that any proposition involving an infinitely complex concept will be contingent. In that case, however, too many propositions would seem to count as contingent. In particular, even identity statements involving complete concepts, such as “Peter = Peter,” would appear to be contingent. And that raises both philosophical and textual difficulties. It presents a philosophical difficulty because – as Gonzalo Rodriguez-Pereyra and Paul Lodge put it – “It is natural to think of identities as necessary” (2011, 231, n. 42). If the morning star is identical to the evening star, then it is presumably the case that the morning star is necessarily identical to the evening star. It presents a textual difficulty because it conflicts with clear assertions made by Leibniz that identity statements are necessary. He tells us, for example, that “An animal is an animal” is true in itself (A 6.4.292 /Log. 42) and that “identical propositions are necessary without any understanding or resolution of the terms, for I know that A is A regardless of what is understood by A” (GP 1.194 /PPL 187). Attention to the details of Leibniz’s advanced understanding of logic turns out – disappointingly – to make his second theory of contingency more rather than less puzzling. For Leibniz’s understanding of logic makes it difficult to see how he could possibly think that contingent propositions do not admit of finite demonstrations. One might, of course, suppose that the trouble here lies with Leibniz. One might suppose that Leibniz simply failed to see a rather obvious and fatal objection to a theory of contingency that he enthusiastically, but somewhat naïvely, entertained for decades. Perhaps. But perhaps the fault lies with us. Perhaps we have not yet fully appreciated what Leibniz is trying to get at with his formal theory of contingency. In the next two sections, we will suggest that looking to Leibniz’s meta-logical insights provides a promising, alternative picture of what Leibniz has in mind with his formal theories of contingency and necessity, a picture, incidentally, on which the Problem of the Lucky Proof, as a problem, simply never arises.

4. A Meta-Logical Theory of Contingency As noted above, Leibniz’s interest in ideal languages led him to reflect not only on the construction of formal systems of logic but also on what might be established by means of such formal systems. Leibniz’s interest in meta-logical considerations suggests an alternative way of understanding what he was trying to get at with his formal theory of contingency. Framed in terms of his intuitive understanding of the notion of decidability, the core thought would be that a proposition is contingent if and only if there is no algorithmic, formal procedure guaranteed to discover (and output) its proof. Even if we were equipped with a perfect language, we would have no algorithmic means, no method analogous to multiplication or division, that we could apply in order to arrive with certainty at a proof of the relevant proposition. Put alternatively in terms of his intuitive understanding of computability, the core thought would be that no machine could be built by us that, working from definitions alone, and following an algorithmic procedure, would be guaranteed to halt at a proof of a contingent proposition. Even if we were equipped with a fantastically expanded and idealized version of Leibniz’s 18

For critical discussion, see Hawthorne and Cover 2000, 155–156, Maher 1980, 239, Merlo 2012 and Steward 2014, 32–37.

Leibniz’s Formal Theory of Contingency

29

Step Reckoner – a modern computer, if you like – our “rational calculator” might run forever without arriving at a proof of a contingent proposition. For ease of expression, let us call such an interpretation of Leibniz’s formal theory of contingency, a meta-logical interpretation. 19 On a meta-logical interpretation, Leibniz’s proposed demarcation of contingent propositions would be formal, not epistemic: whether or not something is decidable or computable is a formal matter, not an epistemic one. But, of course, the suggestion that contingent propositions are not, in the relevant sense, decidable or computable does have epistemic implications, and those implications might be seen as furnishing the intuitive idea behind Leibniz’s technical demarcation. For, of course, it is quite plausible that the truth of contingent propositions cannot be established by appeal to non-empirical axioms, definitions and formal procedures alone. If we want to know whether or not Peter is a denier of Christ, this dog is a labradoodle, or it rained last Tuesday, it seems our reasoning must at some point touch base with experience. Someone must witness Peter’s denial, examine the dog, or have gotten caught in a downpour. Leibniz, of course, couldn’t think that that intuitive idea alone might provide a fully satisfying demarcation of contingent truths. For he allows that God can know that Peter is a denier of Christ, that my dog is a labradoodle, and that it rained last Tuesday a priori; that is to say, Leibniz allows that even contingent truths are, strictly speaking, knowable even in the absence of ordinary experience. With his formal theory of contingency, however, Leibniz could still offer an objective, non-epistemic demarcation of contingent propositions that nonetheless explains, and thus can draw support from, the intuitive idea that contingent propositions are knowable by us – by finite creatures – only with the aid of experience. Again for ease of exposition, let us call that intuitive idea the driving idea behind Leibniz’s formal theory of contingency. A meta-logical interpretation and its driving idea fit nicely – although not necessarily uniquely – with many of Leibniz’s texts. Consider, for example, Leibniz’s letter to Henry Oldenburg dated 28 December 1675 (A 3.1.326-334 /PPL 165–166). In it, Leibniz makes mention of his “combinatorial characteristic,” which he describes as “a higher science” than algebra but similar to it in that with it “we cannot err even if we wish and that truth can be grasped as if pictured on paper with the aid of a machine.” He boasts to Oldenburg that “nothing more effective” than his new method “can well be conceived for perfecting the human mind and that if this basis for philosophizing is accepted, there will come a time, and it will be soon, when we shall have as certain knowledge of God and the mind as we now have of figures and numbers and when the invention of machines will be no more difficult than the construction of geometric problems.” Having extolled the virtues of his characteristic, however, and most remarkably for our purposes, Leibniz goes on to imply that we should not expect his characteristic, on its own, to settle contingent truths about nature. He writes “when these [combinatorial] studies have been completed [. . .] men will return to the investigation of nature alone, which will never be entirely completed,”

19

We leave open the possibility that, for Leibniz, a contingent proposition might be decidable by an infinitely complex procedure and that an infinitely complex machine might be guaranteed to halt at a proof of a contingent proposition. And, in fact, perhaps a monad’s law of the series is just such a procedure, and the monad, or the natural machine that is its body, is just such a machine. On this point, see also Hacking 1978, 191. Special thanks to Tomas Feeney for drawing our attention to this point.

30

Jeffrey McDonough & Zeynep Soysal

adding later “Once men carry our [combinatorial] method through to the end, therefore, they will always philosophize in the manner of Boyle,” that is, empirically (A 3.1.332 / PPL 166). In perfect keeping with the spirit of a meta-logical interpretation, Leibniz, in his letter to Oldenburg, thus suggests that, even once perfected, his combinatorial characteristic won’t provide an algorithmic procedure guaranteed to settle contingent propositions. According to Leibniz, an ideal language will be of great use in establishing the truth of contingent propositions – it will be a great tool to mathematicians and natural philosophers alike. But it will be of practical use in settling contingent propositions only when supplemented by experience. Another significant text is provided by Leibniz’s letter to Herman Conring of 19 March 1678 (GP 1.193-199 /PPL 186–191). In it, Leibniz attempts to respond to Conring’s “criticisms regarding analysis and demonstration.” Focusing on demonstration, Leibniz first explains that “only identities are indemonstrable”; he maintains that even axioms are strictly speaking demonstrable even though “they are mostly so clear and easy that they do not need demonstration.” Leibniz then provides an account of his understanding of demonstration in which he makes it clear that he sees the demonstration of contingent propositions as presupposing empirical observation: [I]t is clear that demonstration is a chain of definitions. For in the demonstration of any proposition, nothing is used but definitions, axioms (with which I here include postulates), theorems which have been demonstrated previously, and observations. Since the theorems again must themselves be demonstrated, and axioms, except for identities, can also all be demonstrated, it follows that all truths can be resolved into definitions, identical propositions, and observations – though purely intelligible truths do not need observations. After the analysis has been completed, it will become manifest that the chain of demonstrations begins with identical propositions or observations and ends in a conclusion but that the beginning is connected with the conclusion through intervening definitions. In this sense I said that a demonstration is a chain of definitions. (GP 1.194 /PPL 187)

Leibniz’s account of demonstration here again fits remarkably well with a meta-logical interpretation and its driving idea. Setting aside formal identities, and taking a practical context for granted, Leibniz thinks that all propositions can be demonstrated. Necessary propositions (to which we’ll return in the next section) can be demonstrated ultimately from definitions alone (since postulates and axioms can themselves be demonstrated). Contingent propositions, however, can be demonstrated ultimately from definitions only with the aid of empirical observations. Leibniz’s ideal language is not guaranteed to settle the truth of all propositions on it is own. And, in particular, in the case of contingent propositions it serves only as a tool aiding experience, not as an algorithmic method for establishing contingent propositions a priori. A final text worth considering here has been dated to 1680 and entitled “Precepts for Advancing the Sciences and Arts” (A 6.4.692-713 /Sel. 29–46). In this work, Leibniz makes more explicit how he sees his work on ideal language as dovetailing with his views on scientific method more generally. As is so often the case, Leibniz presents himself as staking out a moderate, intermediate position. Against what he sees as immoderate empiricism, which he clearly associates with the Royal Society, Leibniz emphasizes the importance of formal tools, including logic and mathematics. He thus reports, for example, “they confessed to me in England that the great number of experiments they have amassed gives them no less difficulty than the lack of experiments gave the ancients”

Leibniz’s Formal Theory of Contingency

31

(A 2.1.554 /Sel. xxiii). Leibniz’s emphasis on formal tools, however, should not be taken to imply that he thinks that all contingent propositions can be established by pure reasoning alone. On the contrary, he emphasizes, often with a barb directed at Descartes and his followers, that progress is generally to be made in the sciences by joining formal tools to careful observation and choice experiments. As emerges clearly in Precepts for Advancing the Sciences and Arts, the theory of perspective and of musical harmonies and dissonances serve, for Leibniz, as scientific paradigms. They are powerful theories rooted in a few observations or experiments with implications drawn out by careful reasoning. Leibniz thus rejects immoderate rationalism no less than immoderate empiricism, an attitude that lies behind his famous comment “I prefer a Leeuwenhoek who tells me what he sees to a Cartesian who tells me what he thinks. It is [. . .] necessary to add reasoning to observations” (Leibniz 1691, 641). Leibniz’s understanding of science, as set out in his Precepts for Advancing the Sciences and Arts thus once again fits nicely with both a metalogical interpretation of his formal theory of contingency and its driving idea. Even armed with an ideal language, and fully exploiting formal tools, it will be possible for us to establish the contingent propositions of science only with the aid of experience. Beyond textual considerations, a meta-logical interpretation also provides an elegant resolution to the Problem of the Lucky Proof. As we’ve seen, the Problem of the Lucky Proof originally arose in the context of logical interpretations. In that context, it raises a rather obvious worry that directly challenges the guiding thought of such interpretations, namely, that a truth is contingent if and only if it does not admit of a finite demonstration. In the context of a meta-logical interpretation, however, things look significantly different. On a meta-logical interpretation, Leibniz’s formal theory of contingency isn’t particularly invested in whether or not there are finite demonstrations of contingent propositions. It is concerned rather with the question of whether or not there is an algorithmic procedure guaranteed to find finite proofs. Given a meta-logical interpretation, it is therefore not so surprising that Leibniz never seems to have worried about the possibility of a lucky proof. Moreover, a meta-logical interpretation suggests two, closely related, ways in which Leibniz could have responded to the Problem of the Lucky Proof if he had considered it. On the first way, he could allow that lucky proofs are possible but deny that they represent a threat to his formal theory of contingency. For if a lucky proof is precisely a proof that one luckily “hits” upon without following an algorithmic procedure, then such proofs do not present even a prima facie challenge to Leibniz’s formal theory of contingency on a meta-logical interpretation. On the second way, Leibniz could maintain that the very notion of a lucky proof is incoherent. In order to take this route, he would have to stipulate that a proof essentially involves a sequence of definitions arrived at by application of an algorithmic process. Given such an understanding of what a proof is, a lucky proof would be as incoherent for Leibniz as the notion of an infinite proof is for many today. The first way of responding to the Problem of the Lucky Proof would cleave closer to our understanding of what a proof is; the second way would allow Leibniz to deny that contingent propositions admit of finite proofs. Both ways of responding are sufficient to undercut the Problem of the Lucky Proof, both draw on Leibniz’s attention to meta-logical considerations, and both would rest on purely formal considerations. On a meta-logical interpretation, the Problem of the Lucky Proof is no problem at all. A meta-logical interpretation of Leibniz’s formal theory of contingency also offers insight into a worry that has recently been revived by Rodriguez-Pereyra and Lodge.

32

Jeffrey McDonough & Zeynep Soysal

They suggest that behind the Problem of the Lucky Proof “there is a deeper and more substantive problem about Leibniz’s infinite analysis conception of contingency”: For even if we are unlucky and it takes a long time to uncover a particular predicate in the definition of the subject, it will always be uncovered in some finite number of steps. The point can be seen more clearly if we associate each one of the infinitely many concepts constituting Peter’s concept with a natural number and we imagine that our analysis uncovers those constituent concepts according to the order of natural numbers. Then no matter what number the concept ‘denier of Christ’ is associated with, it will take only a finite – but probably very large – number of steps to reach this concept from the beginning of our analysis. In this case, although the full decomposition of the infinitely complex ‘Peter’ will not be completeable in a finite number of steps, every concept composing ‘Peter’ can be found in ‘Peter’ after a finite number of steps. (Rodriguez-Pereyra and Lodge 2011, 223; see also Mayer 1980, 239)

Rodriguez-Pereyra and Lodge call this allegedly deeper problem the Problem of the Guaranteed Proof. It represents a prima facie challenge to proof-based interpretations because it suggests that every contingent proposition should admit of a finite proof. That specific challenge needn’t worry us, of course, since we are not defending a proof-based interpretation. But the Problem of the Guaranteed Proof also implies a prima facie challenge to our meta-logical interpretation because it implies that there might be an algorithmic procedure – for example “unpacking” in the order of the natural numbers – that would be guaranteed to find a finite proof for any contingent proposition. If that were the case, then Leibniz’s formal theory of contingency would be doomed to failure even on a metalogical interpretation. It has been claimed that the Problem of the Guaranteed Proof is, in fact, a non-starter. On the way to offering his own (extra-formal) solution to the Problem of the Lucky Proof, Giovanni Merlo suggests that the Problem of the Guaranteed Proof rests on a rather elementary confusion: Think again of a bag containing infinitely many marbles, each numbered with a different natural number. Sure enough, we can imagine a sequence of draws in which marble number ‘2’ is hit upon after finitely many attempts (here is one sequence: 1, 3, 7, 11, 2, 34, . . .). But of course there are many ‘unlucky’ sequences as well: think of any sequence going from marble number ‘150’ onward. Rodriguez-Pereyra and Lodge invite us to “imagine that our analysis uncovers [the] constituent concepts according to the order of natural numbers.” Now, sure enough, if our analysis unfolds according to the order of natural numbers, concept number ‘56’ will be hit upon after 56 steps. But the point is precisely that whether or not our analysis unfolds according to the order of natural numbers is a matter of luck: there are vastly many ‘unlucky’ analyses that evolve randomly and take infinitely long detours [. . .]. So even if there is a problem of lucky proof, I do not think this problem generalizes into a problem of guaranteed proof. (Merlo 2012, 14)

Supposing that the analysis of complete concepts is analogous to drawing marbles from a bag, Merlo denies that there is a Problem of the Guaranteed Proof. For he maintains that there are infinitely many procedures that would not result in a proof of a given contingent proposition. Supposing that the predicate needed to complete a proof is numbered by 2, we might “draw” predicates from the bag forever without finding 2 if, for example, we were to begin our search with 3 and follow the order of the natural numbers. Although instructive, we think that neither side in the debate over the Problem of the Guaranteed Proof has quite put its finger on the deep lesson the challenge offers. Both sides assume that the concepts contained in Peter’s complete concept can be “num-

Leibniz’s Formal Theory of Contingency

33

bered” with the natural numbers (see Merlo 2012, 32–33, n. 20). If this means that the concepts contained in Peter’s complete concept can be exhaustively listed in the order of the natural numbers in an effective manner – if they are recursively enumerable, as it were 20 – then Rodriguez-Pereyra and Lodge will be right in suggesting that any contained, sought-after predicate can be found in a finite number of steps. The fact that there would still be infinitely many procedures that will fail to find the sought-after predicate would be entirely beside the point. If, however, the assumption that the concepts contained in Peter’s complete concept are “numbered” isn’t meant to imply that they can be exhaustively listed in the order of the natural numbers (or in a similarly well-behaved sequence) – that is, if they are not recursively enumerable – then Merlo will be right in suggesting that there is no guarantee that a contained, sought-after predicate will be found in a finite number of steps. The deep lesson of the Problem of the Guaranteed Proof is that there will be a guaranteed finite proof if the domain of predicates specified by a genuine subject’s complete concept, or (perhaps equivalently) the domain of proofs of contingent propositions, can be recursively enumerated. And that deep lesson is exactly what we should expect given a meta-logical interpretation of Leibniz’s formal theory of contingency. For if, for example, the domain of predicates contained in Peter’s complete concept can be recursively enumerated, then it should be possible to algorithmically “search” for precisely the predicate needed in order to construct a finite proof of any true proposition concerning Peter. But if, as the meta-logical interpretation implies, Peter’s complete concept is not recursively enumerable, then there should be no such procedure; an attempt to reduce “Peter is a denier of Christ” to an explicit identity statement might go on forever. On a meta-logical interpretation not only does the Problem of the Lucky Proof go away but the Problem of the Guaranteed Proof vanishes as well. 21 All interpretations of Leibniz’s formal theory of contingency will have to be, to some extent, both constructive and speculative. On this topic especially, Leibniz’s texts suggest a work in progress, an incomplete project with details still being worked out. Nonetheless, there is much to recommend a meta-logical interpretation of Leibniz’s formal theory of contingency. As we argued in the Section 2, Leibniz’s work on ideal languages provides him with the resources for thinking, even if without contemporary precision, about contingency in either logical or meta-logical terms. As we argued in the Section 3, however, attempts to understand Leibniz’s formal theory of contingency in logical terms have all met with serious objections. A meta-logical interpretation offers a promising alternative. 20

More technically, a set of integers is said to be “recursively enumerable” if and only if it is the domain of some partial recursive function. Sets that are recursively enumerable have a search procedure: an effective procedure that, applied to an integer n, eventually terminates if n is in the set but does not terminate if n is not in the set. Metaphorically, we only need to look through the integers, consecutively, and terminate the process once we find the integer that represents the concept p, and keep looking, infinitely, if p isn’t part of the complete concept. 21 Incidentally, we can also now see more precisely what, by Leibniz’s lights, is illegitimate about our derivation above of Peter’s denial of Christ. In a sense, the proof itself is fine; it is formally valid by the rules of Leibniz’s logic. But in assuming that Peter’s complete concept can be represented with the letters “mdy,” where “d” represents the predicate “is a denier of Christ,” we effectively assume that Peter’s complete concept is recursively enumerable, that is, put more intuitively, that there is a procedure that has allowed us to find within Peter’s complete concept precisely the predicate we are looking for and write down “p = mdy.” Absent that assumption, we might apply Leibniz’s rules of substitution and inference forever without arriving at an explicit identity statement.

34

Jeffrey McDonough & Zeynep Soysal

It can be seen as being motivated by an intuitive idea, namely, that the truth of contingent propositions cannot be established with certainty by appeal to non-empirical axioms, definitions and formal procedures alone. In order to settle contingent truths, we must, in practice, appeal to experience. That intuitive, driving idea, in turn fits well with key Leibnizian texts, and, furthermore, solves and provides insight into the most important, long-standing challenges associated with Leibniz’s formal theory of contingency. Without wishing to deny that there are competing threads and lacunae in his treatment, we suggest that, all in all, a meta-logical interpretation provides the most promising approach to Leibniz’s formal theory of contingency. In the next section, we’ll argue that a meta-logical approach also provides an intuitive account of Leibniz’s formal theory of necessity.

5. A Meta-logical Theory of Necessity Propositions, for Leibniz, are either contingent or necessary: if a proposition isn’t contingent, it’s necessary. Leibniz’s formal theory of contingency thus implies a formal theory of necessity, and our interpretation of Leibniz’s formal theory of contingency implies an interpretation of his formal theory of necessity. Framed in terms of his intuitive understanding of the notion of decidability, on our reading, for Leibniz a proposition is necessary if a perfect language would provide us with an algorithmic means – a method analogous to multiplication or division – that we could apply in order to arrive with certainty at a proof of the relevant proposition. Framed in terms of his intuitive understanding of computability, on our reading, for Leibniz a proposition is necessary if a machine could, in principle, be built by us that, working from non-empirical definitions and axioms alone, and following an algorithmic procedure, would be guaranteed to halt at a proof of that proposition. A suitably sophisticated descendent of Leibniz’s Step Reckoner, for example, would be guaranteed to find a proof of any necessary proposition provided that we turned the crank – or left the power on – long enough. The meta-logical interpretation of Leibniz’s formal theory of contingency thus has a natural correlative, namely, a meta-logical interpretation of his formal theory of necessity. On a meta-logical interpretation, Leibniz’s proposed demarcation of the class of necessary propositions would again be formal rather than epistemic. Nonetheless, it too would have epistemic implications that might be seen as providing the intuitive idea or drive behind his formal distinction. For on a meta-logical interpretation, Leibniz’s formal theory of necessity would imply that we can know necessary truths by appeal to non-empirical axioms, definitions and formal procedures alone, that is to say, his formal theory of necessity implies that we can know necessary truths without appealing to ordinary experience. And that, of course, should seem quite plausible. For we do seem to be able to know necessary truths such as 2 + 2 = 4 and the Pythagorean theorem without, say, counting our fingers or measuring bits of paper. As before, Leibniz cannot think that the epistemic property of being knowable independently of ordinary experience might itself provide a satisfying criterion of necessary truth. For he thinks that God at least can know both necessary and contingent propositions without the aid of ordinary experience. Nonetheless, Leibniz’s formal demarcation of necessary propositions entails, and can thus draw support from, the intuitive idea that necessary propositions seem to be knowable by non-empirical means. Echoing our terminology from the previous section, we might

Leibniz’s Formal Theory of Contingency

35

call this intuitive epistemological thought the driving idea behind Leibniz’s formal theory of necessity. That driving idea might be further fleshed out by distinguishing two senses in which necessary propositions may be said to be analytic. In one rough but common sense, a proposition may be said to be semantically analytic if it is true simply in virtue of the concepts involved and the way they combine in the proposition (see for instance KrV A6-7 / B10-11). “Tricycles have three wheels,” for example, might be thought to express a proposition that is true in virtue of the concepts involved and the way they combine in the proposition. Analyticity in this sense suggests one possible ground for holding that analytic propositions can be known without the aid of experience: if analytic propositions are true simply in virtue of the concepts they involve and their combination, then we might expect that anyone who understood those concepts would thereby be in a position to recognize their truth. As competent speakers of English, for example, we are in a position to know that tricycles have three wheels in virtue of our understanding of the concepts tricycle and wheel; we don’t need to conduct experiments or carry out observations in order to know how many wheels tricycles have. Leibniz could allow that all true necessary propositions are analytic in this first sense, that is, that all true necessary propositions may be said to be true in virtue of their constituent concepts. In this sense, however, all true contingent propositions will also be analytic for Leibniz. The proposition expressed by “Peter is a denier of Christ” is, for him, no less true in virtue of the concepts it involves than is the proposition expressed by “Tricycles have three wheels.” This first sense of analyticity therefore does nothing to distinguish between necessary and contingent truths as Leibniz understands them. In another broad but intuitive sense, a proposition might be said to be formally analytic if it is derivable from axioms and definitions. Although less familiar today, formal analyticity was once championed by Rudolf Carnap and gestured at by other logical positivists. 22 This second sense of analyticity suggests a different ground for thinking that analytic propositions can be known to be true without the aid of ordinary experience: if analytic propositions are derivable from axioms and definitions alone, then we might expect that anyone armed with those axioms and definitions will be in a position, at least in principle, to establish an analytic proposition without consulting the empirical world, indeed even without grasping the meanings of the terms used to express that proposition. 23 As competent logicians, we may know that 2 + 2 = 4 by appealing to axioms, definitions, and derivation rules, and we may do so even if we do not grasp the meanings of “2,” “ + ,” “=,” and “4”; indeed we may establish that 2 + 2 = 4 even if we are non-conscious computers performing mechanistic operations. If we say that a proposition is derivable only if it can be established by a finite derivation following a general algorithmic procedure or rule, 22

More precisely, Carnap proposed that analyticity might be understood as a property of sentences of formal languages with an analytic sentence (an “L-true” sentence) being one that is true in virtue of the syntactic (or, in his later period, semantic) rules of the relevant formal system. See, for example, Carnap 1934 and 1939, 13, and Ayer 1934, 70, n. 1. Carnap’s later definition of analyticity is equivalent, in more modern terms, to Tarski’s inductive definition of truth. 23 We set aside here complications generated by so-called “conceptual role semantics.” If the meanings of terms are given by their inferential roles, then the distinction between what we are calling semantic and formal theories of analyticity might collapse. In that case, we could say that contingent propositions are not semantically analytic for Leibniz. For further discussion of these issues, see for instance Boghossian 1996.

36

Jeffrey McDonough & Zeynep Soysal

then formal analyticity will serve as a distinguishing feature of analytic truths as Leibniz understands them. For Leibniz, necessary truths are formally analytic, contingent truths are not. The view that at least mathematical propositions are formally analytic was plausible enough that it was widely embraced in the early part of the twentieth century, most prominently by David Hilbert and his followers. 24 Nonetheless, Leibniz himself may have had some reason for concern. His thinking about the modal status of propositions in terms of finite and infinite analyses seems to have been sparked by his early work on infinite numerical series. 25 And, indeed, it is easy to see something analogous between the suggestion that, say, 2 = 1/1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 etc. and the suggestion that (say) Peter = an early leader of the Christian Church, a denier of Christ, a martyr under Emperor Nero, etc. But the analogy also raises a rather obvious puzzle, a puzzle that has been surprisingly overlooked by Leibniz’s commentators (although, see Sleigh 1990, 87). To the extent that we think that statements such as “2 = 1/1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 etc.” express truths, we are inclined to think that they express necessary truths. If the sum of the reciprocal triangular numbers equals 2, then presumably it equals 2 necessarily. But, in spite of the analogy, or, indeed, paradoxically because of the analogy, it seems we are – on Leibniz’s formal theory of necessity – supposed to draw exactly the opposite conclusion in the case of statements involving complete concepts and their predicates. That is to say, the analogy is supposed to support the disanalogous conclusion that statements such as “Peter = an early leader of the Christian Church, a denier of Christ, a martyr under Emperor Nero, etc.” express not necessary but rather contingent truths. For the sake of shorthand, let us call this apparent difficulty the Surprising Tension. 26 There is textual evidence that Leibniz recognized the Surprising Tension himself. In a difficult passage from the main text of his most developed treatment of logic, his General Inquires about the Analysis of Concepts and Truths (1686), Leibniz writes: [I]f, when the analysis of the predicate and of the subject has been continued, a coincidence can never be proved, but it does at least appear from the continued analysis (and the progression and its rule which arise from it) that a contradiction will never arise, then the proposition is possible. But, if in analyzing it, it appears from the rule of progression that the reduction has reached a point at which the difference between what should coincide is less than any given difference, then it will have been proved that the proposition is true. If, on the other hand, it appears from the progression that nothing of this sort will ever arise, then it has been proved to be false – that is to say, in the case of necessary propositions. (C 374 /P 63–64; see also A 6.4.760-761) 27 24

For an engaging discussion of Hilbert and his program see Davis 2000, 83–106. Leibniz’s studies of infinite series can be found in A 7.3. For helpful, but advanced, introductions to those studies see the Akademie editors’ introduction (Einleitung) to that volume as well as Arthur 2006. For a more accessible introduction see Arthur 2014, 86–89. 26 Now it is, of course, possible to prove that 2 = 1/1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 in a finite number of steps. So, such propositions are not necessarily inconsistent with Leibniz’s formal theory of necessity. Nonetheless, insofar as they can be proved in a finite number of steps they are – by Leibniz’s lights – disanalagous to statements such as Peter = an early leader of the Christian Church, a denier of Christ, a martyr under Emperor Nero, etc. The tension is not that the “2-series” is necessary and the “Peter-series” contingent, but rather that the necessary “2-series” is supposed to provide us with insight, or a model, for understanding the contingency of the “Peterseries.” We would like to thank an anonymous referee for pressing us on this point. 27 We have followed C 374 and Log. 63–64 in rendering the last sentence of this passage. Couturat uses corner brackets “〈. . .〉” to “enclose words or phrases added by Leibniz,” and renders the last sentence: “〈sin contra 25

Leibniz’s Formal Theory of Contingency

37

On a natural reading, Leibniz means to suggest here that where an infinite series converges on a limit, a proposition stating the equality of that series with that limit expresses a necessary, true proposition; and, conversely, where an infinite series either converges on a different limit, or no limit at all, then the same statement expresses a necessary, false proposition. As a view concerning the truth conditions and modal status of a certain class of propositions, that all seems reasonable enough. Leibniz, however, sees that it stands in tension with his formal theory of necessity. In the margin of the passage just quoted, he writes: A doubtful point: is everything true which cannot be proved false, or everything false which cannot be proved true? What, then, of the cases of which neither of these holds? It must be said that both truth and falsity can always be proved, at any rate by an analysis which is carried to infinity. But then it is contingent, i. e. it is possible that it is true, or that it is false. The same is the case with concepts: namely, that in an analysis which is carried to infinity they are manifestly true or false, that is, to be admitted to existence, or not. (C 374 /P 64, n. 1; see also A 6.4.761, n. 30)

Leibniz’s marginal remark is prompted, we conjecture, by his seeing a tension between his first thought that propositions stating the equality of infinite series with limit values are either necessarily true or necessarily false, and the implication of his formal theories of contingency and necessity that such propositions should be reckoned to be contingently true or contingently false. If that’s right, it appears that Leibniz himself may have recognized that the very sorts of examples that seem to have sparked his formal theory of necessity stand in tension with one of our most basic intuitions concerning the modal status of propositions, namely, that mathematical propositions are necessarily true or necessarily false. Perhaps in response to such concerns, late in the General Inquires, Leibniz offers a possible response to the Surprising Tension. He writes:

apparet ex progressione tale quid nunquam oriendum, demonstratum esse falsam 〈scilicet in necessariis.〉〉” It is clear from checking the manuscript (LH 4 7C Bl.24 v) that that is what Leibniz wrote. Couturat’s conjecture that the fragment “sin . . . necessariis” was added after the next line of text was written is also plausible from the manuscript as the fragment appears to be squeezed in between two lines of text. His conjecture that the fragment “scilicet in necessariis” represents a further addition is, in our opinion, not implausible but also not strongly supported by the manuscript. Those words do appear more cramped in the manuscript, and could be a still later addition, but the writing might also be cramped simply because of the size of the words appearing below them, and perhaps that is the more likely explanation. In the Akademie edition, however, the end of the sentence is rendered as “scilicet in 〈contingentibus〉” which would raise difficulties for our interpretation of the passage above. The Akademie edition rendering, however, represents both a small typographical error and an editorial decision. It represents a typographical error insofar as, given the conventions of the Akademie edition, the word “contingentibus,” as an editorial addition, should be enclosed in square brackets rather than corner brackets, which are used in the Akademie edition to indicate a conjecture concerning words that cannot be made out with certainty. It represents an editorial decision insofar as it replaces in the main text what Leibniz wrote (“necessariis”) with a conjecture about what he meant to write (“contingentibus”). There is no doubt about what Leibniz actually wrote (“necessariis”). We respectfully disagree with the editorial decision. The replacement (“contingentibus”) would indeed make better sense of the main text itself, but the original reading (“necessariis”) makes far better sense overall once Leibniz’s marginal note is taken into consideration. Although it is impossible to know with certainty even from the manuscript, our own considered view is that Leibniz wrote the fragment “sin . . . necessariis” after the sentence that follows it, later noticed the philosophical tension we discuss above, and subsequently added the marginal note beginning with “Dubium . . ..” We are grateful to Dr. Stephan Meier-Oeser of the Leibniz-Forschungsstelle Münster for invaluable discussion of this passage and for providing us with a copy of the manuscript.

38

Jeffrey McDonough & Zeynep Soysal (133) A true necessary proposition can be proved by reduction to identical propositions, or by reduction of its opposite to contradictory propositions; hence its opposite is called ‘impossible’. (134) A true contingent proposition cannot be reduced to identical propositions, but is proved by showing that if the analysis is continued further and further, it constantly approaches identical propositions, but never reaches them. [. . .] (135) So the distinction between necessary and contingent truths is the same as that between lines which meet and asymptotes, or between commensurable and incommensurable numbers. (A 6.4.776 /Log. 77)

In this passage, Leibniz seems prepared to bite the bullet implied jointly by his formal theory of necessity and his understanding of propositions involving infinite series. Pressed by the Surprising Tension, one could, after all, simply give up the conviction that all mathematical propositions are necessarily true or necessarily false. Leibniz thinks that some mathematical propositions can be finitely, algorithmically demonstrated, and those are to be said to be necessarily true or necessarily false. Leibniz thinks other mathematical propositions cannot be so demonstrated. In the passage just above, he appears ready to say that those mathematical propositions are to be said to be contingently true or contingently false. This response to the Surprising Tension would provide us with at least one right result: the analogy between propositions involving infinite series and propositions involving complete concepts would be upheld and both kinds of propositions could be counted as true. Nonetheless, this “solution” to the Surprising Tension would clearly come at a high cost. For the thought that mathematical propositions, if true or false, must be necessarily true or necessarily false, might reasonably be regarded as a touchstone upon which the success or failure of a theory of the modal status of propositions can be measured. Biting this bullet would seem to be more reckless than brave. Nowadays, of course, we don’t think that demonstrations of summations involving infinite series must require infinitely many steps. Nonetheless, insofar as the Surprising Tension arises from the undecidability of some mathematical propositions, we can recognize that Leibniz was right to be worried about the implications of his formal theory of necessity. As we’ve noted, intuitive notions of derivability, decidability, and computability were given rigorous formulation with the explosion of meta-logic in the late nineteenth and early twentieth centuries. In particular, Gödel’s first incompleteness theorem showed that, for any sufficiently strong consistent formal system, there are formulas that are (formally) undecidable in that formal system. By reflecting on the construction, we see that the particular undecidable formulas that Gödel constructed are in fact true (and, presumably, thus also necessarily true). So, contrary to the implications of Leibniz’s formal theory of necessity, for any formalization of mathematics, there will be necessarily true propositions for which there is no computational procedure that will output their proof from that formalization (for a more precise characterization of Gödel’s results, see for instance Raatikainen 2015). Leibniz may have been wrong in seeing a worry on the horizon arising specifically from infinite series, but he was surely right to worry that all mathematical truths might not admit of finite demonstrations as his formal theory of necessity requires. 28 28

Of course, a formula that’s (formally) undecidable within a given formal system may be decidable relative to a suitable extension of that formal system (and that extension will in turn have undecidable sentences of its own).

Leibniz’s Formal Theory of Contingency

39

If the present account of Leibniz’s formal theories of contingency and necessity is on track, its greatest irony is that of the two halves of Leibniz’s proposal, it is the half concerning necessary truths that should be reckoned the more suspect. Commentators have generally seen Leibniz’s logical commitments as pushing him into the arms of necessitarianism. His formal theory of contingency has been scrutinized and is often viewed as a last-ditch, unsuccessful effort to resist the conclusion that all propositions are necessary. Leibniz’s formal theory of necessity, in contrast, has generally been ignored, its success, as it were, seemingly guaranteed by the failure of his formal theory of contingency. As we read him, however, this familiar story gets things nearly backwards. Leibniz has a plausible and, in spirit at least, even successful formal theory of contingency. Although we may trifle over details, Leibniz is essentially correct in suggesting that contingent propositions cannot be algorithmically demonstrated. Furthermore, as we read him, Leibniz has an interesting, substantive, and even plausible theory of necessity. Again, while we may trifle over details, it is easy to sympathize with his view that all necessary propositions should be demonstrable from non-empirical definitions and axioms, that is, that they should be formally analytic. Developments since Leibniz’s time have done nothing to undermine his formal theory of contingency; we should still agree with Leibniz that in order to determine the truth of contingent propositions we must ultimately consult with experience. Developments since Leibniz’s time have, however, undermined his formal theory of necessity. If standard interpretations of Gödel’s incompleteness results are correct, we should no longer agree with Leibniz that all necessary propositions must be demonstrable from a single fixed set of definitions and axioms alone. Leibniz’s formal theory of necessity thus seems to be less well founded than his formal theory of contingency, although it should be added immediately that even its most serious difficulties are evident now only in light of some of the most astounding results to have ever occurred in the history of mathematics and logic.

6. Conclusion The aim of the present essay has been to offer a novel interpretation of Leibniz’s notorious “infinite analysis” theory of contingency. In the broadest strokes, we’ve argued that Leibniz’s theory should be understood against the backdrop of his lifelong interest in ideal languages, his formal understanding of logical demonstration, and his intuitive grasp of the meta-logical notions of decidability and computability. According to Leibniz’s formal theory of necessity, necessary propositions are guaranteed to be demonstrable by means of an algorithmic, formal procedure and therefore are guaranteed to be knowable, in principle, a priori even by finite creatures. According to Leibniz’s formal theory of contingency, contingent propositions are not guaranteed to be demonstrable by means of an algorithmic, formal procedure and therefore are not guaranteed to be knowable, even in principle, a priori by finite creatures. Placed in their proper context, and with an

As we read him, Leibniz is thinking that necessary propositions are decidable relative to a unique, complete formal system – the one given by the unique, complete, ideal language. It would therefore not be in the spirit of the view we are attributing to him to suppose that propositions are necessary if they are decidable in some formal system or other.

40

Jeffrey McDonough & Zeynep Soysal

appreciation of the sophistication of Leibniz’s logical efforts, we can see Leibniz’s formal theories of necessity and contingency for what they are, namely, genuinely profound attempts to draw a distinction between necessary and contingent propositions in terms of the formal properties of the statements that would be used to express them in an ideal language. Although it is, of course, still possible to object to Leibniz’s theory, most obviously by challenging its background assumptions and by drawing on the full resources of contemporary mathematical logic, standard objections of the sort that we might have expected Leibniz to appreciate, simply fall away. While not unassailable, Leibniz’s formal theories of necessity and contingency turn out to be, when properly understood, both surprisingly plausible and eerily prescient. Contra Bennett (2001, 329), it is, we think, hard to see how Leibniz’s efforts to draw a formal distinction between necessary and contingent propositions should not be of interest to philosophically engaged historians of philosophy (as opposed, presumably, to mere “antiquarians”). For Leibniz’s efforts in this regard lie at a crucial, if still not well-understood, intersection of philosophical concerns that date from Leibniz’s earliest philosophical insights. His formal theories of necessity and contingency are fed by, and in turn feed into, his thinking about truth, language, logic, thought, and the foundations of mathematics. And that is just with respect to Leibniz’s own work. Taking a broader view, Leibniz’s formal theories of necessity and contingency, and the foundations upon which they rest, are important themes in the long conceptual history of logic, they are characters that emerge in a time of crisis, are unduly neglected in Leibniz’s own time, and reemerge in new guise in the twentieth century renaissance of mathematical logic. There is much here – we suggest – for philosophically minded historians of philosophy to explore. Finally, it is even easy, we think, to see how Leibniz’s efforts to draw a formal distinction between necessary and contingent propositions might be of interest even to nonhistorically-minded contemporary philosophers. As is the case with many of his most important mathematical studies, Leibniz enjoyed both the daunting challenge but also immense freedom of working on enduring foundational issues before a dominant consensus had formed. This absence of constraints can make understanding his efforts difficult. Setting out on his own, he often chases down dead ends, explores contradictory paths, and abruptly changes his mind. But the absence of constraints also means that he often considers connections, leads and possibilities that we, conditioned by consensus, are apt to overlook. Many of those options have, of course, been closed down for good reason, and in such cases we gain the most from Leibniz’s forays by emerging with a better appreciation of why consensus has formed in the way that it has. But it is always possible that in some of those options Leibniz saw something to which we are now blind, a possibility or way forward that we might better glimpse by standing on his shoulders. The likes of Frege, Gödel, and Carnap all thought that in connection with the tissue of concerns discussed above Leibniz had had profound insights that are merely waiting to be rediscovered. They might still be right. 29

29

Versions of this paper were presented at the Libori Summer School at the Center for the History of Women Philosophers and Scientists at the University of Paderborn, at the Chicago Modern Philosophy Roundtable at Roosevelt University, to the Leibniz Society of North America at the American Philosophical Association Eastern Division Meeting, to the Philosophy Department at the University of Notre Dame and to a seminar

Leibniz’s Formal Theory of Contingency

41

Bibliography Adams, R. 1994. Leibniz: Determinist, Theist, Idealist. Oxford: Oxford University Press. Antognazza, M. R. 2009. Leibniz: An Intellectual Biography. Cambridge: Cambridge University Press. Arthur, R. T. 2006. The Remarkable Fecundity of Leibniz’s Work on Infinite Series. Annals of Science 63, 221–225. Arthur, R. T. 2014. Leibniz. Malden, MA: Polity Press. Ayer, A. J. 1934. Language, Truth and Logic. 2nd ed. London: Victor Gollancz Ltd. Beeley, P. 2014. Review of Nicholas Rescher, Leibniz and Cryptography: An Account on the Occasion of the Initial Exhibition of the Reconstruction of Leibniz’s Cipher Machine. The Leibniz Review 24, 111–122. Bennett, J. 2001. Learning from Six Philosophers: Descartes, Spinoza, Leibniz. Vol. I. Oxford: Oxford University Press. Blumenfeld, D. 1985. Leibniz on Contingency and Infinite Analysis. Philosophy and Phenomenological Research 45, 483–514. Boghossian, P. A. 1996. Analyticity Reconsidered. Noûs 30, 360–391. Carnap, R. 1934. The Logical Syntax of Language. Smeaton (tr.) 1937. New York, NY: Humanities. (Original: Carnap, R. 1934. Logische Syntax der Sprache. Vienna: Springer.) Carnap, R. 1939. Foundations of Logic and Mathematics, International Encyclopedia. Vol. I, no. 3, Chicago, IL: University of Chicago Press. Carriero, J. 1993. Leibniz on Infinite Resolution and Intra-mundane Contingency. Part One: Infinite Resolution. Studia Leibnitiana 25, 1–26. Carriero, J. 1995. Leibniz on Infinite Resolution and Intra-mundane Contingency. Part Two: Necessity, Contingency, and Divine Faculties. Studia Leibnitiana 27, 1–30. Church, A. 1936. An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics 58, 354–363. Couturat, L. 1901. La Logique de Leibniz: D’après des Documents Inédits. Paris: Felix Alcan. Curley, E. M. 1972. The Root of Contingency. In: Frankfurt, H. (ed.). Leibniz: A Collection of Critical Essays. Garden City, NY: Doubleday Anchor, 69–97. Davis, M. 2000. The Universal Computer: The Road from Leibniz to Turing. New York, NY: W. W. Norton and Company. Eco, U. 1993. The Search for the Perfect Language. Fentress (tr.) 1997. Malden, MA: Blackwell Publishers Inc. (Original: Eco, U. 1993. La Ricerca della Lingua Perfetta nella Cultura Europea. Roma and Bari: Laterza.) Frege, G. 1884. The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number. Austin (tr.) 1980. Chicago, IL: Northwestern University Press. (Original: Frege, G. 1884. Die Grundlagen der Arithmetik: Eine logisch-mathematische Untersuchung über den Begriff der Zahl. Breslau: Koebner.) Gödel, K. 1986. On Undecidable Propositions and Formal Mathematical Systems. In: Feferman, S. et al. (eds.). Collected Works I. Publications 1929 – 1936. Oxford: Oxford University Press, 346–371. Goldfarb, W. 2001. Frege’s Conception of Logic. In: Floyd, J. /Shieh, S. (eds.). Future Pasts: The Analytic Tradition in Twentieth Century Philosophy. Oxford: Oxford University Press, 25–41. Goldfarb, W. 2011. On Gödel’s General Philosophical Viewpoint. Unpublished manuscript.

at Harvard University. We would like to thank audiences at those events as well as two anonymous referees for their helpful feedback. We are also grateful for discussions with Patricia Blanchette, Douglas Blue, Thomas Feeney, Jens Kipper, Sam Newlands, and Charles Parsons as well as written feedback from Paul Lodge and Gonzalo Rodriguez-Pereyra. Special thanks are due to Sam Levey for many helpful discussions and insightful feedback and to the Center for Philosophy of Religion at the University of Notre Dame for its generous support of a sabbatical leave for Jeffrey McDonough during which much of this paper was drafted.

42

Jeffrey McDonough & Zeynep Soysal

Hacking, I. 1973. Leibniz and Descartes: Proof and Eternal Truths. Proceedings of the British Academy 59, 175–188. Hacking, I. 1974. Infinite Analysis. Studia Leibnitiana 6, 126–130. Hacking, I. 1978. A Leibnizian Theory of Truth. In Hooker, M. (ed.). Leibniz: Critical and Interpretive Essays. Baltimore, MD: The Johns Hopkins University Press, 185–195. Hawthorne, J. /Cover, J. 2000. Infinite Analysis and The Problem of the Lucky Proof. Studia Leibnitiana 32, 151–165. Ishiguro, H. 1972. Leibniz’s Philosophy of Logic and Language. London: Duckworth. Kluge, E. H. W. 1977. Frege, Leibniz, et alii. Studia Leibnitiana 9, 266–274. Leibniz, G. W. 1685. Leibniz on His Calculating Machine. Kormes (tr.) 1929. In: Smith, D. (ed.). A Sourcebook in Mathematics. New York, NY: McGraw-Hill, 173–181. (Original: Leibniz, G. W. 1685. Aufzeichnungen von Leibniz zur Rechenmaschine. LH XLII 5, Bl. 69. URL: 〈http: // digitale-sammlungen.gwlb.de / resolver?id=00066559〉.) Leibniz, G. W. 1691. Leibniz an Huygens Hannover ce 20/30 de Février 1691. In: Gerhardt, C. I. (ed.) 1899. Der Briefwechsel von Gottfried Wilhelm Leibniz mit Mathematikern. Berlin: Mayer and Müller, 639–641. Levey, S. 2014. Logical Theory in Leibniz. In: Look, B. C. (ed.). The Bloomsbury Companion to Leibniz. New York, NY: Bloomsbury, 110–135. Locke, J. 1689. An Essay Concerning Human Understanding. Nidditch, P. (ed.) 1975. Oxford: Oxford University Press Maher, P. 1980. Leibniz on Contingency. Studia Leibnitiana 12, 236–242. Malink, M. /Vasudevan, A. 2016. The Logic of Leibniz’s Generales Inquisitiones de Analysi Notionum et Veritatum. The Review of Symbolic Logic 9, 686–751. Mates, B. 1986. The Philosophy of Leibniz: Metaphysics and Language. New York, NY: Oxford University Press. Menger, K. 1994. Reminiscences of the Vienna Circle and the Mathematical Colloquium. Dordrecht: Kluwer Academic Publishers. Merlo, G. 2012. Complexity, Existence and Infinite Analysis. Leibniz Review 22, 9–36. Parsons, C. 2010. Gödel and Philosophical Idealism. Philosophia Mathematica 3, 167–192. Parsons, C. 2014. Analyticity for Realists. In: Kennedy, J. (ed.). Interpreting Gödel. Cambridge: Cambridge University Press, 131–150. Raatikainen, P. 2015. Gödel’s Incompleteness Theorems. In: Zalta, E. (ed.). The Stanford Encyclopedia of Philosophy (Spring 2018 Edition). URL: 〈https://plato.stanford.edu /archives /sum2018 /entries / goedel-incompleteness / 〉. Rescher, N. 1954. Leibniz’s Interpretation of his Logical Calculi. The Journal of Symbolic Logic 19, 1–13. Rescher, N. 2012. Leibniz and Cryptography: An Account on the Occasion of the Initial Exhibition of the Reconstruction of Leibniz’s Cipher Machine. Pittsburgh, PA: University of Pittsburgh Library System. Rodriguez-Pereyra, G. /Lodge, P. 2011. Infinite Analysis, Lucky Proof, and Guaranteed Proof in Leibniz. Archiv für Geschichte der Philosophie 93, 222–236. Rutherford, D. 1995. Philosophy and Language in Leibniz. In: Jolley, N. (ed.). The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press, 224–269. Sleigh, R. C. 1990. Leibniz and Arnauld: A Commentary on their Correspondence. New Haven, CT: Yale University Press. Steward, S. 2014. Solving the Lucky and Guaranteed Proof Problems. Leibniz Review 24, 29–46. Turing, A. M. 1937. On Computable Problems, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 2.42, 230–265. van Atten, M. /Kennedy, J. 2015. On the Philosophical Development of Kurt Gödel. In: van Atten, M. Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Switzerland: Springer International Publishing, 95–145.

Leibniz’s Formal Theory of Contingency

43

van Atten, M. 2015. Gödel’s Dialectica Interpretation and Leibniz. In: van Atten, M. Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Switzerland: Springer, 65–74. van Heijenoort, J. 1967. From Frege to Gödel. Cambridge, MA: Harvard University Press.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism Julia Borcherding, New York University

Abstract Leibniz’s claim that it is possible for us to gain metaphysical knowledge through reflection on the self has intrigued many commentators, but it has also often been criticized as flawed or unintelligible. A similar fate has beset Leibniz’s arguments against materialism. In this paper, I explore one of Leibniz’s lesser-known arguments against materialism from his reply to Bayle’s new note L (1702), and argue that it provides us with an instance of a Leibnizian “argument from reflection”. This argument, I further show, does not constitute a flawed appeal to mere introspection, but is in fact securely grounded in an important corollary of the Principle of Sufficient Reason: Leibniz’s Principle of Intelligibility.

1. Introduction While modern commentators have offered different readings of Leibniz’s argumentative strategy against materialism, nearly all of these readings commit Leibniz to an argument from ignorance. Leibniz, it is claimed – usually with an eye towards his famous “Mill Argument” in Monadology § 17 – infers from the fact that we can find nothing in matter, however organized, to explain mentality that there could not be such an explanation. 1 It is then pointed out that this is an argument bound to fail, because it, in the words of Paul Churchland, “simply assumes without question that the expected failures of perception will reflect the absence of the target phenomenon rather than the absence of the ability to recognize them.” (Churchland 1995, 192–193). In this paper, I argue that a little-known argument against materialism from Leibniz’s reply to Pierre Bayle’s new note L (1702) escapes this objection. Far from being a weak inference to the best explanation, I suggest that this argument presents us with a compelling instance of a Leibnizian “argument from 1

See Wilson 1974, Rorty 1979, 26–27, Searle 1983, 267–268, Seager 1991 and Churchland 1995, 191–193, among others. Unlike the argument I will consider here, the Mill Argument in Mon. 17 turns on the notion of perception simpliciter: “Moreover, we must confess that perception, and what depends upon it, is inexplicable in terms of mechanical reasons, that is through shapes and motions. If we imagine that there is a machine whose structure makes it think, sense, and have perceptions, we could conceive it enlarged, keeping the same proportions, so that we could enter into it, as one enters a mill. Assuming that, when inspecting its interior, we will find only parts that push one another, and we will never find anything to explain a perception. And so, one should seek perception in the simple substance and not in the composite or in the machine” (GP 4.609 /PE 215). In addition to the abbreviations for editions and translations of Leibniz’s text listed in the reference section of this volume, I will use the following abbreviations for Leibniz’s texts: DM = Discourse on Metaphysics; PNG = Principles of Nature and Grace, Based on Reason; Mon. = The Principles of Philosophy, or, the Monadology (cited by paragraph number; quotations generally follow the translation by Ariew and Garber [PE]); New Essays = New Essays on Human Understanding (cited by book, paragraph, and section number; quotations generally follow the translation by Remnant and Bennett [NE]).

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

45

reflection” that moves from an internal reflective experience of ourselves (in this case: an experience of ourselves as engaging in the action of thought, conscious perception, or reflection) to a metaphysical conclusion (that we are immaterial substances). I show that this argument, while seemingly reliant on brute appeals to inexplicability and perceptual immediacy, finds a solid foundation in a principle Donald Rutherford has termed Leibniz’s “Principle of Intelligibility” (henceforth: PI), a powerful corollary of the Principle of Sufficient Reason. (Rutherford 1992) To an extent, the interpretation I offer in this paper can be viewed as an attempt to unify two interpretative strands that have been proposed with respect to Leibniz’s strategy against the materialist: A classic interpretation by Margaret Wilson, who suggests that Leibniz mainly relies on considerations about unity or simplicity, and two readings proposed more recently by Marleen Rozemond and Paul Lodge, who both argue that the notion of action or activity may in fact be central to Leibniz’s argument. (Wilson 1974; Rozemond 2014; Lodge 2014) Moreover, my discussion expands on the idea, put forward by both Rozemond and Stewart Duncan, that considerations regarding conceivability or intelligibility may have an important role to play for Leibniz when it comes to arguing against the materialist. (Rozemond 2014; Duncan 2011) However, while these interpretations keep their focus on Leibniz’s Mill Argument, I will mainly concentrate on the “reflection argument” that I take him to provide in his response to Bayle and some related texts. 2 My plan is as follows: I first contextualize Leibniz’s argument by briefly outlining the important function Leibniz attributes to our internal experience in uncovering metaphysical truths. In the first half of the paper, I then go on to provide a detailed reconstruction of a Leibnizian “reflection argument” against materialism, based on Leibniz’s reply to Bayle as well as a number of related writings. This argument turns on the claim that we know from internal experience that we are engaging in thought, conscious perception, or reflection, and, further, that thoughts, conscious perceptions and reflections are spontaneous actions involving a simple awareness. 3 These features of thought, however, Leibniz contends, are inexplicable as modifications of a material substance. In the second half of the paper, I show that this argument is not a weak inference to the best explanation, but a compelling argument from conceivability supported by the PI.

2. The Power of Reflection In § 30 of the Monadology, Leibniz explains how our knowledge of necessary and eternal truths distinguishes us from animals, and grounds our capacity for abstract reasoning and reflection. 4 This claim about the role of reflection in constituting human reason is familiar from tradition, and has stirred little controversy among interpreters. However, Leibniz then goes on to make a further claim that has caused considerably more puzzlement.

2

For the purposes of this paper, I will bracket the potentially very difficult question whether the mill passage could or should ultimately be interpreted along the same lines as the texts I discuss here. 3 For the sake of brevity, I will sometimes use “thought” to encompass both reflection and conscious perception. 4 “But it is the knowledge of necessary and eternal truths which distinguishes us from simple animals and gives us reason and the sciences, lifting us to the knowledge of ourselves and of God. It is this within us which we call the rational soul or mind,” Mon. § 30 (GP 6.612 /PE 217).

46

Julia Borcherding

Our capacity for reflection, he argues, enables us to direct our reflective attention on our own minds, and in doing so, become acquainted with the nature of substance and other metaphysical concepts: It is also through the knowledge of necessary truths and through their abstractions that we rise to reflective acts, which enable us to think of that which is called “I” and enable us to consider that this or that is in us. And thus, in thinking of ourselves, we think of being, of substance, of the simple and of the composite, of the immaterial and of God himself, by conceiving that that which is limited in us is limitless in him. 5

Leibniz emphasizes the power of reflection to unearth metaphysical concepts and truths, and his commitment to this idea can hardly be doubted. In a note written after 1704, for example, he asserts that internal experience shows us that we are substances, since we would not even be acquainted with substance, were it not for “our own intimate experience when we perceive the self.” (Grua 2.558) Moreover, against Malebranche’s skeptical stance regarding the scope and certainty of self-knowledge, he argues that he [Malebranche] has said that we know our soul by an interior feeling of consciousness and that because of this the knowledge of our soul is more imperfect than that of things, which we know in God. [. . .] The truth is that we see everything in our souls, and that the knowledge we have of the soul is very true and correct provided we have paid attention to it; and that it is by the knowledge we have of the soul that we know being, substance, and even God. (GP 6.578) 6

Finally, in a letter to Burnett, Leibniz extends his claims about the power of reflection even further, arguing that Locke did not sufficiently comprehend that our knowledge of necessary truths does not depend on the senses, “but on the consideration of the nature of the soul, which is a being, a substance, having unity, identity, action, passion, duration, etc.” We ought not to be surprised, he continues, that “these ideas and the truths which depend on them are found in us, although we need reflection to perceive them, and sometimes need experiences to elicit our reflection or attention.” 7 In view of such passages, Nicholas Jolley observes that there is a “marked tendency” in Leibniz’s writings “to emphasize the knowledge of mind that we have a posteriori through reflection or introspection.” 8 And Margaret Wilson similarly points out that Leibniz at times writes “as if we could self-evidently experience ourselves as simple or immaterial

5

Mon. § 30 (GP 6.612 /PE 217); see also PNG § 5 (GP 6.600-601); Echantillon de Reflexions sur le II. Livre (GP 5.23): “It is very true that our perceptions or ideas come either from the exterior senses, or from the internal sense, which can be called reflection: but this reflection is not limited to the operations alone of the mind, as is stated (chap. 1, par. 4); it reaches even to the mind itself, and it is in the consciousness of self, that we perceive substance.” 6 See also GP 5.23: “It is very true that our perceptions or ideas come either from the exterior senses, or from the internal sense, which can be called reflection: but this reflection is not limited to the operations alone of the mind, as is stated (chap. 1, par. 4); it reaches even to the mind itself, and it is in the consciousness of self, that we perceive substance.” 7 Leibniz to Thomas Burnet, 26 May 1706 (GP 3.307-308), my italics. Cf. Leibniz to Bierling, ca. 1709 (GP 7.489). Further passages include: DM 27; DM 34; GP 3.339, 479; GP 4.502; New Essays pref. (GP 5.45); New Essays I.iii.3; New Essays II.vii.1; Dut. 2.223; PNG § 5; Mon. § 29–30. 8 Jolley 1998, 180. Different aspects of Leibniz’s account of self-knowledge have been examined by McRae 1976; Brown 1985; Kulstad 1983 and 1991; Schüssler 1992; Cramer 1994; Jolley 1998; Gennaro 1999; Wilson 1999; Bobro 2005; Di Bella 2005; Leduc 2010; Thiel 2011. However, there is no comprehensive, unified study.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

47

entities.” 9 However, she adds, he also “is extremely inexplicit” about how we can move from our apprehension of the self in conscious perception to warranted conclusions about our substantial nature. (Wilson 1974, 508) Wilson’s assessment is shared by a number of other commentators, who then typically display one of two reactions: The first response (call this the “pessimistic” response) is to assert, as Wilson eventually does, that Leibniz’s views on the subject are at best incomplete, and at worst incoherent. (Wilson 1999, 379; Jolley 1998, 173; see also Mackie 1976, 213–214) Moreover, we may wonder whether they are not at odds with his own critical stance towards a Cartesian epistemology based on introspective experiences of the self. For at least prima facie, it is surprising to find a philosopher so vehemently critical of Cartesian epistemology for its supposedly naïve reliance on introspection and psychological criteria of distinctness arguing that some of the most fundamental notions and truths of metaphysics could be grounded in this way. 10 In contrast with this skeptical attitude, a second line of response (call this the “optimistic” response) to Leibniz’s assertions regarding the power of reflection suggests that perhaps his views on the matter only seem obscure because we were expecting explanations where there were never meant to be any. Such commentators typically emphasize the basic and immediate nature of our apprehension of the self for Leibniz. Robert Sleigh, for instance, argues that it was “a basic brute intuition of the self” that “told Leibniz [. . .] that he is a simple substance”, while Robert McRae explains along very similar lines that for Leibniz, we simply have a “direct apprehension” of ourselves “as being, as one, as acting”, and as a consequence acquire the ideas of being, or unity, or action.” 11 On such a reading, the puzzlement experienced by Wilson and others is merely due, as Marc Bobro puts the point, to our expecting “to find something a bit more sophisticated” in place of the very simple answer Leibniz in fact provides. (Bobro 2005, 30) Even though I lack the space to fully argue this point here, I believe that neither Wilson’s pessimism nor Bobro’s optimism are warranted. To begin with, both the tone of Leibniz’s remarks on Malebranche’s stance towards self-knowledge and the cognitive language he employs in both the Monadology passage as well in his remarks to Burnet should make us wary of the optimistic reading. Against Malebranche, he cautions that reflective knowledge of the soul is “very true and correct provided we have paid attention to it.” (GP 6.578, my italics) And to Burnet, he writes that it is “the consideration” (la consideration) of the nature of the soul as we find it in internal experience which furnishes 9

Wilson 1974, 508. According to Wilson, Leibniz holds both that “I” denotes a particular substance, and that selfconsciousness can provide us with an original and true understanding of the general nature of substance (of which we are instances). 10 For some of Leibniz’s various criticisms of Cartesian epistemology, see DSR 57–67; GP 1.369-74; C 94–95, 196– 203; and the writings against Cartesianism collected in GP 4.274-406. On Leibniz’s extensive agreement with the anti-Cartesianism of French sceptics such as Foucher, Bayle, and Huet, see Popkin 1966. Note, however, that while there is considerable agreement between Leibniz and the sceptics over the inadequacy of Cartesian foundationalism (especially where Descartes’ use of the truth-rule and his perceived dogmatic commitment to our extensive knowledge of certain and necessary truths is concerned), there is considerable disagreement between them over how to meet the challenge that arise from this critique. For some further discussion, see Pelletier 2013. 11 Sleigh 1990, 76; McRae 1976, 93–94. Similar interpretations are offered by Brown 1984, Kulstad 1991, 42, Bobro 2005 and Jorgensen 2011, 193–195. Jorgensen, however, also points out that it remains “puzzling” on such an account how self-knowledge would help us to come by knowledge of metaphysical and necessary truths.

48

Julia Borcherding

us with knowledge of substance. This suggests that, in contrast to Malebranche’s emphasis on “interior feeling”, Leibniz does not conceive of our internal experience as simple introspection, as the optimist claims. Rather, he appears to view it as the starting point of a more complex reasoning process which, with the help of additional considerations (both epistemological and metaphysical) can generate metaphysical knowledge. Indeed, in what follows – now turning our gaze towards the pessimist – I would like to suggest that a passage in Leibniz’s reply to Bayle’s note L, once fleshed out more fully, may plausibly be read as an instance of precisely such an “argument from reflection”, and that this argument can prove far more compelling than the pessimist’s stance would have us expect.

3. Leibniz’s Reflection Argument Against Materialism The argument I would like to consider is found in Leibniz’s response to Bayle’s new “Note L” in the second edition of the Dictionnaire, which Bayle had used to deepen his engagement with Leibniz’s New System (henceforth, using Woolhouse /Franck’s abbreviation: PB6). 12 It occurs as part of a larger discussion of materialism in PB6, by means of which Leibniz intends to defend his theory of Pre-established Harmony (PH) against Bayle. Leibniz’s main strategy in PB6 is to proves both “halves” of PH through establishing – first with a little help from the materialist, and then by refuting her – that there can be no causal interaction between mind and body in either direction. On the one hand, Leibniz argues, the materialists have successfully shown that bodily movements cannot be explained by appealing to the soul causally acting on the body, and thereby have established the mind-body direction of PH: They have shown that “everything happens in the body as if there were no soul.” Indeed, Leibniz emphasizes, “[n]othing which happens on the outside of man is capable of refuting their [i. e., the materialist] doctrine.” 13 On the other hand, however, they go wrong in asserting that something material could cause mental states. Thought and perception cannot be explained on purely material grounds, and this impossibility establishes the body-mind direction of PH: “that everything happens in the soul as if there were no body.” Nothing outside of us, Leibniz concedes, may be capable of refuting the materialist who claims otherwise. However, what is inside of us is. For our internal experience of the “I”, which apperceives

12

GP 4.554-71 /NS 107–125. The manuscript of this text was sent to Bayle by Leibniz in 1702, and would eventually be published in the Histoire critique de la République des lettres of 1716. 13 GP 4.559 /NS 112, translation modified. I shall follow Lodge 2011 in assuming that Leibniz’s arguments against materialism primarily directed against what Lodge has called “mechanical materialism”, i. e. against a view that regards, as Lodge puts it, “material things as mechanical systems, i. e., as entities whose behavior can be accurately and exhaustively explained by adverting to nothing other than the sizes and shapes of impenetrable particles,” 81. In particular, Leibniz aims to show in the passages under consideration that mechanical materialism lacks the explanatory resources to account for the possibility of thinking matter, a position that had been argued for by both Locke and Toland, with both of whom Leibniz engaged extensively. Besides Toland, Leibniz in a letter to Bayle of 1702 [?] (GP 3.65 ff. /NS 127) lists Epicurus, Hobbes, and Spinoza as defending the view that the soul is “a modification of matter.” On the exchange between Leibniz and Toland, see Brown 2002, Duncan 2012, and Heinemann 1945. On Leibniz’s engagement with Hobbes’ materialism, see Duncan 2010.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

49

what happens in the bodily realm, forces us to admit that the subject of perception must be an indivisible substance: [I]nternal experience (l’expérience interne) refutes the Epicurean doctrine: This [experience] is the consciousness within us of this “I” (la conscience qui est en nous, de ce moi) which apperceives things which happen in the body (qui s’aperçoit des choses qui se passent dans le Corps); and that perception cannot be explained by shapes and movements, establishes the other half of my hypothesis, and forces us to recognize an indivisible substance in us, which must itself be the source of its phenomena. 14

Prima facie, this passage seems to lend support to an optimist reading of Leibniz which holds that – given our powers of introspection – reflection can make us directly aware of ourselves as unities, or even as immaterial. The optimist thus views Leibniz as arguing very much like Descartes does when he observes in the Meditations that since I am unable to distinguish any parts within myself when I consider myself qua res cogitans, my mind must be indivisible. 15 In what follows, however, I will suggest that the argument Leibniz offers in PB6 is both more intricate and more defensible than the optimist suggests. In brief, rather than merely asserting that we can in some way directly experience ourselves as immaterial substances, we should read Leibniz here as claiming that if we assume the truth of materialism, our internal experience is rendered inexplicable. 16 Let us begin by considering more closely the Leibniz’s first and key claim in the passage from PB6: that “internal experience refutes the Epicurean doctrine.” What exactly is the internal experience that refutes materialism? And how does it do so? With respect to the first question, we can begin by observing that the passage characterizes our internal experience as “the consciousness which is in us of the ‘I’ which apperceives what happens in the body.” It is tempting to read Leibniz here as appealing to what Kant would later call the “unity of apperception”, and in fact this is exactly what Margaret Wilson, in her 14

GP 4.559-60 /NS 112, translation modified. Partly because of an ambiguity in the French, it is difficult to determine how exactly Leibniz intends the first half of the passage (“But besides [. . .] body”) and its second half (“And that [. . .] phenomena”) to be related. The original French in the Histoire critique de la République des lettres reads: “[. . .] l’expérience interne refuse la doctrine Epicuréenne: c’est la conscience qui est en nous de ce moy qui s’aperçoit des choses qui se passent dans le corps; et la perception ne pouvant estre expliqué par les figures et les mouvemens [. . .] et nous oblige d’admettre en nous une substance indivisible, qui doit être ellemême la source de ses phénoménes.” Should la perception here be taken to refer to perception in general, or to the particular kind of perception Leibniz talks about in the first half of the passage? Compare also the widely differing translations of Loemker (PPL 578), who reads “la perception” as referring back to “internal experience”, and Woolhouse /Franks (NS 112), who suggest a more neutral translation similar to the one I have given here. However, the context of the passage makes it very clear that Leibniz’s argument against the materialist here does rest on an appeal to internal experience, and that this appeal is what is meant to help establish “the other half” of PH. The punctuation (which accurately represents the punctuation in the original text) equally suggests that the two halves are closely connected. It remains an open question, however, how Leibniz would justify this transition from our reflective experience of thought to “perception” in general. I discuss this difficulty in more detail in section 3.2 below. 15 “[W]hen I consider the mind, or myself insofar as I am merely a thinking thing, I am unable to distinguish any parts within myself; I understand myself to be something quite single and complete,” AT VII.86 /CSM 2.59. 16 On this reading Leibniz’s argumentative strategy still turns out to bear a family resemblance to a Cartesian argument, just not in the way the optimist would suppose. For as Rozemond 2014, 9 points out, and as we will see more clearly in the next section, Leibniz’s strategy against materialism here and elsewhere crucially depends on a stronger version of Descartes’ claim that modes presuppose the nature of their substance (see e. g. Principles I.53 [AT VIIIA.25]).

50

Julia Borcherding

interpretation of the mill argument of Mon. § 17, has suggested we do (see Wilson 1974). According to Wilson, Leibniz holds that conscious perceptions are endowed with a particular unity. In analyzing conscious perception, her Leibniz further argues, we find both the “true unity” of the perceiving ‘I’, as well as “a manifoldness or variety in object of content.” (Wilson 1974, 508) Yet material things, being infinitely divisible, cannot give rise to such a unity. However, as Wilson herself concedes, this way of reading Leibniz’s argument leaves it vulnerable to a number of objections. To begin with, as Lodge and Bobro have pointed out, Wilson’s interpretation renders Leibniz’s argument dependent on a feature of conscious thought, whereas Leibniz regards the representation of a multiplicity in a unity as constitutive of all perceptions, not just conscious ones. (Lodge /Bobro 1998, 561) Furthermore, this reading seems to make Leibniz’s argument vulnerable to Kant’s famous charge against rationalist psychology in the Paralogisms: that this form of argument illicitly infers an underlying metaphysical unity from the merely phenomenal unity experienced in consciousness. 17 Finally, note that in PB6, Leibniz makes no explicit mention of unity at all, as we might plausibly expect him to do if this was really the main feature of mentality he intended the argument to turn on. 18 But if it is not the unity involved in consciousness, what then is the relevant feature of our internal experience that refutes materialism because it “cannot be explained by shapes and movements”? In order to provide a fuller answer to this question, we need to look beyond our passage from PB6. Doing so, I will argue, reveals that the relevant internal experience is the reflective awareness which, for Leibniz, implicitly or explicitly is involved in all thought. This awareness, I will further show, is in turned characterized by Leibniz as an internal action that is both spontaneous and simple. A state that has these features, finally, according to Leibniz is explicable only as a modification of an “indivisible substance [. . .] which must itself be the source of its phenomena”, thus establishing his claim at the end of our passage in PB6.

3.1

Reflective Awareness as Internal Action

Apart from PB6, Leibniz describes both thought and reflection as internal actions in numerous other writings. In a letter to Sophie Charlotte of the same year, for instance, he argues that [t]o say that the self, or what a person conceives through reflection on himself, can come from sensible things or from the body is something for which there is no probability: supposing whatever traces, machines, or motions you like in the brain, one will never find the source of perception or of the reflection on oneself, which is a truly internal action [. . .] A skeptic who denies 17

This is Kant’s famous criticism of the “Achilles of all dialectical inferences of the pure doctrine of the soul” in the Paralogisms (KrV A351). Wilson argues that Leibniz’s argument is indeed the main target of the Second Paralogism (Wilson 1974, 507–513). While engaging Leibniz and Kant on this point is both interesting and rewarding, I unfortunately lack the space to do so here. Ultimately, I do not think that Leibniz’s argument is liable to Kant’s criticism (and, moreover, I think there is good reason to suppose that neither did Kant). For a careful discussion of Kant’s argument and its likely targets, see Dyck 2014, 104–141. For detailed discussions of the Achilles argument in various philosophers’ writings, see the papers collected in Lennon /Stainton 2008. 18 As I will argue in more detail below, I do think, despite these caveats, that the unity we experience in conscious thought may well play a role in Leibniz’s argument, just not the one Wilson had in mind.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

51

that there are bodies cannot be refuted by what the letter says against him; the skeptic will say that these are only appearances. But he cannot deny that he thinks. 19

Just as in the PB6 passage, Leibniz here appeals to our experience of the self, or “what a person conceives through reflection on himself”, and then proceeds to claim that material figures or motions could not possibly be “the source of perception or of the reflection on oneself.” However, he here then also goes on to provide a reason for why we should think this to be so: Reflection on the self, Leibniz explains, is “a truly internal action.” Moreover, he adds, this is a result the skeptic cannot deny. The skeptic can doubt the existence of bodies, but he cannot deny his own internal experience of this internal action: he cannot deny that he thinks. In the same vein, Leibniz explains to Damaris Masham in a letter written the following year that our own internal experience of the actions of the soul establishes PH, since “we have experience of bodies acting on one another according to mechanical laws, and of souls producing within themselves various internal actions, but we see no way of conceiving action of the soul on matter, or of matter on the soul, or anything which corresponds to it.” 20 A final piece of evidence in support of this reading of PB6 comes from a second letter from Leibniz to Bayle, like the first written in 1702 (henceforth: PB7a). In this letter, Leibniz adds some detail to his characterization of our minds as “indivisible active mirrors”, which he had also used in PB6. The closest analogy to perception or thought that can be found in “visible things”, Leibniz explains there, is the image we find in a mirror. But, he further points out, while the mirror is capable of accurately representing the object it mirrors, it cannot perceive it. 21 And as in the letters to Sophie and Masham, he then again proceeds to characterize thought as “an action of one thing on itself” that “has no place among shapes and motions, which could never provide the basis of a truly internal action.” (GP 3.69 /NS 128) This remark also further clarifies Leibniz’s mirror analogy: Unlike our soul, the mirror is entirely passive. It does not produce its own image, but merely reflects something outside of it and thus lacks the capacity for genuine perception, which involves activity. In sum, in all the passages surrounding PB6 we have now considered, Leibniz argues that our reflective experience of ourselves as thinking reveals thought, or the reflective awareness involved in thought, as a “truly internal action” inexplicable through “shapes and motions”. Assuming that this is indeed the correct way of interpreting Leibniz’s claim that our internal experience refutes materialism, a number of further questions now arise: How should we understand the claim that thought is an internal action? And what entitles Leibniz to argue that such an internal action is only explicable as the state of a simple, and thus immaterial substance? Moreover, Marleen Rozemond – pursuing a similar line of interpretation with respect to the Mill Argument – suggests that while Leibniz clearly appeals to the notion of an internal action in his attempts to refute the materialist, the prospects of such an appeal may not be especially bright. Understanding “internal action” to mean a perceptual state of a substance that is not externally caused by 19

Leibniz to Sophie Charlotte, August – early November 1702 (Strickland [ed]. 2011, 259, my italics). Leibniz to Masham, May 1704 (GP 3.340 /NS 206). 21 “Among visible things there is nothing which more closely approaches thought than the image in a mirror, and the traces in the brain could not be more exact, but the accuracy of that image does not produce any perception in the place it is in,” GP 3.69 /NS 128; see also GP 4.558 /NS 110.

20

52

Julia Borcherding

another thing, but generated by the substance itself, Rozemond worries that this notion may not be of much use in battling the materialist, because it seems to rely on features deeply embedded in Leibniz’s own system, but not in that of his Epicurean opponent. In particular, she points out, such an argument may be thought to presuppose PH (which of course implies that all perceptions are internal actions in this sense), which would be “philosophically unfortunate.” 22 As many of the passages just considered make clear, such reliance on PH would be philosophically unfortunate indeed. For in them, Leibniz’s is appealing to internal action precisely to prove PH. Taking the principle of charity to heart, we should thus assume that Leibniz did not in fact mean to rely on PH to make his argument. But how, then, should we understand it? In the following sections, I will take a closer look at Leibniz’s conception of an “internal action”, in the hope that gaining a better understanding of its features will also provide us with further insight into how Leibniz might justify his claim that such actions can only be states of an immaterial substance.

3.2

The Spontaneity and Simplicity of Thought

Some further insight into Leibniz’s notion of an internal action can be gleaned from a passage from On Nature Itself (1698), where Leibniz appeals to the “immanent actions” of substances in service of his attack on occasionalism. Indeed, if this view [sc. occasionalism] were extended so far as to eliminate even the immanent actions of substances, [. . .] then it would be as distant as it could possibly be from reason. For who would call into doubt that the mind thinks and wills, that we elicit in ourselves many thoughts and volitions, and that there is a spontaneity that belongs to us? (GP 4.509-10 /PE 161)

This passage indicates that the internal (or, following scholastic terminology, “immanent”) actions of a substance are spontaneous actions: They are actions that originate from our own depth. Instead of relying on features of his own system (such as PH), Leibniz in this text equally appeals to our “innermost experience” in order to convince us that there truly are such internal actions, arguing that if this experience of our inner spontaneity were called into doubt, it would “fly in the face of the testimony of our innermost experience and consciousness.” (GP 4.509-510 /PE 161) Moreover, Leibniz use of the scholastic terminology of “immanent action” further suggests that internal actions are actions in which the agent and the patient are identical (as opposed to an action in which one thing acts upon another). 23 Leibniz also emphasizes the reflexive nature of thought qua internal action in the earlier text De Mundo Praesenti (1684 /1986), where he explains that “[e]very substance has within it a kind of operation and this operation is either of the same thing on itself [eiusdem in seipsum], in which 22

Rozemond 2014, 18. Leibniz clearly identifies all perceptions of a substance as actions. See, e. g., “Reflections on the Souls of Beasts” (GP 7.328-332; also quoted by Rozemond), where he argues that “it is obvious that perception cannot be deduced from bare matter since it consists in some action. The same thing can be understood about any type of perception.” 23 According to Aquinas, ST I 54, 2, while a “transient action” is an action which is directed towards a patient outside the agent, an immanent action is an action that “does not pass outwards, but rather remains within the agent”, insofar it “takes place entirely in the agent.” Knowing and striving, Aquinas further explains, are instances of such activities: they take place entirely within the subject, and further perfect it.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

53

case it is called reflection or thought [reflexio sive cogitatio] and such a substance is spiritual, i. e. a mind”. (A 6. 4. 1506-1507) Structurally, reflection and thought are thus internal actions insofar as they are actions of the mind on itself. This additional feature is further borne out by the New Essays’ definition of “consciousness” (conscience, consciosité) as an awareness of the self (sentiment de moi). 24 In thought, Leibniz explains to Arnauld, we consciously experience the representation of something “divisible and material [. . .] in an indivisible being or substance [. . .] endowed with a true unity.” This experience of the “I”, Leibniz maintains, is constitutive for thought or conscious perception. 25 Thought and reflection, for Leibniz, therefore, are acts that are always directed towards the thinking, perceiving subject itself, and involve an awareness of it. We have, as Leibniz explains in our initial passage from PB6, an internal experience of “the consciousness within us of this “I” (la conscience qui est en nous, de ce moi), which stands opposed to the multiplicity that forms the intentional object of its perception when it “apperceives things which happen in the body.” 26 In appealing to our internal experience of thought and reflection as internal actions, Leibniz thus appeals to our internal experience of a spontaneous action, which involves an awareness of ourselves as the subjects of this action. Moreover, he asserts that both of these features of an act of thought or reflection are inexplicable on a materialist account. The question we are facing now is why that should be so. 24

New Essays II.xxvii (A 6.6.236). For a comprehensive inquiry into the Leibnizian notions of thought and consciousness see Kulstad 1991 and McRae 1976. In the New Essays alone, Leibniz uses a variety of terms to express consciousness and self-awareness. In addition to several French expressions for “consciousness” (conscience, consciosité, conscienciosité), he speaks of “reflection” (New Essays II.xxvii.9), “apperception” (New Essays II.xxvii.14), and “consciousness or reflection” or “immediate memory” (New Essays II.xxvii.13). Furthermore, some passages suggest that apperception also denotes consciousness of the self, and thus that there is no distinction between apperception, consciousness and self-awareness (see e. g., New Essays II.xxvii.9, where Leibniz talks about the “consciousness or the sense of I”). This has led some commentators to conclude that apperception simply is self-consciousness (Rescher 1979, Cramer 1994, Poser 2008; against this, see McRae 1976, 33 and Thiel 2011, 298). Other interpreters have distinguished between different forms of apperception and reflection. Schüssler 1992 and Gennaro 1999, for instance, distinguish between two and three kinds of selfconsciousness, respectively, while Kulstad 1991, 148, finds two distinct types of reflection in Leibniz (“simple or mere” reflection’ and “focused” reflection). A further question that has received much attention in the literature is whether Leibniz meant to defend a first-order or a higher-order theory of consciousness. The latter has been suggested by Kulstad 1991, Gennaro 1999, and Simmons 2001, the former by Jorgensen 2009. For a good overview of these and other interpretative puzzles, see Thiel 2011, 295–301. 25 Leibniz to Arnauld, 9 October 1687 (GP 2.112 /PPL 339). Similarly, Leibniz emphasizes to Burnet that in reflection, I am not only aware of my mental actions, but also of myself as the mental agent who performs them (Leibniz to Thomas Burnet, 2 August 1704 [GP 3.299]). Also compare the following passages from the Paris Notes: “In our mind, there is perception or a sense of itself as of a certain specific thing; this is always in us, because, as often as we use the name, we at once recognize it,” Jag., 108 /PPL 161–162, my italics. 26 GP 4.559-560 /NS 112. See also Leibniz’s letter to Sophie quoted above, where he identifies “the self, or what a person conceives through reflection on himself” as what is inexplicable on a materialist view, as well as Mon. § 16 (the paragraph preceding the Mill Argument): “We, ourselves, experience a multiplicity in a simple substance, when we find that the most trifling thought of which we are conscious involves a variety in the object.” However, as Duncan 2011 points out, the argumentative aim of this passage from the Monadology is importantly different. Unlike the passages we are considering, which explicitly appeal to internal experience to refute materialism, Mon. § 16 addresses all those who – like Leibniz and Bayle – “acknowledge that the soul is a simple substance.” Leibniz’s point there, Duncan argues, does not seem to refute materialism, but to support his definition of perception as the representation of a multitude in a simple through arguing that reflection on our perceptual awareness establishes the possibility of the presence of a multiplicity in a simple subject.

54

Julia Borcherding

Let us begin by considering the first feature of thought and reflection: spontaneity. Why would a state that has this property be inexplicable as the state of something material? Drawing on Leibniz’s frequently repeated view that matter is purely passive, a fully fleshed out Leibnizian argument in support of the incompatibility between matter and spontaneous thought could run as follows: Thoughts and reflections are clear instances of states that we ourselves internally produce, and thus are instances of genuine activity. But matter, as Leibniz frequently asserts, is “devoid of all activity” (New Essays II.xxi.1 [A 6.6.169]). Hence, thoughts and reflections are only explicable as modifications of an immaterial substance. Besides turning on a claim integral to the defense of Leibniz’s metaphysics as a whole (the passivity of matter), this reading finds further support in a recent interpretation of the mill argument proposed by Paul Lodge, who suggests that this argument also may rely on Leibniz’s claims about the passivity of matter. 27 In particular, Lodge cites a passage from a short text, On the Souls of Men and Beasts, in which Leibniz first advances the claim that “it is obvious that matter is something merely passive, since its attributes and variations involve no action”, and then proceeds to argue that “[i]n the same way, it is obvious that perception cannot be deduced from bare matter since it consists in some action” (GP 7.328-329 /Strickland [ed.] 2006, 64). What about the second feature of thought qua internal action, namely our awareness of ourselves as the subjects of the action? Prima facie, Leibniz’s emphasis on this point seems to support Wilson’s interpretation of his case against the materialist. Recall that according to Wilson, Leibniz appeals to the unity of the perceiving “I” to infer the existence of an underlying immaterial substance, and thereby becomes liable to Kant’s famous criticism in the Paralogisms. However, as I believe an intriguing text from Leibniz’s earlier writings makes clear, his point is in fact a slightly different one. For consider this passage from the Confession of Nature Against Atheists (1669), in which Leibniz aims to prove that our soul is immaterial by describing the reflective awareness involved in thought as follows: For thought is that ‘something, I know not what’ which we perceive when we perceive what we think. But when, for example, we perceive that we have thought of Titius, we not only perceive that we have the image of Titius in our mind, for this has parts, of course; such an image is not enough for thinking. For we have images in the mind even when we do not think of them, but we perceive, besides, that we have been aware of this image of Titius, and in this awareness of our images itself we find no parts. For if someone’s action is immediately perceptible, without a perception of parts, then this certain action is a thing without parts. For a quality immediately perceived in a thing actually belongs to it. (Confessio Natura Contra Atheistas [GP 4.109 /PPL 113], translation modified)

Akin to the contrast he draws in his replies to Bayle between genuine thought or perception on the one hand, and a mirror which represents an object by reflecting its image on the other, Leibniz equally emphasizes in this passage that while thought involves representation, this representation alone does not suffice to constitute an act of thought. Rather, when we reflect on our act of thought or perception, we always also experience an awareness that accompanies this representation. And while the representation itself has parts, the accompanying awareness which renders it a thought does not. Moreover, 27

See Lodge 2014, esp. 92–97. In addition to this appeal to the passivity of matter, PB7a (GP 3.69 /NS 129) provides an argument based on the nature of composites: Since the reality of compound beings depends on the existence simples, so does their ability to change.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

55

Leibniz adds, since this awareness is an “immediately perceptible” action, we can be certain that this action is “a thing without parts”, since such reflective experience, being immediately perceptible, could not deceive. This passage suggests that what Leibniz is pointing towards when he appeals to our awareness of the “I” in thought to support his argument against materialism is not so much our awareness of a simple, unified subject (as Wilson suggests), but the simplicity and unity of this awareness itself. As Alison Simmons points out, the unity and simplicity involved in Leibnizian mental representation relies not so much on the idea of consciousness, as it relies on the idea of a point of view: In corporeal representation, spatially distinct parts of the representing thing (the mirror) represent spatially distinct parts of the thing represented (the object reflected), whereas in mental representation, a perceiving subject represents a multiplicity of parts as unified into a single point of view. 28 It is this awareness that constitutes this point of view that is said to be simple: We can break up the complex content of our perception into parts, but not the simple awareness which unifies this content into a single point of view. Now, for this second feature of thought qua internal action, there is again a familiar Leibnizian line of reasoning available which might help us explain why he considers a state that has this feature inexplicable as the state of a material substance: All there is in an extended body are externally related parts. However, as Leibniz famously holds, where there are only external relations, there can be no genuine unity. 29 Applying this line of thought to the case at hand, we thus get the following argument: In thought or conscious perception, what is represented has parts, but the awareness accompanying this representation itself is simple, and unifies these parts. But this awareness could not be accounted for by anything corporeal, because merely externally related parts, like the parts of an extended body, could never give rise to such a simple, unified state. It therefore must occur in a substance that is itself a true unity, and thus immaterial. 30 Summing up our results so far, we have seen that Leibniz views thoughts as internal actions, which as such have two features that Leibniz takes to be inexplicable as the states of a material substance: their spontaneity, and the simplicity of the reflexive awareness involved in them. Moreover, Leibniz argues, we know from reflection on our mental activity that thoughts truly do have these features, since – as Leibniz asserts in the Confession – being immediate, our internal experience cannot deceive. It therefore, as Leibniz claims in our passage from PB6, “refutes the Epicurean doctrine.” While these results do provide us with the means to fill in the blanks of the argument Leibniz presents in PB6 in a way that seems well-supported by other passages, they may also raise the worry that such an interpretation of Leibniz’s “reflection argument” falls prey to Lodge’s first objection against Wilson’s “unity of consciousness” interpretation. 28

See Simmons 2001, 42. Leibniz often likens perceiving substances to mathematical points: “Mathematical points”, he argues in the New System, “are the points of view from which [simple substances] express the universe, GP 4.483 /PE 142. 29 For further discussion of this point, see Mugnai 1992, 18. 30 In addition, Pauline Phemister (2015, 137 ff.) has argued that both Leibnizian causation and preformation require a simple (and thus immaterial) soul. Since the entire cause must be preserved in the effect, the organic body must have a soul which can hold the infinity of impressions this body receives in a single perceptual experience. Moreover, only an immaterial soul, Phemister argues on behalf of Leibniz, can unify a monad’s past, present and future states into a single complete representation.

56

Julia Borcherding

Similar to Wilson’s reading of the mill, the interpretation of PB6 we are now considering rides on our reflective experience of features of thought or conscious perception. However, as Lodge points out against Wilson, Leibnizian perception is not restricted to conscious beings, but applies to all monads, and encompasses both conscious as well as unconscious representation. So, Lodge asks, even if we can show that conscious perception is inexplicable on material grounds, what warrants the generalization of this result to perception simpliciter? 31 Call this the “generality worry”. In response, note first that, philosophically speaking, the difficulty posed by the generality worry may not be too great. For in order to disprove the materialist claim that matter could give rise to thought that Leibniz seems primarily concerned with in the writings we have been considering, it seems entirely sufficient to show that there are features of thought which could never arise from something material. 32 Moreover, in a number of texts closely related to PB6, Leibniz indeed seems perfectly happy to use “perception” and “thought” interchangeably. 33 This may suggest that, at least in those texts, Leibniz may, by “perception”, simply just mean “conscious perception” and not perception in general as in the Monadology and other writings. However, even if Leibniz did in fact intend his reflection argument to generalize, he may have some resources at his disposal to ground such a transition. One such way to bridge the gap is suggested by PB7a, when Leibniz concludes one of his arguments against the materialist by concluding that “internal changes in simple things are of the same kind as we observe in thought, and we can say that, in general, perception is the expression of the multitude in the unity” (GP 3.69 /NS 129) While only our reflective experience of our act of thought involves a conscious experience of this simplicity and spontaneity, the same features of internal action that we can observe reflectively in thought are in fact present in all perceiving substances, down to the lowest monad: Any substance generates, through its appetite, its own perceptual states – whether these states are thoughts or unconscious petites perceptions – and any such perception is a representation of a plurality in a simple. 34 Moreover, while Leibniz acknowledges that it is only our own inner experience of conscious thought that provides us with an instance of this, he then often proceeds to highlight the crucial role of knowledge gained by analogy, in particular through analogies grounded in our reflective experience of the self. 35 What warrants such analogical 31

32

33 34

35

See Lodge /Bobro 1998, 560–561. Note that when stating the conclusion of the argument in PB6, Leibniz also speaks not merely of thought, but of perception in general. Moreover, as Rozemond 2014, 13 points out, it is certainly not obvious why we should think of all perceptions – in particular sense perceptions – as actions. This is different in the case of Wilson’s interpretation, since she offers it as a reading of the mill that, unlike the passages I am considering here, only turns on the notion of perception simpliciter. However, nothing seems to exclude the possibility (and in fact, much seems to suggest it) that Leibniz may pursue several different strategies against materialism, some of which turn on perception in general, while others turn on notions of conscious perception or thought. As, for instance, in his discussion at the end of PB7a (GP 3.68-69 /NS 128–129). In a very similar vein, Leibniz writes to Masham that “in this [pre-established harmony] I am doing no more than attributing to souls and bodies always and everywhere what we experience in them whenever the experience is distinct, that is to say, mechanical laws to bodies, and internal actions to souls,” Leibniz to Masham, May 1704 (GP 3.340 /NS 206). For further discussion of this passage, and of some of the various challenges Leibniz might face because of his commitment to such uniformity, see Duncan 2010. See, e. g., Leibniz to Arnauld, 28 Nov. /8 Dec. 1686 (GP 2.76-77); DM 12 (GP 4.436); GP 4.479; C 522 f.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

57

generalizations is a Leibnizian principle sometimes called the “Principle of Uniformity” (PU), a corollary of the Principle of Plenitude according to which “everywhere and all the time, everything’s the same as here.” 36 In a letter to de Volder, for instance, Leibniz uses the PU to establish his claim that action in bodies “is most intelligible because there is something in it analogous to what is in us, namely perception and appetite. For the nature of things is uniform, and our nature cannot differ infinitely from the other simple substances of which the whole universe consists.” 37 In the same way, Leibniz may be able to appeal to the PU to justify his inference from our internal experience of thought to all perceiving substances.

4. Introspection, Explainability, and the Natural Order of Things Even with the generality worry out of the way, however, we might still wonder whether our Leibnizian “argument from reflection” is truly a philosophically satisfying one. Indeed, Leibniz himself seems to raise a number of worries against similar appeals to internal experience which, at least prima facie, seem to bear equally on his own. At the same time, the fact that Leibniz himself points to these difficulties should at the very least indicate to us that he was aware of them, and should motivate us to search for answers that he may be able to give in response to them. The goal of this section will be to address two such objections that strike me as particularly grave ones – the charge of confusing inexplicability with mere ignorance, and the charge of inviting skepticism about internal experience.

4.1

Ignorance and Intelligibility

In his Conversations of Philarète and Ariste (1711), Leibniz criticizes Malebranche’s argument that thoughts could not be states of matter because they lack certain material properties such as being spatially measurable. 38 The materialist, Leibniz argues, could just respond that the fact that we cannot measure thoughts is due to our faulty knowledge of them and that if we knew the corpuscles which form thoughts and their movements that are necessary for that, we would see that thoughts are measurable, and are the workings of certain subtle machines. (GP 6.587 /PPL 623, translation modified)

Thoughts, Leibniz objects, may in fact turn out to be measurable – we merely did not know enough about them to realize this, and thus were unable to attribute such a property

36

As Leibniz points out to Sophie Charlotte (Leibniz to Sophie Charlotte, May 8, 1704 [GP 3.343]) he adapted this phrase from Fatouville’s Arlequin, empereur dans la lune. See Phemister 2004 for this reference and further discussion of the grounds of the PU, as well as of its role in justifying analogical inferences 37 Leibniz to de Volder, 30 June 1704 (GP 2.270 /PPL 537); see Leibniz to Wagner, 4 June 1710 (GP 7.530), for a parallel passage. Similarly, Leibniz explains to Masham that his whole theory “comes down to recognizing in substances beyond our sight and observation something parallel to what we see in those which are within our range,” Leibniz to Masham, May 1704 (GP 3.339 /NS 204). 38 Entretien de Philarète et d’Ariste, suite du premier entretien d’Ariste et de Théodore, ca. 1711 (GP 6.579-594 /PPL 618–628).

58

Julia Borcherding

to them. 39 But while certainly a plausible criticism of Malebranche’s view, Leibniz’s objection here raises the worry that his own argument could be subjected to a very similar critique: For why should it not equally be the case that our inability to explain the features of our thought qua internal action identified by Leibniz as the states of a material substance is merely due to our ignorance of how such features could come about? Indeed, this is precisely what a number of Leibniz’s contemporary commentators have suggested. William Seager, for instance, comments on our reflection argument in PB6 as follows: This sort of argument moves from an epistemological premise to an ontological conclusion, a direction of argument which is, I think, deeply disturbing. [. . .] If the conditions governing the creation of some phenomenon exceed the grasp of the human mind, then that phenomenon’s inexplicability will tell us precisely nothing about its nature. (Seager 1991, 87) 40

However, I do not think that we need to share Seager’s distress. To begin with, consider the following passage from the New Essays (thus written around the same time as PB6), which also clearly shows that Leibniz is aware of the issue raised by Seager: I note, indeed, that I recognize that we are not allowed to deny what we do not understand, though I add that we do have the right to deny (at least in the order of nature) what is absolutely unintelligible and inexplicable. [. . .] I maintain that the conception of creatures is not the measure of God’s power, but that their conceptivity, or ability to conceive, is the measure of God’s power; everything in conformity with the natural order can be conceived or understood by some creature. (New Essays pref. [A 6.6.65], my italics)

Very much like Seager, Leibniz emphasizes in this passage that we are not simply allowed to deny what we do not understand. However, he then adds, if we find that the phenomenon in question is genuinely unintelligible and inexplicable, then we are entitled to deny it. For while the present state of our understanding may not be a measure of God’s power, our ability to conceive of a phenomenon at all is. The reason for this, Leibniz concludes, is that “everything in conformity with the natural order can be conceived or understood by some creature.” 41 Why should this be so? Following Leibniz’s fundamental commitment to anti-voluntarism, everything that happens within the order of nature must have a reason, and that 39

Leibniz criticizes Descartes’ argument against materialism in the Principles on similar grounds (see Animadversiones (1692) [GP 4.359]). Descartes’ observation that we seem able to imagine that we could be without a body, but not that we could be without thought, Leibniz argues there, does not suffice to establish the claim that we could not be corporeal – it merely establishes that we can doubt that we are. We could only establish the stronger claim if we had knowledge of the soul sufficiently perfect to show that it could not possibly be corporeal. As long as this is not the case, our present inability to conceive of thoughts as extended could equally be due to a mere lack of imaginative power or understanding. 40 Like Seager, Wilson 1974 and Searle 1983 notice and criticize Leibniz’s appeal to the inexplicability of perception. However, since Seager provides by far the most extensive presentation of this criticism, I will mainly focus on his commentary here. 41 Note that the conception of explanation Leibniz is appealing to in this passage and elsewhere is much stronger than the conception Seager assumes here. For Leibniz collapses causa and ratio: to truly understand something or to be able give an explanation of something precisely is to know its true cause. For further discussion of this point, see Mates 1973, 158–162, and di Bella 2002. At the same time, Leibniz does not in fact commit the category mistake of confuting objects with propositions, as is suggested by Mates. Rather, he clearly distinguishes the two orders when declaring their correspondence (see, e. g., New Essays IV.xvii.3, where Leibniz claims that “a cause in the realm of things corresponds to a reason in the realm of truths”, A 6.6.475).

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

59

reason cannot simply be that God willed it to be so, because God himself was guided in creation by the intrinsic natures of things. 42 Consequently, nature – our created world – is ordered in such a way that all states or properties of things arise intelligibly from the natures of things they are states of modifications of. “In the order of nature (setting miracles aside”), Leibniz continues in the same section of the New Essays, God does not arbitrarily give these or those qualities indifferently to substances; he never gives them any but those which are natural to them, that is to say, those that can be derived from their nature as explicable modifications. (New Essays pref. [A 6.6.66])

Leibniz here gives expression to an important corollary of the Principle of Sufficient Reason (PSR), which Don Rutherford has termed the “Principle of Intelligibility” (PI): PI We can find no natural truth in a thing which does not arise from the thing as an explicable modification. 43 The PI, Rutherford emphasizes, “defines nature as a system that can be comprehended by the human mind.” (Rutherford 1995, 240) A world governed by the PI – our world, the best possible one – is a world in which all phenomena must be intelligible by an appeal to the natures of things alone. Thus, Leibniz argues, all its phenomena must, at least in principle, be explicable by us. 44 Conversely (very rare occurrences of divine miracles aside), if a phenomenon cannot be explained by an appeal to the nature of things, it simply cannot be part of this world. 45 Given the PI, therefore, conceivability in fact is a guide to possibility. Applied to our reflection argument, the PI provides powerful support for the inference from our internal experience of certain features of our mental states to the nature of the substance whose states or modifications they are. In reflection, we saw Leibniz argue, we experience our thoughts and conscious perceptions as internal actions, which are 42

Against Descartes and other voluntarists, Leibniz emphasizes time and time again that God is an intelligent being like us, whose will is not absolute, but always guided by his supreme wisdom and goodness. In a letter to Hartsoeker, for instance, Leibniz argues that “God’s will is not a sufficient ‘why’ when it comes to natural things, if the reasons for willing aren’t found in the object, and means for executing this will which conform to the order of nature,” Leibniz to Hartsoeker, 8 February, 1712 (GP 3.532-33). He also stresses that voluntarist explanations are not genuine explanations (see, e. g., Leibniz to Clarke, 25 February 1716 [GP 7.364-65]). 43 See also Rutherford’s more formal definition of the PI: “Within the order of nature, for any entity a and any property F that is truly predicable of a, (i) there is a reason why a is F; (ii) this reason explains a’s being F in terms of F’s being an ‘explicable modification’ of the nature of a”, Rutherford 1992, 36. Leibniz also states a version of the PI in the Specimen Dynamicum (GM 6.244 /PPL 441). 44 Why should human minds in particular receive this privileged status? Besides Leibniz’s strong commitment to the imago dei doctrine, according to which human minds are superior to all other minds because they are made in the image of God, Rutherford 1995, 240 points out that for Leibniz, the maximization of pleasure ought to compel God to create a world that is intelligible to human reason, because it offers the greatest opportunities for human happiness. This interpretation gains further support through Leibniz’s line of argument in the Discourse on Metaphysics, which both emphasizes that the happiness of minds is essential to best world, and also connects this happiness to the indefinite potential of finite minds to acquire knowledge of both God and creation. For a close analysis of Leibniz’s argument in the Discourse, see Jolley 2004. For further discussion of Leibniz’s commitment to the imago dei doctrine, see Craig 1987, Jolley 2005 /1990, and Hillman 2010. 45 In spite of this, Leibniz still maintains that there can be genuine miracles in this world, which are in fact incomprehensible to us. However, in his refutation of occasionalism (see, e. g., PE 82–83), he argues that the simplicity of God’s ways requires that these be very rare (thus excluding phenomena such as thought), and hence they do not genuinely seem to threaten the PI.

60

Julia Borcherding

both spontaneous and involve a simple awareness. However, given the nature of matter, which is both passive and composed of parts, these features of internal action are only conceivable as originating from a simple, active substance. Given the PI, therefore, in reflectively recognizing our thoughts to be spontaneous, simple actions, we are entitled to infer that they must be modifications of immaterial minds.

4.2

Does Immediacy guarantee Veridicality?

Besides his charge against Malebranche of delivering an argument from ignorance, Leibniz raises a further criticism that equally may be thought to apply to his own line of reasoning, this time in his annotations to a treatise entitled Meditations sur la métaphysique (1678). For upon reading the author’s claim that “I am convinced by an inner sentiment that all things are in me”, Leibniz underlines the passage and notes: There! For the first time, one speaks with conviction: And the cause of this conviction is the inner feeling (sentiment intérieur). But how come these inner feelings are certain? This has to be explained. I’ve told myself that this is because without such inner feelings, one could not be certain of anything at all. ‘So be it’, a skeptic would perhaps reply. But I am not of this opinion and I believe that one can say something more satisfactory. 46

The certainty of our internal experience, Leibniz points out, cannot simply be taken for granted. Rather, we need an argument against a skeptic who may doubt it, and, he adds optimistically, “something more satisfactory” can indeed be said here. However, did Leibniz actually succeed in providing such a justification for the certainty of our internal experience? Above, we saw Leibniz appeal to the immediacy of our internal experience to guarantee its veridicality. However, we may well worry whether such an appeal to the immediacy of our internal experience is really convincing. I will now show that Leibniz’s claim that the immediacy of our internal reflective experience warrants its veridicality is equally undergirded by an appeal to the PI. To begin with, consider Leibniz’s appeal to the PI in the service of immediate inner experience in the following passage from the New Essays: We can be deceived by memory across an interval – one often experiences this and one can conceive of a natural cause for such an error. But present or immediate memory (souvenir), the memory of what was taking place immediately before – or in other words, the consciousness or reflection which accompanies inner activity – cannot naturally (naturellement) deceive (tromper) us. [. . .] I have already said that there can be an intelligible reason for the element of error in perceptions which are mediate and outer, but with regard to immediate inner ones such a reason could not be found except by having recourse to God’s omnipotence. (New Essays, II.xxvii.13 [A 6.6.238])

Reflection, Leibniz asserts in this passage, is a form of memory. However, unlike other forms of short-term or long-term memory, it is “a present or immediate memory”: it directly refers back to an immediately prior cognitive state. And as such, he concludes, it cannot naturally deceive.

46

Robinet 1955, 112–113. Leibniz believed this work to be by Malebranche; however, it was in fact authored by the Abbé de Lanion.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

61

Let us start by investigating Leibniz’s first claim, that reflection is immediate memory (souvenir). 47 According to Leibniz, given that my reflection and its object are acts with different intentional contents, they must also constitute numerically different acts. 48 Moreover, the object of a reflective act is always what is immediately past. Reflection, Leibniz concludes, thus is a special form of memory. 49 As Ezio Vailati points out, for Leibniz, the main difference between a memory that is a reflection and an ordinary memory of a past event appears to be a causal one: In the case of reflection, the perception that is the object of the reflexive act is the immediate cause of this act. In the case of mediated memory, by contrast, the perception that is the direct cause of my memory is not the original perception, but a new perception with the same or similar representational content (depending on the distinctness with which I remember). Within a Leibnizian framework, reflection thus turns out to be immediate in two ways. First, reflection is immediate insofar as it is direct: Unlike ordinary memory, in reflection no mediating entities come between the reflective act and the perception that is its direct cause. Moreover, given this immediate causation, reflection also turns out to to be immediate temporally, since on Leibniz’s relational view of time, the causal order of perceptual states fixes their temporal order. Note, however, that Leibniz’s claim that reflection is a form of memory does not preclude the possibility that a reflection can take place while the perceptual state that is its object still remains (as indeed often will be the case). It only requires that this reflection always be a moment behind. 50 Moving on to Leibniz’s second claim in the New Essays passage – that this immediacy guarantees veridicality – we can begin by observing that it is not unique to the New Essays, but is paralleled in a passage from On the Method of Distinguishing Real from Imaginary Phenomena. In this intriguing text, Leibniz explains that there are two first truths of fact, which can be judged “without proof, from a simple perception or experience”: the existence of myself, “who am thinking of a variety of things”, and “the varied phenomena or appearances which exist in my mind.” 51 As in the New Essays passage, Leibniz here

47

48

49 50 51

To the best of my knowledge, Leibniz never provides an explicit argument for this claim, but see Vailati 1987 for a more detailed investigation into how such an argument might run. My perception of a color, for instance, is of that color only, while my reflection on this perception also involves an awareness of myself as the perceiving subject: “This thought of myself, who perceives sensible objects, and of my own action which results from it, adds something to the object of sense. To think of some color and to consider that I think of it – these two thoughts are very different, just as much of color itself differs from the ego which thinks of it,” On What Is Independent of Sense and Matter, 1702 (GP 6.502). Compare also the following passage from the Paris Notes: “In our mind there is perception or a sense of itself as a certain specific thing [. . .] As often as we will, we recognize that we perceive our thoughts, that is, that we have thought a little earlier. Therefore, intellectual memory consists not in what we sense but in that we sense – that we are those who sense”, Jag. 99 /PPL 251–2. McRae 1976, 44–45, also speaks of the “the essential pastness” of the object of reflection. For further discussion, see Vailati 1987, 251–253. De modo distinguendi phaenomena realia ab imaginaris, date uncertain, ca. 1683–1685 /6 (A 6. 4. 1500 /PPL 363). As Leibniz explains in his comments on Descartes’ cogito, there are “as many primary truths of fact as there are immediate perceptions, or if I may say so, consciousnesses.” However, “since I am conscious not only of myself thinking but also of my thoughts, the first truths of fact can be reduced to two fundamental truths: ‘I think’, and ‘Various things are thought by me’”, Animadversiones (GP 4.357 /PPL 385); cf. New Essays IV.ii.1. Leibniz also argues that all other truths of fact depend on these first truths of fact or “immediate perceptions”, and,

62

Julia Borcherding

argues that these reflective judgments could not fail to be true, because their immediacy guarantees their veridicality: “Since both of these namely are perceived immediately by the mind without the intervention of anything else, they can be accepted without question.” (A 6. 4. 1500 /PPL 363, my italics) The New Essays passage, however, goes beyond this earlier text by providing a further, deeper explanation as to why immediacy should guarantee veridicality: Since reflection is immediate memory, it cannot “naturally” deceive. While there can be “an intelligible reason for the element of error” in external perception, with respect to inner, immediate perception, no such reason is conceivable within the natural order. Rather, error in immediate perception would be explicable only “by having recourse to God’s omnipotence.” However, such an appeal to divine intervention is precisely what is blocked by the PI. For the PI requires that everything that occurs within the natural order must arise from created beings within that order as an explicable modification. But, Leibniz now argues, given that reflection is immediate memory, no such natural source of error can be found. Taking into account this appeal to the intelligibility of the order of nature, we thus arrive at the following Leibnizian argument for the veridicality of immediate experience within the natural order: Reflection, the argument begins, is immediate memory. Given this immediacy, the only possible source of error in reflection is a divine intervention. However, God’s absolute power is outside the order of nature. Within the natural order, the PI holds, which demands an intelligible reason for error. However, absent divine omnipotence, no such reason is conceivable. Reflection, the argument concludes, therefore cannot naturally deceive. If successful, this argument would help answer the skeptical challenge raised by Leibniz himself and lend support to his claim that our internal experience of thought as a simple action is veridical, as he had claimed in the Confessio. 52 Now, clearly, much of its success hinges on the plausibility of Leibniz’s claim that, unless we appeal to the absolute power of God, there can be no intelligible natural reason for error in immediate perception. In both of the passages we just discussed, Leibniz leaves this claim undefended and instead relies on its intuitive appeal. Provided that it has such appeal, he thereby shifts the burden of proof to the skeptic: Assuming the skeptic accepts Leibniz’s definition of reflection as a form of memory (or fails to provide a plausible alternative), the question Leibniz challenges her to answer is how such immediate memory could go wrong. Ordinary memories can fade, can be distorted and can even be fundamentally changed by

consequently, that if their immediacy could not guarantee their veridicality, then no truth of fact could ever be secure knowledge. This reductio strategy to ground the veridicality of immediate perception is also present both in the Confessio and in the New Essays passage discussed above (“[I]f these immediate experiences are not certain, there will be no truth of fact of which we can be assured,” NE II.xxvii.13; “The cause of error is the medium, for if an object of perception were the cause of error, it would also be perceived falsely; if the subject were the cause, it would always perceive falsely”, Confessio, L 113). However, as this attempt at refuting the skeptic does not seem to me to be a particularly promising one – unless it is backed by a number of additional and very substantive Leibnizian assumptions – I will set it aside for the purposes of this paper. 52 It is worth noting the crucial importance this argument for the veridicality of immediate memory occupies within Leibniz’s thought. For he not only stakes a substantial part of his case against materialism on its success, but also the fate of morality as a whole: “Since minds must keep their personality and moral qualities [. . .] it is necessary for them to preserve in particular a kind of recollection, consciousness or power to know what they are, upon which depends the whole of their morality”, GP 2.160.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

63

further experiences. However, it seems decidedly less plausible to suppose that the same could happen to a perception that we register before it is fully past, and which thus forms the immediate cause of our reflective act. If, for instance, I recall last year’s visit to the Rijksmuseum, the immediate cause of this memory is not my original perception of The Night Watch, but a new perception with the same or similar representational content. But suppose I did, there and then, standing in the museum, reflect on my act of perceiving Rembrandt’s painting. In this case, my original perception of The Night Watch itself is at least a partial cause of the immediate memory that is my reflection (its other cause being the act of my will directing my attention towards the act itself, rather than merely to its content). While in ordinary memory, the reproduced perception itself could be a cause of error, the same does not seem to hold true of reflection, since it does not involve a new representation of the perception in question, but rather the original perception, which is now both immediate cause and immediate object of my reflection. Leibniz’s argument thus challenges the skeptic to explain what could cause reflection to go awry, given that it is immediate in this sense. If natural error in immediate perception is supposed to be possible, then, according to PI, its coming about has to be conceivable by appealing to the natural order of things alone. But what in this order would explain it? Despite some initial promise, however, this second attempt to invoke the PI ultimately turns out to be less convincing than the first. On the one hand, Leibniz’s strategy to ground our knowledge from internal experience certainly goes beyond a brute appeal to immediacy, and thus lends further strength to his reflection argument. But on the other, it also seems that a sceptic may have some answers to the challenge Leibniz raises for her. To start with, a Humean skeptic may argue that the simplicity I seem to be aware of in reflection is merely apparent, and indeed masks a deep complexity. She may grant to Leibniz that immediacy does guarantee the veridicality of my perception. However, she then further points out, all this means is that I can be certain that I am indeed having the states that I am subjectively aware of having, as they appear to me. We cannot be mistaken about the fact that we are thinking, nor can we be mistaken about how our act of thinking appears to us. But this, she argues, does not seem enough. For it still leaves open the possibility that while our thoughts appear to us to have such and such a feature (say, simplicity) they in fact may not have those features at all. Leibniz himself, she points out, often notes that our perceptions of sensible qualities such as colors seem simple to us, but are in fact infinitely complex. 53 And couldn’t we say the same of my reflective experience of a thought? Even if there is no intermediate state between the perception that is my reflection, and the state it is directed towards, could it not be the case that even though this state appears to be simple, it is in fact highly complex? There are no mediating states

53

Against Locke, who argues that the idea of a color is a simple idea representing the power that caused it, Leibniz argues that “these sensible ideas appear simple because they are confused and thus do not provide the mind with any way of making discriminations within what they contain [. . .] It is obvious that green, for instance, comes from a mixture of blue and yellow; which makes it credible that the idea of green is composed of the ideas of those two colours, although the idea of green appears to us as simple as that of blue, or as that of warmth. So these ideas of blue and of warmth should also be regarded as simple only in appearance [. . .] we should undertake the analysis of them by means of further experiments, and by means of reason”, New Essays II.ii.1 (A 6.6.120). For further discussion of Leibniz’s analysis of color perception, see Pearce 2016 and Puryear 2011.

64

Julia Borcherding

here, nor is there an appeal to God’s absolute power, but – at least on the face of it – the immediacy of reflection here still does not seem to warrant its veridicality. 54 Moreover, the skeptic may further point out, even if we should grant Leibniz’s contention that reflection’s immediacy to its object excludes the possibility of error, we are still left with the worry that our reflective acts themselves may be flawed. We could, for example, be unfocused or sleepy, or distracted by external stimuli. In such cases, even though our access to the object of reflection is direct and unmediated, mistakes, it seems, could still arise. One possible way for Leibniz to meet this challenge might be through an appeal to his further definition of reflection as “nothing but attention to what is within us.” 55 Unlike mere conscious awareness, which may arise gradually out of unconscious perception when enough petites perceptions group together to draw our attention, Leibniz considers reflective awareness as a form of consciously directed attention, with the specific aim of examining its object. 56 Pointing to this conception of reflection as focused attention, Leibniz could then argue that cases of erroneous awareness due to sleepiness or inattentiveness ought not to be counted as instances of reflection in the first place, because they simply do not involve the requisite attention. However, it seems that more would need to be said in defense of such a definition. 57 In sum, while Leibniz’s second appeal to the PI certainly lends a more solid foundation to his claim that the immediacy of our internal reflective experience implies its veridicality, this appeal may ultimately not be sufficient. Leibniz’s argument may thus perhaps most charitably be read as shifting the burden of proof to the skeptic, who (assuming the truth of PI) will have to suggest another, yet unidentified source of natural error in reflection, or offer a valid argument for rejecting Leibniz’s definitions of reflection altogether.

5. Conclusion: The Reflection Argument against Materialism as an Argument from Conceivability Having reviewed the important role of the PI in supporting Leibniz’s appeals to our reflective experience of thought, we are now finally in a position to give a fully fleshed out reconstruction of Leibniz’s reflection argument against materialism:

54

The case of reflection on our own mental activity seems just like the case of color perception insofar as in both instances, it appears to be possible for us to be in error not only about the contents of our mental acts, but also about their structural features. In the case of color perception, the problem is not only that we are inferring the presence of a uniform color where there isn’t any, but rather that we are mistaken about a salient feature of our perceptual state itself (namely, its apparent simplicity). And it seems that exactly same may be said with respect to the (perhaps deceptively) simple awareness involved in each act of thought which, according to Leibniz, reflection reveals to us. 55 New Essays pref. (A 6.6.51). Conversely, “attention is nothing but reflection” (PPL 113). 56 This aspect of reflection is brought out by Leibniz’s definitions of attention as “as an act of thought (cogitatio) with the desire of knowing” (C 493) and “a determination of the soul to know something (determinatio animi ad cogitandum) in preference to other things” (Grua 2.525). 57 Alternatively, Leibniz’s claim about the veridicality of reflection could perhaps be amended to say that awareness of a perception is veridical if it is (a) causally immediate, and (b) involves undivided attention.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

65

The Reflection Argument (P1) We are reflectively aware of ourselves as thinking, or as apperceiving things that happen in the body. In reflection, we experience ourselves as engaged in spontaneous, simple actions. (from internal experience) (P2) Reflection is immediate, and thus veridical. (veridicality argument from PI) (P3) We therefore know from reflective internal experience that our thoughts and conscious perceptions are spontaneous, simple actions. (from P1, P2) (P4) All natural states or actions of a substance must arise from its nature as explicable modifications. (PI) (P5) But spontaneous, simple actions are only explicable as the modifications of a simple, and thus immaterial substance. (passivity of matter, matter merely externally related parts) (C) Therefore, thought and conscious perception must be states of simple, immaterial substances. (from P3, P4, P5) In internal experience, we are reflectively aware of ourselves engaging in thought, conscious perception, or reflection (in case of higher-order reflections). This internal experience, which we know to be veridical, reveals these states to be spontaneous actions directed at a representation which has parts, yet themselves consist of an awareness which is entirely simple. Moreover, according to PI, any phenomenon that is the result of a natural substance needs to be explicable in terms of the properties or nature of this substance. However, the argument proceeds, given the passivity of matter, and its constitution of merely externally related parts, internal actions are inexplicable as the actions of a purely material thing. Therefore, thought cannot be a modification of matter, since the phenomenon, as we experience it, would then remain unintelligible. In sum, Seager is right to claim that Leibniz infers from the fact that we are unable to explain fundamental features of thought that we are immaterial substances. But this should not lead us to assume that Leibniz is simply arguing from ignorance. Rather, he can supply the PI to justify this inference. According to the PI, the properties or natural effects of things have to be conceivable as intelligible consequences of their nature. However, a material thing could never give rise to states that have the features, that we, through our reflective internal experience, know thought and reflection to have. Seager’s contention that a phenomenon’s inexplicability “will tell us precisely nothing about its nature” is thus precisely what Leibniz would disagree with. Assuming the veridicality of our reflective experience of our own mental activity, we are therefore warranted in concluding that our minds cannot be purely material. Of course, ultimately it must remain an open question whether Leibniz’s argument can really get us all the way to this conclusion. As we saw in Section 4.2, Leibniz’s appeal to the immediacy of reflection remains open to a number of skeptical challenges. Further, while Leibniz’s solution escapes Seager’s criticism, it of course relies on strong metaphysical principles that are themselves in need of further justification: the PI, and, ultimately, the PSR. Such justification ultimately may take the form of a priori considerations regarding the character of God’s wisdom, which compelled him to create a world that manifests the rational order expressed by the PI. But whether such considerations can be defended,

66

Julia Borcherding

and whether Leibniz adheres to them throughout his writings, are questions which lie beyond the scope of this paper. Even though in the end, all may thus not be as well as it could be, it has become clear that criticizing Leibniz’s argument does not merely involve calling into question a mere brute appeal to intuition, but rather an attack on some of the most fundamental principles of Leibniz’s system as a whole. Moreover, it is intriguing to see how Leibniz’s reflection argument, very much in the spirit of classic empiricism, fundamentally relies on experience to disprove the materialist, but at the same time provides a solid backing for such reliance by means of a fundamentally rationalist principle. The existence of one such argument alone is of course far from sufficient to conclusively make the case that this type of reasoning is indeed what Leibniz had in mind when making his numerous claims about the epistemic powers of reflection. In order to show this, further investigation into such arguments in Leibniz’s writings is needed. However, the force of the argument considered here seems to suggest that such a line of investigation may be a fruitful one to pursue, and gives us reason to suppose that Leibniz indeed found a promising middle ground between the optimist’s cheerfulness and the pessimist’s gloom. 58

Bibliography Bobro, M. 2004. Self and Substance in Leibniz. Dordrecht /Boston /London: Kluwer Academic Publishers. Bobro, M. /Lodge, P. 1998. Stepping Back Inside Leibniz’s Mill. Monist 81, 553–572. Brown, S. 2002. The Leibniz-Toland Debates on Materialism and the Soul at the Court of the Queen of Prussia. In: Poser, H. (ed.). Nihil Sine Ratione: Mensch, Natur, und Technik im Wirken von G. W. Leibniz. VII. Internationaler Leibniz-Kongress. Vol. 1. Berlin: G. W. Leibniz Gesellschaft. Brown, S. 1984. Leibniz. London: The Harvester Press. Churchland, P. 1995. The Engine of Reason, the Seat of the Soul. Cambridge, MA: MIT Press. Craig, E. 1987. The Mind of God and the Works of Man. Oxford: Clarendon. Cramer, K. 1994. Einfachheit, Perzeption und Apperzeption. Überlegungen zu Leibniz’ Theorie der Substanz als Subjekt. In: Cristin, R. (ed.) 1994. Leibniz und die Frage nach der Subjektivität (Studia Leibnitiana Sonderheft 22). Stuttgart: Franz Steiner Verlag. Descartes, R. 1641, Meditations on First Philosophy. In: The Philosophical Works of Descartes. Vol. 1. Haldane /Ross (trs.) 1970. Cambridge: Cambridge University Press. di Bella, S. 2005. The Science of the Individual: Leibniz’s Ontology of Individual Substance. Dordrecht: Springer. di Bella, S. 2002. Leibniz on Causation: Efficiency, Explanation and Conceptual Dependence. Quaestio 2, 411–448. Duncan, S. 2012. Toland, Leibniz, and Active Matter. Oxford Studies in Early Modern Philosophy 6, 249–278. Duncan, S. 2011. Leibniz’s Mill Argument Against Materialism. The Philosophical Quarterly 62, 250– 272. Duncan, S. 2010. Leibniz on Hobbes’ Materialism. Studies in History and Philosophy of Science Part A 41, 11–18.

58

I would like to thank Christian Barth, Martha Bolton, Michael Della Rocca, Stephen Engstrom, Nabeel Hamid, Martin Lenz, Samuel Levey, Paul Lodge, Sam Newlands, Marleen Rozemond, Don Rutherford, Justin Smith, Kenneth Winkler and all anonymous referees for their very helpful comments on various drafts of this paper.

Reflection, Intelligibility, and Leibniz’s Case Against Materialism

67

Dyck, C. 2014. Kant and Rational Psychology. Oxford: Oxford University Press. Gennaro, R. J. 1999. Leibniz on Consciousness and Self-Consciousness. In: Gennaro R. /Huenemann, C. (eds.) 1999. New Essays on the Rationalists. Oxford: Oxford University Press. Heinemann, F. H. 1945. Toland and Leibniz. Philosophical Review 54, 437–457. Hillman, T. A. 2010. Leibniz on the Imago Dei. Oxford Studies in Early Modern Philosophy 5, 171–213. Jolley, N. 2005. Leibniz. Oxford /New York: Routledge. Jolley, N. 2004. Leibniz and the Excellence of Minds. In: Carrara, M. /Tomasi, G. (eds.) 2004. Individuals, Minds, and Bodies: Themes from Leibniz (Studia Leibnitiana Sonderheft 32). Stuttgart: Franz Steiner Verlag. Jolley, N. 1990. The Light of the Soul. Theories of Ideas in Leibniz, Malebranche and Descartes. Oxford: Clarendon Press. Kulstad, M. 1991. Leibniz on Apperception, Consciousness and Reflection. München: Philosophia. Kulstad, M. 1983. Leibniz’s Theory of Innateness in the New Essays, Followed by a few Remarks on the Possible Impact on Kant. In: Leibniz. Werk und Wirkung. Fourth International Leibniz Congress. Hannover. Leduc, C. 2010. Substance, individu et connaissance chez Leibniz. Montréal: Les Presses de l’Université de Montréal. Lodge, P. 2014. Leibniz’s Mill Argument Against Mechanical Materialism Revisited. Ergo 1(3), 79–99. Mackie, J. L. 1976. Problems from Locke. Oxford: Oxford University Press. Mates, B. 1973. Leibniz and the Phaedo. In: Akten des 11. Internationalen Leibniz – Kongresses (Studia Leibnitiana, Supplementa Bd. XII). Stuttgart: Franz Steiner Verlag. McRae, R. 1976. Is Adam in His Cognitive Nature Made in the Image of God? In: Dascal, M. /Yakira E. (eds.) 1976. Leibniz and Adam. Tel Aviv: University Publishing Projects, 79–84. McRae, R. 1976. Leibniz: Perception, Apperception and Thought. Toronto: University of Toronto Press. Mugnai, M. 1992. Leibniz’ Theory of Relations. Stuttgart: Franz Steiner Verlag. Pearce, K. 2016. Leibniz on the Veridicality of Color Perceptions. Philosophers’ Imprint 16, 1–17. Puryear, S. 2011. Leibniz on the Metaphysics of Color. Philosophy and Phenomenological Research 86, 319–46. Pelletier, A. 2013. Leibniz’s Anti-Scepticism. In: Charles, S. /Smith, P. J. (eds.) 2013. Scepticism in the Eighteenth Century: Enlightenment, Lumières, Aufklärung. Dordrecht: Springer. Phemister, P. 2015. the Souls of Seeds. In: Nita, A. (ed.) 2015. Leibniz’s Metaphysics and Adoption of Substantial Forms. Dordrecht: Springer. Phemister, P. 2004. ‘All the Time and Everywhere Everything’s the Same as Here’: The Principle of Uniformity in the Correspondence Between Leibniz and Lady Masham. In: Lodge, P. (ed.) 2004. Leibniz and His Correspondents. Cambridge: Cambridge University Press. Popkin, R. H. 1966. Leibniz and the French Sceptics. Revue Internationale de Philosophie 20, 228–248. Robinet, A. 1955. Malebranche et Leibniz: relations personnelles. Paris: J. Vrin. Rorty, R. 1979. Philosophy and the Mirror of Nature. Princeton, NJ: Princeton University Press. Rutherford, D. 1995. Leibniz and the Rational Order of Nature. Cambridge: Cambridge University Press. Rutherford, D. 1993. Natures, Laws and Miracles: The Roots of Leibniz’s Critique of Occasionalism. In: Nadler, S. (ed.) 1993. Causation in Early Modern Philosophy. Philadelphia: Penn State Press. Rutherford, D. 1992. Leibniz’s Principle of Intelligibility. History of Philosophy Quarterly 9, 35–49. Schüssler, W. 1992. Leibniz’ Auffassung des menschlichen Verstandes (intellectus). Eine Untersuchung zum Standpunktwechsel zwischen ‘système commun’ und ‘système nouveau’ und dem Versuch ihrer Vermittlung. Berlin: De Gruyter. Seager, W. 1991. The Worm in the Cheese: Leibniz, Consciousness and Matter. Studia Leibnitiana 23, 75–91. Searle, J. 1983. Intentionality. Cambridge: Cambridge University Press.

68

Julia Borcherding

Strickland, L. (ed.). 2006. The Shorter Leibniz Texts: A Collection of New Translations. London /New York: Continuum. Strickland, L. (ed.). 2011. Leibniz and the Two Sophies: The Philosophical Correspondence. Toronto: Iter. Sleigh, R. C. 1990. Leibniz and Arnauld: A Commentary on Their Correspondence. New Haven, CT: Yale University Press. Thiel, U. 2011. The Early Modern Subject: Self-Consciousness and Personal Identity from Descartes to Hume. Oxford: Oxford University Press. Vailati, E. 1987. Leibniz on Reflection and its Natural Veridicality. Journal of the History of Philosophy 25, 247–262. Wilson, M. D. 1999. Ideas and Mechanism. Essays on Early Modern Philosophy. Princeton: Princeton University Press. Wilson, M. D. 1976. Descartes: The Epistemological Argument for Mind-Body Distinctness. Nous 10(1), 3–15. Wilson, M. D. 1974. Leibniz and Materialism. Canadian Journal of Philosophy 3, 495–513.

Leibniz’s Justification of the Principle of Sufficient Reason (Mainly) in the Correspondence with Clarke Paul Lodge, Mansfield College, University of Oxford

Abstract The aim of this paper is to shed light on Leibniz’s justification of the Principle of Sufficient Reason. It approaches this issue through a close textual analysis of the correspondence with Samuel Clarke and a more abstruse and lesser-known writing, ‘Leibniz’s Philosophical Dream’.

1. Introduction The aim of this paper is to shed some light on a relatively neglected aspect of Leibniz’s philosophy, namely his justification of the Principle of Sufficient Reason (PSR). I approach this issue through a close textual analysis of his correspondence with Samuel Clarke. It is well-known that in this correspondence Leibniz appeals to the PSR in connection with his arguments against the Newtonian conception of space and time. But, in addition, not only are there a number of places in which Leibniz discusses the basis for his commitment to the PSR, sections 18–20 and sections 125-130 (the last six sections) of Leibniz’s final letter 1 contain an extended discussion of precisely this issue. Partly for reasons that I shall mention later, we should approach with some caution the thought that this represents Leibniz’s definitive views on the justificatory status of the PSR. However, as we shall see, Leibniz offers a wide range of considerations in a philosophical swansong that was dispatched on August 18, 1716, only three months before his death. I will begin by clarifying how Leibniz characterizes the PSR in the Clarke correspondence. Then I will turn to the sections mentioned above and use them as the basis for organizing other pertinent remarks scattered among Leibniz’s five letters. This will yield a surprisingly large number of different justifications of the principle, which I will present in turn along with critical commentary. I will finish the paper in a rather speculative way. At the very end of his 5th Letter, Leibniz alludes to a justification of the PSR which he tells Clarke is “too abstruse for the present dispute” (Letter 5, Sec. 130 /LC 96), and which he does not provide. I will take the liberty of using this as an opportunity to consider, among other things, a justification that we might take from a reading of one of Leibniz’s more abstruse and lesser-known writings, which might also help resolve some of the worries arising in connection with those he does present.

1

In fact, the ‘correspondence’ comprises a set of extracts from and addenda to letters that were sent to Caroline, Princess of Wales. However, I shall refer to the texts as ‘letters’.

70

Paul Lodge

2. Leibniz’s characterization of the PSR Leibniz introduces the PSR to Clarke in the first section of his 2nd Letter as one of two principles, the other being the Principle of Contradiction (PC). He presents it as follows: “the principle of sufficient reason, viz. that nothing happens without a reason why it should be so, rather than otherwise” (Letter 2, Sec. 1 /LC 16). The PSR is characterized again at the beginning of the swansong in the 5th Letter, but here things are slightly more complex, with Leibniz talking of “the principle of the want of a sufficient reason; in order to any things existing, in order to any events happening, in order to any truth’s taking place” (Letter 5, Sec. 125 /LC 95). At first glance it might appear that we can take the first statement to be a truncated version of the second. However, there is a crucial element in the 2nd Letter that is missing in the 5th Letter, namely the explicit assertion that the sufficient reason should account for both ‘why’ and ‘why not otherwise’. 2 In what follows I am going to take the PSR to be the most generous combination of the two, namely as: PSR The principle of the want of a sufficient reason for a thing to exist rather than not exist, for an event to happen rather than not happen, for any truth’s taking place rather than not taking place. Whilst not explicitly labelled as the PSR, something close to this version can be found in Confessio Philosophi which dates all the way back to 1672–73: [N]othing ever exists unless it is possible (at least for one who is omniscient) to assign a sufficient reason why it exists rather than not, and why it is thus and not otherwise. (A 6.3.118 /CP 33)

Furthermore, a version of this characterization is endorsed by Clarke in his 3rd Letter, where he says “Undoubtedly nothing is, without a sufficient reason why it is thus, rather than not; and why it is thus rather than otherwise” (Letter 3, Sec. 2 /LC 30), and it coincides closely with what we find in another of Leibniz’s relatively late writings, the Monadology, in section 32 of which the PSR is said to be: [the principle] by virtue of which we consider that we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise, although most of the time these reasons cannot be known to us. (GP 6.612 /PE 217)

Another important feature of the way that the PSR is invoked in the Clarke correspondence is that there is only one occasion on which Leibniz offers an example of a sufficient reason, namely in section 9 of his 5th Letter. Here he observes that “the principle of what is best”, i. e., the proposition that God acts on the basis of his choice of the best is “the sufficient reason for the existence of things” (Letter 5, Sec. 9 /LC 57). It is unclear just what to make of this. However, one might plausibly read it as implying that neither the efficient causes cited in natural philosophical explanations nor the reasons that might be consciously considered during the deliberation of created rational beings could count as sufficient reasons for the explananda nor the decisions made 2

As we shall see later, the ‘why not otherwise’ also fails to occur in a passage from Demonstrations of Primary Propositions of 1671–72(?) (A 6.2.483), which has often been presented as crucial locus for our understanding of Leibniz’s commitment to the PSR.

Leibniz’s Justification of the Principle of Sufficient Reason

71

respectively. Furthermore, given Leibniz’s commitment to the limited nature of the cognitive capacities of created beings and the actually infinite structure of created universe, it is hard to see how he could regard things as otherwise. 3 And it also seems that Leibniz alludes to this with his parenthetical remark about omniscience in the passage from the Confessio above. Thus, these very general considerations point to the thought that the PSR is intimately connected with the fact that the universe results from divine choice, and that it is ineliminably a principle of final causation. Finally, it is worth noting that the passage from the Monadology reminds us that Leibniz sometimes wishes to extend the notion of a sufficient reason to include all truths, including those which are necessary, and those whose truth is governed explicitly by PC. The relation between these two principles is a complex one, but I will bracket these considerations in the context of the current essay. For when Leibniz is concerned with the justification of the PSR in the correspondence with Clarke, it is solely in connection with contingent truths concerning the created world and the divine activity by which it was produced. 4

3. Leibniz’s swansong Whilst the PSR is invoked in all of Leibniz’s letters to Clarke, the issue of whether it is legitimate for Leibniz to invoke it does not arise until late in the correspondence. Clarke begins his 4th Letter by criticizing Leibniz’s insistence that the will of God must be determined by a reason that differentiates the things chosen from those not chosen. In addition to claiming that such a view would lead to necessitarianism, he questions Leibniz’s grounds for rejecting the situation in which “there may be a very good reason to act, though two or more ways of acting may be absolutely indifferent” given that he [Leibniz] “supposes the contrary, as a principle; but gives no proof of it, either from the nature of things, or the perfection of God” (Letter 4, Secs. 1–2 /LC 45). Leibniz takes this to be an explicit critique of the PSR, and in his response he provides what appears to be a proof of each kind, as well as offering a number of additional considerations which speak to the challenge. But he also observes “I shall speak more largely at the conclusion of this paper, concerning the solidity and importance of this great principle” (Letter 5, Sec. 20 / LC 60). And, true to his word, he returns to the issue in Sections 125–130, confident by the penultimate sentence of his last letter to Clarke, that he has “said what is sufficient to justify [the PSR]” (Letter 5, Sec. 130 /LC 96). I will draw on other parts of the correspondence as I proceed, but for the present I want to focus on what I am calling ‘Leibniz’s swansong’, namely his comments on why one should adopt the PSR at the end of his 5th Letter. Since it will be important to attend to the flow and interconnections of the claims that Leibniz makes here, I will begin by quoting the relevant passages in full, along with sections 18–20 of the same letter:

3

In Sec. 66 of his 5th Letter Leibniz observes that unlike God, “Men, being such limited creatures, as they are, may act in this manner. They may resolve upon a thing and then find themselves perplexed about the means, ways, places, and circumstances,” (LC 78). However, he stops short of saying that this will always be the case. 4 For a helpful discussion the relationship between the PSR and the PC, and for Leibniz’s views on the PSR in other writings, see Rodriguez-Pereyra 2013.

72

Paul Lodge 18. [. . .] [’T]is very strange to charge me with advancing my principle of the want of a sufficient reason, without any proof drawn from the nature of things, or from divine perfections. For the nature of things requires, that every event should have beforehand its conditions, requisites and dispositions, the existence whereof makes the sufficient reason of such an event. 19. And God’s perfection requires, that all his actions should be agreeable to his wisdom; and that it may not be said of him, that he has acted without a reason; or that he preferred a weaker reason before a stronger. 20. I shall speak more largely at the conclusion of this paper, concerning the solidity and importance of this great principle of the want of a sufficient reason in order to every event; the overthrowing of which principle would overthrow the best part of all philosophy. ’Tis therefore very strange that the author should say, I am herein guilty of a petitio principii; and it plainly appears he is desirous to maintain indefensible opinions, since he is reduced to deny that great principle which is one of the most essential principles of reasoning (Letter 5, Secs. 18–20 /LC 60) 125. I shall conclude with what the author objected against me at the beginning of his Fourth Reply: to which I have already given an answer above (Numb. 18, 19, 20. But I deferred speaking more fully upon that head, to the conclusion of this paper. He pretended that I have been guilty of a petitio principii. But, of what principle, I beseech you? Would to God less clear principles had never been laid down. The principle in question, is the principle of the want of a sufficient reason; in any order to any thing’s existing, in order to any event’s happening, in order to any truth’s taking place. Is this a principle, that wants to be proved? The author granted it, or pretended to grant it, Numb. 2 of his Third Paper; possibly, because the denial of it would have appeared too unreasonable. But either he has done it only in words, or he contradicts himself, or retracts his concession. 126. I dare say that, without this great principle, one cannot prove the existence of God, nor account for many other important truths. 127. Has not everybody made use of this principle, upon a thousand occasions? ’Tis true, it has been neglected, out of carelessness on many occasions: but that neglect has been the true cause of chimeras; such as are (for instance,) an absolute real time or space, a vacuum, atoms, attraction in the scholastic sense, a physical influence of the soul over the body, and a thousand other fictions, either derived from erroneous opinions of the ancients, or lately invented by modern philosophers. 128. Was it not upon account of Epicurus’s violating this great principle, that the ancients derided his groundless declination of atoms? And I dare say, the scholastic attraction, revived in our days and no less derided about thirty years ago, is not at all more reasonable. 129. I have often defied people to allege an instance against that great principle, to bring any one uncontested example wherein it fails. But they have never done it, nor ever will. ’Tis certain, there is an infinite number of instances, wherein it succeeds [or rather it succeeds] 5 in all the known cases in which it has been made use of. From whence one may reasonably judge, that it will succeed also in unknown cases, or in such cases as can only by its means become known: according to the method of experimental philosophy which proceeds a posteriori, though the principle were not otherwise justified by bare reason, or a priori. 130. To deny this great principle, is likewise to do as Epicurus did; who was reduced to deny that other great principle, viz. the principle of contradiction, which is that every intelligible enunciation must be either true, or false. Chrysippus undertook to prove that principle against

5

The square brackets indicate an interpolation that was added by Leibniz in his own copy subsequent to the dispatch to Caroline.

Leibniz’s Justification of the Principle of Sufficient Reason

73

Epicurus; but I think I need not imitate him. 6 I have already said what is sufficient to justify mine: and I might say something more upon it, but perhaps it would be too abstruse for this present dispute. And I believe, reasonable and impartial men will grant me, that having forced an adversary to deny that principle is reducing him ad absurdum. (Letter 5, Secs. 125–30 /LC 96– 97)

Whilst it is hard to pick apart all the strands in these passages, I want to suggest that we can usefully distinguish five distinct approaches which comprise responses to Clarke’s demand for a proof of the PSR. They are all worthy of attention, though I will have more to say about those that appear in Sections 18, 19 and 130 than the others. Before moving on to the things that look like justifications of the PSR, or at least claims that might the bases for such justifications, it is worth noting the way in which Leibniz approaches Clarke’s demand in Section 125: Is this a principle that wants to be proved? The author granted it or pretended to grant it, Numb. 2 of his Third Paper; possibly, because the denial of it would have appeared too unreasonable. (Letter 5, Sec. 125 /LC 96)

Leibniz’s initial move is to question whether there is really any need to prove the PSR, and elsewhere in the correspondence he refers to the PSR as an “axiom” (Letter 3, Sec. 7 / LC 27). In light of this, one might be tempted to think Leibniz took the PSR to be in need of no support because it is a self-evident foundational claim. However, setting aside the issue of just how the term ‘axiom’ is intended in this context, Leibniz makes clear it elsewhere that being an axiom entails neither foundational status nor self-evidence. He does exclude the need to prove “primary axioms” (NE 75), where these are propositions that fall into the class of “identities” (NE 406), i. e., those whose truth is self-evident in virtue of their form rather than their content; or to put it a little anachronistically, analytic truths whose analyticity has been represented explicitly. However, Leibniz also takes there to be “secondary axioms”, and he insists on “the importance of demonstrating all secondary axioms by bringing them back to axioms which are primary” (ibid.). It is surely the case that if the PSR falls into either of these categories it is the second. Assuming this is so, then Leibniz appears to be committed to the idea that the axiomatic status of the PSR could in some way be rendered perspicuous in terms of some “primary axiom /s”, whose truth was analytic and self-evident as a matter of the form in which it they were expressed. But whether Leibniz conceived of things explicitly in these terms or not is moot in the context of this paper. For there is nothing in the Clarke correspondence that looks like an attempt to articulate such a “bringing back” as a justification. Given these considerations, it seems to me that we should take Leibniz’s initial comment as nothing more than an allusion to the fact that it seems odd for Clarke to demand a proof of the PSR given that he is willing to accept it. That said, as we shall see later on, this apparent agreement masks some serious differences.

6

As Alexander observes, this is reported in Cicero’s De Fato, X (LC 96, n. 1).

74

Paul Lodge

4. A proof from the nature of things As we have seen, Clarke’s 4th Letter includes the accusation that Leibniz has not proved the PSR “either from the nature of things, or the perfection of God” (Letter 4, Secs. 1–2 / LC 45). Leibniz responds directly to the first of these charges in Section 18 of his 5th Letter. For the nature of things requires, that every event should have beforehand its conditions, requisites and dispositions, the existence whereof makes the sufficient reason of such an event. (Letter 5, Sec. 18 /LC 60)

A number of commentators have suggested that we should regard this as a version of an argument that occurs much earlier in Leibniz’s career, namely the one in the Demonstrations of Primary Propositions and the Confessio Philosophi. 7 As presented in the Demonstrations, the argument runs as follows: Proposition: Nothing is without a reason, or whatever is has a sufficient reason. Definition 1. A sufficient reason is that which is such that if it is posited the thing is. Definition 2. A requirement is that which is such that if it is not posited the thing is not. Demonstration: Whatever is, has all [its] requirements. For if one [of them] is not posited the thing is not by def. 2. If all [its] requirements are posited, the thing is. For if it is not, it will be kept from being by the lack of something, that is, a requirement. Therefore all the requirements are a sufficient reason by def. 1. Therefore whatever is has a sufficient reason. Q. E. D. (A 6.2.483 /Adams 1994, 68)

This argument has been roundly criticized on the grounds that it begs the question against those who would deny the PSR. Thus Robert Adams observes: “anyone who denies the Principle of Sufficient Reason will suppose that when all the necessary conditions of a thing’s existing are given, there might still be the possibility of its existing and a possibility of its not existing” (Adams 1994, 68). My main interest here, however, is not with the plausibility of the demonstration. Instead (though ultimately, this must surely be a related claim), I want to suggest that we should be wary of assuming that the demonstration of 1671–72(?) is really the same argument as the one Leibniz presents to Clarke in his 5th Letter. For one thing, as I noted above, the formulation of the PSR in this text differs from the one in the Clarke correspondence, in that there is no reference to a “rather than”. So, there is a sense in which a truncated repetition of this argument could not be fully adequate to the task set by Clarke. But there are other prima facie reasons to think they are different. To begin with one might wonder why Leibniz did not offer the 1671–72(?) demonstration in full if he intended to convey the same justification. But we also find differences as we turn to the content that is presented in each case. In the Clarke correspondence, rather than things “having all their requirements”, it is the “existence” of the “proper con-

7

See Sleigh 1983, 203 and CP 151 n. 23; Adams 1994, 68; Look 2011, 205. Versions of the argument are also found in On Existence (A 6.3.587 /DSR 113) and On Freedom (PE 94).

Leibniz’s Justification of the Principle of Sufficient Reason

75

ditions, requisites, and dispositions” that are said to “make the sufficient reason” (Letter 5, Sec. 18 /LC 60). And perhaps more importantly, embracing Clarke’s language, Leibniz claims that “the nature of things requires” that which he equates with the PSR, rather than offering definitions of ‘sufficient reason’ and ‘requirement’ (a term which appears to be equivalent to ‘requisite’ in the correspondence) and demonstrating the PSR from them. Indeed, I think the differences become even clearer if we look at the context in which the comments of Section 18 occur. If we focus on Section 18 alone, it may seem that Leibniz has nothing more in mind than the considerations of the Demonstrations, given that he prefaces the brief claim that he does make by observing “[’T]is very strange to charge me with advancing my principle of the want of a sufficient reason, without any proof drawn from the nature of things, or from divine perfections” (ibid.). However, the content of Section 18 is informed by the contents of Sections 14–17. Crucially, these include an elaboration of Leibniz’s views that rational agency requires that what emerges from such activity is fully determinate, and that this in turn entails that everything that is required to bring about the determinate outcome is also in place, i. e., the conditions that serve as a sufficient reason. Furthermore, in the background is a commitment shared by Clarke to the fact that the “the nature of things” is the result of divine rational agency. Thus, there is at least a case for interpreting Leibniz as suggesting that it follows from the nature of things (i. e., created things) that everything contingent has a sufficient reason because of the way in which created reality is produced. Assuming this is what Leibniz intended, there is, perhaps, something rather disappointing about this kind of justification. For however effective this proof may be in the context of debates with those who regard rational agency as the basis for all contingent truths, it falls short of explaining why this conception of the source of contingent truths should be embraced. Furthermore, it becomes hard to see how it differs from the “proof from divine perfections” that we shall consider next. However, it is unclear to me how concerned we should be about the latter. Although I am presenting what Leibniz says in Sections 18 and 19 as two distinct justifications, Section 18 is very short and opaque. So it may just be that we are being offered two complementary ways of expressing the same considerations, one starting with the effect and one with the cause.

5. A proof from divine perfections Leibniz’s second response to Clarke’s challenge is as follows: And God’s perfection requires, that all his actions should be agreeable to his wisdom; and that it may not be said of him, that he has acted without a reason; or that he preferred a weaker reason before a stronger. (Letter 5, Sec. 19 /LC 60)

At first pass it is hard to see that Leibniz is doing any more in this section than asserting the connection that Clarke has asked him to demonstrate, namely that the nature of God as a rational agent requires that the PSR holds of his activity and what that produces. However, the response echoes a good deal that has been said in earlier letters and it is possible to gain a better sense of why it is that Leibniz thinks that the divine perfections entail the PSR in light of these.

76

Paul Lodge

In his 2nd Letter, Clarke claims to support Leibniz’s endorsement of PSR, but only to add that this is “oft-times no other, than the mere will of God” (Letter 2, Sec. 1 /LC 20), on the grounds that to deny that the divine will “could act without a predetermining cause [. . .] would tend to take away all the power of choosing and to introduce fatality” (Letter 2, Sec. 1 /LC 21). Leibniz’s initial response is two-fold: First, he attacks Clarke on the grounds that he is “falling back into the loose indifference”, which he claims to have “confuted at large, and showed to be absolutely chimerical, even in creatures, and contrary to the wisdom of God” (Letter 3, Sec. 7 /LC 27); second, he defends his own conception of choice as determined by a sufficient reason as involving a benign kind of “fatality”, which he equates with “the wisest order of providence” (Letter 3, Sec. 8 /LC 28) as opposed to a “blind fatality or necessity, void of all wisdom and choice, which we ought to avoid” (ibid.). Clarke’s response to these claims is uncompromising and reveals more about his own understanding of divine activity and the way in which he interprets Leibniz’s alternative: Where there is any difference in the nature of things, there the consideration of that difference always determines an intelligent and perfectly wise agent. But when two ways of acting are equally and alike good (as in the instances before mentioned;) to affirm in such a case, that God cannot act at all, or that ’tis no perfection in him to be able to act, because he can have no external reason to move him to act one way or another seems to be a denying God to have in himself any original principle or power of beginning to act, but that he must needs (as it were mechanically) be always determined by things extrinsic (Letter 3, Secs. 7 and 8 /LC 32–33)

Clarke agrees with Leibniz that where the objects of choice differ, God (qua perfectly wise agent) will be determined in his choice by his “consideration of that difference”. But this still allows for cases in which consideration reveals equally good options, and hence no difference that could provide a basis for choice. And, to Clarke’s mind, Leibniz’s claim that God could not act in such a situation is to deny that God has an internal power to initiate change, and to insist that God is always determined to act by extrinsic causes. The significance of these claims was clearly not lost on Leibniz, given that his 4th Letter begins with a somewhat terse response: 1. In things absolutely indifferent, there is no [foundation for] 8 choice; and consequently no election, nor will; since choice must be founded on some reason, or principle. 2. A mere will without any motive is a fiction, not only contrary to God’s perfection, but also chimerical and contradictory; inconsistent with the definition of the will. (Letter 4, Sec. 2 /LC 36)

And Leibniz returns to the issues in Section 18 of his 4th Letter, observing that “A will without reason would be the chance of the Epicureans. A God, who should act by such a will, would be a God only in name” (Letter 4, Sec. 18 /LC 39), adding in Sections 19 and 20: 19. When two things which cannot both be together, are equally good; and neither in themselves, nor by their combination with other things, has one any advantage over the other; God will produce neither of them. 20. God is never determined by external things, but always by what is in himself; that is by his knowledge of things, before any thing exists without himself. (Letter 4, Secs. 19–20 /LC 39)

8

The bracketed material was added by Clarke.

Leibniz’s Justification of the Principle of Sufficient Reason

77

We can see how radical the difference is between Leibniz’s and Clarke’s conceptions of divine activity in these passages. But, nonetheless it is clear that both men believe that the activity of God as they conceive it is wise and in accordance with the PSR. One crucial difference that feeds into Clarke’s 4th Letter and Leibniz’s 5th Letter is Clarke’s apparent willingness to embrace the idea that God’s activity may in some situations be determined by things external to the divine nature, namely in those situations where alternative courses fail to be “equally and alike good” (Letter 3, Secs. 7 and 8 /LC 32) and their natures, as conceived correctly by God, determine the way God acts. This is then contrasted with situations in which God’s activity is not so determined due to indiscernibility (such as deciding where to locate matter in infinite homogeneous space), and here Clarke insists that rational activity proceeds via spontaneous internal act of divine will. Leibniz objects to this view for two reasons. One is the very familiar idea that God would refrain from acting were there no best option, but the other is less prominent in his writings. For Leibniz finds himself needing to make the point that God is “never determined by external things” (Letter 4, Sec. 20 /LC 39). In his 4th Letter Clarke returns to the charge that Leibniz’s conception of divine action “leads to a universal necessity and fate” (Letter 4, Secs. 1 and 2 /LC 45), but he also draws on an analogy that Leibniz himself had introduced in the first section of his 2nd Letter (Letter 2, Sec. 1 /LC 16). Clarke suggests that Leibniz is assimilating the way in which motives are related to the will to the way in which weights act on a balance – the stronger motive determining the agent as a heavier weight would, and cases in which the motives are “equally alike and good” leaving the agent unmoved like a balance in equilibrium. Clarke insists that the analogy is inappropriate. A balance is no agent, but is merely passive and acted upon by the weights; so that when the weights are equal, there is nothing to move it. But intelligent beings are agents; not passive, in being moved by motives, as a balance is by weights; but they have active powers and do move themselves, sometimes upon the view of strong motives, sometimes upon weak ones, and sometimes where things are absolutely indifferent. In which latter case, there may be very good reason to act, though two or more ways of acting may be absolutely indifferent. (Letter 4, Secs. 1 and 2 /LC 45)

Here Clarke attempts to articulate a view which allows both that intelligent beings act “upon the view of” of external conditions and yet “move themselves”, as opposed to the “merely passive” changes that occur when weights are placed on a balance and the arms move (or not). Leibniz’s response in Sections 14 and 15 of his 5th Letter reveal the inadequacies that he sees in Clarke’s sketch of the disanalogy. In Section 14 Leibniz claims that it is incorrect to think that the patterns of motion when weights are placed on a balance sometimes involve activity and sometimes not. Both the balance and the weights are active whatever the scenario, with the pattern of motion due to the resolution of this activity. However, more importantly, in Section 15 Leibniz tells us how we should conceive what is going on in agency “properly speaking” (Letter 5, Sec. 15 /LC 59). Central to this account is the claim that “motives do not act upon the mind [. . .] but ’tis rather the mind that acts by virtue of the motives, which are its dispositions to act” (ibid.). It is not entirely clear how Clarke conceives of motives. However, he seems not to think of them as intrinsic features of an agent. Rather they seem to be extrinsic features that may be acted upon or not as a matter of the agent’s

78

Paul Lodge

preference, where the content of the preference is not amenable to characterization that is independent of the extrinsic motives. Leibniz appears to adopt such a reading, insisting that Clarke’s view is one which “divide[s] the mind from its motives, as if they were without the mind [. . .] as if the mind had, besides motives, other dispositions to act by virtue of which it could reject or accept motives” (ibid). In contrast, he insists that his own view is one on which “the motives comprehend all the dispositions, which the mind can have to act voluntarily; for they include not only the reasons, but also the inclinations arising from passions or other preceding impressions” (ibid). For Leibniz, reasons are a subset of the motives that give rise to mental activity, thus for him it is “a manifest contradiction” to claim, as Clarke does, that there could be reasons to act and yet the mind remain indifferent with regard to them, or even choose in spite of them. The model of agency that Leibniz employs is one on which activity arises from a resolution of the motivational power of all the dispositions to act, whether rational or otherwise. As he observes, “if the mind should prefer a weak inclination to a strong one, it would act against itself, and otherwise than it is disposed to act” (ibid). But Clarke’s response to this in his 5th Letter, to which Leibniz never responded, is unsurprising. He insists that Leibniz is “denying the mind to have in itself a principle of action”, and he continues to claim that “the motive, or thing considered as in view, is something extrinsic to the mind” and that “the impression made upon the mind by that mind is the perceptive quality, in which the mind is passive” (Letter 5, Secs. 1–2 /LC 97). For Leibniz rational agency is to be conceived univocally, with the source of activity entirely internal to the mind of the agent. What seems to be at issue here is that, by contrast, Clarke embraces a characterization of rational agency that is equivocal. In situations where there are differences in the goodness of external circumstances these determine the choice that is made, but in other cases rational agency is of a completely different character. For it is something that involves determination of the mind that is wholly spontaneous and uninfluenced by the external conditions given that they are identical in all relevant respects. And, perhaps most importantly for the current debate, Clarke is adamant that there are situations in which God’s activity is in accordance with the PSR whilst being an entirely spontaneous choice between situations whose nature (and hence goodness) is identical – a central case being God’s decision to create matter at a determinate position in an infinite homogeneous space (see Letter 3, Secs. 7 and 8 /LC 32). If we take a step back from the issue of the possible resolution of the debate between Leibniz and Clarke, something else comes into view, namely a disagreement regarding the content of the concept to which each of the two men attach the word ‘God’. Furthermore, it is a disagreement that is rendered particularly opaque, given that they each take it to be the case that God’s nature conforms to the traditional triune conception. For this entails that both men take God’s action to result from divine wisdom, and take divine wisdom to be the paradigm for rationality. In other words, both Leibniz and Clarke in their own way are committed to taking something that is plausibly termed ‘the Principle of Sufficient Reason’ as a principle that holds of the created world and the divine activity that gave rise to it. And they justify this in the same way, namely by appeal to the fact that God is the source of all contingent truths concerning the created world. We are now in a position to understand a crucial difference between these conceptions of rational agency. For, at least in the divine case, it is Leibniz’s view that acting on a

Leibniz’s Justification of the Principle of Sufficient Reason

79

reason requires: (1) that the content of that which is willed be internal to the agent and fully determinate; and (2) that the activity takes place in virtue of an awareness of that determinacy and the fact that it is the best option available. However, for Clarke, God can be a fully reasonable agent and yet there be an indeterminacy among the objects of choice with regard to their goodness, and hence a situation in which divine action emerges through a decision in favour of a course of action, the content of which cannot be rendered fully and determinately intelligible even by God. What we are not in a position to do, however, is to see how Leibniz thought this impasse might be resolved. Leibniz’s and Clarke’s Gods seem to be different, and their agency and that which emerges from it has a different character. But Leibniz has not told us why his should be regarded as the proper conception of God and the created world. When Leibniz returns to the PSR at the end of his 5th Letter a number of additional claims are made that appear to speak to why he thinks we should adopt the principle and I will turn to those in sections 5–7 below. Unfortunately, it seems to me that they take us little further in resolving the impasses that have been exposed. However, in section 9 I will suggest that one interpretation of what Leibniz may have had in mind when he spoke of the ideas that he deemed “too abstruse for the present dispute” (Letter 5, sec. 130 /LC 96) might go some way toward a resolution.

6. PSR and the truths of natural philosophy and metaphysics In section 126 of his 5th Letter, Leibniz suggests that “without this great principle [i. e., the PSR], one cannot prove the existence of God, nor account for many other important truths” (Letter 5, Sec. 126 /LC 95). This is a recapitulation of a point made in his 2nd Letter in slightly more grandiloquent terms. Here, in addition to “the being of God”, the PSR is said to enable us to “demonstrate [. . .] all the other parts of metaphysics or natural theology; and even, in some measure, those principles of natural philosophy that are independent upon mathematics” (Letter 2, Sec. 1 /LC 16). Throughout the correspondence, we find various examples of things that Leibniz attempts to establish on the basis of the PSR, or mentions as dependent on it, which fill out these more abstract claims. Most famously it is employed in arguing against the existence of absolute space (e. g., Letter 4, Sec. 13 /LC 38). 9 But Leibniz also invokes the PSR to reject the existence of atoms and the vacuum (Letter 4, postscript /LC 44) and to argue for the Principle of the Identity of Indiscernibles (Letter 5, Sec. 21 /LC 61 and Sec. 26 /LC 61–62). 10 Among the things that are mentioned as positive consequences of the PSR, we are told, “in order to proceed from mathematics to natural philosophy, another principle [i. e., the PSR] is requisite” (Letter 2, Sec. 1 /LC 15). And, as mentioned above, Leibniz illustrates this by claiming that the PSR plays this bridging role in Archimedes On the Equilibrium of Planes when “[Archimedes] takes it for granted, that if there be a balance, in which everything is alike on both sides, and if equal weights are hung on the two ends of that balance, the whole will be at rest” (Letter 2, Sec. 1 /LC 16.). Closer to home, Leibniz also 9 10

For helpful discussion of these arguments, see section 2 of Brown (forthcoming). For differing views of the ways in which this argument proceeds, see Jauernig 2008, 208–212, and Rodriguez-Pereyra 2014, 104–14.

80

Paul Lodge

suggests the PSR is used to establish “the dynamic principles or the principles of force (Letter 2, Sec. 1 /LC 16). Some of the claims that count as “important truths” receive no further elaboration in the correspondence. Others that are rejected by Leibniz are presented as at odds with the claim that they are truths about a world created through the rational agency of God. But, perhaps unsurprisingly, Clarke is unmoved. For, as we have seen, he takes the will of God, in at least some cases, to be a sufficient reason in a way that is completely independent of any specification of the content of that will. Thus (to take one example), the fact that there is no difference between two atoms does not preclude their coming into existence at particular places for Clarke. They simply belong to the class of created beings whose existence emerges from a divine decision that is not wholly explicable by appeal to the nature of that which was chosen. That said, one truth on which both men agree, of course, is the proposition that God exists. A number of puzzles arise in connection with Leibniz’s suggestion that the PSR is required to demonstrate this. It is not surprising to find Leibniz claiming that God’s existence can be proved in this way, given that it is a cosmological argument, one of the most common forms of argument for God’s existence in natural theology. But it is prima facie surprising that Leibniz suggests that without the PSR one could not prove God’s existence. It is true that Leibniz sometimes emphasizes this kind of reasoning in considering the existence of God and that there are contexts where it is presented alone. 11 However, he employs several other strategies for arguing for God’s existence throughout his career, and in the contemporary Monadology we find a version of the ontological argument (Section 45, GP 6.614 /PE 218). 12 The text of the correspondence does not allow us to resolve this puzzle. But one possibility is that Leibniz thought that the other arguments would have been dialectically impotent in the context of a discussion with Clarke, or at least that the cosmological argument would have been uncontentious in a way that might not have been true of the others. As Ezio Vailati observes (1998, 195, n. 2), Clarke not only offered a version of this argument, the whole of his A Demonstration of the Being and Attributes of God And Other Writings can be regarded as an extended cosmological argument. However, this still leaves us without a way of defending Leibniz’s claim that the fact that the PSR can be used in this way provides justification for the PSR itself. Moreover, it is hard to see how such a strategy could go. One might also worry that Leibniz appears to be opening himself up to a charge of circularity by claiming that the PSR is required to prove God’s existence whilst offering it as an argument for the PSR. Two avenues seem worthy of consideration here. We have already seen that Leibniz embraces non-PSR grounded arguments for God’s existence. But it is also worth noting that the argument occurs in the context of a correspondence in which his opponent has granted that God exists. And, as we have seen, a central part of the dispute concerns the relation between two competing conceptions of divine agency and what is involved in a commitment to the PSR. Both men agree that the two go hand 11

For example, it is the focus of detailed elaboration in the piece On the Ultimate Origination of Things of 1697 (GP 7.302-8 /PE 149–55) and it is the only argument for God’s existence that appears in Leibniz’s only published book The Theodicy. (GP 6.106-07 /T 127–28). 12 See Look (2014) for a useful overview of Leibniz’s arguments for the existence of God.

Leibniz’s Justification of the Principle of Sufficient Reason

81

in hand. Thus, at least in this context, it might have been legitimate for Leibniz to regard the circle as virtuous, since there is a sense in which, absent the PSR, Leibniz would lack a demonstration that the ground of contingent beings had the characteristics that his concept of God includes. But, again, it leaves the claim that the PSR can be independently justified on the basis of its employment in proving God’s existence looking implausible. Section 127 is also devoted to claims about the relation between the PSR and natural philosophy. Here Leibniz suggests that there are “chimeras” (Letter 5, Sec. 127 /LC 96), “fictions [or] spectres of imagination” (LC 5.48 /Al 72), belief in which has resulted from the fact that that “it [i. e., PSR] has been neglected, out of carelessness, on many occasions” (Letter 5, Sec. 127 /LC 95). Leibniz offers several examples, namely “an absolute real time or space, a vacuum, attraction in the scholastic sense, a physical influence of the soul over the body [and of the body over the soul] 13 and a thousand other fictions, either derived from erroneous opinions of the ancients, or lately invented by modern philosophers” (ibid.), among which he explicitly mentions, for the moderns Henry More’s “spirits that can make themselves impenetrable” (Letter 5, Sec. 48 /LC 72), and for the ancients Epicurus’s “groundless declination of atoms” (Letter 5, Sec. 128 /LC 96). But here again there is little of dialectical significance as Leibniz is drawing attention to claims that Clarke would, or does, either reject or embrace on different grounds.

7. The ubiquitous use of PSR The previous section was concerned with arguments that turn on the relation between particular empirical truth claims and the PSR. But Leibniz also tries to argue for the PSR on more generic empirical grounds. In section 127 of the 5th Letter, we find the observation “Has not everybody made use of this principle upon a thousand occasions?” (Letter 5, Sec. 127 /LC 95). Leibniz does not say more about why he takes this to be significant. But we might assume that he is suggesting that some kind of support for the PSR is to be found by observing that everyone is aware of having themselves relied on the principle to govern their activity and are aware that other people seem to have acted in this way as well. Construed literally, the claim that we know from experience that everyone uses the PSR on many occasions is clearly problematic. But a more charitable reading, namely that experience shows that people generally employ the principle is more persuasive, at least if we understand it to mean that people generally engage in the practice of looking for reasons for things until they take themselves to have found a reason that satisfies their search. Perhaps the significance of the claim is supposed to lie in the thought that an, as yet, unfalsified commitment to the truth of a given proposition is good enough grounds for holding it true. That this is what Leibniz intends receives further support from section 129 of the 5th Letter where Leibniz turns again to facts about the actual use of PSR. Here he observes that he has “often defied people to allege an instance against that great principle, to bring any one uncontested example wherein it fails. But they have never done it, nor ever will” (Letter 5, Sec. 129 /LC 96). In light of this, Leibniz suggests that “one may reasonably judge, that it will succeed also in unknown cases, or in such cases as can only by its means 13

Material in brackets added by Clarke.

82

Paul Lodge

be known” (ibid.) and that the principle can be justified “according to the method of experimental philosophy which proceeds a posteriori” (ibid.). In other words, Leibniz is suggesting that there is an inductive case to be made for the truth of the PSR, given that our natural tendency to regard it as true is something that survives attempts to find counterexamples. The claim that Leibniz has challenged people to come up with counterexamples parallels the better-known claim he makes about challenging companions to find two identical leaves in defence of the Principle of Identity of Indiscernibles (see Letter 4, Sec. 4 /LC 36). However, it is much less clear what he has in mind in this case. As I noted at the beginning of the paper, Leibniz provides no examples of sufficient reasons, and leaves us with the thought that “the principle of the best” might really be the only one where we are restricting our attention to claims about created reality. But, in addition to this, some of the best-known receptions of Leibniz’s writings provide us with examples that strike some people as clear cases that defy the PSR if it is conceived as a principle that requires an appeal to divine reason. Here I am thinking of the various examples of ‘senseless’ suffering in Voltaire’s Candide and the only slightly less famous passages from Dotoevsky’s The Brothers Karamazov, in which Ivan discusses the problem of evil with his brother Alyosha and contemplates the torture of innocent children – focusing in particular on the case of an eight year old deliberately torn apart by hunting dogs in front of his mother on the command of a nobleman for a minor misdemeanor. (Dostoyevsky 1958, 284). We can interpret these examples in the conventional way, namely as challenges to Leibniz’s thesis that the actual world is the best of all possible worlds and, by extension, to the thesis that a God who conforms to a traditional theistic conception exists. But another way to put the point is to suggest that, insofar as there are events of this kind, they are events for which no sufficient reason could be given as Leibniz conceives of such a thing. For even if such a world were the best among those that could have been created, there would remain the issue of whether the creation of nothing remained the better option. At least as problematic is Leibniz’s claim that the methods of experimental philosophy, i. e., inductive reasoning, can be used to justify the PSR. This is perhaps most straightforwardly read as the claim that past experience of the kind evinced suffices for no more than the rational expectation that PSR will succeed in future cases. But Leibniz makes the stronger claim that those who attempt to provide a counterexample “never will”, i. e., that the PSR is both an infallible principle and that this can be established through induction. Indeed, this is something that is further compounded by the fact that Leibniz is committed to the existence of an actual infinity of created beings (e. g., see GP 1.416; A 6. 4. 1393 /LoC 234–235). There is clearly scope for turning to Leibniz’s views about the logic of experimental philosophy at this point. But, to the extent that he is serious in his claim that the PSR holds universally, it is hard to see how there could be a plausible empirical justification. For all of this, however, it is hard to shake the thought that Leibniz is onto something. It is hard to deny that a commonplace aspect of human thinking and communication is the tendency to ask why, and to be satisfied only when one has been given reasons that render events, situations, and truths intelligible to one. And, whilst it may not be the case that the answers in such cases are sufficient reasons in the strict sense, there is a more ordinary sense in which we relent in a satisfied way when, and only when, we discover,

Leibniz’s Justification of the Principle of Sufficient Reason

83

or are convinced, that conditions the obtaining of which suffice for that about which we asked have been found to obtain. One need only interact with an inquisitive three year old to be reminded all too much of this phenomenon. That said, such requests often seem to fall short of the demand for a reason in Leibniz’s sense, i. e., one that will render them intelligible as the products of rational deliberation. Furthermore, they still leave us without a clear sense of why the tendency to make such demands should be regarded as grounds for the truth of the claim that there is such a reason. Indeed, interactions with three year olds often seem to suggest just the opposite. But whatever is the case here, it becomes clear from the following section of the 5th Letter that Leibniz does not want to rest his case entirely on such claims.

8. To deny PSR is to be reduced to absurdity When offering his a posteriori justification in section 129 of his 5th Letter Leibniz adds that it would hold “even if the principle were not otherwise justified by pure reason, or a priori” (Letter 5, Sec. 129 /LC 96). And, whilst he is not explicit, it appears that section 130 is intended to provide this a priori justification. Here Leibniz observes that “To deny this great principle, is likewise to do as Epicurus did; who was reduced to deny that other great principle, namely, the principle of contradiction; which is that every intelligible enunciation must either be true or false” (Letter 5, Sec. 130 /LC 96). Leibniz does not explain just what the connection is between the denial of the PSR and the PC, however he adds “I believe reasonable and impartial men will grant me that having forced an adversary to deny that principle [i. e., the PSR] is reducing him ad absurdum” (Letter 5, Sec. 130 /LC 96 – 97). What we seem to be hovering around at this point is the thought that it is somehow a requirement on being a “reasonable” person that one accept the PSR, just as it would be unreasonable to deny the PC. One might wonder whether there are resonances here with the justification of induction that we find in the work of P. F. Strawson, namely that it is constitutive of the practice of thinking rationally about unobserved cases that we utilize induction (see Strawson 1952, 256–263). Might Leibniz be claiming that is constitutive of thinking rationally more generally that one think in accordance with the PSR? If this is the position, one obvious worry is that Leibniz is yet again doing no more than offering his preferred conception of divine wisdom and presenting it as the blueprint for what it is think properly. And if this is the case, we seem to face the very same impasse that has arisen again and again in the debate between the two men. For why couldn’t Clarke make exactly the same Strawsonian move employing his own conception of rationality? In the next section, I will build on this thought in offering a speculative rendition of the “abstruse” justification that Leibniz did not share with Clarke. Before turning to this part of my discussion, I think it is worth taking stock a little. One conclusion of my discussion of all the preceding justifications might be that, given the views to which Clarke is wedded, Leibniz is in fact begging the question throughout. He repeatedly reasserts the connection between the fact that the universe emerges through rational activity as he conceives it and a view about what the rational structure of the universe consists in. But this conception of the emergence of the created universe from the uncreated ground is not itself motivated via an appeal to any common commitments.

84

Paul Lodge

The discussion has exposed fundamental differences between the commitments of the two men regarding the concepts that terms like ‘God’ and ‘sufficient reason’ express. But, given this, it seems clear that there could never have been a genuine expectation of agreement. Furthermore, it seems clear that this emerges much earlier in the discussion than the swansong. At this point, we might wonder what Leibniz was really trying to do. Did he think he could convince Clarke? Indeed, was he even trying to do this, or was he perhaps playing to others whom he thought the correspondence might be reaching? We should remember that Clarke was liaising with Newton and that the discussions were always passing through the hands of Princess Caroline. Furthermore, he could have reasonably expected that the correspondence would be published. But, interesting as these questions are, there is nothing in the correspondence that seems to help us answer them. However, in my account of the ‘abstruse justification’, I will try to offer an account of how Leibniz might have spoken in favour of these fundamental commitments had he decided to elaborate on it.

9. The abstruse justification? At this point we have covered almost all of what Leibniz has to say in favour of the PSR in his swansong. Indeed, previous misgivings notwithstanding, in section 130, the very last of the correspondence, Leibniz claims that he has “already said, what is sufficient to justify [the PSR]” (Letter 5, Sec. 130 /LC 96). But he then adds “I might say something more upon it, but perhaps it would be too abstruse for this present dispute” (ibid.). Unfortunately, nothing more is said, but at the risk of going completely off piste, I want to end with some speculative thoughts about what Leibniz’s abstruse thoughts might have been, based on writings other than the correspondence. As we have now seen, the debate between Leibniz and Clarke appears to turn on a dispute over the proper conception of rationality, and the concept of God that embodies this conception. The question at hand is what other abstruse reason Leibniz might have given for arbitrating. I want to consider three separate approaches that have some basis in things that Leibniz says elsewhere, in order of abstruseness. Clearly, it is impossible to know which, if any, of these Leibniz in mind. But I want to use the opaque nature of his claim to take the opportunity to engage in some rather liberal exegesis, recognizing that the main part of what I will say invites and demands a good deal of further exploration. The first kind of consideration that Leibniz may have had in mind is perhaps not abstruse enough, given that it is a complaint that he levels throughout his life at those whom he perceives as defending a voluntarist conception of God. 14 But I think it is nonetheless worth mentioning. As we have seen, Clarke allows that divine willing might have taken place where there was no intelligible content that differentiated that which was willed and that which was not. For Leibniz, this leaves Clarke in the position where there is no intellectual basis on which a judgement of the goodness of God’s action can be determined. Furthermore, Leibniz believes that this leaves Clarke (assuming that he 14

For a particularly clear discussion, see the Meditation of the Common Concept of Justice dating from 1703 (PW 45–51), and for useful discussion see Arthur 2014, 170–171.

Leibniz’s Justification of the Principle of Sufficient Reason

85

wishes to claim that God’s activity is good) in an untenable position. For he is required to maintain that God’s activity and its consequences are good simply in virtue of God’s having willed them so, much as he was happy to claim that God’s activity is reasonable simply because it is the product of his wisdom. The problem with this from Leibniz’s perspective is that it entails that anything that God had willed would have counted as good, something that to his mind reduces God to a tyrant who is to be feared, rather than a good God who deserves love. Aside from the fact that this justification is too commonplace in Leibniz’s writings to really deserve the title ‘abstruse’, it again moves the debate along no further. For, as should be obvious by now, this kind of response would not have moved Clarke. It is simply a part of the package to which he was self-consciously committed. Indeed, it may have been for this reason that Leibniz did not think it worth adding this consideration explicitly despite its being common in his other work. Another strategy that Leibniz might have adopted is more abstruse, at least in the sense that it is not one that he appeals to often. Indeed, the only occasion of which I am aware in which he does use this strategy is in a letter to Burcher de Volder, with whom he corresponded between 1698 and 1706. One of the key disputes between the two men concerns the proper conception of substance. Whilst the debate is very complex, we need take note of very little of that here. What is of interest is one among a number of Leibniz’s response to De Volder’s claim that substance is that which can exist independently of anything else. 15 In his letter of July 6, 1701 we find: “I might point out that your concept of substance does not seem to agree with those things that are commonly so called” (LDV 207). And Leibniz elaborates in his letter of December 27, 1701: I admit that you are within your rights to understand the word substance so that God alone is a substance and other things are called something else. But it is my intention to look for a notion that will apply to others and agrees with ordinary ways of speaking, according to which you, I and others are counted as substances. (LDV 223)

What we see here appears to offer a means by which Leibniz might try to arbitrate between his and Clarke’s conception of God, namely on the grounds that the proper conception ought to track the extension of the term ‘God’ as commonly employed. But, interesting as this strategy is, it is again hard to see that Clarke should have been moved by anything of this kind. For one thing, the analogy with the concept of God is a little awkward. In the case of substance, Leibniz points to the fact that a class of entities that would generally be called substances, namely human beings, do not fall under the extension of De Volder’s definition of the term. But Leibniz and Clarke are arguing about the properties that should be ascribed to a being to which they both take themselves to have successfully referred, and which they both regard as the creator of the universe. Nonetheless, one might think that Leibniz could appeal to the thought that appeal to traditional understanding of the term should prevail in the case of the dispute over the proper understanding of the divine nature. But, again, whatever the merits in the case of the term ‘substance’, this strategy would have been weak in the current context. It is true that in being adamantly opposed to divine voluntarism, Leibniz stood in a long line of philosophical theologians, stretching 15

For further discussion of De Volder’s views and other responses that Leibniz offered, see LDV li – lx.

86

Paul Lodge

at least as far back as St Thomas Aquinas, who would have agreed with him. But there is an equally well-established tradition of divine voluntarists, including Duns Scotus and William of Ockham, who would have opposed him. Thus, to the extent that Leibniz could have appealed to common usage, he would have met equivocation of a kind that would have helped neither him nor Clarke. Thus, I want then to turn to another, even more speculative suggestion. This consideration is drawn from a discussion of a little-known piece that probably dates from around 1693, which was given the title “Leibniz’s Philosophical Dream” by an early keeper of Leibniz’s papers. 16 In this complex piece, which might be thought to be Leibniz’s attempt at a version of Plato’s allegory of the cave, a journey is described in which Leibniz is brought by a pair of guides to the use of “intelligence or reason”. My analysis of it will be based on the, admittedly questionable, hermeneutic principle that we should take it as an account of Leibniz’s actual experiences in its essentials if not in all its imagery. At the start of the piece Leibniz portrays himself as someone who “naturally loved to act well and to know the truth,” (LH 108) but he adds: “I was satisfied with what I was among men, but I was not satisfied with human nature” (ibid.). He describes the problem as arising because he “often considered with chagrin the hardships to which we are subjected” (ibid.) The particular hardships that Leibniz mentions at this point are “the shortness of our life, the vanity of glory, the improprieties that are born of sensual pleasure, the illnesses that overwhelm even our spirit; finally, the annihilation of all our greatness and all our perfections in the moment of death, which appears to reduce to nothing the fruits of our labors” (ibid.) Leibniz then adds: “these meditations left me full of melancholy,” and that “it appeared that I punished myself unnecessarily, that a successful crime was worth more than an oppressed virtue, and that a madness that is content is preferable to an aggrieved reason” (ibid.) Implicit here is the thought that Leibniz was tempted to turn away from acting well and the pursuit of truth, given the despair he suffered when contemplating the stark reality of a finite human existence and the fact that acting well was often less well-rewarded than “successful crime” (ibid.). But next we are told that, at this point in his life, he “resisted these objections and directed [his] spirit on the right course by thinking about the divinity who must have given a proper order to everything and who sustained my hopes with the expectation of a future capable of redressing everything” (ibid.) However, he goes on to suggest that this alternate focus on a mode of life governed by religious belief was of limited help: This conflict was renewed in me by the sight of some great disturbance, either among men, when I saw injustice triumph and innocence chastened, or in nature, when hurricanes or earthquakes destroyed cities and provinces and caused thousands to die without distinguishing the good from the wicked, as though nature cared no more for us than we trouble ourselves about ants

16

See LH 108–111. This piece is also in the original Everyman edition of The Philosophical Writings of Leibniz which was translated by Mary Morris and published in 1934 (PWL 253–257). However, it is notable that it was left out of the volume, which was the standard introductory selection for many years, when it was re-edited by G. H. R. Parkinson in 1973 (PW). I quote from the translation by Donald Rutherford, from whom I take the dating, at 〈http: // philosophyfaculty.ucsd.edu/faculty/rutherford/Leibniz/translations/Dream.pdf〉.

Leibniz’s Justification of the Principle of Sufficient Reason

87

or worms that we encounter in our path. I was greatly moved by these spectacles and could not stop myself pitying the condition of mortals. (ibid.)

What follows next is a description of a dream which is said to have occurred at some point when Leibniz found himself “fatigued from these thoughts” (ibid.). The dream comprises a situation in which Leibniz finds himself in a cavern surrounded by people pursuing “luminous trifles they called ‘honors’, or glittering little flies they called ‘riches’” and by “many who searched the ground for bright bits of wood they called ‘sensual pleasures’” (LH 108–109). The fates of those following these “evil lights” vary. Some are said to have switched from one evil to another, some “quit the chase altogether because of exhaustion or despair”, some “who ran blindly and often believed they had reached their goal fell into crevasses” and some “were bitten by scorpions and other venomous creatures that left them wretched and often mad” (LH 109). But not only does the dreamscape contain people who are drawn to worldly pursuits and suffer as a consequence, they are people who are presented as bound to this fate. For Leibniz adds: Yet neither these examples nor the arguments of persons better informed stopped others from chasing the same hazards and even entering into fights in order to forestall rivals or keep themselves from being forestalled. (ibid.)

In the world of the dream, the tendency to fall prey to the horrors that are met by those who choose worldly pursuits is portrayed as impervious both to the observation that it yields misery and to the persuasion of those who might be able to provide arguments for behaving otherwise. It is natural to ask at this point, where Leibniz positions himself in this scenario. But this is only possible once we add his description of the ultimate escape route. In the vault of this huge cavern there were little holes and almost imperceptible cracks. Here a trace of daylight entered; yet it was so weak that it required careful attention to notice it. One frequently heard voices which said, “Stop you mortals, or run like the miserable beings you are.” Others said, “Raise your eyes to the sky.” (ibid.)

Leibniz suggests that “no one stopped” on account of these additional features. But this is not meant to imply that no one paid attention, since he quickly adds “I was one of those who was greatly struck by these voices. I began often to look above me and finally recognized the small light which demanded so much attention” (ibid.) As the dream continues, the light becomes the focal point of attention. Leibniz tells us that: It seemed to me to grow stronger the more I gazed steadily at it. My eyes were saturated with its rays, and when, immediately after, I relied on it to see where I was going, I could discern what was around me and what would suffice to secure me from dangers. (ibid.)

At this point, Leibniz is told that the light signifies “what is called ‘intelligence’ or ‘reason’ in us” by a “venerable old man who had wandered for a long time in the cave and who had had thoughts very similar to mine” (ibid.). In conjunction with the passage above, we can see that Leibniz is constructing a story according to which he chances upon the faculty of reason, is drawn to and overcome by it, and then relies on it. Leibniz is not explicit about the nature of this faculty, but throughout the discussion with Clarke we have seen Leibniz return to the thought that commitment to his version of the PSR is at least partially constitutive of what it is to think properly and engage in rational activity. Indeed, it seems to me that this is what is

88

Paul Lodge

implied in sections 31 and 32 of the contemporary Monadology, when Leibniz observes that “Our reasonings are based on two great principles, that of contradiction [. . .] and that of sufficient reason” (GP 6.612 /PE 217). Thus I want to suggest that Leibniz’s reliance on guidance by this “light” is another statement of his commitment to a practice which involves a faculty whose operation includes taking things to accord with the PSR, and hence involves a commitment to the truth of the PSR. 17 This is clearly related to the Strawsonian idea mentioned above, but here there is something additional. For Leibniz suggests that “a venerable old man”, i. e., someone with legitimate authority (Plato himself perhaps?) has anchored the terms ‘reason’ and ‘intelligence’ to that faculty. In this context there is no other game in town, so the contrast with Clarke’s conception of intelligence or reason is not made explicit. But there can be no doubt that it is the one that is favoured by Leibniz himself that is being discussed and sanctioned and, as such, that Clarke’s is being implicitly rejected. Thus, we find something that, to Leibniz’s mind at least, might lead us out of the impasse in his dealings with Clarke and voluntarism more generally. For what we also see is that Leibniz offers considerations that speak to why we might commit to a mode of being which is grounded in acting in accord with his conception of reason, and hence taking the PSR to be true. More precisely, he suggests that in virtue of this commitment he could: 1) see where he was going; 2) see what was present in his environment; and 3) see what would protect him from danger. If we take these claims to be expressions of a justification for the PSR, they are perhaps best construed as pragmatic. For it is not so much that the PSR yields beliefs in propositions that are true, or indeed that the PSR is itself true that stands in its favour. Rather, it is because relying on the PSR (and thus taking it to be true) is constitutive of a practice whose value is said to lie in the facilitation of behavior that leads the world to show up to Leibniz in a particular way. Namely, it enables Leibniz to avoid the dangers to which other less luminous beings fall foul. So, in addition to the Strawsonian claim that Leibniz thinks of the taking the PSR to be constitutive of rational engagement with the world, we have a higher-order, a posteriori, justification for taking this conception of rational agency seriously. But, of course, it is not one whose grounds are represented as plausible as a matter of inductive generalization. If it is to provide additional warrant, we need to trust Leibniz the author as a reliable authority independently of our own practice, or the practice of others. If this were all Leibniz said, it would be interesting. But this is not the end of the dream, and what follows will perhaps be even more surprising to some readers. As dream-time proceeds, Leibniz describes himself exploring the ways in which reason might operate. Here he starts to make more of the fact that there is more than one hole through which the light shines, and talks of “chang[ing] position in order to test” (ibid.), presumably with regards to the benefits mentioned above. These experiments lead him to discover situations in which “several beams could be seen at once from their true point of view,” and observes that in cases such as these “I found a collection of rays which greatly enlightened me. This technique was of great help to me and left me more capable of acting in the darkness” (ibid.)

17

As Sleigh 1983, 192–196 points out, the matter is complicated by the fact that Leibniz often appears to invoke other principles. However, the constitutive nature of the PSR and the PC does not appear to be in much doubt.

Leibniz’s Justification of the Principle of Sufficient Reason

89

Finally Leibniz “was led by [. . .] good fortune” to a position that “was unique and the most advantageous in the cave, a place reserved for those whom the divinity wished to remove completely from this darkness” (LH 109–10). At this point he became “surrounded by a bright light shining from all sides [and] the whole cave and its miseries were fully disclosed to [his] eyes” (LH 110). Next Leibniz goes on to describe a more enlightened state to which he is led by “a celestial messenger” (ibid.) The messenger tells him “Give thanks to the divine goodness which releases you from this madness,” and takes him beyond the cave altogether to “a high mountain, which revealed to [him] the face of the earth” (ibid.) Here Leibniz finds he has a kind of telescopic vision available which allows him to focus on any part of the world and magnify it so that he can “see it as though it were next to [him]” (ibid.). Leibniz mentions two consequences of this: First he reports that it “gave me a marvelous pleasure” (ibid.); but in addition that it “emboldened me to say to my guide: ‘Mighty spirit – for I cannot doubt that you are of the number of those celestial figures who make up the court surrounding the sovereign of the universe – since you have wanted to clarify so my eyes, will you do as much for my mind?’” (ibid.) The celestial figure, at whose identity we can but guess, then grants the wish, given that he believes that Leibniz “holds wisdom above the pleasure of those vain spectacles the world presents to [his] eyes,” (ibid.) with the following promise: However, you will lose nothing that is substantial in those same spectacles. You will see everything with eyes clarified in a completely different way. Your understanding being fortified from above, it will discover everywhere the brilliant illumination of the divine author of things. You will recognize only wisdom and happiness, wherever men are accustomed to find only vanity and bitterness. You will be content with your creator; you will be enraptured with the vision of his works. Your admiration will not be the effect of ignorance as it is with the vulgar. It will be the fruit of knowledge of the grandeur and marvels of God. Instead of scorning with men the unraveled secrets, which in earlier times they regarded with astonishment, you will find that when you are admitted into the interior of nature your raptures will go on growing the farther you advance. For you will only be at the beginning of a chain of beauties and delights that go on growing into infinity. The pleasures that enchain your senses and that Circe of your legends who changes men into beasts will have no hold on you, so long as you attach yourself to the beauties of the soul, which never die and never disappoint. You will belong to our fold and will go with us from world to world, from discovery to discovery, from perfection to perfection. With us you will pay court to the Supreme Being, who is beyond all worlds and fills them without being divided. You will be at once before his throne and among those who are distant from it. For God will establish his siege in your soul and heaven follows him everywhere. (LH 110–111)

What Leibniz depicts here is an initiation into a mode of being which involves transportation into the presence of the “supreme being” with “eyes clarified in a completely different way”. In other words, there is another step on the journey which involves commitment to the truth of the PSR. And it appears to offer something even more precious as a reward for adherence to that principle, namely acquisition of capacity for intellectual perception of a different order that allows telescopic acquaintance with the whole endlessly rich universe and the ability to navigate it seamlessly. Arguably then there is another justification for taking the PSR to be true. It relies on the thought that doing so will eventually lead one to be inducted into a practice that is ‘cognitive’ and yet not governed by the PSR, i. e., a beatific vision which arises from intuitive cognition of the way things are and which

90

Paul Lodge

is also attended by a sense of being in the presence of the divine and of being a cosmic traveler. If anything like this reading is correct, then we are being offered yet another a posteriori justification for the PSR, but, of course there is an added dimension. For in order to find any of this remotely motivating one would have to be willing to listen to the testimony of the dreamer who is telling the story in ways that might sound even less plausible than the story about the security brought through taking the PSR as a principle that governed one’s activity. Moreover, what we would be trusting is that a transformation, whose nature is not described at all, other than as something delivered by a “celestial figure”, will take place if we become servants of reason in the more straightforward sense. Here it seems that what we will have to take on trust can perhaps only be characterized as a report of the fruits of an instance of personal revelation to Leibniz, albeit one which chimes with claims made by many authors in the Platonic tradition and, arguably, in non-Western traditions as well. Leibniz seems to be suggesting that the capacity to live in accordance with the PSR and belief in its truth is a gift he received at some point by chance by trusting the authority of another, and that this led him first to a situation in which he could cope in the world, but also on a road to an even more mysterious path where he was led by another authority to a place where he acquired a mode of cognition that transcended this. Now, of course none of this was revealed to Clarke, and one can imagine why. Leibniz had not managed to persuade Clarke that his version of PSR was constitutive of rationality using his more mundane tools, which at least have the appearance of possessing argumentative structure. By contrast here he is saying something that might be thought to amount to little more than “trust me in the way I have trusted others”. But setting its relation to Clarke aside, there is of course the question of whether this could have been what Leibniz thought. There is nothing even this explicit in any other writing of Leibniz’s that I know – though I think one might be able to marshal a case that there are hints in the places where he is writing about natural theology in ways that break free of its relation to Christianity. So in pointing to these passages I certainly do not take myself to be making a scholarly case. But, if I am right, what we seem to find on offer is an additional, and perhaps the ultimate, justification for taking the PSR to be true. For if we trust the authority of Leibniz, however mysterious the process by which this is to be ultimately achieved, commitment to the truth of the PSR is justified as part of the journey to ultimate enlightenment. 18

18

I would like to thank the following people for their helpful comments and advice on earlier versions of this paper: Greg Brown, Michael Della Rocca, Sam Levey, Owen Pikkert, Eric Schliesser, Amia Srinivasan, Mark Wrathall, and an anonymous reviewer for this journal. I would also like to thank members of audiences in Houston and Berlin to whom the paper was presented and, especially, John Whipple for his formal response in Houston.

Leibniz’s Justification of the Principle of Sufficient Reason

91

Bibliography Adams, R. M. 1994. Leibniz: Determinist, Theist, Idealist. Oxford: Oxford University Press. Antognazza, M. R. 2016. Leibniz: An Intellectual Biography. Cambridge: Cambridge University Press. Arthur, R. 2014. Leibniz. Cambridge: Polity Press. Brown, G. (forthcoming). The Leibniz-Clarke Correspondence. In: Lodge, P. /Strickland, L. (eds.). G. W. Leibniz: Key Philosophical Texts. Oxford: Oxford University Press. Dostoyevsky, F. 1958. The Brothers Karamazov. Magarshak (tr.) London: Penguin. Jauernig, A. 2008. Kant’s Critique of the Leibnizian Philosophy: Contra Leibnizians, but Pro Garber, D. /Longuenesse, B. (eds.). Kant and the Early Moderns. Princeton: Princeton University Press. Look, B. 2011. Grounding the Principle of Sufficient Reason: Leibnizian Rationalism and the Humean Challenge. In: Fraenkel, C. /Perinetti, D. /Smith, J. E. H. (eds.). The Rationalists: Between Tradition and Innovation. Dordrecht: Springer. Look, B. 2014. Leibniz’s Arguments for the Existence of God. In: Antognazza, M. R. (ed.) The Oxford Handbook of Leibniz. DOI: 10.1093 /oxfordhb/9780199744725.013.010. Rodriguez-Pereyra, G. 2013. The Principles of Contradiction, Sufficient Reason, and Identity of Indiscernibles. In: Antognazza, M. R. (ed.). The Oxford Handbook of Leibniz. DOI: 10.1093 /oxfordhb/9780199744725.013.002. Rodriquez-Pereyra, G. 2014. Leibniz’s Principle of Identity of Indiscernibles. Oxford: Oxford University Press. Sleigh, R. C.Jr. 1983. Leibniz on the Two Great Principles of our Reasoning. Midwest Studies In Philosophy 8, 193–216. Strawson, P. F. 1952. Introduction to Logical Theory. London: Methuen. Vailati, E. 1998. Leibniz and Clarke: A Study of Their Correspondence. Oxford: Oxford University Press.

Simples, Representational Activity, and the Communication among Substances: Leibniz and Wolff on pre-established Harmony Gastón Robert, King’s College London

Abstract This article aims to make further progress in revising the standard account of Wolff’s philosophy as a popularisation and systematisation of Leibniz’s doctrines. It focuses on the topic of the communication among substances and the metaphysics of simples and activity underlying it. It is argued that Wolff does not accept the pre-established harmony (PEH) in its orthodox Leibnizian version. The article explains Wolff’s departure from Leibniz’s PEH as stemming from his rejection of Leibniz’s construal of the activity of every simple as representational power and of the metaphysics of unity and activity in which that construal is rooted.

1. Introduction In his Éloge du Monsieur Leibnitz, Fontenelle characterises Leibniz as a thinker who loves “to see the plants for which he had furnished the seeds growing in other people’s gardens” 1. According to the standard story of Leibniz’s reception in eighteenth-century Germany, the philosophy of Christian Wolff (1679–1754) was one of those gardens in which the growth and unfolding of Leibniz’s seeds were promoted. For instance, at the outset of the chapter on Wolff in his Lectures on the History of Philosophy, Hegel says that “the philosophy of Wolff is directly connected with that of Leibnitz, for really it is a pedantic systematisation of the latter” (HS 348). 2 A similar appraisal can readily be found in histories of modern philosophy and philosophical textbooks, which usually credit Wolff with having organized and put together ideas that Leibniz bequeathed to posterity in a fragmentary and detached form. In this sense, Wolff and Leibniz have popularly been viewed as advocating a single, uniform Leibnizian philosophy – the so-called ‘LeibnizianWolffian system’. 1 2

Quoted in Garber 2009, xv. In addition to the conventions adopted in the general legend of this volume, I will use the following abbreviations: Discourse = G. W. Leibniz, Discourse on Metaphysics, Arriew /Garber (trs.); Disp. Met = F. Suárez, Disputationes Metaphysicae, Rábade /Caballero /Puigcerver (eds.); Elements = L. Euler, Thought on the Elements of Bodies, in which the theory of the Simple Things and Monads is examined and the true essence of bodies is discovered, Hirsch (tr.); Enquires = D. Hume, Enquiries concerning Human Understanding, Nidditch (ed.); HS = G. W. F. Hegel, Lectures on the History of Philosophy, Haldane /Simons (trs.); New System = G. W. Leibniz, New System of the Nature of Substance and their Communication, and of the Union which Exists between the Soul and the Body, Woolhouse /Francks (trs. & eds.); Sum. Theol. = Aquinas, Thomas Aquinas, Sancti Thomae Aquinatis Summa Theologiae. Full details about the editions I have used can be found in the Bibliography.

Simples, Representational Activity, and the Communication among Substances

93

In the last decades, however, both Wolff and Leibniz scholars have reacted against this reading. 3 Following the line of criticism opened up by these scholars, the overarching aim of this article is to make further progress in revising the popular account of Wolff’s thinking as a mere epigone of Leibniz’s views. To do this, I focus on the specific topic (or family of topics) of the communication among substances and the metaphysics of simples and activity underlying it. The general thesis I defend is this: Wolff does not embrace Leibniz’s theory of pre-established harmony (henceforth PEH) because he does not embrace the metaphysics of simples and activity on which Leibniz’s PEH is grounded. I break this thesis down into more specific claims of the following argument. Leibniz’s PEH relies on an ontology of simples whose activity is construed as representational activity or perception, the specific type of activity which allows the infinite plurality of non-causally related individuals existing in this world to become members of one unified world. In turn, this interpretation of the nature of activity trades on Leibniz’s conception of simples as entities whose explanatory role concerns not the particular constitution of spatio-temporal appearances, but rather their metaphysical foundation. But Wolff, I argue, rejects such a conception and hence the representational nature of simples’ powers. Instead, with the exception of the human soul, Wolff conceives of simples as physical points endowed with force capable of motion. 4 As a result, he is bound to reject PEH in its orthodox Leibnizian version. His rejection of it notwithstanding, Wolff continues to favour PEH as an explanation of the relation between the body and the soul. Yet, I argue further, even here what he favours cannot be Leibniz’s soul-body PEH: while Wolff’s soul-body PEH is intended as a solution to the problem of how to explain the relation between ontologically heterogeneous entities, Leibniz’s soul-body PEH relies on an ontology which cuts that problem at its very roots. 5 Since this is a long article, it will be helpful to be clear on its structure from the outset. It is divided into two main parts. The first is devoted to Leibniz’s PEH, and more particularly to PEH’s reliance on the perceptual powers of simples. In 2.1, I trace a line of thought which begins with Leibniz’s considerations about the necessity of simples or indivisible 3

See Corr 1974 and 1975, École 1964, Rutherford 2004, Watkins 2006, and n. 5 below. It is interesting that the phrase “Leibnizian-Wolffian” – as employed in epithets such as “Leibnizian-Wolffian system”, “LeibnizianWolffian School”, and the like – was probably coined by Rüdiger and Budde, two overtly declared enemies of Wolff’s philosophy. See Beck 1969, 257. This makes it reasonable to think that, as Wundt 1964, 150, suggests, it was purposely concocted in order to detract from the novelty of Wolff’s thought. 4 On the level of created reality, a further exception would have to be made in order to accommodate the existence of angels. For the purposes of my argument, however, the relevant exception is the human soul. 5 The premise that Wolff rejects, or is agnostic about, Leibniz’s view that all simples are endowed with representational power has been advocated by other scholars. See École 1964 and Rutherford 2004 for the first option, and Watkins 2006 for the second. I owe much of the initial impetus for the present work to reading their papers. However, I develop the premise and provide further support for it through a number of new arguments grounded on a broader range of texts. Moreover, the general position I shall be putting forward is in contrast with that of some of these scholars, particularly Watkins’. Perhaps most notably, whereas Watkins is favorably disposed towards Wolff’s re-elaboration of Leibniz’s monadology, I shall try to show that Wolff broke with Leibniz’s philosophy precisely with respect to those points which, in my opinion, make it a cogent and appealing theoretical alternative. More particular points of (dis)agreement will be noted in subsequent footnotes (see especially n. 52, 55, 69). In any case, as will be treated here, Wolff’s rupture with Leibniz’s perceiving simples is only one step within a wider set of discrepancies which ultimately explain, or so I shall argue, Wolff’s rejection of Leibniz’s pre-established harmony – both his pre-established harmony between all substances and that between the soul and the body.

94

Gastón Robert

active unities (construed as forms). In this context, two Leibnizian arguments for simples are discussed, aiming to give a clear sense of the purely metaphysical character of Leibniz’s motivations for introducing simples into his ontology. In 2.2, I focus on Leibniz’s interpretation of the activity of these simples in terms of representational power, the analysis of which will lead us to a discussion of his project of laying the metaphysical foundations for the (accidental) unity and (phenomenal) reality of bodies as aggregates. I argue that the representational activity of simples performs an indispensable function in Leibniz’s model of aggregate unification. In 2.3, I argue that this model – and hence perception – is at the basis of Leibniz’s understanding of PEH as an explanation of the unity of the world, thereby closing my argument for the coalescence of perception and PEH. A further conclusion at which we arrive is that, like the very principles on which it rests with respect to bodies, the primary function of Leibniz’s PEH is that of providing the metaphysical grounding for the (accidental) unity and (phenomenal) reality of the world. In Part 2 we turn to Wolff. Its structure is roughly delineated by the topics discussed in Part 1. Thus, in 3.1, I analyse two Wolffian arguments for the necessity of simples, putting special emphasis on the differences between Wolff’s position and that of Leibniz. I argue that although Wolff follows Leibniz in defending the necessity of simples, his motivations differ significantly from those of Leibniz, which I identify as an important preliminary step in the chain of reasoning which will ultimately lead Wolff to break with Leibniz’s version of PEH. In 3.2, I concentrate on Wolff’s rejection of perception as a property of every simple. As we shall see, Wolff’s actual remarks about the perceptual nature of the activity of simples are rather elusive and ambiguous. However, on the basis of the results of 3.1 and building on passages from Wolff’s VGG (1720) and CG (1731), I develop two systematic lines of argument in support of the claim that he cannot coherently have endorsed Leibniz’s view that perception is a property of universal applicability. Section 3.3 explains how Wolff’s departure from Leibnizian orthodoxy affects his own version of the soul-body PEH. A concluding section offers some remarks on the role that Wolff’s re-elaboration of Leibniz’s doctrines played in eighteenth-century debates on causation. My suggestion here will be that Wolff’s separation of simples from the purely metaphysical function they performed in Leibniz’s philosophy made it impossible for PEH to accommodate the truth of mechanics, which in turn triggered the decline of PEH as an attractive causal theory. One caveat is in order before moving on. The argument of this paper turns partly on the claim that Leibniz’s PEH relies on an ontology of simples endowed with the property of perception, that is, an idealistic ontology. 6 This will surely raise some eyebrows, for there is evidence that Leibniz first adopted PEH, in all its essentials but the name 7, around the time period of the Discourse and the correspondence with Arnauld 8, a period 6

Or, more precisely, on an ontology which deploys such simples alongside the claim that they are all there really is. 7 The name ‘pre-established harmony’ (harmonie pre-établie) was used by Leibniz in public for the first time in his so-called “First Explanation of the New System”, published in the April 1696 issue of the Journal des Savants and which contains Leibniz’s answer to Foucher’s objections to the New System. See GP 4.496. For further details, see Antognazza 2009, 351–352. 8 If not before, as Mercer 1995 and Lodge 1998 (in different senses) have proposed. For the received view – as Lodge calls it – that PEH emerged by the time period of the Arnauld correspondence and the Discourse, see e. g. Beck 1969, 226, Brown 1988, 118, Wilson 1989, 112, Kulstad 1993, 116 and 93, and Schönfeld 2000, 140.

Simples, Representational Activity, and the Communication among Substances

95

in which his commitment to idealism is far from clear. For reasons of space, I cannot dwell on this difficulty here. However, I would like to mention two points, if only in passing. The first is that I believe that, in fact, Leibniz’s commitment to PEH during the so-called middle period does constitute a powerful case for idealistic readings of his metaphysics in that period. 9 In my opinion, Leibniz’s PEH only works on the basis of an interpretation of the activity of forms /simple substances as representational power, and such a power does not yield the kind of unity that is required for a matter-form compound to be transformed into a true corporeal substance. 10 Yet, of course, powerful cases for realistic strands in Leibniz’s middle period (and later) have been made too. 11 An adequate defence of the indispensability of idealism for Leibnizian PEH would have to take those cases into appropriate account, and we shall not undertake that task here. At any rate – and this is the second point I want to mention – we might do well to remind ourselves that, considered as a philosopher, the eighteenth-century Leibniz, and more particularly Wolff’s Leibniz, was the full-fledged idealist thinker of the Monadology and related writings. 12 That this Leibniz may not have been as permanent and stable as it used to be thought before Garber’s groundbreaking 1985 article is an exegetical option that became possible, at least partly, through the analysis of texts that were not even available to Wolff. Any attempt at comparing the views of two philosophers must endeavor to set forth their doctrines in a way that would have made sense to them, and I have tried to incorporate this principle throughout my presentation of Leibniz’s views. 13 Without further ado, let us move on.

2. Leibniz 2.1.

Form, unity, activity: the necessity of simples

On many occasions, Leibniz presents his mind-like perceiving simples in close connection with forms and souls. However, while in his mature writings he moves quite freely from one to the others, it is important to note that the equation “form /soul /mind-like 9

For a comprehensive development of this line of argument, see Rutherford 2008 and 1995, 265–288. Canonical argumentation in this direction is developed in Adams 1994 and Rutherford 1995. I think that this underwrites the sort of charge levelled by Tournemine against Leibniz’s PEH, namely that it does not bring about “union” or “essential connection” between the body and the soul. Leibniz’s answer is that, indeed, it does not. See GP 6.595-6. In my view, the best account of this and related topics continues to be Rozemond 1997. 11 As is well-known, the milestone here is Garber 1985. See also Broad 1975, Jolley 1986, Hartz 1998, Bolton 2004, Garber 2009. For an insightful reappropriation and extension of Garber’s views, see Levey 2007 and 2008. That Leibniz was essentially committed to an idealistic ontology from ca. 1686–7 until his death has been defended by Sleigh 1990, Adams 1994, Rutherford 1995, Look 2011, among others: I line up with them and am indebted to their research throughout. As one would expect, there are many more interpretations. Summaries of them can be found in Look 2011, 90, and Garber 2009, 385–386. 12 Here I am disregarding the fact that, for some scholars, not even the Leibniz of the Monadology and related writings is a full-fledged idealist. For different takes on this insight, see Levey 2007 and 2008, Phemister 2005, Loptson 1999. 13 I will sometimes consider Leibnizian texts which were not available to Wolff – mainly unpublished letters. But I think none of these texts contains ideas that would have seemed unfamiliar to Wolff had he been able to see them.

10

96

Gastón Robert

simple” implies a great deal of philosophical interpretation and novelty on Leibniz’s part. Particularly, Leibniz’s conception of simples as mind-like entities having perception can be viewed as a combination of three complementary tenets: what we can call ‘pan-formalism’, ‘pan-psychism’, and ‘pan-mentalism’. As I see them, the third of these tenets is an interpretation of the second, and the second of the first. As a first step towards establishing PEH’s reliance on substances’ representational activity, let us pick up the thread by focusing on pan-formalism. According to pan-formalism, the form is a constitutive principle of every real being. In advocating forms, Leibniz rehabilitates the Aristotelian tradition. The most significant opponent he faced in this connection is, of course, Descartes, whose ontology of the physical world is sufficiently well known not to require extended exposition here. For my purposes, it will suffice to be clear on its most distinctive metaphysical thesis and the main claims from which it derives. Briefly, we can put them in the form of the following argument: (P1) Bodies are nothing more than matter (P2) Matter is nothing more than extended stuff (C) Therefore, bodies are nothing more than extended stuff On Descartes’ view, extension is thus the essence of bodies because bodies are matter alone and extension is the essence of matter. 14 With Descartes, Leibniz endorses (P2): (Cartesian) matter is nothing but extended stuff. 15 Against him, however, he thinks that bodies are not purely extended stuff. Accordingly, he rejects (P1): alongside matter, form must be a constitutive principle of body. Before going into Leibniz’s reasons for this thesis, a preliminary remark must be made here about the level of reflection at which he argues for it. According to Leibniz, forms are not to be invoked in order to account for particular phenomena or the spatio-temporal order of appearances. He writes in Discourse, § 10: “I agree that the consideration of these forms serves no purpose in the details of physics and must not be used to explain particular phenomena” (GP 4.434 /PE 42). As far as the “detail of physics” goes, Leibniz thinks the Cartesian position is essentially correct. 16 Yet, in his judgement, the question about particular phenomena and their derivative features does not exhaust the domain of ontological inquiry into bodies. To achieve a full understanding of them, it is necessary to descend from the level of phenomena to that of their ultimate ontological grounds, from the domain of mechanics and geometrical properties to the domain of the metaphysics of nature: forms are necessary in order to explain the being of physical entities. 17 14

See Principia Philosophiae II, § 11 (AT VIII, 46). That body /matter is for Descartes nothing but extension has been questioned by some Cartesian scholars. See e. g. Della Rocca 2003. Here I assume that (C) expresses Descartes’ actual view, an assumption which is in fact required for Leibniz’s criticism to make sense, as will emerge. 15 The qualifier ‘Cartesian’ is important, for Leibniz distinguished at least three senses in which matter is spoken of, namely matter as extension (“Cartesian matter”), secondary matter, and primary matter. It is the first of these meanings that I take to be relevant to Leibniz’s rehabilitation of forms, however. As will emerge, it is precisely because matter is extension that he takes the Cartesian account to fall short of an adequate explanation of the bodily realm. 16 See GP 4.444, GP 4.478. 17 See GP 4.434, 444; GP 7.478. That forms ground the being of bodies is not to say that bodies are turned into substances when they are informed by a form: being or reality comes in degrees. See A 6.4.399. The same holds

Simples, Representational Activity, and the Communication among Substances

97

The metaphysical scope of Leibniz’s pan-formalism becomes particularly clear when one considers his reasons for reintroducing forms into natural philosophy. Leibniz gives (at least) two arguments for forms, one based on the concept of unity (hereafter ‘Argument from unity’ = AFU), the other on that of activity or force (hereafter ‘Argument from activity’ = AFA). 18 We will look at these arguments in turn. Consideration of them will allow us to detect views which will later be resumed in our discussion of Wolff. I shall lay stress upon those points which will be relevant to that discussion, leaving others aside. We begin with the AFU. The essentials of Leibniz’s AFU emerge from a consideration of § 3 the New System: [I]t is impossible to find the principles of a real unity in matter alone, or in what is only passive, since this is nothing but a collection or aggregation of parts ad infinitum. Now, a multiplicity can derive its reality only from true unities [. . .]. So, in order to get to these real unities, I had to have recourse to a formal atom, since a material thing cannot simultaneously be material and perfectly indivisible, or possessed of a genuine unity. So it was necessary to recall and, as it were, to rehabilitate substantial forms. (GP 4.478 /NS 139)

Underwriting the AFU is the premise that only what is truly one is truly real. In advocating it, Leibniz draws from the Scholastic doctrine of the transcendental properties of being. Unity is not a predicamental property – not a res addita, as both Aquinas and Leibniz put it – but a transcendental one: ens et unum convertuntur. 19 Hence, what is real must be one. Once this underlying premise has been established, Leibniz’s reasoning proceeds as follows: (P1) (P2) (P3) (P4) (P5) (C)

Only what is truly one is truly real Matter is not truly one (and thus not a principle of unity) A form is truly one (and thus a principle of unity) Bodies are matter alone or matter plus form Bodies must have (at least some degree of) reality Bodies cannot be matter alone but must have a form

(P1) is an axiom. 20 (P3)–(P5), on the other hand, are assumed in the passage. 21 So, the bulk of Leibniz’s reasoning focuses on (P2).

18

19

20 21

for unity. See A 6.4.401, A 6.4.301. According to these texts, the basic categories which delineate Leibniz’s ontology of concrete being are substantial being /accidental being (including phenomena, aggregates) and, corresponding to them on the side of unity, per se unity /accidental unity. Interestingly, in a passage from the Arnauld correspondence Leibniz entertains the view that, if deprived of a formal principle, Cartesian matter would not even be an aggregate. See GP 2.72. But in other passages from the correspondence his opinion seems to be that, without form, bodies would be aggregates /phenomena but not substances. See e. g. GP 2.58. For discussion, see Lodge 2002. See n. 23. The centrality of unity and activity to Leibniz’s theory of forms has been duly emphasised by Garber 2009, 55– 181, and Antognazza 2016, 74–85. See also Levey 2007. “Transcendental unity (unum transcendens) is not an added thing (res addita)” (GP 4.18). “Unity (Unitas) follows entity (Entitatem) in concept (in conceptu), they are the same in the thing (in re)” (GP 4.24). “I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, that what is not truly one being is not truly one being either” (GP 2.96-7 /PE 86). For Aquinas, see Sum. Theol. I, q. 11, a. 1 See the third passage quoted in the previous note. I shall revert to (P3) shortly, whose analysis will provide us with the specific link between Leibniz’s AFU and the AFA, and thereby between the notions of unity and activity. (P5), and more particularly the issue of the sort of reality which bodies have on Leibniz’s view, will be discussed in 2.2.

98

Gastón Robert

His argument for this premise centers upon the problem of the infinite divisibility of matter. In short, Leibniz’s point seems to be this. Matter is infinitely divisible 22, for extension, in which the essence of matter consists, is infinitely divisible. Now, that matter is infinitely divisible means that it is nothing but a collection or aggregation of parts ad infinitum. That is, it consists of an infinite plurality of parts. Yet, if matter consists of an infinite plurality of parts, it has no ultimate parts: each material part, qua extended, is subject to further division. Therefore, as (P2) states, matter is not one. Now, if compelling, this reasoning yields the negative conclusion that, contrary to Descartes’ view, body is not only extended matter. But it also allows Leibniz to establish the positive thesis that forms are necessary in order to give a satisfactory account of body. For if matter is not one, then, given (P1), matter lacks reality, which entails that, on the Cartesian account, bodies lack reality as well. But this is inconsistent with (P5). So, in order to explain the ontological status of material objects, something in itself nonextended or simple must ground the unity and reality of bodies. And this something is form, as (P3) holds. Note that the AFU’s point is not then to deny the infinite divisibility of matter in order to save the reality of bodies: to Leibniz’s mind, matter-qua-extension is infinitely divisible or “only a collection or aggregation of parts ad infinitum”. 23 The point, rather, is that unless one posits a form or true unity, such a collection or plurality would not even be possible: unity is a condition for something to be, and an infinitely divisible aggregation of parts outside parts fails to meet this condition. As we read elsewhere, “there is no plurality without true unities” (GP 2.97). 24 Now, this argument presupposes that forms are sufficient for explaining the unity of bodies. Why? According to (P3), a form is in itself a unity or simple entity. But why can forms, being unities in themselves, bestow unity and hence reality on something which lacks unity and reality of its own? In other words, what it is that makes forms good candidates for principles of the unity of the collection in which body-qua-matter consists? To answer this question, we must turn to Leibniz’s second argument for forms, the argument from activity. The chief thesis articulating the AFA is that forms are essentially active. The argument is sometimes presented in connection with the problem of motion. 25 In order to get at a metaphysically satisfactory explanation of motion, it is necessary to distinguish between the quantity of motion and its force, a distinction which cannot be drawn if bodies are nothing more than matter, the essence of which is purely passive extension. Now, forms, 22

Or infinitely divided, as Leibniz says in his 30 April 1687 letter to Arnauld (GP 2.77). See also GP 2.268 /LDV 301: bodies are “actually subdivided (actu subdivisa)”. 23 See also GP 2.77, GP 4.482. That there can be a collection or aggregation of parts is contravened by a text from Leibniz’s 28 November /8 December 1686 letter to Arnauld: “Thus one will never find a body of which it may be said that it is truly one substance. Or rather, it will not be a real entity, since the parts making it up are subject to the same difficulty, and since one never arrives at any real entity, because entities made up by aggregation has only as much reality as exist in their constituent parts” (GP 2.72 /LA: 88). According to this passage, Cartesian matter fails to be in every sense in which “being” is spoken of: it fails to be substance and it fails to be an aggregate /phenomenon, for it lacks proper constituents. Be this as it may, the point remains that simple constituents are necessary in order to ground the reality of body. 24 See also C 523 /PE 34: “Something lacking extension is required for the substance of bodies, otherwise there would no source (principium) for the reality of phenomena or for true unity. There is always a plurality of bodies, and never one, and therefore, in reality, there is not even a plurality”. See also GP 2.267, GP 4.483. 25 See e. g. Mendelson 1995, 37.

Simples, Representational Activity, and the Communication among Substances

99

unlike matter, are essentially active. Hence, forms can serve as a basis for a satisfactory metaphysical explanation of motion. There is no question that Leibniz resorted to the quantity /force of motion distinction in order to motivate his rehabilitation of forms. 26 Nevertheless, I think there is another way of understanding the AFA. Let us revert to the passage from § 3 of the New System quoted above. In particular, reconsider its opening sentence: [I]t is impossible to find the principles of a real unity in matter alone, or in what is only passive (ce qui n’est que passif) since this is nothing but a collection or aggregation of parts ad infinitum. (GP 4.478 /NS 139; my italics)

Here Leibniz explicitly equates “matter alone” with “what is only passive”. On the face of it, this is not surprising, for matter and passivity – as well as the correlative notions of form and activity – are intimately interwoven notions in the Aristotelian tradition, and Leibniz is drawing on that tradition. However, the fact that Leibniz deploys the notion of matter alongside that of passivity in connection with the problem of unity is, in my opinion, relevant. For given the “matter /what is only passive” equation in this specific context, the following conclusion follows: what is only passive is not a principle of unity. In turn, this suggests that what is active is a principle of unity. And these conclusions suggest two things. First, it is precisely the passivity of matter that renders it a bad candidate for something that bestows unity and hence reality on body. Secondly, it is precisely the activity of forms that renders them good candidates for something that performs such a function. If this is granted, we can put Leibniz’s AFA thus: (P1) (P2) (P3) (C1) (P4) (C2)

What is merely passive is not a principle of unity What is active is a principle of unity Matter is merely passive Matter is not a principle of unity Forms are active Forms are principles of unity

What I want to emphasise here is that, so understood, Leibniz’s AFA can be read as complementing, and indeed sustaining, the AFU, and more specifically AFU’s (P3): while that premise presupposes that a form, insofar as it is a unity in itself, is sufficient for accounting for the unity of bodies, the AFA shows us the reason for this presupposition: forms or simples can bestow unity and reality on physical objects because they are active. As Leibniz writes to De Volder, a natural substance “is actuated by one Entelechy, without which there would be in it no principle of true Unity” (GP 2.250 /PPL 529). 27 Thus Leibniz’s rehabilitation of forms is based not only on the idea that matter, being essentially extension, is infinitely divisible and therefore lacks unity. It also springs from the view that, being merely passive, matter cannot function as a unifying factor of bodies’ infinite plurality of parts and hence as a principle of their reality. So I think we can say that, for Leibniz, in a sense at least, activity is metaphysically more fundamental than unity: activity grounds 26 27

See GP 4.442-4. See also GP 3.260: “[. . .] the principle of the unity contains the primitive Active power (la puissance Active primitive) or the primitive force (force primitive)”.

100

Gastón Robert

the unity of body and hence their reality. 28 Qua unities or in-themselves-simples, forms allow stopping an infinite regress in the division of the infinite collection of parts in which bodies-qua-matter consist: they are, in Leibniz’s words, “the final elements in the analysis of substantial things” (GP 4.482 /PE 142). Qua active, on the other hand, forms work as unifying principles of the collection: they are, Leibniz adds, “the first absolute principles of the composition of things (premiers principes absolus de la composition des choses)” (GP 4.482 /PE 142). 29 In this sense, the activity of substances grounds not only what we might call “diachronic plurality” or substances’ “unity in succession”, but also the unity of a coexistent or synchronic plurality of members: it unifies the passive extended mass – the continuously repeated multitude that it involves – which contains no source of unity. 30 The centrality which this interpretation ascribes to the activity of simples is in keeping with the fact that, after focusing on the problem of the unity of matter in New System § 3, Leibniz immediately goes on to say that the very nature of forms “consists in force (la force)” (GP 4.479): forms are essentially “primary forces, which contain not only actuality [. . .] but also an originating activity (activité originale)” (GP 4.479 /NS 12). Also, it sits well with Leibniz’s oft-repeated thesis that the capacity to act is the very “mark of substance” (GM 6.235) or what most formally defines the substantiality of substances: “activity is of the essence of substance in general” (GP 5.58 /NE 68). 31 It is important to bear this point in mind, for, as I shall argue in Part 2, Wolff breaks with this characteristically Leibnizian claim, which in turn paves the way for his rupture with Leibniz’s perceptually-equipped simples and thereby with his version of PEH. Hitherto, we have seen that forms must be rehabilitated because unity is a condition of being and activity is a condition of unity. But nothing has so far been said about how Leibniz’s active simples are supposed to bestow unity on the collections they constitute. That is, an explanation of AFA’s (P2) is still missing. This leads us from the topic of the necessity of simples to that of the nature of simples and their activity, and thus from Leibniz’s pan-formalism to pan-psychism and pan-mentalism.

28

That activity plays a metaphysically more fundamental role than unity is suggested, though in passing, by Look and Rutherford in the introduction to their edition of the correspondence between Leibniz and Des Bosses. See LDB, xli. 29 Note that Leibniz does not say here that unities “compose” things. What he says, rather, is that they are the “principle” of their composition. As a purely metaphysical principle, a Leibnizian simple does not then relate to body as a part relates to a whole. See GP 2.265 /LDV 303: “[A]ccurately speaking, matter is not composed of constitutive unities, i. e., from real unities; rather it results (resultat) from them, since matter, i. e., extended mass, is nothing but a phenomenon founded (fundatum) in things”. 30 For Leibniz’s characterisation of extension as coexistent parts, see GP 2.169. For extension as involving a continuously repeated multitude, see GP 4.394. Textual basis for the distinction between successive and coexistent plurality is also found in GP 4.394. 31 See also GP 4.588 /WF: 163: “[E]nergy or activity [. . .] constitutes the nature of a substance”. GP 6.598 /PE 207: “A Substance is a being capable of action”. GP 3.464: “The nature of each substance consists in the active force”. Also GP 3.58; IV, 469, 470, 482, 508, 594; VI, 350, 354, 598; VII, 316, 508.

Simples, Representational Activity, and the Communication among Substances

2.2.

101

Representative activity and unity of the collection: the nature of simples

In rehabilitating forms as active principles of unity Leibniz does more than merely align himself with the Aristotelian tradition. For he also advocates the view that every form is a soul-like principle of reality, a view which Jean École has called Leibniz’s “pan-psychism” or pan-animism (École 1964, 9). This represents an advance over pan-formalism insofar as the kind of activity that forms bestow upon bodies is conceived on the model of living things: substances “have something of the nature of life”, as Leibniz puts it in New System § 11 (GP 4.483 /NS 16). In this respect, Leibniz distances himself from the Aristotelian tradition, showing advocacy of a (neo-)Platonic view: there is a kind of animation on every level and in everything in the world. 32 Yet this is still not specific enough. For, on Leibniz’s view, pan-psychism is subject to one important further qualification: forms or souls are construed as mind-like entities. Accordingly, the specific kind of life that the form or soul possesses is perceptual or representational. Thus, in a paper from the late 1680s, we find Leibniz saying that perception belongs “to all forms” (A 6. 4. 1625 /PW 85) and, as early as 1676, he claims that “perception [is] everywhere” (A 6.3.522-3 /DSR 83). This is what I have earlier referred to as ‘pan-mentalism’. 33 Given the results of my analysis of Leibniz’s AFA, the question that this doctrine prompts is: How is it that the representational activity that a mind-like entity possesses can bestow unity and hence reality on something which lacks unity and reality of its own (body)? To address this question, we need first to briefly outline another characteristic Leibnizian doctrine and some distinctions it involves: phenomenalism. As I see it, Leibniz’s phenomenalism consists of two main claims. The first is familiar: bodies, considered as pure extension and deprived of any formal principle, are not real beings. This can be seen as a direct implication of Leibniz’s idealistic metaphysics: if mind-like entities are the only real beings, then bodies, insofar as they are corporeal, must lack reality. Yet, as Leibniz himself cautions, his idealistic metaphysics does not “eliminate” bodies but only “reduces” them to what they are. 34 Phenomenalism’s second claim is that bodies – and their motions – are phenomena grounded on, or resulting from, simples. 35 Quite how extended bodies result from simple entities is, of course, a complex question, one the adequate treatment of which would lead us far beyond what is feasible in the present context. Here we shall content ourselves with one assertion: bodies are phenomena grounded on, or resulting from, simples in the sense that they 32

See Look 2011, 92. For the view that everything is animated, see especially Mon. §§ 63–70 (GP 6.618-9). See also Plato, Timeaus 34b; Plotinus, Ennead V.1, 2. 33 The terminology might seem inappropriate, for having perception is not of course enough to be a mind, a term which properly applies to substances capable of consciousness (apperception) or rationality. However, the argument Leibniz offers (or, at any rate, the only one in my ken) for ascribing perception to all substances consists in generalizing, via the application of a version of the principle of continuity, what we find in our minds to everything else: “[I]f we were to attribute an inherent force to our mind, a force for producing immanent actions, or to put it another way, a force for acting immanently, then nothing forbids, in fact, it is reasonable to suppose that the same force would be found in other souls or forms, or, if you prefer, in the natures of substances” (GP 4.510 /PE 161). See also NE 51–52. While this does not mean that everything is a mind, it does entail that everything is either a mind or a mind-like entity. And the expression “pan-mentalism” I have chosen to adopt is meant to capture this. 34 See GP 2.275 /LDV 319: “I do not really do away with body (tollo), but reduce (revoco) it to what it is”. 35 See GP 2.275. See also GP 3.636.

102

Gastón Robert

ontologically depend on simples, that is, they borrow their unity and hence their being from the activity of simples. The following distinctions may help us to refine this assertion. There is a twofold way of considering bodies, in an absolute sense and in a relative sense. In the former sense – i. e. considered as such – bodies are not real beings since they lack true unity. In a relative sense, however, bodies are real beings, though in the qualified sense of phenomenal beings: they are “phaenomena realia” (GP 2.262). A body is not an unum per se and hence not an ens per se, but only an unum ab alio or per accidens: a collection or aggregate can only be one and have some degree of reality if a certain externally imposed relation holds among its members. As Leibniz puts it: “Bodies are nothing but aggregates constituting something which is one accidentally (per accidens) or by an external denomination, and therefore they are well-founded phenomena” (GP 7.344 /PE 319). 36 So, the chain of conceptual connections articulating the chief insight of Leibniz’s phenomenalism is this: bodies are phenomena insofar as they have only a relative reality – a reality in virtue of a certain relation to something other – and they have only a relative reality because they lack intrinsic or per se unity and hence per se being. Thus, the thesis that bodies are phenomena cannot be divorced from the thesis that they are aggregates. Nor are these theses in conflict with one another. 37 Since Leibniz, as we saw in his AFU, endorses the reciprocity of one and being, the fact that bodies lack unity implies that bodies are not capable of being through themselves but only by reference to, or as a manifestation of, something ontologically more basic, which is precisely what it means for something to be a phenomenon. As Adams puts it, bodies are phenomenal beings “because they are aggregates” (Adams 1994, 219). Now, the principle from which bodies derive their unity and phenomenal ontological status is perception: bodies are “phenomena of perceivers (percipientium phenomena)” (GP 2.270 /LDV 307). A clue as to how this happens I take to occur in Leibniz’s discussion about compound ideas in the NE: The unity of the idea of an aggregate is a very genuine one; but fundamentally we have to admit that this unity that collections have is merely a respect or a relation, whose foundation lies in what is the case with each of the individual substances taken alone. So the only perfect unity that these entities by aggregation have is a mental one, and consequently, their very being is also in a way mental, or phenomenal, like that of the rainbow (GP 5.133 /NE 146). 38

Two points from this passage are relevant to our topic: 39 (i) This passage reinforces the claim that aggregates do have a certain unity, but that their unity is not that of substances. That is, instead of being intrinsically or per se one, aggregates have an accidental or relational unity that obtains among a plurality of entities by virtue of the activity of truly-one, grounding entities. So, the unity of aggregates is

36

See also GP 6.586 /PPL 1013: “[A] body (corps) is not a true unity; it is only an aggregate, which the Scholastics call a being per accidens, a collection like a herd”. 37 Against this is Jolley 1986, 41 ff. See also Loeb 1981, 299–309. Space does not allow me to delve further into this. 38 In this passage, Leibniz considers the unity of a collection of individual substances, not that of an aggregation or collection of parts, as he does in the quoted passage from New System § 3. Cf. n. 23. In this article I shall disregard this issue, focusing on a simplified model of aggregate-unification which contains a unifying factor on the one hand, and a plurality of “members” on the other, whatever these members may be. There is much more to Leibniz’s notion of an aggregate than this, however. For details, see Lodge 2001. 39 In commenting on this passage I have been helped by Watkins 2006, 271–272.

Simples, Representational Activity, and the Communication among Substances

103

possible only if the unifying, grounding entities have certain properties on their own – or “taken alone” – properties which allow the members of the plurality to enter into certain relations to each other, thereby becoming a certain unity. As Watkins observes, this means that the members of the plurality cannot be so united when taken alone or separately: otherwise no unifying principle would be required in the first place (Watkins 2006, 271). In other words, for a relation to obtain between the members of an aggregate, something must take them together. Now, it is at this stage that representative activity enters into play: those truly one entities which ground the unity of the aggregate must actively represent the members of the multitude as standing in relations to one another. A mind-like entity bestows unity and reality on aggregates by representing together the multiplicity of distinct entities it comprises. Leibniz condenses this view in the following words to Des Bosses: “The aggregates themselves are nothing but phenomena, since besides the monads that enter into them, the rest is added by perception alone, by the very fact that they are perceived together” (GP 2.517). 40 (ii) This has important consequences for Leibniz’s understanding of the ontological status of bodies. We have seen that bodies are phenomena, and that this is so because they are aggregates: insofar as they lack intrinsic unity and being per se, the only way in which a body can be said to “be” is by conceiving it as a manifestation of an ontologically primitive, per-se-one and per-se-real entity. But if aggregates have unity by being represented as one, then the unity of bodies, as the very principle on which they ontologically depend, must be mental in kind. Given the reciprocity of one and being, it follows from this that the phenomenal being of bodies must be mental in kind as well. The passage is explicit about this: “So the only perfect unity that these entities by aggregation have is a mental one, and consequently, their very being is also in a way mental, or phenomenal, like that of the rainbow” (my italics). Thus bodies are phenomena because they are aggregates, and because they are phenomena they are mental in nature: metaphysically considered, a body is an ideal being.

2.3.

From the ideal unity of bodies to the ideal unity of the world: PEH as a system of representative unity

The import of the foregoing remarks can be expressed in a single sentence: the principle of the accidental unity and phenomenal reality of bodies as aggregates is the representational power of the simple entities which constitute them. How does this relate to Leibniz’s theory of PEH? What I would like to propose is that, understood as an explanation of the collective unity of all substances, the theory of PEH is an extension of, or is conceived by analogy with, Leibniz’s theory of bodies as aggregates. Jointly considered, the following texts provide evidence for this proposal: [a] The world (monde), which is the whole assemblage (l’assamblage) of contingent things. (GP 6.106 /T 127) I call “World” (Monde) the whole succession and the whole collection (collection) of all existent things. (GP 6.107 /T 128)

40

Translation in Adams 1994, 249.

104

Gastón Robert The world (Mundum) [is the] aggregate (aggregatum) of finite things. (GP 7.322) The actual universe is nothing but a collection (collection) of [. . .] compossibles. (GP 3.573) [b] [b1] Beings through aggregation [. . .] are only semi-beings (semientia), whose reality consists in the union which a mind makes or in an extrinsic denomination or relation. [b2] Such is [. . .] the pre-established harmony, which makes that one thing seems to influence another; these are therefore mental or relational results. (LH IV, III, 5e, Bl. 23) 41

The quotations in [a] offer a general definition of the world: the world is an aggregate, collection, or assemblage. 42 Although this definition does not make explicit what it is that makes the world one world, we can fill out its content by relying on our discussion of the unity of aggregates in the previous section, whose main claims are actually summarised by [b1]: the unity and reality of an aggregate consists in a relation imposed by a perceiver on the diversity it involves, which means that distinct members are joined together by the representative activity of that perceiver. By itself, this yields the conclusion that the unity and reality the world possesses is the unity and reality of an aggregate, that is, an ideal or representational unity and reality. The more important point for the view I am advancing is given, though, by [b2]. For, after having summarised his conception of the unity of aggregates in [b1], in [b2] Leibniz decisively relates this conception to his theory of PEH: “Such is [. . .] the pre-established harmony”, he says. This suggests that, as Leibniz sees things, the mechanism through which PEH unifies the world is the same as the mechanism through which the elements of an aggregate are unified: the world is unified insofar as it is represented as one by the simple entities it comprises. One might object that Leibniz’s model of unity by aggregation might perhaps explain substances’ unity as coexistent entities, but not the unity of their successive states, which is of course essential to PEH. However, Leibniz’s model of unity by aggregation is wide enough to apply to a multiplicity of items existing at successive times, too. For instance, Leibniz is ready to talk of an aggregate of “Roman Emperors”, as well as of aggregates of “times”. 43 As he sees things, moreover, whenever there are entities or items that can coexist, all the states ascribable to them must also be consistent at every time. For a world comprising a plurality of distinct entities is, of course, a possible world. Now, if a world is possible, then the members it comprises must be compossible. By Leibniz’s lights, this means that their perceptual states must agree at every time: “I have reasons for believing that not all species are compossible in the universe, great as it is; not only with regard to things existing at the same time (ensemble en mème temps), but also with regard to the whole succession of things (à toute la suites des choses)” (GP 5.286 /NE 307). Note that what I am saying here remains non-commital as to whether a plurality of compossible items is sufficient for those items to perceive one another – let alone to harmonize with one another. A set of items representing one another does, however, entail that they are compossible, and this is all that my reply demands.

41

I take this passage and translation from Rutherford 1994, 271–272. Leibniz employs these terms interchangeably in more than one place. See e. g. GP 6.589 and, for more references, Lodge 2002, 469. 43 See e. g. A 6.4.162. See Lodge 2002, 471, n. 17.

42

Simples, Representational Activity, and the Communication among Substances

105

Let us recapitulate. First, in reflecting on Descartes’ account of bodies as extended matter alone, Leibniz is led to rehabilitate forms as active unities capable of bestowing unity and reality on bodies (2.1). These active unities are conceived of as mind-like entities endowed with perception or representational power. This permits Leibniz to explain how his active unities ground the derivative unity and phenomenal reality of bodies, namely by representing as one the multiplicity they involve (2.2). Finally (2.3), this explanation is used by Leibniz as a basis for articulating his conception of the collective unity of all substances: while Leibnizian substances are “windowless” and therefore neither admit nor emit any causal impetus, the multiplicity that the world comprises is “compensated” or “reduced” to unity by the perceptions of substances. 44 To be sure, there is much in this argument that requires further elaboration. 45 What it does for us here, however, is to establish a clear link between Leibniz’s claim that perception is a property of every substance and his theory of PEH: without mind-like entities endowed with representational power there is no Leibnizian PEH. Also, it allows us to appreciate that the level of reflection on which this connection is predicated is the metaphysical level: like the perceptions of simple substances with respect to bodies, PEH is offered (at least in part) as an answer to a question of fundamental ontology, namely that of how an infinite plurality of noninteracting substances can nevertheless be one plurality and hence be in some sense. And, with this in place, we are now in a position to turn to Wolff.

3. Wolff 3.1.

Wolff on the necessity of simples

Wolff opens the Preface of PP by complaining about the situation in which “first philosophy” finds itself after the rise of Cartesianism and by suggesting a certain line of continuity between the metaphysical enterprise he is about to begin and the metaphysics of the Scholastics: like Leibniz, Wolff wants to rehabilitate some Aristotelian-Scholastic

44

As Antognazza 2007, xxi, 9–10, 45–47 observes, the general idea of harmony as multiplicity reduced to /compensated by unity can be traced back to some of Leibniz’s earliest writings. See e. g. his 1671 De Conatu et Motus, Sensu et Cogitatione, where harmony is defined as “unitas plurimorum” and “diversitas identitate compensata” (A VI, 2: 283). Interestingly, already in this early text the role of reducing variety to unity is ascribed by Leibniz (though perhaps not exclusively) to the activity of a mind: “Thinking is nothing but the sense of comparison or, more succinctly, the sense of many things simultaneously or one in many” (A 6.2.28). See also A 2.1.174, A 6.3.116. 45 For example, throughout my discussion I have been implying that the perceiving entities which unify an aggregate – whether bodies or the world as a whole – are internal to that aggregate. Many of Leibniz’s preferred examples of aggregates suggest, however, that the unifying principle of an aggregate is external to it: think of a pile of logs (A 6.4.401), an army (GP 2.96), or a flock of sheep (GP 2.252). Yet, on the other hand, Leibniz does talk of bodies – a sheep, a log – simply as aggregates (GP 6.586), or else as aggregates of substances /monads (GP 7.501, GP 2.193, GP 2.205, among many others). The idea of the world as an aggregate can, in my opinion, accommodate both views – that is, the principle of grouping of the world can be internal or external to it. With respect to the latter option, I am quite sympathetic to Rutherford’s view that, ultimately, the ground of the unity and reality of aggregates is the representational activity of the divine mind – which is external to the world. See Rutherford 1994, 75. But defending this thesis is not an easy task. For some difficulties, see Lodge 2002, 477, who thinks that God cannot aggregate.

106

Gastón Robert

doctrines. 46 This is reflected by his position on the necessity of simple beings, which he develops in Section II (“On simple being”) of Part II (“On the species of beings and their reciprocal relations”) of PP. 47 Although Wolff does not set out the topic in terms of “matter alone” versus “form” 48, his main argumentative strategy follows the general Leibnizian pattern of argument for the necessity of forms and against Descartes’ account of body as purely extended stuff. With Leibniz and against Descartes, Wolff thinks that an adequate explanation of compound bodies can only be attained by having recourse to simpler, grounding entities: composition (plurality) requires simplicity (unity). Wolff offers two different arguments for the necessity of simples in this section of PP. The first is based on the idea that the sufficient reason of composites’ being cannot be found in composition itself (henceforth ‘Argument from composition’=AFC). The second argument – which is implicit in Wolff’s text – centres upon the theses that composite beings have an accidental being and that simples are the only truly substantial beings (henceforth ‘Argument from substantiality’ = AFS). As we did with Leibniz’s AFU and AFA, we shall consider Wolff’s arguments in turn. In PP § 673, Wolff defines “simple beings” (entia simplicia) as entities lacking parts. 49 In a previous paragraph, “composite beings” (entia composita) are defined as entities which consist of a plurality of distinct parts. 50 On the basis of these definitions, in § 686 Wolff argues as follows: If there are composite beings, then there must be also simple beings, or, without simple beings composite [beings] cannot exist. For composite beings are composed of parts that are distinct from each other mutually (§ 531). But if those parts were composed once more of parts that are distinct from each other mutually, then they, too, would be composite beings (§ 531). Therefore, as long as other, smaller parts are admitted from which larger parts are composed, the question continuously arises, whence they are composed, consequently, it is not yet intelligible, whence, in the end, the smallest composite beings result that make up the composition of the other composites. Because, in this way, the sufficient reason is not contained in the notion of the composite, why it is composed (§ 56), yet a composite being cannot exist (§ 70) without a sufficient reason why it is a composite being rather than not a composite being, the sufficient reason of a composite being is to be sought outside the composite being, and therefore in a simple being (§ 665). If, therefore, composite beings should exist, simple beings must exist as well, or, without simple beings, a composite being can neither be conceived nor exist. 51

In its general structure, the argument can be put thus: 52

46

47 48 49 50 51 52

“Philosophia prima invidendis elogiis a Scholasticis exornata; sed, postquam Philosophia Cartesiana invaluit, in contentum adducta omniumque ludribio exposita fuit.” Since translations of Wolff’s writings into English are scarce, I have used those found in the secondary literature (specific sources in the footnotes) as it suited my purposes. In other cases I supply my own. Passages quoted in the footnotes are left untranslated. See PP §§ 673–850. On this change in terminology, see below n. 61. “Ens simplex, quod partibus caret.” See also PP § 675: “Ens [. . .] simplex partes nullas habet.” See PP § 531: “Ens compositum dicitur, quod ex pluribus a se invicem distinctis partibus constat.” See also VGG § 51. Translation in Watkins 2006, 277–278. For a parallel passage, see VGG § 76. In the formal presentation of this argument for simples I draw partially from Watkins 2006. My analysis and assessment of it differs, however, from his. More specifically, Watkins thinks that, despite ostensible differences, there is “no fundamental difference [. . .] that is of importance” between Wolff’s argument and Leibniz’s – the differences are “merely apparent” (2006, 277).

Simples, Representational Activity, and the Communication among Substances

107

(P1) Everything must have a sufficient reason (P2) Beings are either simple or composite (P3) A composite being consists of a plurality of distinct parts, each of which consists in turn of a plurality of further distinct parts (P4) The reason for composite beings cannot be found in composite beings themselves, but in something other (C1) The reason for composite beings must be found in simple beings (C2) Simple beings are necessary The burden of Wolff’s argument relies on (P4), the premise that the ground of composition lies outside composition itself. Composite beings, Wolff appears to be saying, are metaphysically reducible entities and, as such, their ultimate reason cannot be found in composition alone. But given that everything – as (P1) claims – must have a sufficient reason and that everything – as (P2) states – must be either simple or composite, it follows that the reason for composite beings must be found in simple beings. But what is Wolff’s argument for (P4)? The passage suggests that the reason for this premise lies in the definition of composite being deployed by (P3), and more specifically in the problem of infinite regress that seems to arise in connection with that definition: since composite beings are nothing more than pluralities of parts having parts, the question continuously arises as to whence a part and, in the end, the composite being itself is ultimately composed. But while Wolff explicitly connects (P4) with the problem of infinite regress, he offers no clue as to why, in this precise context of inquiry, an infinite regress must actually come to an end. This is important. Reconsider the argument that Leibniz gives in support of (P2) of his AFU. According to this premise, recall, matter is not truly one and thus not a principle of unity. Like Wolff’s argument for (P4), Leibniz’s argument for this premise also revolves around the issue of infinite regress. Unlike Wolff, however, Leibniz does not only assert that if there were no simples, one would be led into an infinite regress in the division of bodies: he also gives a reason why this regress is philosophically problematic. For Leibniz, an infinite regress is problematic because something which is infinitely divisible lacks unity. In turn, this is problematic because something which lacks unity cannot be. Thus, Leibniz’s rejection of the possibility of collections or aggregates of parts having no ultimate constituents is not based on the problem of an infinite regress as such. Rather, it springs from a deeper ontological claim, namely that one and being are convertible. Leonhard Euler, one of the harshest critics of Leibniz-Wolffian metaphysics, makes an interesting remark in this connection. In his Elements (1746), after having presented the problem of bodies’ infinite divisibility, he writes: Mr. von Leibnitz appears to admit this infinite divisibility by maintaining that infinitely many monads are required to represent the smallest body. In this Mr. Wolff is of a totally different opinion by maintaining that the divisibility of bodies does not proceed infinitely far. (Elements II, § 3; my italics)

Euler’s remark may perhaps be inaccurate in some respects, but I think he is right to imply that, for Leibniz, the problem of an infinite regress in the division of body has not to do with the infinity of the regress itself. In other words, Leibniz sees no problem in accepting infinites qua infinites: for he actually thinks that each body (considered as secondary matter) involves infinitely many simple entities. Rather, what he deems problematic is

108

Gastón Robert

to accept infinites of something which is not one, namely infinites of material parts, just partes extra partes to infinity. Wolff seems untroubled by this subtlety of Leibniz’s view: infinites are just unacceptable qua infinites. Consequently, it remains unclear why the reason for composition cannot be contained in composition itself, and hence why simples are necessary in order to explain composites in the first place. As I anticipated, however, there are other passages in Wolff’s PP from which a different argument for the necessity of simples can be extracted. In a sequence of paragraphs from the second chapter of his treatise on simples, 53 we find the following claims: (C1) § 789: The essence of a composite being consists in nothing but mere accidents (C2) § 791: Accidents cannot exist without substances (C3) § 793: There are no substances other than simple substances 54 Although these claims, in the context in which they appear, are not meant to serve as premises of an argument for the necessity of simples, they can nonetheless provide us with the materials to produce one. We can put the AFS as follows: (P1) (P2) (P3) (C1) (C2)

Simples are the only substances (= C3) Accidents require substances (= C2) Composite beings have an accidental way of being (= C1) Composite beings require substances (from P2 and P3) Composite beings require simples (from C1 and P1)

The AFS claims composites to require simples because accidental beings – the type of being to which beings through composition belong – require substantial beings, and simples are the only truly substantial beings. For the purpose of comparing Leibniz’s and Wolff’s views, the argument is interesting both (1) for what it says and (2) for what it omits. Let us see. (1) Although Wolff’s AFS does not parallel either Leibniz’s AFU or his AFA, its main insight seems to run close to some of the ideas we encountered in our presentation of Leibniz’s phenomenalism. According to Leibniz, we saw there, bodies are not real beings in the full sense of being-real but only in the derivative sense of entities “resulting from”, and therefore requiring, simples. This thesis, we also saw, is built on a distinction between being per se and being per accidens. In particular, bodies have a derivative, phenomenal reality – a reality ab alio – insofar as they are incapable of existing entirely through themselves (per se): they are aggregates of simple constituents. For this reason, they are said to be mere accidentia or beings per accidens. Now, since in the AFS the relationship between composites and simples is couched in terms of accidental beings requiring substantial beings, it can be read as built on the per se /per accidens distinction and therefore as essentially aligned with Leibniz’s views. 55 Three considerations might be used to support this reading. First, a few paragraphs before 53

See PP §§ 703–795: “De Modificationibus rerum, praesertim simplicium”. See also PP § 792: “In ente composito nihil datur substantiale praeter entia simplicia”; § 794: “Substantia adeo simplex est, quae proprie substantia dicuntur”; CG § 177: “In corporibus nihil datur substantiale praeter entia simplicia.” 55 For this reading, see Watkins 2006, 208, to whom Wolff is not “genuinely breaking with Leibniz, much less misreading his position”. Indeed, Watkins thinks that, in this argument, Wolff is “making a more efficient use of the resources implicit in Leibniz’s account” (2006, 208). I agree with Watkins that there are ways of reading

54

Simples, Representational Activity, and the Communication among Substances

109

(C1) – (C3) occur, Wolff says that the account of substance as that which has being per se is “the clearest of all”. 56 So, substances are per se entities for Wolff. It follows from this that simples are per se entities, for simples are the only substances, as we read in (P1). Second, in PP §§ 701–702, Wolff explicitly uses the Leibnizian “resulting from” idiom to characterise the sort of relation holding between composite and simple beings: “Simplicia, unde compositum resultat”, he writes. Finally, Wolff’s way of characterising the kind of accidental reality that composite beings have resembles Leibniz’s. On Leibniz’s view, the accidental reality of body consists in an accidental relation holding among the plurality of members that body-qua-matter involves. Similarly, in a chapter devoted to explaining the essence of composite beings 57, Wolff explains that a composite is “a certain whole” (§ 532: totum aliquod) whose essence consists “in the way in which its parts are combined with each other”, that is, in a relation. 58 The same explanation is repeated in PP § 768, whose heading is reproduced in (C1). In light of these considerations, it seems reasonable to take Wolff’s main insight in the AFS as a genuinely Leibnizian one: simples are necessary to explain composites because composition – as Leibnizian aggregation – is an accidental relation. Hence, it can only obtain among the plurality of members involved in composite bodies if there is something per se real which grounds the relation or from which the relation results. 59 (2) However, even if there is a way of interpreting Wolff’s AFS so as to make it fit with some Leibnizian ideas, more interesting for my goal is to consider those of Leibniz’s ideas which Wolff’s AFS omits. In particular, there are two conspicuous omissions in Wolff’s reasoning to which I would like to draw attention, namely (i) the thesis that one and being are convertible and (ii) the notion of activity (i) We have seen that both Leibniz and Wolff agree to the general proposition that composites require simples because composites are only accidentally real and an accidental being requires something per se real as its foundation. Yet Leibniz’s position is more complex than this. On his view, a composite requires something per se real because it lacks unity and unity is a condition of reality. More particularly, Leibniz’s way of understanding the composite /simple relationship in terms of per accidens entities which require per se beings is, as I see it, this: given that composites lack unity in their own right, and given the reciprocity of one and being, composites are incapable of being entirely through themselves (per se), from which it follows that they require something per se as the source of their phenomenal reality. In this sense, we can say that, for Leibniz, it is

56

57 58

59

Wolff’s argument that suggest he is endorsing some essentially Leibnizian views. As I shall argue in a moment, however, I think there are other aspects of Wolff’s argument – particularly the ideas it omits – which suggest he is parting company with Leibniz in very fundamental respects. See PP § 771: “Nihil sane notius est, quam quod substantia in philosophia Aristotelico-Scholastica definita fuerit per ens, quod per se subsistit [. . .].” Shortly afterwards, nevertheless, Wolff says that this definition contains something obscure, since it does not explain what exactly means for a substance to be “through itself”. In PP § 772, he holds that something is (subsists) through itself if it “needs nothing other than itself to exist” (“nulla alia re indigere ad existentiam”). I must confess I cannot see how the idea of “something needing nothing other than itself to exist” may help clarify the idea of “something capable of existing through itself”. See PP Part II, Section 2, chap. 1: “De Essentia Entis Compositi” (§§ 531–543). See PP § 533: “Essentia entis compositi consistit in modo quo tales partes [sc. the composite being’s parts] invicem combinantur”. This last point is also made by Watkins 2006, 279.

110

Gastón Robert

precisely composites’ lack of intrinsic or per se unity that explains their need of something per se real as a foundation. The transcendental character of unity plays, then, a pivotal role in Leibniz’s view of the grounding relation holding between simples and composites. This point is of importance, not least because it gives a clear indication of the strictly metaphysical character of Leibniz’s motivations for his “foundationalism”: simples are invoked so that bodies can satisfy minimal metaphysical conditions, namely possessing (some degree of) unity and thereby having (some degree of) reality. Yet in Wolff’s AFS the premise is omitted. True, this does not entitle us to draw any positive conclusion about Wolff’s motivations for simples and the precise explanatory role he ascribes to them. But it does give me occasion to anticipate an idea that the discussion of Wolff’s doctrine of elements in the next section will confirm: unlike Leibniz’s, Wolff’s simples are invoked to explain what is actually perceived at the derivative level of the material world – recall at this point Leibniz’s view in Discourse § 10, quoted above: “I agree that the consideration of these forms serves no purpose in the details of physics and must not be used to explain particular phenomena” (GP 4.434 /PE 42). 60 (ii) Closely related to the problem of composites’ unity as it appears in Leibniz’s philosophy is the notion of activity. We saw earlier that activity occupies a prominent place in Leibniz’s explanation of the derivative reality of aggregates: bodies borrow their accidental unity and phenomenal reality from the (representational) activity of simples – activity is the ground of unity, as I argued when discussing Leibniz’s AFA. Yet in Wolff’s AFS there is no mention of activity. 61 This may be viewed as a natural consequence of Wolff’s omission of the notion of unity: if unity and activity work in tandem, then the omission of the former might explain the omission of the latter. I think, however, that there is a deeper reason underpinning Wolff’s omission. In PP § 794, one paragraph before concluding his treatise on simples, he writes: That existent simple substances are endowed with force cannot be demonstrated here [sc. in the PP] (hic nondum demonstrare potest) [. . .] For which reason the Leibnizian notion of substance, which distinguishes a substance from its accidents by reference to active force, could not be established here (hic stabiliri nondum potuit).

Here Wolff claims that active force, and consequently Leibniz’s dynamical account of substance, falls outside the domain of ontology. As I read it, this striking declaration has its roots in one of the most characteristic features of Wolff’s rationalism, namely what we may call his “ontological logicism”. 62 Roughly, it involves three claims: (a) being is mere 60

Taking into account other passages of PP, the contrast between Leibniz’s view and that of Wolff can be drawn in yet another direction. In PP § 771, Wolff says that substances are per se beings and complements this by saying that a substance is also that which “sustains” accidents (“quod per se subsistit et sustinet accidentia”). This is interesting because it makes room for spelling out Wolff’s interpretation of the per se (simples) /per accidens (composites) grounding relation in terms of a relation of inherence: Wolff’s per se beings would ground composites insofar as they work as composites’ bearers, whereas Leibniz’s per se beings (at least primarily) grounds composites insofar as they work as composites’ unifiers (and hence as principles of their reality). 61 This might explain why, as mentioned earlier, Wolff formulates the issue of the necessity of simples in terms of “simples versus composites”, rather than in terms of “forms versus extended matter”: since he is only interested in the simplicity of simples, he might have regarded the notion of form – which involves both unity and activity – as unnecessary. On this, see Wolff’s note to CG § 361 and Soto Bruna’s 1991, 358 comments on this passage. See also PSR § 644. 62 See Soto Bruna 1991, 359 ff.

Simples, Representational Activity, and the Communication among Substances

111

possibility 63; (b) possibility is logical non-contradiction 64; and (c) ontology is the science of being in general or being as being. 65 Wolff’s definition of ontology in (c) is of course traditional. But his view of “being” in (a) strongly affects the way in which the ontological science is to be understood. For if being is – as (a) claims – mere possibility, then the proper subject matter of ontology is beings’ possibility or being qua possible. Further, if possibility is conceived – as we read in (b) – as non-contradiction or minimal conceptual intelligibility, then the proper subject matter of ontology is being insofar as it lacks selfcontradiction. These claims commit Wolff to a radically logicist conception of ontology, one according to which the ontological science, the complete system of propositions and tenets it contains, must move exclusively within the limits of pure conceptual possibility or relations of logical compatibility. We need not delve further into the details of this view here. 66 What makes it relevant for the issue at hand is that, as it seems to me, it can help us understand Wolff’s conspicuous exclusion of activity from ontology and, as a result, from his AFS. For if being is absorbed in the purely logical sphere of possibility and non-contradictoriness, it seems natural to infer that active force will not properly belong to the science devoted to its study: the conditions for the actual reality of beings do not pertain to the strictly ontological domain. Consequently, Leibniz’s account of substance, insofar as it takes activity to be the very mark and essence of substantiality, will not belong to the strictly ontological domain either. 67 This does not mean that activity is completely absent from Wolff’s system of nature. As we shall see, in CG and VGG Wolff advances a conception of simples as indivisible points of force. However, the fact that activity is ruled out from ontology and hence from the realm of beings’ fundamental ontological determinations already suggests that Wolff’s dynamical conception of simples will significantly differ from that of Leibniz. In Leibniz’s philosophy, activity is a basic ontological concept aimed at satisfying basic ontological conditions. Even though we are not yet in a position to pin down Wolff’s positive conception of activity, we have reasons to suspect that it will not be the metaphysical conception which is so characteristic of the philosophy of his putative master.

63

64

65 66

67

See PP § 135: “Quod possibile est, ens est”; § 134: “Ens dicitur, quod existere potest, consequenter cui existential non repugnant”. See also VGG § 30. See PP § 85: “Possibile est, quod nullum contradictionem involvit, seu quod non est impossibilem”; PP, § 79: “Impossibile dicitur, quidquid contradictionem involvit.” See PP § 1: “Ontologia seu Philosophia prima est scientia entis in genere, seu quatenus ens est.” More extended expositions of it can be found in Gilson 1952, 113 ff., and Burns 1966, 18–21. See also the references given in the next note. Here I am in agreement with Corr, for whom “throughout his metaphysics Wolff concentrates on demonstration at the level of essential possibility. In ontology [. . .] essence [. . .] does not entail the characteristic dynamism of the Leibnizian essence in striving for existence” (Corr 1974, 16). See also Campo 1980, 10: “In Wolff the notions of ‘being’, ‘subject’, and ‘substance’ become attenuated, tend to disappear and to be resolved into being’s attributes, predicates or notes. The metaphysical kernel of being is replaced by the logical side of essence”. See PP § 153, where Wolff equates essence with possibility.

112

Gastón Robert

3.2.

Wolff on the nature of simples: the “elementa rerum” and the physicalisation of simples and activity

The analysis of Wolff’s arguments for the necessity of simples has led us to two main conclusions, namely that the activity with which Wolff’s simples are endowed is not strictly metaphysical in kind, and that its explanatory role does not concern the metaphysical problem of the unity of bodies. As presented so far, however, these conclusions are rather abstract. Moreover, both of them are based on mere omissions. In order to get a firmer and a more concrete grip on Wolff’s take on Leibniz’s views, we need to turn to his actual remarks about Leibnizian simples and their activity. Or so we might expect. For, as a matter of fact, Wolff’s actual remarks about Leibnizian simples and their activity are not as clear as one would like. To begin with, consider these texts: 68 [a] We defend only the simplicity of the elements of material things, but we remain undecided (in dubio relinquamus) about what the innate force is in them (PSR § 644). [b] I have left undecided (in medio relinqui) the concept of Leibnizian monad [. . .] and so I have also refrained from using the name (Mor., Praef. ix). [c] But when we consider a simple being, we are not concerned with the monad of More or the monad of Leibniz (PP § 684). [d] I leave to Leibniz his opinion about monads (Leibnitio suam de monadibus sententiam relinquo) [. . .] For me it is the same whether someone makes Leibnizian monads the most important things, or condemns and rejects them (CG, Praef. xiv). These texts do not all represent the same Wolffian attitude towards Leibnizian monadology. But none of them gives clear-cut evidence that Wolff rejects Leibniz’s perceiving simples. In [a] and [b], Wolff says that he neither rejects nor accepts Leibniz’s conception of monads – he declares himself agnostic. 69 Suggestively, [a] shows that the particular aspect of Leibniz’s conception which Wolff wants to leave “undecided” is not whether simples are or are not endowed with “innate force” – they are, according to Wolff. Rather, his indecision concerns the specific nature of this force – “what the innate force is”. This explains Wolff’s refusal to use Leibniz’s terminology, as he tells us in [b]. 70 However, Wolff is happy to leave the issue of the nature of force open, without adopting any definite stance. As for [c] and [d], they are admittedly stronger. For instead of declaring himself agnostic, Wolff tells us he is “not concerned” with Leibniz’s monads: “Leibnitio suam de monadibus sententiam relinquo”. Again, nevertheless, this is far from decisive, for the question still remains as to exactly which aspect of Leibniz’s view Wolff is “not concerned with”. 68

I owe the translations of [a] – [d] to Rutherford 2004, 235–236, n. 21. The thesis that Wolff is merely agnostic about Leibnizian monadology has been defended by Watkins. See Watkins 2005, 47–48, 2006, 281–283, and 1998, 140. See also Laywine 1993, 151, n. 12. Against this rather weak positon see Rutherford 2004, 236, n. 21, and what follows. For other passages apparently speaking in favour of Watkins’ reading, see VGG §§ 598–600. 70 As we shall see, Wolff uses the term ‘element’ (when not just ‘simple’) instead of ‘monad’.

69

Simples, Representational Activity, and the Communication among Substances

113

But while these statements about Leibniz’s simples and the nature of force are not particularly helpful, other texts from the Wolffian corpus might perhaps seem more promising. Consider these: [e] The elements of material things are atoms of nature [. . .] They can also be called ‘physical atoms’. (Elementa rerum materialium sunt atomi naturae [. . .] Dici etiam poterant atomi physicae). (CG § 187) [f] [T]he atoms of nature, which are certain physical points ([A]tomi Naturae, quae physica quaedam puncta sunt). (CG § 216) ‘Element’ (Element, elementum) is the term Wolff uses in VGG and CG to refer to the simple beings which make up composite bodies. 71 The elements about which Wolff is talking in these passages are then the same entities for whose necessity he argued in the AFC and AFS: the true substances on which composite beings are grounded. 72 So texts [e] and [f] do seem to display a glaring lack of fit between Wolff’s position and that of Leibniz. For Leibniz’s simples are “atoms of substance” (atomes de substance) and “metaphysical points” (points metaphysiques) (GP 4.482), whereas Wolff’s simples, as we learn from these passages, are “atoms of nature” (atomi naturae), “physical atoms” (atomi physicae) or “physical points” (puncta physica). And yet, this is still not sufficient to settle the matter. For the difference between Wolff and Leibniz on this point could be merely terminological. 73 In support of this, the following consideration might be advanced. Wolff, it is true, describes his elements as “atoms of nature” and “physical points”. Now, the terms ‘natural’ and ‘physical’ can be seen as semantically equivalent. But ‘physical’ – and hence ‘natural’ – need not mean ‘corporeal’ or ‘material’: it could only mean ‘real’. In fact, this use of ‘physical’ can be found in other authors – both Scholastic and Modern – all of whom relate to Wolff’s philosophy in one way or another. For instance, in his Metaphysical Disputations, Suárez says that “God is a physical (physica) cause as He creates, and also angels when generate motion whether in heaven or in themselves”, where he clearly does not want to attribute either to God or angels the status of material causes but rather that of “real” causes – “causalitatem realem”, as Suárez clarifies (Disp. Met. XVII, ii, 6). 74 The same meaning of ‘physical’ is adopted by Kant in his Metaphysik Herder (Ak 28: 53) 75 and by Baumgarten in his Metaphysica (Met. § 450). So, in describing his simples as natural atoms or physical points, Wolff could simply be saying that his simples are real points – unlike, say, mathematical points, which are only limits. And this is something Leibniz would not of course disavow. Indeed, in the New System, Leibniz calls his simples “unités reelles” (GP 4.478, GP 4.482). Therefore, even though Wolff’s characterization of simples in texts [e] and [f] might seem not very Leibnizian at first sight, it can prima facie be rendered consistent with Leibniz’s views. 71

See CG section II, chapter 2: “De Elementis corporum” (§§ 176–214) and VGG § 582. See CG § 182: “Substantiae simplices sunt elementa corporum.” Note, though, that ‘simple substance’ and ‘element’ are not coextensive concepts: the human soul, on Wolff’s view, is a simple substance but not an element. We enter into this point in the next section. 73 For this reading, see Burns 1966, 82. Against it, see Corr 1975, 256, and below. 74 Wolff knew Suárez’s work well. See e. g. PP §§ 169, 502, 527, 586, 684. See École 1961, 124, according to which Wolff’s philosophy makes possible the continuity between Suarezian and post-Suarezian Scholasticism and Kantian and post-Kantian thought. 75 See also Ak 20: 283. 72

114

Gastón Robert

So, in addressing Wolff’s views on Leibniz, no definite progress can be made by concentrating on his actual remarks about Leibnizian monads and the nature of simples. In the remainder of this section I would like to concentrate on two more implicit aspects of Wolff’s theory of elements which, in my opinion, reveal his rupture with Leibnizian orthodoxy with particular clarity. (i) The first concerns Wolff’s interpretation of the force of elements as moving force (bewegende Kraft, vis motrix). (ii) The second relates to his account of the origin of spatial extension. (i) As is well-known, Leibniz distinguished between two main types of force, namely primitive and derivative. Primitive forces govern the metaphysical realm of monads and their perceptions (and appetitions), whereas derivative forces rule the mechanical domain of bodies and their motions. 76 This distinction plays an important systematic role in Leibniz’s philosophy. For one thing, it provides Leibniz with a basis for articulating a dynamical science of a purely metaphysical, non-mechanical character. For another, it sets a framework for conceptualising the active forces of substances as representational power. By this I do not mean to suggest that Leibniz’s primitive /derivative force distinction is enough to motivate an interpretation of substances’ forces as perceptual in nature. However, such an interpretation would not be possible if the concept of force simpliciter were conflated with the mechanical concept of force capable of local motion. But Wolff’s account of elements and their force, I want to suggest, favours such a conflation. In brief, his account can be divided into three steps. The first two steps draw on broadly Leibnizian premises. First, in VGG § 623, Wolff holds that since all the modifications of bodies are generated by virtue of motion, bodies must be endowed with a “moving force” (bewegende Kraft). This moving force, he says in VGG § 624, consists in a “continuous striving to move matter”. 77 Later on, secondly, discussing the origin of this force in VGG § 697, Wolff contends that it must be found in the elements of bodies: Before we have seen that the force must be something persistent. But in bodies we find nothing persistent save the elements from which (daraus) matter is originated. For this reason, the force must be found in these elements.

Wolff’s claim here seems to reveal no departure from Leibniz’s position. Like Wolff, Leibniz also claims the derivative forces of bodies – and hence moving force as an instance of derivative force 78 – to rely on, or result from, the primitive forces of simples. 79 After this, however, Wolff and Leibniz part ways. For, thirdly, Wolff appears to think that, given that the force of elements is the source of the moving force of bodies, the intrinsic activity of elements must be of the same kind of that of bodies, that is, force capable of motion. 76

See GP 2.251, GP 2.262, GP 2.270, GP 3.457, GP 6.150. This is a simplified way of stating Leibniz’s view, which involves further distinctions within the primitive and derivative categories – namely active and passive instances within each category. See GP 2.281, GP 4.395, GM 6.236. 77 See also CG § 137: “[. . .] vis illa corporum dicitur motrix, quia nempe motui locali adheret.” 78 For Leibniz’s characterisation of motive force as derivative force, see GP 4.473. 79 The precise sense in which derivative forces “rely on” or “result from” primitive ones is a vexed issue. In light of the interpretation I favour of the simple /aggregate relationship, one might be inclined to read the primitive / derivative force relationship as a metaphysical grounding relation: derivative forces would depend on primitive ones qua being. Leibniz’s view, however, is more complex than this, for he says that derivative forces are “modifications”, “limitations”, and “accidental variations” of primitive forces, as they figure in relation to extension. See GP 2.251, GP 2.270, GP 3.356, GP 3.457, GP 4.473, GP 6.352. For discussion of this and related topics, see Adams 1994, 378–399.

Simples, Representational Activity, and the Communication among Substances

115

Now, Wolff does not explicitly draw this conclusion. But I think he implies it. Two points support my claim. 80 First, in VGG § 700, Wolff says that given his explanation of the origin of moving force by reference to the force of elements, “there is no need of having recourse to an originating activity (ursprüngliche Kraft), but it suffices to rely on those forces which can be explained by the motion (Bewegung) of a subtle fluid matter found in the empty spaces of bodies”. Interestingly, “originating activity” (activité originale) is an expression Leibniz employs in New System § 3 to refer to the metaphysical force of substantial forms (GP 4.479). Leaving this terminological matter aside, however, what is worth nothing about Wolff’s move is that it makes clear that, on his view, the innate force of elements is, like that of bodies, physical in kind. If not, why would the derivation of elements’ forces from that of bodies render “an originating activity” unnecessary? A second illuminating pointer comes from Wolff’s position in CG. As in VGG, in CG Wolff also embraces a certain “foundationalist” view: elements must be endowed with “a certain force” (vi quadam) because bodies are endowed with “active or moving force” (vi activa seu motrice) and bodies are grounded on elements (CG § 196). Again, however, he seems to think that this renders any reference to a metaphysical, originating activity unnecessary. What I have in mind is this: Since moving force, in a collision of bodies through which derivative force results, is modified according to the rules of motion, through these [rules] it is understood why in a given case primitive force is modified in one way rather than another, and consequently the reason for the modification is given through these [rules]. (CG § 365; my italics) 81

Ostensibly, here Wolff distinguishes between primitive and derivative forces. Yet the distinction is merely verbal. For both primitive and derivative forces are said to be modified in accordance with the same rules, namely the rules of motion. 82 For Wolff, then, as Rutherford points out, “there is no deeper reason for the modification of primitive forces than the laws of motion themselves”, the laws which govern the mechanical level of bodies (Rutherford 2004, 229). This means that the active forces of Wolffian elements are mechanical forces: vis activa is vis motrix. Like Leibniz, Wolff thinks that composite bodies require simple beings, and that the forces of composite bodies must be grounded on the forces of these simple beings. Yet, against Leibniz, Wolff takes this to imply that the force of elements must be moving force. Note how Wolff is in a sense inverting Leibniz’s way of seeing the relationship between grounding simples and grounded bodies.

80

The claim that Wolff equates Leibnizian active force with moving force is shared by Kant. In GSK, his first published writing (1746), he writes: “Leibniz, to whom human reason owes so much, was the first to teach that an essential force (wesentliche Kraft) inheres in a body and belong to it even prior to extension [. . .]. The inventor gave this force the general name of ‘active force’ (wirkenden Kraft). One should only have followed on his heels in the systems of metaphysics, yet the attempt was made to define this force somewhat more precisely. The body, it is said, has a moving force (begewende Kraft), for it is not seen to do anything except produce motions” (Ak 1: 17–18 /W 22; my italics). As Arana 1988, 334 argues in his commentary, “systems of metaphysics” stands here for “Wolffian systems of metaphysics” – including Wolff himself and some of his followers. 81 Translation in Rutherford 2004, 230–231. 82 That is, Newton’s rules of motion. See CG section II, chapter 4 (“De Legibus Motus”), especially §§ 309, 318, 346, 348. See also VGG § 610. For discussion of Wolff’s reception of Newton’s laws, see Watkins 1997, 316–321. Also Schönfeld 2000, 142, mentions Newton’s influence on Wolff.

116

Gastón Robert

For Leibniz, as seen earlier, the fact that the unity and being of bodies is grounded on the perceptual power of simples entails a ‘mentalisation’ of bodies and their motions. Wolff puts things the other way around. Since the force of the elements grounds the force that we perceive at the spatio-temporal level of material things, their force must be mechanical force. Bodily forces and their effects – local motions – enjoy priority for Wolff. Accordingly, bodies’ reliance on simples entails not a mentalisation of bodies and their motions but rather a physicalisation of simples and their actions. (ii) We saw that the role of Leibniz’s simples is to fulfil a basic ontological function, namely that of bestowing unity and hence reality on bodies, and that this thesis is intimately related to Leibniz’s view that substances’ powers are representational in nature. I want to argue that Wolff breaks with it. That this is so might seem to be already implied by the fact that, as I have just argued, Wolff equates the active force of elements with bodily moving force. For if the force with which elements are endowed is nothing but force capable of motion, and if all the modifications of bodies – as Wolff says in VGG § 624 – are to be accounted for by reference to motion, then the force of elements is meant to explain all the modifications of bodies and not only their unity and being. However, there is another, in my opinion more interesting, feature of Wolff’s conception of elements that I would like to develop here. 83 As noted earlier, Wolff conceives of elements as physical points or natural atoms. At the same time, however, he denies that they are material atoms (atomi materiales). 84 A material atom is one which, though naturally or de facto indivisible, has parts and is thus divisible in principle. 85 Contrastingly, an element is indivisible de jure: it is conceptually or “analytically” indivisible. 86 As such, an element is devoid of parts and does not occupy space 87. But Wolff thinks that even if the elements neither have parts nor occupy space, they do nonetheless determine the spatiality of composite beings. This view can found in both VGG and CG: [S]ince [each simple] refers to the rest in a special way according to its internal state, it coexists with the rest in a special way such that none of them can exist with the rest in precisely this way. And thus not only is each one external to the others (ausser dem andern), but many, taken together, also follow each other in an order, and thus many, taken together, fill (erfüllet) a space. (VGG § 602)

Likewise, Wolff writes in CG: § 219: The elements of material things exist externally (extra se) with respect to each other. For the individual elements of material things are different (dissimilia) from each other, and so [sc. as elements exist externally to each other] one can be distinguished from another.

83

In some of the points that follow I am indebted to Rutherford 2004, 231–232. See e. g. CG § 187: “Elementa rerum materialium sunt atomi naturae, non vero atomi materiales.” See also VGG § 583. 85 See CG § 186: “Atomus [. . .] materialis appelatur, quod in se divisibile, sed cui dividendo non sufficiunt aliquae causae in rerum natura existentes.” 86 See CG §§ 186–7: “Atomus naturae dicitur, quod in se indivisibile est, adeoque partibus destituitur, in quas resolvi possit [. . .] Elementa [. . .] sunt atomi naturae.” 87 See CG § 184: “Elementa rerum materialium non sunt extensa [. . .] spatium nullum implent.” 84

Simples, Representational Activity, and the Communication among Substances

117

§ 221: Aggregates of elements are extended (extensa). For when elements are aggregated, they exist externally to each other. 88

Underlying Wolff’s argument is the Leibnizian premise that space is a certain order of entities which coexist externally to each other. 89 On this basis, his reasoning centers upon the relations holding between the notions of plurality (non-identity), externality, and spatiality (or extension, according to the version of CG). Despite their simplicity, Wolff wants us to believe, simples can fill a space or constitute a certain extension because they exist externally to each other – they differ from each other and are thus non-identical – and space is a system of external relations. In other words: space (extension) is entailed by a plurality of coexistent distinct simples (a system of different, non-identical simples) because such a plurality entails that its members exist externally to each other, which is that in which space consists. 90 The argument is weak and can be attacked from more than one flank. 91 For our purposes, however, what is significant about it is the thesis it aims to establish: the spatial dimension or extension of physical objects is to be explained in terms of relations between simples: [S]ince each simple thing is related to those which surround it, many simple things constitute one, and because of this (daher) a composite thing receives an extension in length, breadth, and depth. (VGG § 603)

On Wolff’s account, the explanatory scope of the elements thus transcends the limits Leibniz imposes on them, reaching the level of the actual constitution of appearances: Wolffian simples compose extended bodies. This puts Wolff’s “monadological” enterprise in a particularly vulnerable position. If the spatial extension of bodies is to be explained by reference to simple entities, why the indivisibility of simples is not threatened by the divisibility of bodies? Furthermore, how can a purportedly non-extended, discrete substance compose the continuous magnitude in which extended matter consists? 92 How many points would be needed? 93 Leibniz can successfully eschew these questions because his simples and bodies (in their extensional appearance) pertain to two irreducible 88 89 90

91

92

93

Translations in Rutherford 2004, 232. See also PP § 548 and VGG §§ 52–53. Wolff argues for a relational conception of space in VGG § 46. See also PP §§ 589 ff. Wolff’s version of the argument in VGG differs from that in CG insofar as it moves from the idea of externality to that of spatiality via the intermediate premise that simples stand in a certain ordering relation (“follow each other in an order”), whereas the latter moves directly from the idea of externality to that of extension. As Watkins remarks, however, Wolff does not clarify why spatiality rather than some other kind of order derives from the fact that simples stand in a certain ordering relation. See Watkins 2006, 284, n. 40. Two of which are the following. First: Wolff wants to show that simples can fill a space which does not exist independently of simples: space is a derivative order grounded on, or arising from, simples’ outer relations. But his account of the relation holding between plurality, externality, and spatiality concerns only necessary conditions: whether simples’ external relations suffice to generate space remains unclear. Second: Wolff wants to show that simples can fill a space because space is a derivative order grounded on simples’ outer relations. Yet his way of explaining the connection between plurality and externality could be used to support an absolute conception of space. Simples differ from each other – one might argue – because they exist externally to each other; externality is a condition of plurality. But externality is a spatial category and hence presupposes space. Therefore, simples’ diversity presupposes space: space is a condition of the identity of simples. In VGG § 604, Wolff explains “extension and, with extension, continuity” by reference to elements and their relations. See also PP § 548 and VGG §§ 52–53. These objections were among the favorite in Newtonian anti-Wolffian circles. See Euler, Elements §§ 55 ff.

118

Gastón Robert

ontological levels. The former do not figure into the explanation of the spatial constitution of appearances, but are only presupposed as a necessary condition for bodies to be one and thus be: simples ground matter without composing it. 94 Since Wolff claims his elements are involved in the explanation of spatiality, this strategy is not available to him. 95

3.3.

Wolff and PEH: the “nexus elementorum” and the mind-body problem

I have argued so far that Wolff breaks with Leibniz’s conception of simples as mindlike entities endowed with perception. I have also tried to show that, in doing so, he is not simply dropping Leibniz’s perceiving simples while remaining faithful to other fundamental Leibnizian tenets. Leibniz’s simples are only one step in a larger train of thought, one going from the notion of unity through that of activity to perception. Wolff gets off this train as early as it begins, namely in the notion of unity. So, as a matter of fact, we may say that Wolff is faithful to at least the internal logic of Leibniz’s system: detached from the constellation of ontological views which sustains it, the ascription of perception to every substance remains largely unmotivated. So there is no point in defending it. I think that a similar claim can be made about Wolff’s attitude towards Leibniz’s theory of PEH. For, having refused to embrace Leibniz’s perceptually-equipped simples, there is no room for PEH as a model of cosmological unification in Wolff’s system. Accordingly, he leaves it to Leibniz. Instead, Wolff favors the view that the world is, at every level, a real system of externally connected entities: like material things themselves, “the elements of material things are all reciprocally connected (inter se connexa)” (CG § 204). As was the case in his interpretation of active force as vis motrix, in advancing this thesis Wolff’s reasoning proceeds from the identification of things’ characteristics at the macroscopic, grounded level of physical reality to the determination of things’ characteristics at the atomic, grounding level: Since the ultimate reasons for material things are found in the elements [. . .], the ultimate reason for the connexion of material things (nexus rerum materialium) is also to be found in the elements of things (elementa rerum). Therefore, there is something in the elements wherefrom it is understood why material things are connected with one another (§ 56 Ontol.). Thus, since the elements of material things are connected with one another (§ 204) and their successive states depend on one another (cum elementa rerum materialium inter se connectantur eorumque status successivi a se invicem pendeant) (§ 199), through their connection and dependence among their states the connection of material things can be understood. (CG § 205)

94

See GP 2.268 /LDV 303: “[A]ccurately speaking, matter is not composed of (componitur ex) constitutive unities; rather, it results from them, since matter, i. e., extended mass is nothing but a phenomenon founded in things, like the rainbow or the perihelion. And there is no reality in anything except the reality of unities.” 95 Wolff might have resources at his disposal to avoid the mentioned problems. For instance, he could reply that what constitutes continuous extension is the network of external relations among simples, whereas simples themselves continue to be immaterial and thus non-extended beings. This view was defended by both Baumgarten and the pre-critical Kant. See Met. § 399 and Ak 1: 480, 481, respectively. Its problems, however, are pressing, as the mature Kant knew well. Space is claimed to be constituted by the external properties of simples. But “external” is a spatial category. Hence, external relations presuppose space, rather than constitute it. See KrV A23 /B38.

Simples, Representational Activity, and the Communication among Substances

119

For Wolff, the connection of material things (nexus rerum materialium) entails the connection of the elements of material things (nexus elementorum) because the latter provides us with a reason why bodies are all reciprocally connected rather than not. Now, the connection at the atomic level predicated here is not the mere “externality” which Wolff claimed to be entailed by elements’ non-identity and which constitutes spatial extension. More strongly, the nexus elementorum amounts to an external dependence among their states. Wolff makes this point very clearly when he writes: The elements of things are acted upon by one another (a se invicem patiuntur). There is passive potency (potentia passiva) in bodies (§ 144). Since the ultimate reasons for bodies are found in the elements [. . .], the reason for bodies’ passive potency is also to be found in the elements [. . .]; but a passion consists in a change of state whose reason [ratio: ground], which changes the states of a subject, is found outside that subject. Now, through the active force with which the elements of things are endowed it is not understood why bodies are acted upon (sint passionibus obnoxia). Therefore, it is necessary to admit that there are also passions in elements themselves (sunt etiam in ipsis elementis passiones); or, since there is passive potency in bodies, the elements of things are acted upon by one another. (CG § 207)

Wolff’s pattern of reasoning is familiar. Bodies are acted upon by one another. The reason for what happens in the bodily realm must be found in the elements. Hence, the elements are acted upon by one another. Note the sharp contrast between the last claim in this reasoning and the way Leibniz explains the (purported) passions of monads. As we read in a famous portion of Mon. § 49, “The creature is said to act externally insofar as it is perfect, and to be acted upon (patir) insofar as it is imperfect. Thus we attribute action to a monad insofar as it has distinct perceptions, and passion, insofar as it has confused perceptions” (GP 6.615 /PE 219). Here the active and passive states of a substance are qualitatively differentiated active states of that very substance: a substance’s passions are only apparent, nothing more than a way of describing what philosophically considered are its own spontaneous actions. 96 Interestingly, Baumgarten, a much more orthodox Leibnizian than Wolff, takes precisely this way of accounting for the passions of substances to be the very mark of “ideal influence”: “If the passion of a substance on which another exerts its influence is at the same time an action of the patient itself (simul est ipsius patientis actio), the passion and influence are called ‘ideal’ (ideales). Instead, if the passion is not an action of the patient, the passion and influence are called ‘real’ (reales)” (Met. § 212). Leibnizian monads are closed, their states depending on no finite substance except for themselves. Everything that happens at the atomic level of monads is only the product of processes of immanent causation. By contrast, Wolffian elements are not selfcontained entities but are open to the external influx of other finite entities. Wolff’s world is a totum reale. I shall not dwell on Wolff’s positive account of substances’ interaction here. In light of what we have seen so far, Wolff’s rejection of Leibniz’s PEH and the reasons for this

96

This is what Leibniz calls ‘ideal influence’ (GP 6.615; cf. GP 2.475). In describing substances’ passions and things’ influence as “apparent” I am lining up with the traditional view. See e. g. Sleigh 1990, 161–163, Mates 1986, 206, Wilson 1999, 345. But there are dissenting voices. See Puryear 2010.

120

Gastón Robert

rejection are, or so I hope, sufficiently well established. Instead, I would like to say a final word about Wolff’s view of the soul-body PEH. 97 As I anticipated, in spite of his rejection of PEH as a general model of cosmological unification, Wolff thinks that PEH is the best explanation of the relation between the soul and the body. This restriction of the role of PEH is already suggested by the way Wolff defines the doctrine. At the outset of the fourth chapter of section III of PS, he writes: Pre-established harmony is the system in which the relations (commercium) between the soul and the body are explained through the series of perceptions in the soul and the series of motions in the body, which are harmonious or accord (consentiunt) in virtue of the nature of the soul and the body.

The fact that PEH reappears in Wolff’s psychological investigations is interesting: because it is in this context where the key concept of the theory reappears: that of representative activity. This shows with particular clarity how far Wolff has gone from Leibniz’s teachings. To Leibniz’s mind, representative activity is an ontological concept. In Wolff’s philosophy, the concept of activity is relocated from ontology to cosmology, and that of representation from ontology to psychology. At the same time, however, it is clear that Wolff makes a minimal concession to Leibniz. For, again, he sticks to the strictures of Leibniz’s basic pattern of thought. Without representative power there is no doctrine of PEH. As the concept of representative power reappears in rational psychology, the door that was closed to PEH in Wolff’s cosmology is reopened in his inquiry into the human soul. Indeed, the notion of representation makes its most conspicuous appearance in Wolff’s account of the essence of the human soul: The essence of the soul consists in the force of representing the universe (vi representativa universi) [. . .]. In effect, this force is that which is first conceived of the soul, and that on which the other things found in it depend. Therefore the essence of the soul consists in this force. (PS § 66) 98

The soul is essentially a being capable of representation. Furthermore, it is a simple being (PS § 48). In fact, Wolff thinks that the simplicity of the soul is intrinsically tied to its representative capacity. As it stands in PS, his argument moves from the idea of representation to the idea of simplicity via the intermediate premise that the soul is immaterial. Briefly put, the idea is this: the soul is a being capable of representation (or perception), which is an act by which it presents objects to itself. But this perceptual capacity of the soul is such that the perceptions themselves can be the object of the soul’s own representations. The soul, then, is capable of apperception, an act by which it becomes conscious of its own perceptions by reflecting upon itself (PS § 23) and which is necessary for actual cognition to arise (PS § 44). Now, apperception requires immateriality (PS § 44). 99 Hence, the soul is immaterial or incorporeal (PS § 47). Therefore it is simple (PS § 48), devoid of parts, and unextended (PS § 49).

97

Wolff’s most complete account of the mind-body relation is found in PS, section III (“De commercio inter mentem & corpus”). See also VGG § 760–768. 98 See also VG § 753–755. 99 Wolff argues for this premise in PS § 44 and VGG § 738.

Simples, Representational Activity, and the Communication among Substances

121

So the soul is a simple substance capable of conscious representation. But the body, of course, is not: it is extended and lacks representative capacity (PS §§ 44, 51). Taken together, these claims shape the type of soul-body problem that Wolff must face: if the soul is a simple entity capable of representation and the body is not, how can they interact? 100 In addressing this question he has three prima facie possible answers at hand: real interaction, occasionalism, and PEH. 101 His answer is the latter. Yet Wolff’s mind-body PEH cannot be Leibniz’s mind-body PEH. In a letter of 3 July 1694, Leibniz says to Bossuet that with his PEH he has solved the great problem of the union of the soul and the body (A I, 10: 134 /NS 36). 102 As early modern philosophers see it, the great problem of the mind-body union has a quite defined form. Hume summarises it as follows: “[N]othing can be more inexplicable than the manner in which body should so operate upon mind as even to convey an image of itself to a substance, supposed of so different, and even contrary nature” (Enquiries, 153). Thus described, the problem finds its roots in Descartes’ dualistic ontology. All there is can be sharply divided into two, really distinct kinds of substance, the mental substance and the corporeal substance (AT VIII: 28). As Descartes characterised them in the “Sixth Meditation”, these two kinds of substances are really distinct not only because they are capable of separate existence, but also, and more strongly, because they have contrary attributes: the former is a non-extended, purely thinking substance, whereas the latter a purely extended, non-thinking one (AT VII: 78). When we look at the mind-body problem in this light and consider those passages in which Leibniz – as in his letter to Bossuet – claims that his PEH is a solution to this problem, the immediate temptation is to read PEH as preserving substance-dualism while avoiding the problem of ontological dislikeness entailed by it: the mind and the body do have a “contrary nature” – as Hume put it – and precisely because of this there can be no real interaction between them but only a pre-established agreement. While the mainstream of scholarly work on Leibniz usually recognises that his motivations for PEH are internal to his system, there still persists a “not uncommon view”, to use the words of one commentator, 103 which sees Leibniz’s solution to the mind-body problem in this vein. This is certainly true of those who have only a passing acquaintance with seventeenth century philosophy. 104 Yet echoes of it can also be found in the works of early modern 100

101

102 103 104

That soul and body do interact Wolff takes it as evident on empirical grounds. See PS § 540; VGG §§ 760, 527. On this point, see Blackwell 1961, 349. See PS § 553. This threefold division of causal systems was widely accepted in the period. See e. g. the entry “Rorarius” in Bayle’s Dictionnaire historique et critique; Baumgarten, Met. §§ 448 ff.; Kant, KrV A390. See also GP 4.484-5. This is Mendelson’s description (1995, 33). Roger Woolhouse outlines a “popular” story which will surely make sense to many. It runs as follows. According to Descartes, the mind and the body really interact. But, as Princess Elizabeth rightly observed, this is problematic on Cartesian grounds, for how could two radically different substances interact? Descartes was unable to provide a satisfactory solution to Elizabeth’s pointed worry, but, after Descartes, three main solutions emerged. The most radical among them was of course Spinoza’s, which consisted in denying that mind and body are two distinct kind of substance. Then Malebranche and other occasionalists dealt with the problem by proposing that God is the only true causal agent, finite substances being only “occasions” for his direct causal intervention. Finally, Leibniz introduced his pre-established harmony, which, as his contemporary Foucher didn’t fail to recognise, “is nothing more than Malebranche’s Occasionalism with all the adjustments made at once”. See Woolhouse 1986, 69.

122

Gastón Robert

scholars. For instance, in his New History of Philosophy, W. I. Matson introduces the preestablished harmony in the following way: The Cartesians had the problem, which they did not solve, of making comprehensible the interaction of mind and body. One hypothesis, Occasionalism, was to the effect that God had so arranged the physical and mental series that on the occasion of the occurrence of one event in one, for example a volition, an appropriately corresponding event such as a muscular motion would take place in the other. The series were compared to two clocks that being made and adjusted by the same clockmaker, seem to interact without doing so. Leibniz’s adopted this line of thought, multiplying from two harmonised substances to the infinite of monads. (Matson 1986, 331) 105

To be sure, some of the points in “this line of thought” capture aspects of Leibniz’s position. But the overall impression we get from it is misleading. For Leibniz did not elaborate his PEH within a dualist framework – or not, at any rate, primarily – as Matson’s account suggests. 106 As seen earlier, bodies and their motions are not substances for Leibniz, but well-founded phenomena. As he says to De Volder, “I show that a corporeal mass [. . .] is not a substance, but a phenomenon resulting from (resultans ex) simple substances, which alone have unity and absolute reality” (GP 2.275 /LDV 319). Exactly how bodies as phenomena are supposed to result from simple substances is no doubt a difficult question, the answer to which Leibniz may ultimately have been unable to elaborate to his entire satisfaction. 107 However, one thing that (in my opinion) is clear about it is that, with the fundamentality of perception and phenomenalism in place, its difficulty should not be located in anything related to the sort of dualistic problem stemming from a dualistic outlook. 108 The point of departure of Leibniz’s solution to “the great problem” of the relation of the soul and the body consists in eliminating the problem itself by offering an alternative to the metaphysical framework in which it is rooted. But while foreign to Leibniz, the dualistic view of PEH’s motivations is interesting for the purposes of comparing his position with that of Wolff. For such a view does fit quite well the Wolffian outlook. Wolff maintains the representative nature of the human soul. At the same time, he denies the representative, mind-like nature of the elements which make up material things. As a result, a dualistic picture of reality arises in his philosophy. As Latta long ago put it: “Ostensibly [Wolff’s] philosophy is a Monadology; really it is a kind of combination of Monadology with Atomism [. . .] Dualism is restored in the form of a distinction between spiritual and physical monads” (LM 166). As Wolff writes in PS: “The elements of material things are not minds [. . .] the human soul is mind (Elementa rerum materialium Spiritus non sunt [. . .] Anima humana spiritus est)” (§§ 644, 645). Wolff’s dualism is not exactly Descartes’ dualism. Instead of Descartes’ extended /nonthinking substance versus non-extended /thinking substance dualistic scheme, Wolff 105

See also Russell 1937, 137, Loeb 1981, 311–312, and next note. Loeb 1981, 311–312, argues for the admittedly more sensible view that PEH “was initially” formulated within a dualistic framework. There is no space here to discuss his view, in favour of which there are indeed some early texts. At any rate, such a framework is not a permanent one in Leibniz’s thinking, as Loeb himself acknowledges. 107 This is for instance Garber’s opinion, for whom the problem of “how to understand the relation between the bodies we experience and the monads that are, in some sense, their metaphysical foundation” was “never solved by Leibniz to his complete satisfaction” (2009, xxi): Leibniz’s work was in progress, but he died in medias res (2009, 388). 108 Not all Leibniz scholars agree on this however. See e. g. Loptson 1999.

106

Simples, Representational Activity, and the Communication among Substances

123

proposes a simple /simple sort of dualism: with Leibniz and against Descartes, Wolff claims, simple beings are the only real beings; with Descartes and against Leibniz, he adds, reality is divided into two irreducible sets of real beings; against Leibniz and against Descartes, he finally contends, one of these sets contains physical simples, the other spiritual simples. 109 Even granting this difference, however, the fact remains that Wolff’s position entails some form of dualism, whereas Leibniz’s philosophy undercuts dualism in any of its forms. 110 And as some form of dualism arises, a version of the mind-body problem in its traditional Modern form becomes unavoidable: there is an ontological gap or disproportion which is needed of explanation. It is this explanatory impasse that motivates Wolff’s soul-body PEH. Thus, at Wolff hands, PEH becomes a mere ad hoc solution aiming to bridge the gap between heterogeneous entities and thereby “solve” a pressing problem of rational psychology. We saw already that Wolff rejected PEH as a general model of cosmological unification. Now we can see that, although he advocated a certain version of the soul /body PEH, he also rejected Leibniz’s soul /body PEH. He kept just the name.

4. Conclusion In a sense, Leibniz’s thinking is profoundly systematic. Although it comes in a wide variety of forms and was never formulated as a complete system, there is a functional reciprocity running below the diverse formulations and scattered theses that are found in it. As in the monadic world, in Leibniz’s thinking everything conspires: it is an organic whole. When one modifies one member of such a whole, the whole itself suffers grievously. I have argued in this article that Wolff undermined one of the very foundations of Leibniz’s metaphysics: the representational nature of substances’ powers. This rendered Leibniz’s PEH impossible. In an attempt to solve an old and difficult problem of philosophical psychology, however, Wolff stuck to a certain version of the theory. But the detachment of PEH from its grounds turned it into nothing more than a deus ex machina. Wolff’s philosophy is usually regarded as a paradigm of systematic philosophy. 111 I think we have now good reason to believe that this is only superficially true. Granted, Wolff took pains to set forth his views in the form of a body of deductively related theses, in which the bulk of our knowledge is extracted from rigorous definitions and well-established axioms. On this score, he certainly fared better than Leibniz. But, unlike Leibniz’s, the resulting body is not an organic one. The pieces stand alongside one another without being really integrated. Wolff’s re-elaboration of Leibniz’s doctrines had important consequences for the reception of PEH in eighteenth-century Germany. I should like in closing to briefly outline

109

The combination of Cartesian and Leibnizian elements in Wolff’s philosophy is acknowledged by Tonelli 1967, 340: “Wolff drew his major philosophical tenets from Leibniz, but Wolff”s interpretation of Leibniz was partially Cartesian.” 110 As Corr 1983, 117, has argued, Wolff would not be ashamed of this. On the contrary, while he criticised Descartes for having given an inadequate account of body and matter, he applauded him “for sharply differentiating soul from body, thus undercutting materialism.” 111 See e. g. Kant’s remarks in KrV Bxxxvi. See also Corr 1975, 251–252.

124

Gastón Robert

this point. This will allow me to reinforce one of the most important and, in my opinion, unfortunate aspects of Wolff’s departure from Leibniz’s view. From about 1740 to 1760, German intellectual life was dominated by a series of controversies growing out of the encounter between Leibnizian metaphysics and Newtonian science. 112 The theory of PEH was a recurrent target of Newtonian critics. Briefly put, their objection was this. Every doctrine contrary to the truths of mechanics is false. The principle of inertia is a truth of mechanics. Yet PEH contradicts this principle. For, according to PEH, finite substances do not interact, all their states being only the result of their own intrinsically determining causal powers. But, according to the principle of inertia, bodies cannot change in their states unless they are interconnected in a system of externally impressed forces. Thus, in a universe of causally isolated entities, bodies can do no more than preserve the very same state in which they were created. Therefore, PEH is false. Positively, physical influx is true. 113 Does this objection undermine Leibniz’s PEH? I think it does not. For a conflict between theories to arise, they must be situated at the same explanatory level. But, as we have seen, Leibniz’s theory of PEH is not intended to explain the full range of empirically observable effects that configure our daily experience, as Newton’s laws do. Rather, it is offered as a response to a metaphysical question: how it is that the world, though comprising a plurality of non-interacting substances, can nevertheless be one unified world? In connection with this, it is interesting to note that in more than one passage Leibniz explicitly restricts the scope of PEH to the strictly metaphysical domain of substances, leaving open the possibility of interaction at the mechanical level of bodies. 114 This being the case, the theory of PEH should not compete with but rather complement the laws of mechanics by providing their metaphysical foundation. As in the case of the active unities on which it rests, PEH belongs to the sphere of metaphysics. 115 A perfectly coherent reasoning for an orthodox Leibnizian, this reply was not available on Wolffian grounds. Simple substances – and Newtonians were well aware of this – are supposed to be the sort of entity in which PEH is rooted. But Wolff’s simples are not metaphysical principles of explanation but physical points whose explanatory role reaches the actual order of spatiotemporal appearances. Critics of PEH often looked at the doctrine of monads through Wolffian lenses and hence took PEH to compete with the laws of mechanics. So interpreted, PEH had little chance to thrive. By the mid112

A detailed account of the Leibnizian-Newtonian confrontation can be found in Calinger 1968 and 1969. See also Broman 2012. 113 This line of objection is developed by Euler in his Réflexions sur l’espace et le temps (1748). Also the pre-critical Kant claims PEH to be incompatible with change: change requires external causation. See Ak 1: 410–412. For a more detailed assessment of Euler’s case against PEH, see Laywine 1993, 27–31. 114 For instance, he writes in New System § 17: “It is true that we can easily understand in connection with matter both the emission and the receiving of parts, by means of which we quite properly explain all the phenomena of physics mechanically. But a material mass is not a substance, and so it is clear that action as regard an actual substance can only be explained as I have described [sc. terms of PEH]” (GP 4.486 /NS 20). See also GP 2.251, GP 6.607. However, I register here that some scholars deny that there can be body-body interaction for Leibniz. See Brown 1992. Yet others believe that there is. See Miller 1988. 115 For a comprehensive development of this and related issues, see Antognazza 2016 – though she does not mention the PEH in particular. According to Antognazza, Leibniz’s distinction between the level of analysis of mathematical physics and that of metaphysics is his most distinctive contribution to the process from which modern science eventually emerged as an autonomous enterprise.

Simples, Representational Activity, and the Communication among Substances

125

eighteenth century, physical influx had already established itself as the standard view on causation even within broadly Leibnizian circles. 116 In light of the foregoing, I think it is not unreasonable to say that Wolff was partially responsible for PEH’s decline as a philosophically cogent and appealing explanation of the communication between finite substances. Kant, who always regarded the reconciliation between metaphysics and science as an urgent matter 117, understood this well when saying that, “mistreated by his would-be followers and interpreters” as he was, Leibniz might well have exclaimed: “God protect us only from our friends; our enemies, we can take care of for ourselves” (Ak 8: 247 /Allison /Heath (eds.) 333). 118

Bibliography Adams, R. M. 1994. Leibniz: Determinist, Theist, Idealist. Oxford: Oxford University Press. Allison, H. /Heath, P. (eds.). 2002. Immanuel Kant. Theoretical Philosophy after 1781. Cambridge: Cambridge University Press. Antognazza, M. R. 2016. Leibniz: A very short Introduction. Oxford: Oxford University Press. Antognazza, M. R. 2009. Leibniz. An Intellectual Biography. Cambridge: Cambridge University Press. Antognazza, M. R. 2007. Leibniz’s on the Trinity and the Incarnation. Reason and Revelation in the Seventeenth Century. New Haven: Yale University Press. Arana, J. 1988. I. Kant. Pensamientos sobre la verdadera estimación de las fuerzas vivas. Bern: Peter Lang. Bayle, P. 1607. Dictionnaire historique et critique. Des Maizeaux, P. (ed.). 1734. Amsterdam: Compagnie des Libraires Beck, L. W. 1969. Early German Philosophy. Kant and his predecessors. Cambridge, MA: The Belknap of Harvard University Press. Blackwell, R. 1961. Christian Wolff’s doctrine of the soul. Journal of the History of Ideas 22, 339–354. Bolton, M. 2004. Leibniz to Arnauld: Platonic and Aristotelian Themes on Matter and Corporeal Substance. In: Lodge, P. (ed.) Leibniz and his Correspondents. Cambridge: Cambridge University Press Broad, C. D. 1975. Leibniz. An Introduction. Cambridge: Cambridge University Press. Broman, Th. 2012. Metaphysics for an Enlightened Public: The controversy over monads in Germany, 1746–1748. Isis 103, 1–23. Brown, G. 1992. Is there a Pre-established Harmony of Aggregates in the Leibnizian Dynamics, or Do non-substantial Bodies interact? Journal of the History of Philosophy 30, 53–75. Brown, S. 1988. Leibniz’s Crossing from Occasional Causes to the Pre-established Harmony. In: Heinekamp, A. (ed.). Leibniz: Tradition und Aktualität. V. Internationaler Leibniz-Kongress. Hanover: Leibniz Gesellschaft. Burns, J. V. 1966. Dynamism in the Cosmology of Christian Wolff. A Study in Pre-critical Rationalism. New York: Exposition Press. Calinger, R. 1979. Kant and Newton’s Science. Isis 70, 348–362. 116

This is for instance the case of Martin Knutzen, a revisionist Leibnizian who was the first in Germany to accept Newtonian attraction and physical influx. See Friedman 1992, 1. On the decline of PEH and emergence of physical influx in eighteenth-century Germany, see Watkins 1998. 117 For this feature of Kant’s Weltanschauung, see Ak 1: 107, Ak 1: 473, Ak 4: 472. See Calinger 1979, Friedman 1992, Schönfeld 2000, and Robert 2011, 74–79. 118 I would like to thank Professor Maria Rosa Antognazza for helpful comments and advice throughout the writing of this article.

126

Gastón Robert

Calinger, R. 1969. The Newtonian-Wolffian Controversy: 1740–1759. Journal of the History of Ideas 30, 319–330. Calinger, R. 1968. The Newtonian-Wolffian Confrontation in the St. Petersburg Academy of Science. Cahiers d’ Histoire Mondiale 11, 417–435. Campo, M. 1980. Christiano Wolff e il razionalismo precritico. Hildesheim: Olms. Corr, Ch. 1974. Did Wolff Follow Leibniz? In: Funke, G. (ed.). Akten des 4. Internationalen KantKongresses Mainz. Berlin: Walter de Gruyter. Corr, Ch. 1975. Christian Wolff and Leibniz. Journal of the History of Ideas 36, 241–262. Corr, Ch. 1983. Cartesian Themes in Wolff’s German Metaphysics. In: Schneiders, W. (ed.). Christian Wolff (1679–1754): Interpretationen zu seiner Philosophie und deren Wirkung. Mit einer Bibliographie der Wolff-Literatur. Hamburg: Felix Meiner Verlag. Della Rocca, M. 2003. ‘If a Body Meets a Body’: Descartes on Body-body Causation. In: Gennaro, R. J. / Huenemann, C. (eds.). New Essays on the Rationalists. New York: Oxford University Press École, J. 1961. La Philosophia Prima sive Ontologia de Christian Wolff: Histoire, Doctrine et Methode. Giornale di Metafisica 16, 124. École, J. 1964. Cosmologie Wolffienne et dynamique Leibnizienne: Essai sur les rapports de Wolff avec Leibniz. Les études philosophiques (Nouvelle Série) 19, 3–9. Euler, L. 1746. Thought on the Elements of Bodies, in which the Theory of the Simple Things and Monads is Examined and the True Essence of Bodies is Discovered. Hirsch, E. (tr.). URL: 〈http: // www. 17centurymaths.com / contents / euler / e842 / E81tr.pdf〉. (Original: Euler, L. 1746. Gedancken von der Elementen der Körper, in welchen das Lehr-Gebäude von den einfachen Dingen und Monaden geprüfet, und das wahre Wesen der Körper endecket wird. Berlin.) Frankfurt, H. G. (ed.) 1972. Leibniz: a Collection of Critical Essays. New York: Anchor Books. Friedman, M. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press. Garber, D. /Nadler, S. (eds.) 2006: Oxford Studies in Early Modern Philosophy. Vol. III Oxford: Oxford University Press. Garber, D. 1985. Leibniz and the Foundations of Physics: the Middle Years. In: Okruhlik, K. /Brown, J. (eds.). The Natural Philosophy of Leibniz. Dordrecht: Reidel. Garber, D. 2009. Leibniz: Body, Substance, Monad. Oxford: Oxford University Press. Gilson, E. 1952. Being and Some Philosophers. Toronto: Pontifical Institute of Medieval Studies. Hartz, G. 1998. Why Corporeal Substances Keep Popping up in Leibniz’s later Philosophy. British Journal for the History of Philosophy 6, 193–208. Hegel, G. W. F. 1836. Lectures on the History of Philosophy. Vol. III: Medieval and Modern Philosophy. Haldane, E. S. /Simons, F. H (trs.) 1968. London: Routledge & Kegan Paul (Original: Hegel, G. W. F. 1836. Vorlesungen über die Geschichte der Philosophie. Berlin.) Hume, D. 1748. Enquiries Concerning Human Understanding, Nidditch, P. H. (ed.) 1975. Oxford: Oxford University Press. Jolley, N. 1986. Leibniz and Phenomenalism. Studia Leibnitiana 18, 39–51. Jolley, N. (ed.) 1995. The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press. Kant, I. 1781 /1787. Critique of Pure Reason. Guyer, P. /Wood, A. W. (trs. & eds.) 1998. Cambridge: Cambridge University Press. (Original: KrV) Kulstad, M. 1993. Causation and Pre-established Harmony in the Early Development of Leibniz’s Philosophy. In: Nadler, S. (ed.). Causation in Early Modern Philosophy. Pennsylvania: The Pennsylvania State University Press. Latta, R. (trs.). 1925. The Monadology and other Philosophical Writings. London: Oxford University Press. Laywine, A. 1993. Kant’s early Metaphysics and the Origin of Critical Philosophy. Atascadero: Ridgeview Publishing Company. Leibniz, G. W. 1686. “Discourse on Metaphysics”. In: Ariew, R. /Garber, D. (trs. and eds.). G. W. Leibniz. Philosophical Essays. Indianapolis & Cambridge: Hackett Publishing Company.

Simples, Representational Activity, and the Communication among Substances

127

Leibniz, G. W. 1695. “New System of the Nature of Substance and their Communication, and of the Union which Exists between the Soul and the Body”. In: Woolhouse, R. S. /Francks, R. (trs. and eds.). Leibniz’s ‘New System’ and Associated Contemporary Texts. Oxford: Oxford University Press. Levey, S. 2007. On Unity and Simple Substance in Leibniz. The Leibniz review 17, 61–106. Levey, S. 2008. Why Simples? A Reply to Donald Rutherford. The Leibniz review 18, 225–247. Lodge, P. 1998. Leibniz’s Commitment to the Pre-established Harmony in the late 1670s and early 1680s. Archiv für Geschichte der Philosophie 80, 292–320. Lodge, P. 2001. Leibniz’s Notion of an Aggregate. British Journal for the History of Philosophy 9, 467– 486. Lodge, P. 2002. Leibniz on Divisibility, Aggregates and Cartesian Bodies. Studia Leibnitiana 34, 59– 80. Lodge, P. (ed.) 2005. Leibniz and his Correspondents. Cambridge: Cambridge University Press. Loeb, L. E. 1981. From Descartes to Hume. Continental Metaphysics and the Development of Modern Philosophy. Ithaca, NY: Cornell University Press. Look, B. 2011. Leibniz’s Metaphysics. The Path to Monadology. In: Look, B. (ed.). The Continuum Companion to Leibniz. London: Continuum. Loptson, P. 1999. Was Leibniz an Idealist? Philosophy 74, 361–385. Mates, B. 1986. The Philosophy of Leibniz: Metaphysics and Language. Oxford: Oxford University Press. Matson, W. I. 1989. A new History of Philosophy. II: From Descartes to Searle. San Diego: Harcourt Brace Jovanovich. Mendelson, M. 1995. ‘Beyond the Revolutions of Matter’: Mind, body, and Pre-established Harmony in the earlier Leibniz. Studia Leibnitiana 27, 31–66. Mercer, C. /Sleigh Jr., R. C. 1995. Metaphysics: the early Period to the Discourse of Metaphysics. In: Jolley, N. (ed.). The Cambridge Companion to Leibniz: Cambridge University Press. Miller, R. 1988. Leibniz on the Interaction of Bodies. History of Philosophy Quarterly 5, 245–256. Phemister, P. 2005. Leibniz and the Natural World: Activity, Passivity, and Corporeal Substance in Leibniz’s Philosophy. Dordrecht: Springer. Puryear, S. 2010. Monadic Interaction. British Journal for the History of Philosophy 18, 763–796. Robert, G. 2011. Armonía Preestablecida versus Influjo Físico: un estudio acerca de la interacción de las sustancias naturales en la filosofía temprana de Kant (1746–1756). Pamplona: Publicaciones de la Universidad de Navarra. Rozemond, M. 1997. Leibniz on the Union of Body and Soul. Archiv für Geschichte der Philosophie 79, 150–178. Russell, B. 1937. A Critical Exposition of the Philosophy of Leibniz. London: George Allen and Unwin. Rutherford, D. 1994. Leibniz and the Problem of Monadic Aggregation. Archiv für Geschichte der Philosophie 76, 65–90. Rutherford, D. 1995. Leibniz and the Rational Order of Nature. Cambridge: Cambridge University Press. Rutherford, D. 2004. Idealism Declined: Leibniz and Christian Wolff. In: Lodge, P. (ed.). Leibniz and his Correspondents. Cambridge: Cambridge University Press. Rutherford, D. 2008. Unity, Reality, and Simple Substances: a Reply to Samuel Levey. The Leibniz review 18, 207–224. Rutherford, D. /Cover, J. A. (eds.) 2005. Leibniz: Nature and Freedom. Oxford: Oxford University Press. Schönfeld, M. 2000. The Philosophy of the Young Kant: the Pre-critical Project. Oxford: Oxford University Press. Sleigh Jr., R. C. 1990. Leibniz & Arnauld. A Commentary on their Correspondence. New Haven: Yale University Press. Soto Bruna, M. J. 1991. El significado de la monadología leibniciana en Christian Wolff. Anuario Filosófico 24, 349–366.

128

Gastón Robert

Suárez, F. 1597. Disputationes Metaphysicae, Rábade, S. /Caballero, S. /Puigcerver, A. (eds.) 1960. Madrid: Gredos. Thomas Aquinas, Sancti Thomae Aquinatis Summa Theologiae. Madrid: BAC, 1994. Tonelli, G. 1967. Christian Wolff. In: The Encyclopedia of Philosophy. Vol. 8. New York: Macmillan. Watkins, E. 1997. The Laws of Motion from Newton to Kant. Perspectives on Science 5, 311–348. Watkins, E. 1998. From Pre-established Harmony to Physical Influx: Leibniz’s reception in eighteenth century Germany. Perspectives on Science 6, 136–203. Watkins, E. 2005. Kant and the Metaphysics of Causality. Cambridge: Cambridge University Press. Watkins, E. 2006. On the Necessity and Nature of Simples: Leibniz, Wolff, Baumgarten, and the precritical Kant. In: Garber, D. /Nadler, S. (eds.). Oxford Studies in Early Modern Philosophy. Vol. III. Oxford: Oxford University Press. Watkins, E. (ed.). 2012. Immanuel Kant. Natural Science. Cambridge: Cambridge University Press, 2012. Wilson, C. 1989. Leibniz’s Metaphysics. A Comparative and Historical Study. Princeton: Princeton University Press. Wilson, C. 2005. Compossibility, Expression, Accommodation. In: Rutherford, D. /Cover, J. (eds.) 2005. Wilson, M. D. 1999. Confused vs Distinct perception in Leibniz: Consciousness, Representation, and God’s mind’. In: Wilson, M. D. Ideas and Mechanism. Princeton, NJ: Princeton University Press. Wilson, M. D. 1999. Ideas and Mechanism. Princeton, NJ: Princeton University Press. Woolhouse, R. 1986. Leibniz Reaction to Cartesian Interaction. Proceedings of the Aristotelian Society 86, 69–82. Wundt, M. 1964. Die deutsche Schulphilosophie im Zeitalter der Aufklärung. Hildesheim: Olms.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind Patrick R. Leland, Loyola University New Orleans

Abstract Philosophers after Leibniz used a technical idiom to classify and explain the nature of mental content. Substantive philosophical claims were formulated in terms of this vocabulary, including claims about the nature of mental representations, concepts, unconscious mental content, and consciousness. Despite its importance, the origin and development of this vocabulary is insufficiently well understood. More specifically, interpreters have failed to recognize the existence of two distinct and influential versions of the post-Leibnizian idiom. These competing formulations used the same technical terms and taxonomic relations but assigned different connotations to those terms and employed different criteria for their application. This paper explains the two most influential versions of the post-Leibnizian idiom.

1. Introduction Philosophers writing in the aftermath of Leibniz used a technical idiom to classify different kinds of mental content. The nature of this vocabulary is insufficiently well understood, and this obscures our understanding of important claims formulated in terms of it. The technical idiom consists of Latin and German cognates for the terms ‘obscure’, ‘clear’, ‘confused’, and ‘distinct’. Post-Leibnizian authors used these terms in ways that imply technical connotations, taxonomic relations, and criteria for classifying mental content in terms of these designations. Understanding this is essential for interpreting claims formulated in terms of the idiom. These include claims about the nature of mental representations, concepts, unconscious mental content, and consciousness. 1 The number of post-Leibnizians who employed this vocabulary is extensive. An incomplete list includes Christian Wolff, Ludwig Philipp Thümmig, Johann Christoph Gottsched, Friedrich Christian Baumeister, Alexander Baumgarten, Martin Knutzen, Hermann Samuel Reimarus, Georg Friedrich Meier, Johannes Lambert, and Immanuel Kant throughout his early and late writings. Understanding the technical idiom of post-Leibnizian philosophy is indispensable for interpreting eighteenth-century German philosophy of mind. While there is increasing recognition that philosophers after Leibniz used a technical idiom, the nature of this vocabulary is insufficiently well understood. More specifically, interpreters have failed to recognize the existence of two distinct and influential versions 1

I use the term ‘post-Leibnizian’ to denote philosophers who both worked during the half century following Leibniz’s death and were influenced by him, but who also departed from Leibniz in important respects.

130

Patrick R. Leland

of the post-Leibnizian idiom. These competing formulations used the same technical terms and taxonomic relations but assigned different connotations to those terms and employed different criteria for their application. Interpreting claims formulated in terms of the idiom requires knowing which version the author employs. 2 This paper corrects for the neglect of these issues by examining two distinct and influential formulations of the post-Leibnizian idiom. Properly speaking, this vocabulary originated in Leibniz’s 1684 essay on cognitions and ideas. 3 As I will explain, however, it was Christian Wolff (1679–1754) who offered the first influential statement of the idiom. At the outset of his first and most widely published philosophical work, Wolff appropriates and develops Leibniz’s 1684 account of ideas to explain the nature of concepts. Essential elements of this account were repeated in Wolff’s later German and Latin publications and appropriated by authors of numerous logic compendia, many of which were themselves widely published. As a result, it became common practice to use a specific set of technical terms, taxonomic relations, and associated individuating criteria to explain the nature of concepts. Twenty-six years following Wolff’s influential statement of the post-Leibnizian idiom there emerged a second, distinct, and ultimately influential version of that vocabulary. In his Metaphysica (1739), Alexander Baumgarten (1714–1762) used the idiom expansively to classify representations, in general. He redefined the connotations of the idiom’s most basic terms and revised the criteria traditionally used for individuating representations denoted by those terms. This distinct version of the idiom was then repeated and developed further in the writings of his most influential student, Georg Friedrich Meier (1718– 1777). The historical importance of this is reflected in the fact that Kant used the cognates for ‘obscure’ and ‘clear’ with the connotations Baumgarten and Meier had assigned to those terms. I discuss these developments in what follows. Section two explains Wolff’s influential statement of the post-Leibnizian idiom in the Deutsche Logik [VGK] (1713) and, briefly, its appropriation by subsequent authors in published writings over the next five decades. Section three then explains the emergence of Baumgarten’s distinct version of the idiom in the Metaphysica [Met.] (1739) and, briefly, its modification and dissemination in the writings of Georg Friedrich Meier. I conclude by discussing briefly two important features of Kant’s appropriation of the post-Leibnizian idiom.

2

A number of important studies treat related issues from the period in question. None of these however recognizes the existence of the two influential formulations of the post-Leibnizian idiom that are the focus of this paper. See, for example, Sommer 1892; Grau 1916; Wilson 1995; Oberhausen 2002; Mirbach 2009; Wunderlich 2005; La Rocca 2006; and Thiel 2011. 3 Meditationes de Cognitione, Veritate, et Ideis, GP IV, 422–426. Obviously, seventeenth century Cartesians used Latin and French cognates for the terms in question. The technical idiom with which I am concerned however consists of a specific set of connotations and taxonomic relations that originated in Leibniz’s 1684 essay.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

131

2. Wolff’s formulation of the post-Leibnizian idiom in the Deutsche Logik (VGK) The initial statement of what would become the post-Leibnizian idiom occurred in Leibniz’s 1684 essay, Meditationes de Cognitione, Veritate, et Ideis. Leibniz organized into a taxonomy the terms Cartesians had used for describing ideas, namely, the French and Latin cognates for ‘obscure’, ‘confused’, ‘clear’, and ‘distinct’. Importantly, Leibniz specified necessary and sufficient conditions for classifying concepts, or ‘notions’ (notiones), in terms of this taxonomy. The result is a set of technical terms, taxonomic relations, and individuating criteria that became the technical vocabulary for eighteenth century German philosophy of mind. 4 The necessary and sufficient conditions Leibniz specifies represent different kinds of conceptual abilities. Though Leibniz does not describe his account in this way, these abilities are best understood as different ways of using concepts in perception and reasoning. 5 According to Leibniz’s taxonomy, every concept is either obscure or clear. One’s concept is clear if and only if it enables one to recognize reliably the referent; otherwise, it is obscure. Every clear concept is either confused or distinct. One’s concept is distinct if and only if it contains distinguishing “marks” (notae), or constituent concepts, that denote properties of the referent, properties one can specify when recognizing it; otherwise, the concept is confused. Every distinct concept is either adequate or inadequate. One’s concept is adequate if and only if the distinguishing marks one specifies are themselves distinct in the sense defined above; otherwise, it is inadequate. Orthogonal to this last distinction, every distinct concept is either intuitive or symbolic. A distinct concept is intuitive if and only if one can grasp at once all the distinguishing marks it contains; otherwise, it is symbolic (GP 4.422-3). The immediate influence of Leibniz’s taxonomy was apparently negligible. The 1684 essay appeared in the newly established journal Acta Eruditorum, and the availability of articles in this journal steadily decreased over time. 6 Thirty years following its publication, Wolff complained the work had been ignored by philosophers working on the very issues Leibniz had discussed. 7 Other important writings in which Leibniz employs the taxonomy were not published until much later. These include Nouveaux essais and Discours de métaphysique, first published in 1765 and 1846, respectively (Tonelli 1974). 4

Properly speaking, Leibniz also uses his taxonomy to classify “cognitions” (cognitiones). Clarifying that particular application of the taxonomy, however, is not necessary for present purposes, and so I set it aside. 5 In general, philosophers in the period with which I am concerned do not typically distinguish between a concept and its referent. Ascribing to them such a distinction however is the most charitable way to interpret their respective accounts. Interpreters who ascribe to Leibniz such a distinction include Martin 1966, 100, and 1967, 206; Wilson 1999, 324; McRae 1976, 74; Brandom 1981, 454; Parkinson 1982, 13; Lodge /Puryear 2006, 181; Bolton 2011, 196; and Jorgensen 2015, 56. I will adopt this approach throughout the paper. 6 Wilson 1995, 442–443. Locke was among those who did the read the essay. In a letter to William Molyneux from April 10, 1697, Locke writes: “I must confess [. . .] that Mr. Leibnitz’s great name had raised in me an expectation which the sight of his paper did not answer, nor that discourse of his in the Acta Eruditorum, which he quotes, and I have since read [. . .] From whence I only draw this inference, That even great parts will not master any subject without great thinking, and even the largest minds have but narrow swallows”. Quoted in Antognazza 2009, 408. 7 VGK, Preface, [109]. Page numbers in brackets refer to the reprint edited by Arndt (Hildesheim: Olms, 1965). All translations from German texts are my own.

132

Patrick R. Leland

What appears to have been decisive for the influence of Leibniz’s taxonomy is its appropriation by Christian Wolff. In 1713, Wolff published his first major philosophical work, commonly known as the Deutsche Logik [VGK]. 8 In the preface, Wolff explicitly acknowledges his reliance on the 1684 essay. 9 This is particularly evident in the first chapter wherein Wolff appropriates the vocabulary, taxonomic relations, and individuating criteria Leibniz had proposed for the classification of concepts. Wolff was the most influential German philosopher of the first half of the eighteenth century and VGK his first and most widely published work. Appearing in fourteen editions by 1754, it was one of the most extensively published German logic texts of the period. VGK and its Latin successor PR (first edition 1728) served as models for over a dozen logic textbooks. 10 Some of these, in turn, were themselves either used or published extensively. 11 Wolff’s logic texts were also well regarded by critics and others outside the Wolffian tradition (Arndt 1965, 98–99). In the opening paragraphs, Wolff defines two terms in ways important for understanding his account. He first defines a “thought” (Gedancke) as a conscious mental state. He then defines a “concept” (Begriff) as that which is both a constituent ingredient of a thought and the representation of an object of conscious awareness. His paradigm is conscious, sense-based representations of things external to the mind. Everyone perceives that he senses many things. I assert however that we sense something when we are currently conscious of it [. . .] We call a thought that effect of the soul through which we are conscious [. . .] sensations are our thoughts of occurrent objects [. . .] I call a concept every representation of a thing in our thoughts (Einen Begriff nenne ich eine jede Vorstellung einer Sache in unserm Gedancken). 12

Collectively, these definitions imply a concept is a consciously possessed representation. As I will use that term, a representation is conscious if and only if it is cognitively available for serving as a direct ingredient in a conscious mental state, such that its referent can be an object of conscious awareness. The cognitive availability of a representation for consciousness includes the proximate availability exhibited by representations in ordinary acts of perception and attention, as well as the distal availability exhibited by a representation one recollects only with great effort. A representation that figures in 8

9

10

11

12

The full title reads Vernünfftige Gedancken: Von den Kräfften des menschlichen Verstandes und ihrem richten Gebrauche in Erkenntis der Wahrheit. This and the next paragraph are indebted to Arndt 1965, 7–8; 95–99. VGK, [108–109]. It is unclear which, if any, of Leibniz’s other writings on logic Wolff may have known. Wolff’s logic texts make no reference to any of Leibniz’s many writings on the Ars characteristica combinatoria, including the Dissertatio de Arte combinatoria. Arndt 1965, 63. As an anonymous referee rightly notes, an earlier appropriation of Leibniz’s taxonomy occurs in the Kurzer Unterricht that prefaces Anf. (hereafter KU-Anf). My account focuses on VGK for two reasons. First, it was the most widely published of all Wolff’s writings. Second, it defines “thought” (Gedancke) in a way that makes clear Wolff’s taxonomy of concepts is a taxonomy of consciously possessed representations. I return to this issue below. Arndt 1965, 98; Pozzo 2000, 97–98. Wolff published both a second logic text in Latin, PR (full title: Philosophia rationalis sive Logica, methodo scientifica pertractata, et ad usum scientiarum [1728]), as well as a Latin translation of the original Deutsche Logik, entitled Cogitationes rationales de viribus intellectus humani earumque usu legitimo in veritatis cognitiones (1730). French, Dutch, and Italian translations soon followed. Baumeister’s Institutiones philosophiae rationalis (1735) appeared in twenty editions during the eighteenth century. Kant famously used Meier’s Auszug aus der Vernunftlehre (1752) as the official textbook for his lectures on logic over the course of four decades. VGK, I.1-4. Wolff’s use of the term ‘Gedanke’ to denote a conscious mental state is reiterated seven years later in VGG, § 194; cited in Wunderlich 2005, 18.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

133

tacit awareness and whose referent is noticeable but not an object of attention occupies an intermediate position on this continuum. Each of these forms of representational, conscious awareness was a topic of interest for philosophers in the period under consideration. 13 Recognizing the definition of a concept Wolff employs in VGK allows us to avoid two related, interpretive problems that arise in the context of Leibniz’s 1684 essay. The first concerns the intended scope of the taxonomy and the second a positive, necessary condition for obscure concept possession. Leibniz’s philosophy of mind posits both unconscious and conscious representations. It is unclear however whether his 1684 taxonomy is intended as a classification of all representations or only those possessed consciously. 14 Since Wolff implicitly defines a concept as a conscious representation and appropriates the taxonomy specifically for the classification of concepts so defined, the intended scope of his taxonomy is the classification of conscious representations. This is true even if Wolff ascribes to the mind unconscious representations, as some interpreters claim (Wunderlich 2005, 20–21). 15 Related to the problem concerning the intended scope of Leibniz’s taxonomy is the absence of a positive, necessary condition for obscure concept possession. Leibniz defines an obscure concept negatively, as one which fails to enable recognition of the referent. Beyond this, however, it is unclear what obscure concept possession requires and what possessing a concept of this nature might allow one to do. Wolff follows Leibniz in defining an obscure concept negatively, as one which fails to enable recognition of the referent: a concept is “obscure” (dunckel), he writes, “if it does not suffice for recognizing again the thing (wenn er nicht zulangen will die Sache wieder zu erkennen)”. 16 Wolff’s general definition of a concept in the opening paragraphs is

13

With reference to Wolff’s later writings, Wunderlich writes that ‘Gedanke’ functioned as a terminus technicus for ‘conscious representation’. While approximately true, interpreting ‘Gedanke’ and ‘Begriff’ as denoting conscious mental states and conscious representations, respectively, allows for a more precise reading of VGK. See Wunderlich 2005, 19. It is worth noting that Wolff’s definition of ‘Gedanke’ is absent from his earlier appropriation of Leibniz’s taxonomy in KU-Anf. 14 Interpreters are divided on this point. For contrasting interpretations, see Grau 1916, 151–152; Wilson 1999, 325; Burkhardt 1980, 166; Lodge /Puryear 2006; and Wunderlich 2005, 12. To avoid confusion on this issue, it is important to recognize that Leibniz employs two distinct sets of vocabulary for describing ideas and perceptions, respectively, and that these distinct vocabularies both use cognates for the terms ‘confused’ and ‘distinct’. As a result, one should avoid conflating Leibniz’s account of confused and distinct perceptions with his account of confused and distinct ideas. For discussion of this subtle but crucial interpretive issue, see McRae, 126 ff.; Wilson 1999, 339–340; Brandom 1981, 149–150; Simmons 2001, 53, n. 41; and Jorgensen 2015, 56. Grau appears not to recognize the distinction between Leibniz’s distinct vocabularies and thus uses the 1684 taxonomy of concepts to explicate Leibniz’s account of perception. See Grau 1916, 151–152. 15 To avoid confusion, I do not deny that Wolff sometimes uses the cognates for ‘clear’ and ‘obscure’ more liberally to denote consciousness and lack of consciousness, respectively. See, for example, VGG §§ 201–203. I would note however that lack of consciousness does not entail the presence of unconscious representations. Inanimate objects lack consciousness, but we do not for that reason ascribe to them unconscious mental content. Whether and to what extent Wolff ascribes unconscious mental content to the mind is a topic in need of further study. For present purposes, my claim is that, in the context of Wolff’s 1713 taxonomy of concepts, those cognates refer exclusively to consciously possessed representations. Recognizing this is important for understanding one of Baumgarten’s most important modifications of the post-Leibnizian idiom. 16 VGK I.8. Contrary to what a literal reading might suggest, Wolff is not implying an obscure concept allows for recognition of the referent on one occasion but fails to allow for repeated recognition on other occasions.

134

Patrick R. Leland

important, in part, because it implies a positive, necessary condition for obscure concept possession. If a concept is, or can be, a direct representational ingredient in a conscious mental state, such that its referent is an object of conscious awareness, then this is a constraint on every kind of concept in the taxonomy, including those which are obscure. Recognizing this allows us to see a feature of Wolff’s taxonomy that is arguably distinct. In general, there is an explanatory need for representations of objects and properties one does not recognize. Object recognition is significant, in part, because one can discriminate an object in perception without being able to recognize it. Wolff’s general definition of a concept and his negative definition of an obscure concept suggest this is what an obscure concept allows one to do. One’s concept is obscure if and only if it enables one to discriminate consciously but not recognize the referent. Call the positive condition in this requirement the discriminating criterion. 17 Seven years later, Wolff appeals to something like the discriminating criterion to distinguish the referents of consciously possessed representations. In VGG (first edition 1720), he explains what it means to be conscious of something as follows: “We thus find that we are conscious of things when we can distinguish them from one another [. . .] If we do not notice the differences among the things that are present to us, then we are not conscious of those things as they strike our senses.” 18 Wolff’s account of clear concept possession is nearly identical to that which Leibniz advanced in the 1684 essay. This is true of both the definition and the examples Wolff provides. He defines a clear concept (klarer Begriff) as follows: If the concept we have suffices for recognizing again the things when they occur, as when we know it is the same thing we have seen in this or that place, by this or that name; then it is clear. On the other hand, it is obscure when it will not suffice for recognizing again the thing. We thus have a clear concept of colors, for we can recognize them and distinguish them from one another when they occur. But suppose we see a strange plant in a garden and cannot remember with certainty whether it is the same one we have seen in another place or heard referenced by a particular name; then we must say that we have only an obscure concept of it. (VGK I.8)

As the example of the plant illustrates, the referent of an obscure concept is something one can discriminate consciously but not recognize. Adequacy for the latter is what distinguishes clear concept possession. One’s concept is clear if and only if it enables one to recognize reliably the referent. Call this the recognition criterion. 19

Wolff is simply using a locution implied by Leibniz’s original example of an obscure concept, namely, that of an object one recalls but which one is unable to recognize again: “Obscura est notio, quae non sufficit ad rem repraesentatam agnoscendam, veluti si utcunque meminerim alicujus floris aut animalis olim visi, non tamen quantum satis est, ut oblatum recognoscere et ab aliquo vicino discernere possim” (GP 4.422). 17 If the intended scope of Leibniz’s 1684 taxonomy is restricted to consciously possessed ideas, then this is a point of continuity between that essay and VGK. Some interpreters however think the obscure concepts in Leibniz’s taxonomy are unconscious ideas. If that reading is correct, then this is an important point of contrast between the taxonomies of Leibniz and Wolff. Proponents of the second reading of Leibniz include Wunderlich 2005, 12, 20; and Heidemann 2012, 40. 18 VGG, § 729. Quoted in Wunderlich 2005, 20. See also Dyck 2014, 106–107. 19 There is an important ambiguity in the passage quoted above; one, moreover, which first appears in Leibniz’s account of the distinction between obscure and clear concepts. This concerns the fact that Leibniz’s and Wolff’s examples of a strange plant one does not recognize imply one is in fact able to recognize the object sufficiently well to classify it as a plant, even if one is unable to recognize it in the more determinate sense required for

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

135

As with Leibniz, most of the concepts classified in Wolff’s taxonomy are complex aggregates of other concepts. In their functional role as constituent elements of an aggregate, these latter concepts are “marks” (Merckmahle) that denote properties of the referent. One of the most distinctive features of Wolff’s account is his appropriation of this idea for the purpose of positing degrees of conceptual obscurity. This corrects for what is arguably an explanatory limitation of Leibniz’s original account. Leibniz had defined a clear concept as one that enables reliable recognition of the referent. He then explained the distinction between confused and distinct concepts in terms of the ability to specify distinguishing marks (notas) denoting properties of the referent one recognizes. Leibniz’s paradigm for confused concepts are those we possess for sensible qualities, such as colors, tastes, and smells. He writes that we can recognize these qualities but are unable to specify any distinguishing marks on the basis of which we do so. As a consequence, we experience sensible qualities as being phenomenally simple, “even though it is certain that our concepts of these qualities are composites and can be resolved” (GP 4.422-4.423). In contrast to this, Leibniz asserts one’s concept is distinct if and only if one can both recognize the referent and specify one or more of that concept’s distinguishing marks. Leibniz’s paradigm for distinct concepts are those we possess for objects we apprehend as cognitively complex. The cognitive complexity of the object consists in the fact that one both recognizes the referent and grasps it has having one or more properties corresponding to the concept’s distinguishing marks. In Leibniz’s example, the assayer’s concept of gold is distinct because she can identify distinguishing marks, such as color, heaviness, and solubility in aqua fortis. Her ability to recognize these properties informs her ability for recognizing reliably the referent of her concept. These distinguishing marks contribute to the cognitively distinct character of the assayer’s perception of gold when she sees a gold colored object dissolve in nitric acid. She perceives the color and the dissolution as essential properties of the object. Absent from Leibniz’s account is an explanation of cases involving failed recognition of phenomenally complex objects some of whose properties one recognizes. This is so despite the fact that Leibniz’s examples of obscure concepts include those one possesses for plants and animals one has seen previously but is unable to recognize later. 20 These are phenomenally complex objects one can classify in general terms as, say, a plant or animal but not recognize in the more specific sense Leibniz requires for possessing a clear concept for that specific kind of organism. What the 1684 account requires for these cases are obscure concepts for phenomenally complex objects one fails to recognize in the

recognizing it as the plant one saw earlier. One problem with this approach is that it appears to make the distinction between obscure and clear concepts context-dependent; since what is at issue is not whether one can recognize the object, at all, but rather whether one can recognize the object relative to that context. One explanation for this ambiguity is that Leibniz and Wolff do not have a sufficiently clear notion of the referent of a concept. As a consequence, their examples of clear concept possession approximate reliable recognition of a referent by emphasizing re-identification of an object perceived previously. 20 GP 4.422: “A notion which is not sufficient for recognizing the thing represented is obscure, as, for example, if whenever I remember some flower or animal I once saw, I cannot do so sufficiently well for me to recognize that flower or animal when presented and to distinguish it from other nearby flowers or animals”. The fact that Leibniz illustrates the nature of obscure concepts with examples of objects one is unable to re-identify is arguably symptomatic of the problem explained above in n. 19.

136

Patrick R. Leland

relevant sense despite the fact that one recognizes some of their marks and can classify them in more general terms. One way to develop Leibniz’s account, then, is to posit obscure concepts with recognizable marks to explain failed recognition of phenomenally complex objects. 21 Wolff pursues this line of thought. Immediately after explaining the distinction between obscure and clear concepts, he writes: This obscurity however admits of different degrees. For sometimes in the presence of an object we think of many distinguishing marks (Merckmahlen) that can also be found in another; and sometimes we think of only a few. For example, in the case of the strange plant, we might think that the other one for which we have an obscure concept has leaves which are just as long, spiked, and jagged as the plant before us; it does not however occur to us whether, with regard to other features, the leaves of the former look like the leaves of the plant before our eyes. Now depending on whether we can think of many or only a few distinguishing marks; accordingly, our concept is either somewhat or very obscure. (VGK I.9)

Wolff recognizes that some of the objects we fail to identify are phenomenally complex, and that failures of object recognition vary in degree. Sometimes the referent of an obscure concept exhibits many properties one recognizes and other times only a few. Wolff appropriates Leibniz’s notion of distinguishing marks to explain these cases. One’s concept is obscure if and only if it enables one to discriminate but not recognize the referent. If the referent one fails to recognize is phenomenally complex, then it exhibits discriminable properties. One’s concept is “somewhat” obscure if one recognizes some of these properties and “very” obscure if one recognizes only a few of them. It is important to recognize two features of this account. First, cases involving “somewhat” and “very” obscure concepts, respectively, require an interaction of conceptual obscurity and clarity that is possible only if obscure concepts are conscious representations whose referents are discriminable in conscious awareness. The interaction of conceptual obscurity and clarity is a function of the fact that one fails to recognize the object in the relevant sense as the specific kind it is despite one’s ability to recognize some of its properties and classify it in more general terms. One could not do the latter however if one failed to discriminate the object in conscious perception at all. Wolff’s account of the degrees of conceptual obscurity is thus further evidence for the interpretive claim that obscure concepts are consciously possessed representations individuated in accordance with the discriminating criterion. The second feature to recognize is that, since he endorses the recognition criterion for clear concept possession, Wolff’s account implies whatever characteristics one recognizes are properties for which one possesses clear concepts. Wolff however does not acknowledge this implication. His account emphasizes the question of whether one can recognize the object to which one attends in thought or perception. Properties one recognizes but which are inconclusive for object recognition in this sense occupy a subordinate place in his account. This may explain why he posits degrees of conceptual obscurity instead of degrees of conceptual clarity. As Leibniz had done, Wolff asserts every clear concept is either confused or distinct depending on one’s ability to specify some of its constituent marks. One possesses a

21

Lodge /Puryear 2006, 195, suggest Leibniz would probably allow for degrees of obscurity.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

137

confused concept (verwirreter Begriff) if and only if one can recognize the referent but is unable to specify any of its distinguishing properties. Inability to specify these properties corresponds to an inability to specify the concept’s constituent marks. Wolff’s paradigm for confused concepts are those we possess for colors: “For we can certainly recognize the color red when it appears but are unable to say on what basis we do so” (VGK I.12). In contrast to this, one possesses a distinct concept (deutlicher Begriff) if and only if one can both recognize its referent and specify some of its distinguishing properties. The ability to specify distinguishing properties corresponds to an ability to specify some of that concept’s constituent marks: “One has a clear and distinct concept of a mechanical clock if he can tell us it is a machine that shows the hours through the rotation of the clock hand or indicates the hours through a strike of the clock’s bell” (VGK I.12). It is important to recognize what this account implies about the relation between a distinct concept and its constituent marks, and, with that, the requirements for distinct concept possession. For both Leibniz and Wolff, every mark stands in a material inferential relation to the distinct concept of which it is a constituent. 22 The material inferential character of this relation is exhibited in two ways. First, recognizing the property denoted by a mark is a reason for identifying the object which instantiates that property as the referent of a distinct concept which includes that mark. Second and conversely, recognizing the referent of a distinct concept allows one to infer that the object one recognizes possesses properties corresponding to marks of that concept. To develop Leibniz’s original example, seeing a gold-colored, metallic substance dissolve in aqua fortis is a reason for the assayer to classify that metal as gold. Similarly, knowing on a different occasion that the metal she sees is gold allows the assayer to infer its solubility in aqua fortis. The material inferential character of the relation between a concept and its marks is implicit in both of Wolff’s examples. One’s concept of red is confused because, although one can recognize reliably instances of that color, one is unable to say “on what basis” one does so. Similarly, one possesses a distinct concept of a mechanical clock if and only if one can specify distinguishing marks that explain the meaning of that concept. This account implies a feature of distinct concept possession that distinguishes it in an important respect from the requirements for possessing obscure and clear concepts, respectively. Distinct concept possession requires grasping a material inferential relation between that concept and one of its marks. This, in turn, requires the exercise of a discursive ability that is not obviously necessary for either obscure or confused concept possession, as Wolff describes them. Recognizing this allows us to formulate more precisely the requirements for distinct concept possession implicit in Wolff’s account. One possesses a distinct concept if and only if one recognizes reliably the referent, recognizes one of its properties, and grasps a material inferential relation between them. The first and second conditions on distinct concept possession are instances of the recognition criterion. Call the distinguishing third condition the material inferential criterion. 23 22

The claim that material inferential relations are essential to the meanings of concepts, in general, is developed by Sellars 1953 and Brandom 1994. 23 An anonymous referee raises two concerns. First, the referee suggests my account of the material inferential criterion implies the ability to recognize an inferential relation between a concept and its mark presupposes that one possesses that concept as a distinct concept. In response, I would emphasize that the material inferential

138

Patrick R. Leland

The account of concepts set forth in VGK was reiterated in Wolff’s later writings and appropriated by post-Leibnizian authors well into the second half of the century. Among these authors, it became common practice to classify concepts in terms of the technical idiom, taxonomic relations, and individuating criteria Wolff had used in his 1713 logic text. This is evident in a number of influential works, the initial publications of which span four decades. These include Ludwig Philipp Thümmig, Institutiones Philosophiae Wolfianae (1725); Johann Christoph Gottsched, Erste Gründe der gesammten Weltweisheit (1733); Friedrich Christian Baumeister, Philosophia Definitiva (1738); Hermann Samuel Reimarus, Vernunftlehre (1756); and Johann Heinrich Lambert, Neues Organon (1764). All these works were published in multiple editions, some as late as 1790. In its most general form, the post-Leibnizian idiom consists of Latin and German cognates for the terms ‘obscure’, ‘clear’, ‘confused’, and ‘distinct’, and the taxonomic relations among these terms Leibniz had originally proposed. Wolff’s particular formulation of the idiom exhibits three distinguishing features, all of which were appropriated by the authors mentioned above. First, each of these authors used the idiom to classify concepts, in particular, and followed Wolff in defining a concept as a consciously possessed representation in the sense explained earlier. 24 Second, each of these authors used the recognition criterion as a necessary and sufficient condition for clear concept possession. 25 Third and finally, each of these authors offered accounts of distinct concept possession which imply the relations between a distinct concept and its marks are material inferential relations and that grasping one or more of these is required for possessing a distinct concept. 26 Recognizing these features in the writings of post-Leibnizian authors is important for understanding the influence of Wolff’s formulation of the idiom. It is also essential for disambiguating occurrences of the idiom’s central terms in writings published during the 1740’s and later. The reason for this is that a second formulation of the idiom emerged during this period. This formulation uses the same terms and taxonomic relations but eschews all three of the aforementioned features central to Wolff’s account. As a consequence, fundamental terms in the post-Leibnizian idiom came to acquire significantly criterion is part of a set of necessary and sufficient conditions on distinct concept possession. Possessing a distinct concept entails one can grasp an inferential relation between that concept and one of its marks. Conversely, the ability to grasp an inferential relation between a concept and one of its marks entails one possesses that concept distinctly. Possessing a distinct concept consists in the ability to reason about that concept and one of its marks. The second concern raised by the referee is that the discriminating, recognition, and material inferential criteria are discontinuous, and that this is inconsistent with Wolff’s presentation of the taxonomy as consisting of continuous gradations among concepts. In response, I would note that the criteria are not wholly discontinuous insofar as the first is presupposed by the second, and the second by the third. Insofar as there are discontinuities in the abilities required for obscure, clear, and distinct concept possession, however, these ultimately have their origin in Leibniz’s 1684 essay, as opposed to Wolff’s appropriation of that account, and regardless of Wolff’s characterization. 24 Thümmig 1725, § 4; Gottsched 1733, § 24; Baumeister 1738, §§ 50–51; Reimarus 1756, § 48; and Lambert 1764, I, §§ 1–2, 6–7. The definition of a concept as a consciously possessed representation in the sense explained earlier is sometimes assumed and other times made explicit. 25 Thümmig 1725, § 5; Gottsched 1733, § 25; Baumeister 1738, §§ 73–74; Reimarus 1756, § 82; and Lambert 1764, I, §§ 8–9. 26 Thümmig 1725, § 7; Gottsched 1733, § 27; Baumeister 1738, §§ 76; Reimarus 1756, § 82–83, 85–86; and Lambert 1764, I, §§ 9–11. As with Leibniz and Wolff, the material inferential character of the relation between a distinct concept and its marks is implicit in these authors’ accounts of distinct concept possession.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

139

different connotations. Knowing which version of the idiom an author employs is crucial for interpreting that author’s use of those terms.

3. Baumgarten’s transformation of the post-Leibnizian idiom One of the most important developments in the dissemination of the post-Leibnizian idiom is its transformation in the writings of Alexander Baumgarten (1714–1762). Somewhat ironically, this transformation is motivated by Baumgarten’s commitment to a broadly Leibnizian metaphysics. In contrast to Wolff, Baumgarten followed Leibniz in endorsing a monadic ontology and characterizing monads as vires repraesentativas. 27 Baumgarten’s transformation of the post-Leibnizian idiom is largely a consequence of his using the idiom to classify the representations of monads. The result is a change in the scope of the taxonomy’s intended application, the connotations of its most basic terms, and the criteria employed for individuating representations denoted by those terms. Baumgarten develops his account of the nature of representations within the broader context of his monadic ontology. In Met., he writes that every substance in the world is either a monad or an aggregation thereof (§§ 230–234); that monads are constitutive of the world, in general (§§ 394–395); and that the essence of a monad consists in the activity of representing the universe (§ 400). 28 It is within the context of these ontological commitments that Baumgarten first appropriates the post-Leibnizian idiom. Every monad is said to represent the world either obscurely or clearly, and those that represent clearly do so either confusedly or distinctly (§§ 401–402). Baumgarten’s use of the post-Leibnizian idiom to classify monadic representations entails a significant departure from Wolff in two, related respects. The first of these concerns a difference in the kind of mental content classified and the second a difference in the taxonomy’s intended scope. To understand the first point, it is important to recall that Leibniz had characterized representations using two, distinct but overlapping sets of vocabulary. When discussing the nature of ideas, Leibniz used the cognates for ‘obscure’, ‘clear’, ‘confused’ and ‘distinct’ to classify concepts (notiones) in terms of the criteria and taxonomic relations set forth in the 1684 essay. When discussing the nature of perceptions, however, Leibniz used the cognates for ‘confused’ and ‘distinct’ to denote unconscious and conscious perceptions, respectively. 29 Baumgarten departs from Leibniz by using the first vocabulary for the

27

On Baumgarten’s relation to Leibniz, see Mirbach 2009. The longstanding notion of a “Leibniz-Wolff philosophy” is misleading in that it both exaggerates points of agreement and ignores important disagreements between Leibniz and Wolff. For discussion of this, see Rutherford 2004; Watkins 2005, chapter 1; and Jauernig 2011, 291– 293. The notion of a “Leibniz-Wolff philosophy” was criticized as early as 1747 in an anonymously published essay by G. F. Meier, entitled Erläuterungen des Satzes des zureichenden und determinierenden Grundes. See Schenk 1997, 800. 28 All citations of the Metaphysica are by paragraph number. References are to the fourth edition, published in 1757, which Kant used. Translations are original, though I have benefited from the German translation in Gawlick /Kreimendahl 2011 and the English translation in Fugate /Hymers 2013. 29 See, for example, Leibniz, Monadologie §§ 19, 24 (GP 6.610-11); and Principes de la Nature et de la Grâce § 4 (GP 6.600). For discussion, see Wilson 1999, 324–325, 339. It is important to note that, unlike many of Leibniz’s writings, both the texts just cited were published and available to Baumgarten. Monadologie appeared in

140

Patrick R. Leland

purpose of the second. Whereas Leibniz and Wolff had employed the post-Leibnizian idiom narrowly to classify concepts, Baumgarten uses that vocabulary more expansively to classify every kind of representation, including the perceptual states of monads. This more expansive application of the taxonomy entails important changes in the kinds of representations it is used to classify. One of these concerns the conscious availability of those representations. In VGK, Wolff had appropriated Leibniz’s taxonomy exclusively for the classification of concepts, defined as conscious representations. Baumgarten departs from this by using the taxonomy to classify both unconscious and conscious representations. As one might expect from his commitment to a monadic, representational ontology, Baumgarten follows Leibniz in positing monads that represent in the absence of conscious awareness. Whereas Leibniz had characterized the unconscious representations of bare monads as “confused”, however, Baumgarten instead calls them “obscure”. Monads that represent their worlds are either at least partially conscious of their perceptions when they represent the world to themselves, or not. And hence the monads of this universe represent this world either only obscurely, or at least partially clearly. The former are BARE MONADS (slumbering monads) (Met. § 401; original capitalization).

Baumgarten ascribes unconscious representations to bare monads and uses the adverb ‘obscure’ to denote the activity of representing unconsciously (obscure repraesentant). Since bare monads represent in complete absence of conscious awareness, the unconscious character of their representations is absolute. This contrasts with representations that are unconscious in a weaker sense, such as those one has forgotten or those instrumental in tacit awareness. Baumgarten’s use of the post-Leibnizian idiom to classify the unconscious representations of monads prefigures his account of human representations. In general, Baumgarten offers a unified account that treats the representations of human beings as a species of monadic representations. A monad capable of representing the world both clearly and distinctly is a “spirit”, or a “person” (Met. §§ 402–405), and the “soul” a person’s capacity for representing consciously (§ 504). Baumgarten ascribes to the soul “obscure”, “clear”, and “distinct” representations. Obscure representations are unconscious representations that constitute the “foundation of the soul” (fundus animae) (§§ 510–511, 514). Clear representations are conscious “thoughts” (cogitationes) that are either confused or distinct, depending on one’s ability to individuate their constituent marks (§§ 506, 510).

French (1714), German (1720), and Latin (1721), respectively. Principes de la Nature et de la Grâce appeared in French (1718) and Latin (1737). See Tonelli 1974. The importance of distinguishing between Leibniz’s distinct vocabularies for concepts and perceptions, respectively, has been emphasized by M. Wilson 1999, 324–325, 339–340; Brandom 1981, 149–150; Simmons 2001, 53, n. 41–42; and Jorgensen 2015, 56. Leibniz’s account of the relation between concepts and perceptions is a more complicated matter. If the distinction between confused and distinct perceptions parallels that between unconscious and conscious representations; and if the concepts classified by the 1684 taxonomy are possessed consciously; then one might reasonably interpret the latter as distinct abilities for discriminating, recognizing, and reasoning about conscious mental content. The issue is complicated however for at least two reasons. First, Leibniz sometimes claims sensibility and thought – the provenance of perceptions and concepts, respectively – differ only in degree and not in kind. Second, Leibniz arguably allows for unconscious acts of conceiving. For discussion of these issues, see McRae 1976; Parkinson 1982; Simmons 2001; and Lodge /Puryear 2006.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

141

Baumgarten’s commitment to a monadic ontology is one, though not the only, reason for his ascription of unconscious representations to the human mind. A second is his commitment to a Leibnizian principle of continuity. 30 According to this principle, every change in the world is gradual in the sense that it is a continuous transition from one state to another in accordance with a rule (Met. §§ 383–384). There is no “leap” (saltus) in the natural world (§§ 386–387). What is true of natural events, in general, is true of mental content, in particular. Consciousness does not occur abruptly but rather emerges gradually from unconscious mental states. Obscure representations constitute the “foundation of the soul”, in part, because it is in the midst of unconscious representations that the soul can gradually come to represent consciously in accordance with the principle of continuity. Consciousness emerges in the gradual transition from complex representations whose constituent marks are wholly obscure, or unconscious, to complex representations, some of whose marks are possessed consciously (§ 528). As Baumgarten writes later in Aesthetica (1750), “Nature makes no leaps from obscurity to distinctness” (§ 7) (Fugate /Hymers 2013, 23). Baumgarten’s use of the post-Leibnizian idiom to classify unconscious representations entails a change in the connotations of the idiom’s most basic terms. The most obvious example of this is Baumgarten’s use of ‘obscure’ to denote unconscious representations. A less obvious example is his use of the term ‘clear’. Properly speaking, Wolff and Baumgarten both use that term to denote conscious representations. They differ however in the class of conscious representations they use that term to denote. This becomes apparent once we recognize Baumgarten’s criterion for possessing a clear representation. Wolff had used the discriminating criterion as a necessary and sufficient condition for obscure concept possession. Since obscure concepts are the most primitive concepts in his taxonomy and a concept, in general, a conscious representation, the discriminating criterion functions simultaneously as a criterion for the most primitive kind of conscious representation. Baumgarten follows this in one important respect: he uses the discriminating criterion as a necessary and sufficient condition for possessing the most primitive, conscious representations in his taxonomy. In contrast to Wolff, however, these representations are the ones Baumgarten classifies as being clear but confused. My soul cognizes (cognoscit) some things obscurely and some confusedly. Now, all else being equal, one who perceives a thing and perceives that it is different from other things perceives more than one who perceives but does not distinguish. (Met. § 520) That perception is minimally clear whose marks (notae) are only sufficient for distinguishing it with great difficulty from that which is maximally different. Thus, the easier I can distinguish a perception from an increasing number of more similar perceptions, the clearer that perception is to me; until it is that which is most clear to me, and which I can distinguish easily from all others, including those that are most similar to it. (Met. § 528) 31

30

For discussion of the important role which this principle plays in Leibniz’s philosophy of mind, see Simmons 2001, 45; and Jorgensen 2009 and 2015. 31 It is reasonable to think the capacity for distinguishing the referent of a concept is more basic than the capacity for perceiving it since one might be able to do the former in the absence of the latter. This is especially true if perception is understood in terms of the traditional sense modalities. Baumgarten however has an expansive concept of perception. Similar to Leibniz, Baumgarten treats the activity of perceiving, or representing, as the fundamental activity of a simple substance. Within the scope of this activity discrimination is then construed

142

Patrick R. Leland

For Baumgarten, the act of distinguishing the referent of one representation from that of another is an act of conscious, phenomenal discrimination. 32 One who “perceives but does not distinguish” is one who perceives “obscurely”, or unconsciously. That is, one is unable to discriminate phenomenally any property whatsoever by means of which one might individuate consciously the referent. One who “perceives a thing and perceives that it is different from other things” is one who perceives clearly, or consciously. That is, one can distinguish the referent from other objects or properties in conscious awareness. In either case, what is at issue is one’s ability to distinguish consciously an object or property that is the referent of a representation. This is an explanatorily more basic ability than that of recognizing reliably the referent. In these and related passages, Baumgarten appeals exclusively to the discriminating criterion to individuate clear representations and relative degrees of representational clarity. There is in the Metaphysica simply no appeal to anything like the recognition criterion used by Leibniz and Wolff. 33 Baumgarten’s exclusive use of the discriminating criterion to distinguish between obscure and clear representations entails every representation is clear whose referent is consciously discriminable. In his formulation of the idiom, ‘clear’ denotes every conscious representation in this sense and not merely those whose referents one recognizes reliably. Corresponding to this, ‘obscure’ denotes every representation whose referent is not consciously discriminable. These are the principal connotations Baumgarten assigns to the terms ‘obscure’ and ‘clear’. I designate these as principal connotations because Baumgarten occasionally uses ‘obscure’ in a way that is inconsistent with this practice. This is true also of those who appropriated his formulation of the idiom. Recognizing this is essential for disambiguating occurrences of this term in the post-Leibnizian literature. The inconsistency originates in Baumgarten’s claim that representational clarity and obscurity admit of degrees. This is another important respect in which he appropriates and modifies Wolff’s account. The second quotation immediately above reads in full as follows:

narrowly on the model of consciously distinguishing an object or property. I appreciate the editor’s encouraging me to clarify this point. 32 As with Leibniz and Wolff, the most charitable reading of Baumgarten ascribes to him an implicit distinction between a representation and its referent. In the absence of this, passages such as those just quoted require ascribing to Baumgarten distinct sets of criteria for the individuation of “things” (Met. § 520) and the individuation of “perceptions” (Met. § 528), respectively. An implicit distinction between a concept and its referent is discernible in Baumgarten’s account of the distinction between clear and obscure concepts in Acroasis logica (1761): “A concept is clear whose notes [. . .] are sufficient for consciousness of the object. A concept that is not clear is obscure (Conceptus, cuius notae [. . .] obiecto illius apperciendo sufficient, clarus est. Conceptus non clarus, obscurus est).” Baumgarten 1761, §§ 18–19. 33 To the extent that a related cognate is used at all, it occurs later in the course of Baumgarten’s brief discussion of memory (Met. §§ 579–588). In those passages, ‘recognition’ (recognoscere) is used synonymously with ‘recollection’ (recordor), where the topic of concern is the capacity for recognizing a representation that the mind had produced previously. In contrast to Leibniz, Wolff, and those who appropriated Wolff’s formulation of the idiom, Baumgarten’s Metaphysica makes no use of the cognates for ‘recognition’ (agnoscere, erkennen) traditionally used to explain clear concept possession. Within Baumgarten’s oeuvre, this is a distinguishing feature of the Metaphysica and one that contrasts with Baumgarten’s earlier use of ‘recognoscendum’ to explain the difference between obscure and clear representations. See Baumgarten 1735, § 13.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

143

That perception is minimally clear whose marks (notae) are only sufficient for distinguishing it with great difficulty from that which is maximally different. Thus, the more easily I can distinguish a perception from an increasing number of more similar perceptions, the clearer that perception is to me; until it is that which is most clear to me, and which I can distinguish easily from all others, including those that are most similar to it. That representation is minimally obscure whose marks are simply not sufficient for distinguishing it easily from another that is most similar to it. Thus, the more that a perception cannot be distinguished even with the greatest effort from an increasing number of more different perceptions, the more obscure it is; until it is that perception that is most obscure to me, and which I cannot distinguish from any other, including those that are most different, with all of my effort. (Met. § 528) 34

The degrees of representational obscurity and clarity form a continuum on which every representation can be located. These representations are paradigmatically complex aggregates of constituent marks that are themselves either obscure or clear. A representation’s position on the continuum depends on the number of obscure and clear constituent marks it contains. If one can distinguish the referent of a representation, one does so on the basis of one or more of its clear marks. Baumgarten’s account of the degrees of representational obscurity and clarity is consistent with his formulation of the post-Leibnizian idiom in two important respects. First, the discriminating criterion is the sole criterion used for individuating degrees on the continuum. Second, those representations that are “most obscure” are those whose referents are indiscriminable, and thus representations that are obscure in the principal connotation of that term. There is however an important difficulty with Baumgarten’s account of representational obscurity. He classifies as obscure representations that contain one or more clear marks on the basis of which the referents of those representations are discriminable. These include not only “minimally obscure” representations but every obscure representation on the continuum whose constituent marks are not wholly obscure. The difficulty is that all but the “most obscure” representations satisfy Baumgarten’s criterion for being clear. This introduces an important and influential ambiguity in Baumgarten’s use of the term ‘obscure’. In general, Baumgarten uses that term to denote both representations that are completely obscure as well as those that are only partially obscure. Unfortunately, he frequently uses the term without clarifying which of these connotations he intends. 35 The discriminating criterion plays a central role in Baumgarten’s formulation of the idiom. This is reflected in his account of the difference between obscure and clear representations, as well as that of the degrees of representational obscurity and clarity. It is also reflected in Baumgarten’s account of the distinction between confused and distinct representations. I think some things distinctly and others confusedly. One who thinks something confusedly does not distinguish its marks (notas), though one nevertheless represents or perceives it. For if 34

This passage is one example of Baumgarten’s synonymous use of the terms ‘perception’ (perceptio) and ‘representation’ (repraesentatio). 35 Recognizing this ambiguity is important, in part, because so much of the scholarship on Baumgarten has focused on his aesthetic writings. In Aesthetica (1750), however, Baumgarten is explicit that completely obscure representations fall outside the scope of his aesthetics. Failure to recognize this invites confusion in interpreting Baumgarten’s frequent, unqualified use of ‘obscura’ to denote representations that are only partially obscure, properly speaking. Baumgarten 1750, §§ 15–16.

144

Patrick R. Leland he should distinguish the marks of that which is represented confusedly, then he would think distinctly that which he represents confusedly. If he does not perceive whatsoever the marks of that which is thought confusedly, then he could not by means of them distinguish from others that which is perceived confusedly. Thus, one who thinks something confusedly represents some things obscurely. (Met. § 510) I represent something such that some of its marks are clear and others obscure. A representation of this nature is distinct with regard to its clear marks and sensible with regard to those that are obscure (Met. § 521). Consequently, it is a distinct representation with a mixture of confusion and obscurity, and a sensible representation in which some distinctness inheres. (Met. § 522) Since distinctness is the clarity of a thing and its marks, distinctness can increase by means of both the quantity and the intensive or extensive clarity of its marks (Met. § 531). A representation that has both more and more lively marks than other distinct representations is EXTENSIVELY MORE DISTINCT; one that has intensively more clear marks than other distinct representations is PURER (intensively more distinct). (Met. § 634, original capitalization)

As with Leibniz and Wolff, Baumgarten holds one possesses a distinct representation only if one is able to distinguish one or more of its constituent marks. In contrast to his predecessors, however, Baumgarten appeals exclusively to the discriminating criterion to explain representational distinctness. There is no further requirement that one grasp a material inferential relation between a representation and one or more of its marks. Distinguishing an object or a property of the referent is necessary and sufficient for possessing a distinct representation. This is regardless of whether one grasps that object or property as standing in a material inferential relation to the referent. All representational distinctness requires is the ability to discriminate a constituent feature of the referent. There is in Met. no appeal to the material inferential criterion as a condition for possessing a distinct representation. 36 We are now in a position to summarize the essential features of Baumgarten’s formulation of the idiom. Every representation is either obscure or clear. One’s representation is clear if and only one can distinguish the referent, where this means conscious discrimination but not necessarily recognition; otherwise, one’s representation is obscure. Every clear representation is either confused or distinct. One’s clear representation is distinct if and only if one can distinguish an object or property of the referent, where this means conscious discrimination but not necessarily grasp of a material inferential relation between the representation and a constituent mark; otherwise, one’s representation is confused. 37 In contrast to Leibniz and Wolff, Baumgarten employs the discriminating criterion as the sole principle for individuating representations in the taxonomy. As noted earlier, Baumgarten’s use of this formulation is complicated by his ambiguous use of the term ‘obscure’. This ambiguity consists in his use of that term to denote both

36

Since distinct representations fall outside the purview of poetic representations, Baumgarten does not define representational distinctness in Meditationes philosophicae de nonullis ad poema pertinentibus. See Baumgarten 1735, § 14. 37 As with Wolff, additional distinctions from Leibniz’s original taxonomy are evident in Baumgarten’s writings. These distinctions however are beyond the scope of this essay. See Baumgarten 1735, § 14; and Baumgarten 1739, §§ 620–621, 671.

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

145

representations that are wholly obscure and those that are only partially obscure on account of their containing one or more clear marks. Baumgarten’s formulation of the post-Leibnizian idiom was disseminated in the writings of his most influential student, Georg Friedrich Meier. In works published throughout the 1740’s and early 1750’s, Meier consistently uses the post-Leibnizian idiom to classify representations. The technical connotations and individuating criteria he employs are those specific to Baumgarten’s formulation of the idiom. Thus, we read that every representation is either obscure or clear; that obscure representations are unconscious and clear representations conscious; and that one’s representation is clear if and only if one can discriminate the referent. 38 Similarly, we read that every clear representation is either confused or distinct; and that one’s clear representation is distinct if and only if one can discriminate a property of the referent, where this does not necessarily entail grasp of a material inferential relation between the representation and its mark. 39 There is in Meier’s writings no appeal to either the recognition or the material inferential criterion operative in Wolff’s formulation of the idiom. 40 Baumgarten’s ambiguous use of the term ‘obscure’ is to some extent disambiguated in Meier’s writings. In his logic compendia, Meier distinguishes between representations that are “absolutely obscure” (ganz dunkel) and those that are only “relatively” so (einesteils dunkel). 41 As with Baumgarten, however, Meier frequently uses the term ‘obscure’ (dunkel) without specifying which of the more specific connotations he intends. Care is thus required when interpreting occurrences of this term in his writings.

4. Conclusion Philosophers writing in the aftermath of Leibniz used two distinct versions of a technical idiom to advance a variety of claims about mental content. Recognizing this is essential for interpreting Kant’s use of this vocabulary. A detailed study of this complex issue is beyond the scope of this essay. I pursue it elsewhere. I conclude by noting briefly two of the most important respects in which Kant critically appropriates the post-Leibnizian idiom. 42 It is well known that Kant used Baumgarten’s and Meier’s compendia as official texts for his lectures on logic, ethics, and metaphysics for more than forty years. Throughout this period, Baumgarten’s and Meier’s formulation of the idiom served as the principal technical vocabulary in terms of which Kant formulated pedagogical claims about the nature of mental content. More importantly, Kant’s early and late marginalia and published writings consistently reflect his appropriation of this version of the idiom. This is evident in his use of the cognates for ‘obscure’ and ‘clear’ to denote unconscious and conscious representations, respectively; his claim that consciousness admits of degrees; his use of the 38

Meier 1742, § 44; Meier 1744, § 38; Meier 1749, § 30; Meier 1752a, §§ 27, 155; Meier 1752b, § 13, AA 16: 80. Meier 1744, § 48; Meier 1749, § 31; Meier 1752a, §§ 28; Meier 1752b, §§ 14, AA 16: 80–81. 40 In addition to Meier, Martin Knutzen employs Baumgarten’s formulation of the idiom for the classification of ideas, perceptions, and concepts. See Knutzen 1747, §§ 87 ff. 41 Meier 1752a, § 156; Meier 1752b, § 125, AA 16: 318. 42 For detailed discussion of these issues, see Leland 2018 and (forthcoming). 39

146

Patrick R. Leland

discriminating criterion to individuate “clear” representations; and his characterization of mental states as complex aggregates of obscure and clear constituent marks. 43 Kant’s use of Baumgarten’s formulation was sufficiently extensive that later thinkers could associate it with Kant instead of Baumgarten. In his Wissenschaftslehre (1837), Bernhard Bolzano writes of the distinction between obscure and clear representations: “I should think that one of the best explanations is the Kantian one. ‘If I am conscious of a representation, then it is clear; if not, then obscure’.” 44 While Kant’s use of the cognates for ‘obscure’ and ‘clear’ reflect his appropriation of Baumgarten’s version of the idiom, his early account of concept possession represents a radical departure from Baumgarten and Meier. In his logic compendia and writings on lower organisms, Meier had used the discriminating criterion as a necessary and sufficient condition for ascribing concepts and the faculty of understanding to non-human animals. Kant criticizes this in the compressed remarks that conclude his 1762 essay on logic. Of particular interest for present purposes, Kant appropriates the material inferential criterion Leibniz and Wolff had used as a necessary and sufficient condition for distinct concept possession. What is more, Kant uses this criterion expansively as a necessary and sufficient condition for possessing concepts, in general, and the faculty of understanding. The result is a nascent expression of one of Kant’s most important contributions to the philosophy of mind. This is his commitment to the semantic primacy of judgment, or the view that conceptual content is explanatorily dependent on its role in acts of judgment. 45

Bibliography Antognazza, M. 2009. Leibniz: An Intellectual Biography. Cambridge: Cambridge University Press. Arndt, H. 1965. Einführung des Herausgebers. In: Arndt, H. (ed.). Wolff, Vernünftige Gedanken: Von den Kräften des menschlichen Verstandes und ihrem richten Gebrauche in Erkenntis der Wahrheit. Hildesheim: Olms. Arndt, H. 1983. Rationalismus und Empirismus in der Erkenntnislehre Christian Wolffs. In: Schneiders, W. (ed.). Christian Wolff 1679–1754. Interpretationen zu seiner Philosophie und deren Wirkung mit einer Bibliographie der Wolff-Literatur. Hamburg: Felix Meiner. Bolzano, B. 1837. Wissenschaftslehre. Sulzbach: Seidel. Baumeister, F. C. 1735. Institutiones philosophiae rationalis, methodo Wolfii conscriptae. Wittemberg: Alfeld. Baumeister, F. C. 1738. Philosophia definitiva. Wittemberg: Alfeld. Baumgarten, A. 1735. Meditationes philosophicae de nonullis ad poema pertinentibus. Halle: Grunert. Baumgarten, A. 1739 /1757. Metaphysica = Metaphysik: Historisch-Kritische Ausgabe. Gawlick, G. / Kreimendahl, L. (eds., trs.) 2011. Stuttgart-Bad Cannstatt: Frommann-Holzboog.

43

See, for example, ND, AA 1: 401, 406; VBnG, AA 2: 199; UDG AA 2: 290; KrV), B414-415n; and ApH AA 7: 135 ff. Quoted in Centrone 2010, 261. See AA 9:33 and Bolzano 1837 III, 30–39. The definition Bolzano ascribes to Kant is from the Jäsche Logik, a text which Kant did not write but which is included in the Academy edition of Kant’s writings. Kant explicitly rejects the formulation Jäsche ascribes to him and offers instead a different formulation of the discriminating criterion as a necessary and sufficient condition for the clarity of a representation. See B414-415n. 45 I would like to thank the editors of this volume and an anonymous referee for helpful comments on an earlier draft of this paper.

44

Wolff, Baumgarten, and the Technical Idiom of Post-Leibnizian Philosophy of Mind

147

Baumgarten, A. 1739 /1757. Metaphysics: A Critical Translation with Kant’s Elucidations, Selected Notes, and Related Materials. Fugate, C. /Hymers, J. (eds., trs.) 2013. New York: Bloomsbury. Baumgarten, A. 1750. Aesthetica. Frankfurt ad Oder: Impens. Baumgarten, A. 1761. Acroasis logica. Halle: Hemmerde. Bolton, M. 2011. Leibniz’s Theory of Cognition. In: Look, B. C. (ed.). The Continuum Companion to Leibniz. London: Continuum. Bolzano, B. 1837. Wissenschaftslehre. Sulzbach: Seidel. Brandom, R. 1981. Leibniz on Degrees of Perception. Journal of the History of Philosophy 19, 447–479. Brandom, R. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge: Harvard University Press. Burkhardt, H. 1980. Logik und Semiotik in der Philosophie von Leibniz. München: Philosophia. Centrone, S. 2010. Bolzano und Leibniz über Klarheit und Deutlichkeit. Archiv für Geschichte der Philosophie 92, 256–289. Dyck, C. 2014. Kant and Rational Psychology. Oxford: Oxford University Press. Fugate, C. /Hymers, J. 2013. Introduction. In: Baumgarten, Metaphysics: A Critical Translation with Kant’s Elucidations, Selected Notes, and Related Materials. Fugate, C. /Hymers, J. (eds., trs.). New York: Bloomsbury. Gottsched, J. C. 1733. Erste Gründe der gesammten Weltweisheit. Leipzig: Breitkopfen. Grau, K. 1916. Die Entwicklung des Bewuβtseinsbegriffes im XVII. und XVIII. Jahrhundert. Halle: Niemeyer. Heidemann, D. 2012. The ‘I Think’ Must Be Able To Accompany All My Representations. Unconscious Representations and Self-Consciousness in Kant. In: Giordanetti, P. et al. (eds.). Kant’s Philosophy of the Unconscious. Berlin: Walter de Gruyter. Jauernig, A. 2011. Kant, the Leibnizians and Leibniz. In: Look, B. C. (ed.). The Continuum Companion to Leibniz. London: Continuum. Jorgensen, L. 2009. The Principle of Continuity and Leibniz’s Theory of Consciousness. Journal of the History of Philosophy 47, 223–248. Jorgensen, L. 2015. Leibniz on Perceptual Distinctness, Activity, and Sensation. Journal of the History of Philosophy 53, 49–77. Knutzen, Martin. 1747. Elementa philosophiae rationalis seu logicae. Repr. 1991. Hildesheim: Olms. Kuehn, M. 2001. Kant: A Biography. Cambridge: Cambridge University Press. La Rocca, C. 2006. Das Schöne und der Schatten. Dunkle Vorstellungen und ästhetische Erfahrung zwischen Baumgarten und Kant. In: Klemme, H. /Raters, M. L. /Pauen, M. (eds.). Im Schatten des Schönen. Die Ästhetik des Häβlichen in historischen Ansätzen und aktuellen Debatten. Bielefeld: Aisthesis. Lambert, J. H. 1764. Neues Organon, oder, Gedanken über die Erforschung und Bezeichnung des Wahren und dessen Unterscheidung vom Irrtum und Schein. 2 vols. Leipzig: Wendler. Leland, P. Kant and the Primacy of Judgment Before the First Critique. Journal of the History of Philosophy (forthcoming). Leland, P. 2018. Unconscious Representations in Kant’s Early Writings. Kantian Review 23, 257–284. Lodge, P. and S. Puryear. 2006. Unconscious Conceiving and Leibniz’s Argument for Primitive Concepts. Studia Leibnitiana 38/39, 177–196. McRae, R. 1976. Leibniz: Perception, Apperception, and Thought. Toronto: University of Toronto Press. Martin, G. 1966. Kants Auseinandersetzung mit der Bestimmung der Phänomene durch Leibniz und Wolff als verworrene Vorstellungen. In: Heimsoeth, H. (ed.). Kritik und Metaphysik. Berlin: de Gruyter. Martin, G. 1967. Leibniz. Logik und Metaphysik. Berlin: de Gruyter. Meier, G. F. 1744. Theoretische Lehre von den Gemütsbewegungen überhaupt. Halle: Hemmerde. Meier, G. F. 1751. Beweis: daß keine Materie dencken können. 2nd ed. Halle: Hemmerde.

148

Patrick R. Leland

Meier, G. F. 1752a. Vernunftlehre. Nach der bei Johann Justinus Gebauer in Halle 1752 erschienenen ersten Auf lage in zwei Teilen. 1997. Schenk, G. (ed.). 3 Teile. Halle: Hallescher Verlag. Meier, G. F. 1752b. Auszug aus der Vernunftlehre. Reprinted in volume 16 of Kant, AA. Mirbach, D. 2009. Die Rezeption von Leibniz’ Monadenlehre bei Alexander Gottlieb Baumgarten. In: Neumann, H.-P. (ed.). Der Monadenbegriff zwischen Spätrenaissance und Aufklärung. Berlin: de Gruyter. Oberhausen, M. 2002. Dunkle Vorstellungen als Thema von Kants Anthropologie und A. G. Baumgartens Pyschologie. Aufklärung 14, 123–146. Parkinson, G. 1982. The ‘Intellectualization of Appearances’: Aspects of Leibniz’s Theory of Sensation and Thought. In: Hooker, M. (ed.). Leibniz: Critical and Interpretive Essays. Minneapolis: University of Minnesota Press. Pozzo, R. 2000. Georg Friedrich Meiers “Vernunftlehre”: eine historisch-systematische Untersuchung. Stuttgart-Bad Cannstatt: Frommann-Holzboog. Reimarus, H. S. 1758. Die Vernunftlehre, als eine Anweisung zum richtigen Gebrauche der Vernunft in dem Erkenntnis der Wahrheit, aus zwoen ganz natürlichen Regeln der Einstimmung und des Widerspruchs. Hamburg: Bohn. Rutherford, D. 2004. Idealism Declined: Leibniz and Christian Wolff. In: Lodge, P. (ed.). Leibniz and His Correspondents. Cambridge: Cambridge University Press. Schenk, G. 1997. Appendix. In: G. Schenk (ed.). Vernunftlehre. Nach der bei Johann Justinus Gebauer in Halle 1752 erschienenen ersten Auf lage in zwei Teilen. 3 Teile. Halle: Hallescher Verlag. Sellars, W. 1953. Inference and Meaning. Mind 62, 313–338. Simmons, A. 2001. Changing the Cartesian Mind: Leibniz on Sensation, Representation and Consciousness. The Philosophical Review 110, 31–75. Simmons, A. 2011. Leibnizian Consciousness Reconsidered. Studia Leibnitiana 43, 196–215. Sommer, R. 1892. Grundzüge einer Geschichte der deutschen Psychologie und Ästhetik von WolffBaumgarten bis Kant-Schiller. Würzburg: Stahel. Thümming, L. 1729. Institutiones Philosophiae Wolfianae. 2 vols. Frankfurt: Renger. Tonelli, G. 1974. Leibniz on Innate Ideas and the Early Reactions to the Publication of the Nouveaux Essais (1765). Journal of the History of Philosophy 12, 437–454. Watkins, E. 2005. Kant and the Metaphysics of Causality. Cambridge: Cambridge University Press. Wilson, C. 1995. The Reception of Leibniz in the Eighteenth Century. In: Jolley, N. (ed.). The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press. Wilson, M. 1999. Ideas and Mechanism: Essays on Early Modern Philosophy. Princeton: Princeton University Press. Wunderlich, F. 2005. Kant und die Bewuβtseinstheorien des 18. Jahrhunderts. Berlin: de Gruyter.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science Katherine Dunlop, University of Texas at Austin

Abstract This paper argues that in Christian Wolff’s theory of knowledge, logical regimentation does not take the place of experiential justification, but serves to facilitate the application of empirical information and clearly exhibit its warrant. My argument targets rationalistic interpretations such as R. Lanier Anderson’s. It is common ground in this dispute that making concepts “distinct” (articulating their component marks) issues in the premises on which all deductive justification rests. Against the view that concepts are made distinct only by analysis, which is carried out by the understanding independently of experience, I contend that for Wolff some distinct concepts are arrived at through experience. I emphasize that Wolff countenances empirical methods of obtaining distinct concepts even in mathematics. This striking feature of his view indicates how its empiricist elements can be reconciled with his injunction to follow “mathematical” method.

1. Introduction Before Kant asked how metaphysics as a science is possible, Christian Wolff defined philosophy as “the science of the possibles insofar as they can be”, and argued that it is possible (PD § 29; § 37). 1 Wolff takes mathematics as the model on which all scientific reasoning should proceed, and Kant’s insistence that philosophy follow a different method than mathematics is one manifestation of his break with Wolff. It is widely believed that in his mature philosophy, Kant came to reject Wolff’s rationalism. 2 This paper engages with recent (Anglophone) scholarship in order to show that Wolff grants experience a broader role – even in mathematical reasoning – than is typically supposed, particularly with respect to his influence on Kant. 3 On my reading, there is more to Wolff’s account of mathematical reasoning than just the “analysis of concepts” that Kant finds inadequate. In particular (so I will argue), Wolff relies on experience to establish the possibility of concepts, even in mathematics. His account of this justificatory role for experience is framed within a detailed theory of concept acquisition, which is of independent interest as background for Kant’s view. 1

On at least one occasion when he raises this question, Kant identifies metaphysics with “all of pure philosophy” and makes clear reference to Wolff’s system (KrV A841 /B869 – A847/B875). 2 One reason Wolff is seen as a rationalist is that his views are assimilated to Leibniz’s. I argue in Dunlop 2014 that those writings of Leibniz’s that were available to Wolff allow the involvement of imagination and senseexperience in mathematical cognition. 3 A prominent exception to this generalization is Corey W. Dyck. Further, as the citations in this paper indicate, Wolff’s reliance on experience in the theory of knowledge is more widely recognized outside the Anglophone context.

150

Katherine Dunlop

Wolff’s view is marked as rationalist by his attributing certainty to scientific cognition, as well as modeling all scientific cognition on mathematics. 4 According to Wolff, a body of knowledge qualifies as science when it admits of deductive organization. This regimentation proceeds along two lines. First, it must be possible to derive all propositions of the theory from epistemologically secure “first principles” by rigorous methods of inference. Wolff holds the view, extraordinary in the early modern period, that all correct reasoning in the sciences can be expressed in syllogistic form. Since the modes of inference are exhaustively specified a priori in logic, the only way experience can contribute to the expansion of knowledge is by supplying premises for inferences. Secondly, the terms in which the theory is couched must be defined, in terms that can be presumed as understood. For Wolff, language merely publicizes and records thought, which it is our aim to understand. So it is concepts, rather than words, that are most crucially in need of definition. Part 2 of this paper explains how, in Wolff’s system, concepts encode the bases of syllogistic inferences and predications (and also shows the importance of organizing concepts into genus-species hierarchies). Since concepts, to which definitions primarily pertain, thus suffice to express the justificatory structure of scientific cognition, Wolff’s theory of definition becomes crucial for gauging the extent of his rationalism. Those who count Wolff as a rationalist suppose that for him, the contribution of experience to scientific cognition is either merely etiological or psychological, or else provisional (such as to have no place in a completed science). Recent work shows clearly how his theory of definition offers a way to dispense with experience in the knowledge of premises. For the definition of a concept sets out the elements that it contains. And Wolff takes from Leibniz the view that predicates of true judgments are contained in the concepts of their subjects. Wolff also appears to share Leibniz’s view that in every case, the elements contained in a concept can be made explicit by analysis, which is an operation carried out by the understanding alone. So by this purely logical or rational procedure, we can both arrive at the true judgments that serve as premises for inferences, and grasp the basis for the predications by which syllogisms advance from truth to truth. We can thereby place all knowledge on a rational or logical basis. In Part 3, I introduce a representative interpretation of this sort. On R. Lanier Anderson’s influential reading, Wolff regards syllogisms as sufficient for all science because he supposes science’s end is a unique hierarchy of concepts, corresponding to the system of essences God chose to realize in creating the world, whose containment relations ground the premises and inferential steps of all syllogisms. Anderson takes Wolff to hold that such concepts are obtained by analysis. Although Anderson’s emphasis on the metaphysical significance of the conceptual hierarchy is novel, he joins many others in assuming that distinct concepts are always obtained by analysis. Starting in Part 4, I raise an objection to this line of interpretation: it overlooks Wolff’s distinction between “real” and “nominal” definitions. Roughly speaking, a real definition shows a concept to correspond to something that could exist as part of a natural order, while a nominal definition shows the concept to contain enough detail that it can pick out a unique (kind of) thing. The purely rational operations considered by these interpreters 4

Wolff’s commitment to mathematical demonstrative method features as a rationalist feature of his view even in Vanzo 2015, which emphasizes his reliance on experience.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

151

are guaranteed to yield nominal, but not necessarily real, definitions. I contend that experience’s role in showing the objectivity of real definitions cannot be dispensed with in Wolff’s scientific system. Other commentators have already highlighted the indispensability of experience (in Wolff’s system) for the sort of objectivity that real definitions express. 5 But to my knowledge, there has been no sustained consideration of how this role for experience manifests in the system – namely that of mathematics – on which Wolff models all scientific reasoning. 6 Part 4 of this paper aims to fill this gap. I show that Wolff gives illustrations from mathematics of various ways – several of them empirical – of acquiring nominal and real definitions. I think it is clear that Wolff’s system relies on experience, as he explicitly claims, to establish that “those things [which] are admitted as possible” are indeed possible (PD § 11), in the sense of having a place in a natural order. However, this role for experience could still be seen as psychological or etiological. In Part 5, I argue that the experience by which definitions are acquired justifies their use in syllogistic reasoning. In Part 6, I argue against the view that Wolff dispenses with empirical justification in order to base all knowledge on the principle of non-contradiction. On my reading, his regimentation of scientific knowledge is not intended to supply it with a logical or rational justification, but to facilitate its application and make perspicuous its warrant (which remains empirical in some cases).

2. The structure of Wolff’s logical system 2.1.

Compacting the mind’s operations

In 2.1 through 2.4, I offer a characterization of Wolff’s system that is intended to be neutral between competing interpretations (regarding the extent of Wolff’s rationalism). In “Preliminary Discourse on Philosophy in General” (PD), which appears at the beginning of his Latin logic textbook, Wolff explains that for philosophy to have the certainty that characterizes science, terms must be “explained by accurate definitions”; principles must be “sufficiently proven”; and all other propositions must be “legitimately deduced” from these principles (PD § 33, §§ 116–118). Since logic explains how to “define accurately”, “formulate determinate propositions”, and “demonstrate legitimately”, its rules must be applied in philosophy (PD § 135). Wolff shares the common early-modern view that logic studies the mind’s operations. On this view logic has three main elements, namely concepts, judgments, and inferences. For Wolff, all cognition is either concept or judgment, and the operations required for it are specifically “barely representing” an object (through a concept); forming a judgment immediately on the basis of a single representation; or forming a judgment by means of “ratiocination” from other judgments taken as premises. 7 Wolff takes “ratiocination” to

5

See especially Arndt 1983. In Anglophone scholarship, the point is made (without reference to the theory of definition) in Kuehn 1997. 6 There are cursory mentions of such a role in Kreimendahl 2007 and Cataldi Madonna 2011. 7 Wolff 1733, lxvii. Cited as translated in Wolff 1770.

152

Katherine Dunlop

consist of syllogisms (PR § 50, § 332), so that it always moves to a conclusion from a major and minor premise. The items (concepts, propositions, and syllogisms) produced by these operations are of equal expressive power in that (a) the logical relationship expressed by a syllogism can also be expressed by a proposition, and (b) the logical relationship expressed by a proposition can also be expressed by a concept. The latter sort of “compactness” (as we may call this codifying relationship) is especially important for rationalist interpretations of Wolff, but it will be convenient to begin with the former sort. On (a): Wolff restricts his attention to syllogisms of the first figure on the grounds that they suffice “for all intents and purposes”. 8 In such syllogisms, the subject S and predicate P joined in the conclusion are linked by a middle term that stands as subject with respect to P (in the major premise) and as predicate with respect to S (in the minor premise). Wolff construes the middle term as a “condition” under which P applies to S. That the predicate applies to or agrees with the subject under this condition can also be expressed in the form of a proposition. For, according to Wolff, every proposition is “very easily resolved into two parts:” [First], the condition or hypothesis under which the predicate does or does not agree with the subject, namely, as containing in it this or the other thing, or as being found under this or the other circumstances. [Second,] the position or thesis, which contains that which can or cannot agree [. . .]: As for instance, in the proposition, the warm stone does warm, the hypothesis or supposition lies in the stone’s being warm; but the position, in that it warms: And it may be expressed thus, if the stone is warm, it does warm. (VGK III.6) 9

In this example, the conditioned agreement between subject and predicate would be expressed by this syllogism: “The stone is (a) warm (thing); Warm things warm; Therefore, the stone warms.” In general, conditioned agreement is expressed in propositional form by adjoining to the subject term the condition under which the predicate agrees, either as an adjective, or by means of a copula in the antecedent of a hypothetical proposition. On (b): In his German logic textbook Wolff claims that to judge is to grasp “either that a thing has, or may have in itself something, or even that something may proceed or arise (herrühren) from it”, or that something is or cannot be contained or cannot arise from it (VGK III.1). Wolff’s discussion of judgment in his German metaphysics textbook shows that what is thus grasped does not consist solely in facts, but includes the underlying metaphysical basis for their truth. In judging “we cognize that this or that thing has, or at least could have, this or that intrinsically, or also that something could arise (herrühren) from it”, which means “that one could find in it the ground” of a change in it or an effect on another thing (VGG § 287). This divides the determinations that are attributed to things into intrinsic ones (which are called “attributes”; VGG § 288) and those which arise, as new determinations, through grounds contained either in the subject undergoing

8

Wolff 1733 claims that particular instances of syllogisms in the second or third figures “may, without any trouble, be reduced” to the first”, although “from the school-philosophy” we see that the reducibility of the other figures to the first “cannot be shown in general without much circuition” (lxxx). Wolff argues for the general reducibility thesis in PR § 384, § 398. See Jean École’s Introduction to the Olms reprint (Hildesheim, 1983), lxiv. 9 Wolff’s VGK and Wolff 1733 are cited as translated in Wolff 1770. Wolff’s VGG is cited as translated in Watkins 2009.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

153

change or in some other thing. Intrinsic determinations belong to a thing’s essence in case they comprise “the ground of the rest of what is attributed to” the thing (VGG § 33); other intrinsic determinations are “grounded solely in the essence of the thing” and thus inseparable from the thing, “immutable just as the essence itself is, and [. . .] necessarily and thus continually attributed to [the] thing” (VGG § 44). Thus every determination ascribed in judgment is either part of or grounded solely in the subject’s essence, or has a ground (which brings about the determination only under some further condition) in some other thing or in the subject. We can recognize this as a form of the Principle of Sufficient Reason (PSR). What matters for our purposes is that the concept of the subject or the other thing can be developed to render this ground explicit, so that the concept’s possessor will be in position to ascribe the determination to the subject (in a judgment). How, exactly, this refinement takes place is a point of contention in this paper. Hence just as propositions can express what is known by means of syllogisms, namely that a predicate agrees with a subject under a condition, in the same way concepts can exhibit the underlying basis for linking predicates to subjects.

2.2.

The usefulness of philosophy

On the early modern view of logic shared by Wolff, logic does not merely describe the mind’s capabilities, but teaches the best use of cognitive faculties. 10 Accordingly, the possibility of organizing items of knowledge (concepts, terms, or propositions) in a certain manner is significant for logic only insofar as such organization serves a purpose. We need to know what end is served by the regimentation that marks philosophy as scientific knowledge. Throughout his oeuvre, and especially in the German writings, Wolff indicates how this systematization is useful. PD includes a sustained account of philosophy’s usefulness, which turns on a contrast between “philosophical” and “historical” cognition. Historical cognition is empirical, but not limited to commonplace perceptual observation; it includes observation and experiment in science, because all of this originates in the senses (PD §§ 23–24; cf. VGG § 325). Wolff contrasts it as “bare cognition of the fact”, which does not include the grounds of truth, with philosophical cognition, which “exhibits the reason of the fact so that it be understood why something of this sort could occur” (PD § 7). Indeed, the overall aim of philosophy is to “give a reason”, specifically by demonstrating, why that which is possible can actually occur (PD § 31). Wolff argues that one who “is acquainted with philosophy” and “knows the reason why a thing is or occurs” will “perceive the condition under which something is predicated of a being”, and therefore will only attribute the predicate when the condition is present (PD, § 41). Wolff emphasizes that such knowledge is useful both for science and in everyday life (PD § 122). It helps to prevent mistakes such as attempting to produce, “with the shoots of any tree”, what is achieved with the shoots of rosemary, namely that when “planted into the ground at one end, they take root and grow into a bush”. For

10

For discussion, see Hatfield 1997.

154

Katherine Dunlop he who would search for the reason why this works with rosemary, and discover it, knows the conditions required for success. And as a result, when the conditions are absent, he would abstain from the vain labor of trying to grow something (PD § 41).

Here, conditions under which predicates agree with subjects are assimilated to reasons for truths. Both conditions and (as we saw in the discussion of (b) above) reasons are treated as properties belonging to things of a certain kind. The claim that philosophy supplies reasons by “demonstrating” is crucial for distinguishing philosophical from historical cognition. For both the properties that function as conditions or reasons, and that they so function, are typically known by means of experience (“historically”). In VGK Wolff claims that in experience we perceive not merely “things themselves and their properties”, as that air is elastic, but also “the changes they undergo”, as that air expands due to heat, and their effects on other things, as that air “firmly compresses together exhausted hemispheres” (VGK V.5). In PD, he clarifies that one can know “the reason for the ascent of water in pumps and in artificial fountains” if one cognizes by means of “experiments” that “air has both weight and elasticity”. This is philosophical cognition, but based on historical cognition (PD § 10). For the cognition to be purely philosophical, it would be necessary to demonstrate how the weight and elasticity of air give rise to water’s ascent. Wolff holds that our ability to determine how widely conditions hold is greatly furthered by organizing our kind-concepts into a Porphyrian tree (so-called after Porphyry’s introduction to Aristotle’s Categories). This is a hierarchy of genera and species, in which each genus is portioned into the species that stand under it by an exclusive and exhaustive disjunction (that is, in accordance with the rules of “logical division”), and each species can itself stand as a genus relative to classes into which it is in the same way divided. It falls to philosophy to determine how generally, i. e. how far up in a Porphyrian hierarchy, any given trait obtains. This is because in the context of a hierarchy, the “reason” grasped by philosophical cognition is both a condition under which a predicate applies to a subject and a property that characterizes a node of the tree. As Wolff puts it, one who “knows the reasons of things which are and occur” thereby also knows “whether this reason is contained in the notion of the species or the notion of the genus” (PD § 42). To “discover the reason in the notion of the genus” enables one to “attribute to many species what historical cognition finds in only one species” (VGG § 182). Regimentation of this kind thus forestalls the mistake of “dealing with fewer problems of life than one could”, specifically “applying to things of one species what should be applied to many more things.” For example, one who has historical cognition that “water is moved more quickly if the bed of a river is contracted such that the water flows through a smaller section of the river than before” can apply this knowledge only to water in the bed of a river. But he who has philosophical cognition knows that the motion of the water is accelerated or decelerated not because it is water but because it is a heavy fluid. Consequently, he knows that the motion of any heavy fluid running through an inclined channel can be accelerated or decelerated [. . .] It is also clear to him that the contraction or expansion of the riverbed is to be understood as a larger or smaller aperture. (PD § 42)

Philosophical cognition thus equips its holder to apply the lesson about water in a riverbed to any case of a heavy fluid passing through an aperture, for instance, to “a stronger

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

155

wind being produced by a bellows” (PD § 42). Since the attribution of the predicate to the more general subject-concept is a more compact and general expression of knowledge, Wolff can claim that by means of philosophy “he who is instructed with a less scattered cognition is prepared for more cases” (PD § 43).

2.3.

Syllogism as the culmination of Wolff’s logical system

The doctrine of syllogism is the culmination of Wolff’s entire logical system insofar as syllogistic inference is the main way in which Porphyrian hierarchies (of concepts) are deployed to extend knowledge. 11 Wolff’s regard for the syllogism has been especially noted, by Anderson and other interpreters. What is most striking, and recognized as bold by Wolff himself, 12 is that on his view syllogistic reasoning serves to first discover truths as well as to make their justification explicit. Genus-species relationships make possible the two main kinds of syllogism. The principle that “whatever agrees with a genus or species, must agree with all the particulars contained under that genus or species” makes possible affirmative syllogisms, such as “Light is that which renders the surrounding bodies visible; The moon makes the bodies around me visible; Therefore, the moon is a light” (VGK V.2). The principle that “whatever is denied of a whole genus or species, must also be denied of every particular contained under that genus or species” makes possible negative syllogisms, such as “No man takes his riches with him out of the world; Croesus is a man; Therefore, Croesus can take nothing with him out of the world” (VGK V.3). An obvious way in which syllogisms lead to new knowledge is that they allow us to conclude about a particular (or species) that it has the properties that “agree with”, and lacks the properties that are denied of, its species (or genus).

2.4.

The “prompting” role of experience in demonstration

In addition to Wolff’s regard for the syllogism, another striking feature of his methodology that encourages rationalist readings is his emulation of mathematics. Wolff’s confidence that syllogistic reasoning is appropriate in all areas of inquiry informs his conception of mathematical method and view of its preeminence. We saw that Wolff holds that for a discipline to attain certainty, it must define its terms, prove its principles (by deriving them from definitions), and admit only what follows from the principles by the rules of syllogism. Wolff claims that mathematics (as he has developed it in his Elementa matheseos universae) meets this standard, and argues on this basis that the “rules of mathematical method” are also those of philosophical method – indeed, the only rules by which any discipline can achieve certainty (PD § 139). Wolff claims specifically that by this method, results are “rigorously demonstrated”. In his account of demonstration in mathematics, Wolff identifies a role for experience,

11

Wolff writes that syllogism shows the reason (Ursache) why “it were to be wished that men always framed hteir judgments by genus and species” (1733, lxxi). 12 Wolff indicates that the view that the syllogism can discover truths not already known is counter to such authorities as Descartes and Tschirnhaus (1841, 134–136).

156

Katherine Dunlop

which is fulfilled in classical geometrical proof by observation of the diagram. 13 Wolff explains that to be correct, a demonstration should indicate how the conclusion of each syllogism is supposed to follow from the previously-admitted propositions that serve as its premises. But even though these propositions (Fördersätze) are “required for the form of the inference”, they do not all have to be included, because for a “proficient reader” they “come to mind” (einfället) (1716, 501). In particular, when the conclusion of one syllogism serves as a premise for another, the latter’s second premise is easily called to mind. The cues by which it is evoked are words, citations, and diagrams of geometrical figures: The observation (Anschauen) of a drawn figure, to which one directs one’s thoughts while demonstrating, yields at the beginning a proposition [. . .] This proposition has a part in common with another, which comes to mind due to the same circumstances (der uns um deswillen einfället), and thus we have the other required proposition (1716, 502).

Here as elsewhere, Wolff is concerned to show that mathematical method is applicable to other pursuits. He claims that “not only in geometry does one attend to (nehmen in acht) things of this sort”, but rather all people do “as often as they proceed from a present thought to some other one.” An example of such syllogistic reasoning is how the ringing of the church bells brings Titius to go to church. By “being attentive to what strikes his senses”, Titius cognizes the proposition “that today is the day for church and it is almost twelve o’clock, and one strikes the church bells”. Titius is thereby moved to think (the proposition) that “if one hears the bells shortly before twelve o’clock on a church day, then it is time to go to church”, and concludes therefrom that it is time to go to church (1716, 503). The example indicates that experience conduces specifically to cognizing minor premises of syllogisms and bringing to mind major premises. As I will explain in 3.2, the latter can be regarded as definitions, and it is thus reasonably clear how Wolff can hold that definitions and “indubitable experiences” are the basis of all demonstration. 14

3. A rationalist construal of the conceptual hierarchy 3.1.

Eliminating experience for the sake of metaphysics

Because the preceding characterization of Wolff’s view aimed to be neutral regarding the role of experience, we have yet to consider some remarks which seem to call Wolff’s commitment to rationalism into question. In particular, Wolff emphasizes the value and indispensability of historical cognition. He declares that “historical cognition is the foundation of philosophical cognition insofar as experience establishes those things from which the reason can be given for other things which are and occur, or can occur” (PD § 10). Wolff elaborates that such a foundation is “firm and unshaken” because “only those things which truly exist and occur are admitted as possible”, and that history must not 13

Wolff also claims that “mechanical examination” of figures can supplant demonstration as a means for knowing mathematical truths (PD § 19). Elsewhere he treats mechanical investigation as a species of demonstration, as Shabel explains in (Shabel 2003). I have not counted this use of experience as part of the mathematical method because as far as I know, Wolff does not claim it is practicable outside mathematics. 14 Wolff defines (the German and Latin cognates of) “demonstration” as a series of syllogisms in which only definitions and secure (German: klar, Latin: indubitaba) experiences enter as premises (PR § 498; VGK VI.21).

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

157

only “precede” philosophy but be “constantly joined with it” (PD § 11). This leads him to speak of a “holy marriage throughout all philosophy” of historical and philosophical cognition. 15 Wolff makes clear that the marriage is between equals: despite having “carefully distinguished” historical from philosophical cognition, “we have not deprecated or condemned it” (PD § 12). Yet some commentators find pressures in Wolff’s view that move him to dispense with empirical information, in favor of purely logical relations between concepts. As a representative I will take R. Lanier Anderson, chiefly because he develops the interpretation in unsurpassed detail and with admirable clarity (and also on account of his influence). 16 On Anderson’s reading, what the above characterization of Wolff’s view leaves out, and what overrides his seeming acceptance of empirical claims in philosophy, is the metaphysical significance of the conceptual hierarchy. In contrast to the (rather banal) purposes for the hierarchy suggested in 2.2 above, on this reading the “true hierarchy” matches the “system of conceptual essences” that God recognized as the best possible, and chose to make actual in creating the world (Anderson 2015, 96). It is our goal as knowers to cognize this system. The goal of inquiry, on this reading, is specifically to organize concepts into such a hierarchy by making explicit the elements they “contain”. When articulated, these containment relations between concepts are a sufficient basis for all knowledge. Anderson argues (as I explain in Part 6) that for Wolff, the justificatory force of experience and that of PSR ultimately depend on the principle of non-contradiction (PNC). So it is by this principle, in the final accounting, that all truths are known. Since the truths to which it applies are (in the first instance) of subject-predicate form, their negations will be contradictory only if the predicate stands in an appropriate logical relationship to the subject. The obvious candidate for such a relation is containment. On Anderson’s interpretation, accordingly, the way we grasp the reason for a fact (in philosophy) is by determining whether the connection between the concepts of the subject and the predicate “is a matter of direct containment in the definition of the subject, or whether it is restricted by a certain additional condition”. Whether or not the containment relation is so restricted, establishing it opens a route for knowing the truth “from concepts”, by analysis. Philosophical knowledge also “specifies the relevant condition”, if any, and thus “transforms the initial claim into a genuine containment truth”, in which “the predicate is contained in the concept of the subject-plus-condition” (Anderson 2015, 91). As we saw, Wolff construes the middle term of a syllogism as a condition under which the predicate asserted of a subject in the conclusion actually applies to the subject. On Anderson’s interpretation, the link asserted in the conclusion and the links between each of its terms (S and P) and the middle are containment relations. This yields a “unified presentation of the underlying principle behind syllogistic inference”, which would have been attractive to early modern thinkers “dissatisfied with the intricacies” of medieval theory (Anderson 2015, 53). Most importantly, it makes sense of Wolff’s proposal to reconstruct all scientific knowledge in syllogisms. For syllogisms are now taken to codify

15 16

PD § 12; PR § 985, § 1232. For additional citations see Arndt, “Rationalismus und Empirismus”, 42, n. 1. Shabel 2003 and Sutherland 2010 are studies of the background to Kant’s philosophy of mathematics that reflect Anderson’s influence.

158

Katherine Dunlop

the relations (of containment) that structure the “true hierarchy” that it is science’s goal to discover. It may seem wild to suppose that the explanatorily relevant features of kinds are arranged in a hierarchy satisfying the rules of logical division, and far more so to assume that empirically based natural science will deliver a unique hierarchy of this sort. That eighteenth-century thinkers found this plausible, however, shown by the acclaim that greeted Linnaeus’s systematization of biological kinds. 17 Wolff is more likely to have influenced Linnaeus than to have been influenced by him, 18 but the point is that the climate in which both worked was hospitable to the approach.

3.2.

Distinctness and definitions

To show that Wolff’s texts leave room for interpretive disagreement (thus to motivate a detailed examination of Wolff’s theory of concepts), we may first note that Anderson’s interpretation nicely fits Wolff’s account of experience’s role in Chapter V of VGK. Wolff claims we can know through experience whether a determination belongs to a thing intrinsically (in which case it is an attribute of the thing), or only under some condition, in which case experience also allows us to identify the condition. Wolff holds, specifically, that we sometimes have the power “to remove the things, whose attributes we would know, from the things around them and convey them to the vicinity of quite different things”, 19 and learn thereby whether “the reason for something’s agreement with a thing is intrinsic to the thing”. For instance, I find a piece of wax [. . .] lying in a warm place, that has become soft. I suppose myself still ignorant as to whether wax is at all times soft or not: I take the wax and lay it in a cold place, such as a cellar, and there I find it turns hard. And here I recollect that whatever is not constantly in a thing cannot be an attribute, and [thence] conclude that softness is no attribute of wax: And therefore when wax is soft, the reason is to be looked for in other things which happen to be contiguous, as in our case the sun’s rays, to which it was exposed. (VGK V.6)

This passage seems to be directed against Descartes’s claim (in the Second Meditation) to discover wax’s essential properties through purely rational scrutiny. 20 Yet Wolff stresses that “we may also determine the matter by reasoning, namely from comparing distinct notions both of the attribute in question, and of the matters contiguous to the thing”. For, he claims, “on comparing together these notions, I can easily see whether the contiguous things make any contribution, and can find whether the ground or reason for [a predicate]’s agreement with a thing be in the thing itself, or in the things without it” (VGK V.8). It thus appears that knowledge which is acquired through experience can as

17

Ernst Mayr notes, however, that “the dogma that one particular type of characters is best suited as the basis for classification came under heavy attack already in Linnaeus’s lifetime” (Mayr 1982, 189). Mayr stresses the artificiality of classifications reached by logical division based on a single character (159–160). 18 See the English-language “Summary” in Frängsmyr 1972. 19 Wolff claims that when we cannot move a thing from one place to another, “we are to observe whether at another time, when placed in other circumstances, it still continues to have what it had before.” His example is that when the sun is high above the horizon, it loses the oval shape it has on rising and setting (VGK V.7). 20 Especially in light of Wolff’s other criticisms of Descartes’s methodology in VGK I.15, VII.19, IX.2, and IX.4.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

159

well be achieved through purely rational scrutiny of concepts, as long as the concepts are sufficiently distinct. It is thus appropriate to frame the question of experience’s justificatory contribution (to science) in terms of procedures for acquiring distinct concepts. It should be emphasized that because distinctness conduces to knowledge of the grounds for predications, the acquisition of such concepts is significant for epistemology, not merely psychology. (Showing that experience is necessary for acquiring the concepts does not settle the question concerning Wolff’s rationalism, however. For rationalistic interpreters might acknowledge this epistemological role for experience, yet argue that its contribution is ultimately dispensable. I argue for its indispensability in Parts 5 and 6.) The central relevance of distinct concepts for this issue is also shown by their tight link with definitions. We saw that through syllogisms we may conclude that a particular (or species) has the properties that are affirmed of, or lacks the properties that are denied of, its species (or genus). Hence the major premise of a syllogism must attribute (or deny) a property to a species or genus. If the judgment is framed with maximal generality, so that the property agrees with “only the individuals of the same species or genus”, 21 and the property holds of the items in this class under all circumstances and at all times, the judgment qualifies as a definition for Wolff. For it supplies a criterion by which these items can be distinguished “at any time from all other things, that have any affinity with them” (VGK I.36). Not only is this conception of definition flexible enough to allow alternative definitions of the very same concept, but it does not require the defining property to be more ontologically basic or easily known than the definiendum. Since Wolff does not sharply distinguish between a concept and its definition, this is another instance of compacting information first expressed propositionally into a concept. The expressive power thus accorded to concepts is quite remarkable, since on Wolff’s view definitions (together with experience, however its contribution is to be understood) are a sufficient basis for all formal reasoning. Wolff explicitly holds that other “first” principles (axioms and postulates) traditionally regarded as indemonstrable are actually consequences of definitions. 22 Since definitions are in this way a basis for all scientific reasoning, if they are known independently of experience, they afford a basis for all scientific knowledge. Now Wolff defines a distinct concept as one such that “we can either repeat to another the marks (Merkmale) by which we cognize a thing; or at least can represent them to ourselves, in particular, one after another”. 23 If these marks are sufficient to distinguish the thing (from all others) under any circumstances, the concept qualifies as a definition, and so can be taken as a basis in deductive reasoning. 24

21

As opposed to holding of some higher genus, which would also include individuals that do not fall under the subject-concept. 22 In the “Kurzer Unterricht” that begins Anf. (hereafter “KU-Anf.”), §§ 29–30. Cf. VGK III.13. 23 VGK I.13. In VGK “mark” is not defined, but is used to designate that which allows us to “recollect” that certain properties were “also observed in a thing we have elsewhere seen”; I.10. 24 At VGK I.36 and KU-Anf. § 2, Wolff defines definitions as distinct concepts through which things of a certain kind can always be distinguished from all other things. The definition of definitio in PR § 152 further requires that the concept include only as many marks as are needed to cognize the thing and distinguish it from all others.

160

3.3.

Katherine Dunlop

Anderson on distinctness and analysis

Although Anderson concedes that Wolff gives experience a “fundamental role” as an “original source” for conceptual content (Anderson 2015, 88–89), on Anderson’s reading the content thus derived is made distinct by analysis. So experience’s role in conceptacquisition is construed as solely, or at least primarily, psychological. 25 The view that distinct concepts are achieved only through analysis is common among (Anglophone) commentators. 26 Analysis consists in, specifically, identifying the “higher” genera under which the concept stands in the hierarchy, together with the differentiae associated with each concept in the line of descent. Anderson explains why articulating concepts in this manner yields philosophical cognition, or in his words “the wanted knowledge from grounds” (Anderson 2015, 86). By this, Anderson means that analysis shows the concept to be possible. It is important to understand how the relevant notion of possibility relates to Wolff’s official notion. In his metaphysics textbooks, Wolff defines the possible as whatever contains or involves no contradiction (VGG II.12; PP § 85). Wolff indicates that this sort of possibility confers the “non-repugnance to existence” that constitutes something as a being (ens or Ding) (VGG II.16; PP §§ 133–134). Nonetheless, he resists defining possibility as a capability to exist because that invites confusion between this manner of possibility, which is intrinsic to things, and there being a cause that is sufficient to produce a thing, which is extrinsic to (finite) things themselves (PP § 133n.). Wolff labels the latter notion “extrinsic possibility” (CG § 111). It also confers a manner of being, which is called “being in potentia” to distinguish it from being simpliciter. Being in potentia is further divided into being in potentia proxima and being in potentia remota, according to whether the cause sufficient to produce a thing is in something actual or in something merely possible (PP § 176). The most important point, for present purposes, is that when we inquire into the reason (or sufficient cause) for what actually happens, we are concerned with both kinds of possibility. This is our concern in the sciences, and also in philosophy generally (outside the special province of ontology, which considers being “in general, or insofar as it is being”) (PP § 1; PD § 73). According to Wolff, philosophy’s job is to give reasons “why those things which can occur actually do occur (actu fiant)” (PD § 31). It is also important to note that the causes sufficient to produce (finite) things constitute a “nexus”, or ordered series. 27 On Anderson’s account, analysis can show (the thing corresponding to) a concept to have both kinds of possibility. First, Anderson indicates that the possibility of concepts is ascertained by placing them in the true hierarchy (the one that “cuts the world at its conceptual joints”, by identifying “the system of compossible essences God picked out as best”). The concepts comprising such a hierarchy “have content and refer to objects, since they correspond to possibilities that have been realized [. . .] by God’s choice of the best” (Anderson 2015, 96). They are thus shown to be possible in the sense of corresponding to things that can exist in the order of nature.

25

I explain this qualification in note 29 below. Some examples are Coffa 1982, Hogan 2009, Schönfeld 1998, and Stang 2016. 27 See Peursen 1987 and Rudolph 2011.

26

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

161

Secondly, analysis shows that the concept is possible in the central sense that its defining characteristics are free from contradiction. (The genus that stands immediately above the concept, together with the specific difference that picks out, within the genus, the objects to which the concept applies, serves to define the concept.) Anderson explains that each node of a Porphyrian hierarchy is subject to two requirements: “(1) the member species must exhaust the sphere 28 of the divided genus, and (2) the species exclude one another, so that none can be predicated of any other” (Anderson 2015, 57). The “exclusion rule”, in particular, guarantees that contradictory concepts (those with incompatible differentiae) cannot “overlap in a common subspecies”. So the “incompatibility of two concepts” can be known “simply from their positions in the hierarchy”, specifically, on branches that diverge at a higher node contained in both concepts (or in genera contained in the concepts or in the genera they contain, etc.). Conversely, the compatibility of two concepts is shown by their standing in a relation of direct linear (i. e. non-branching) descent. The same goes for the genus and specific difference that make up (as component marks) a concept whose possibility is under investigation. Note that the compatibility of concepts can be determined by hierarchical relationships only if all concepts can be ordered in a single Porphyrian tree (so that any two concepts distinct from the summum genus at the top node must both be contained under it, either on one line of descent or on branching lines). Analysis thus settles the question of a concept’s possibility without having to be carried so far as to yield either an explicit contradiction, or absolutely simple components (which are assumed to be incapable of contradicting one another). On Anderson’s interpretation, by making concepts distinct analysis promises to eliminate the only role left for experience in the “completed order” of the philosophical system, namely to establish immediately certain first premises (of demonstrations). For it now appears that such facts are encoded in concepts, from which they could presumably be extracted with sufficient care and insight. Anderson explicitly holds that containment relations are opposed to empirical discoveries, and meant to replace them in the completed structure of scientific knowledge: by showing that what we “would take to be [. . .] additional empirical facts about an object” are in fact contained in its concept, as we make the concept distinct, we are entitled to regard our knowledge of these facts as independent of experience (Anderson 2015, 90). Anderson claims specifically that by rendering concepts distinct, analysis keeps empirical concepts from “disturb[ing] the connection of truths in philosophy” (Anderson 2015, 90; quoting PD § 36). Anderson takes this to mean not only that the content included in empirical concepts is to be incorporated within the “true” hierarchy, but that empirical concepts themselves are merely “provisional stabs at the ultimate, fully analyzed” concepts, which will “eventually find their place in a stable scientific hierarchy” (Anderson 2015, 94). 29

28

“Sphere” is used in eighteenth-century texts as “extension” is now used: for the collection of objects to which a concept applies. “Extension” is typically used in these texts to refer to the concepts that stand under a given concept, i. e. that stand to it as species to genus. 29 Supplying these “provisional” empirical concepts seems to be the “incidental” role that Anderson allots to empirical information in “the genuine order of reasons”, while insisting that it “is needed primarily in the order of discovery” (Anderson 2015, 90).

162

Katherine Dunlop

I will argue that Wolff does not intend analysis to replace empirical methods for ascertaining possibility; he does not hold that concepts are shown to be possible by finding their place in the “true” hierarchy, nor regard empirical concepts as merely “provisional”. Later in the paper, I argue more generally against the view that empirical information is needed only in the “order of discovery”, whereas the sufficiency of conceptual containment (as a basis for knowledge) is reflected in the “order of justification” of the completed philosophical system.

3.4.

Problems with the “one hierarchy” view

A merit of this interpretation is that it explains how Wolff’s approach to philosophy came to dominate the German-speaking intellectual world: in virtue of its elegance and simplicity. But this simplicity also creates problems, three of which I will now introduce. We may begin with problems raised by Anderson himself (as “trade-offs” for making the notion of containment fully determinate). First, (1) a hierarchy constructed according to the rules of logical division cannot supply grounds for all truths. According to these rules, a genus can be divided into species in only one way. The uniqueness of division is required to infer the incompatibility of concepts from the divergence of their lineages. So classifications cannot “cross-cut” one another: once plants, for example, are divided into biological categories, they cannot be reclassified as edible or inedible, cultivated or wild, or cool- or warm-season crops. Such rigidity is perhaps to be expected in a hierarchy that reflects, not our interests and purposes, but the relationships God takes into account in deciding to create the world. But as Anderson argues, a hierarchy that represents “only one kind of affirmative relation among concepts” cannot express basic arithmetical truths, such as that 7 plus 5 equals 12. 30 The rules also prohibit differentiae from appearing at more than one node of a hierarchy: for example, pentamerism (five-fold radial symmetry) cannot be the distinguishing feature of both starfish and bush honeysuckle. It is, again, to be expected that from a God’s-eye point of view each discrete kind of thing is marked by a unique trait or feature. But, as Anderson notes, (2) the inability to “express that there is something common to things falling under different parts of the tree” renders our concepts “much less contentful, and much less explanatory, than they seemed” (Anderson 2015, 124). (The inability to represent, for instance, morphological features shared by an animal with other things would make the concepts useless for understanding biological mimicry or camouflage.) A deeper problem with Anderson’s interpretation is that (3) analysis as Anderson construes it will not necessarily yield philosophical cognition as Wolff defines it, because it may not deliver the requisite insight into the possibility of things. Anderson maintains that analyzing a concept into the predicates that fix its place in the hierarchy is an alternative to analyzing it into absolutely simple components. But it seems clear that placing a concept underneath those that it contains will establish its possibility only if the higher concepts are guaranteed not to harbor a contradiction. (Placing the concepts of round squares, triangles, etc. under the concept “round polygon” will not establish 30

Crucial to Anderson’s argument is that the concept “7 plus 5” stands in a different (“orthogonal”) relation to the concepts of 7 and 5 than to the concept 12. No hierarchy can express both relations without violating the division rules (Anderson 2015, 252).

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

163

their possibility.) It thus appears that the higher concepts reached at a given stage of analysis must themselves be placed under those they contain, until we reach the most general concept(s) at the apex of the hierarchy. But then it is not clear what advantage is offered by the procedure Anderson outlines, over the sort of analysis that terminates in ultimately simple constituents. 31 As I understand Wolff’s method, it is not subject to these objections, because it does not aim to capture all knowledge within a single hierarchy of concepts. 32 In particular, Wolff does not hold that a concept’s possibility is demonstrated only by fixing its place in a comprehensive hierarchy reflecting God’s plan for the universe. Rather, he holds that a concept’s possibility can be proved either by analysis or through experience (specifically either observation or generation of an object falling under the concept), and I will argue that it is ultimately up to experience to ensure that “only those things which truly exist and occur are admitted as possible” (PD § 11). Because the concept’s possibility is secured independently of those ranked above it, problem (3) is eliminated. When the procedures Wolff outlines are followed, the same concept can occur in multiple hierarchies of generality. So Wolff’s usage of Porphyrian trees does not, in fact, limit their expressive power in the ways indicated under (1) and (2). To be sure, when the requirement that all concepts be ordered in a single hierarchy is given up, hierarchical relationships cannot after all determine the pairwise compatibility of concepts or the possibility of concepts defined through a genus and specific difference. But that is a defeat only if Wolff needs a rational basis for all cognition of truth (of judgments) and possibility (of concepts). I will argue that Anderson does not succeed in showing that there must be such a basis.

4. Experience’s role in forming mathematical concepts and making them distinct 4.1.

Wolff on concept-formation and the kinds of definition

Now that I have introduced the rationalist interpretation to which I wish to contrast my own, it is time to consider Wolff’s theory of concepts and definitions in detail. I will argue that even in mathematics – which Wolff construes as the model for all scientific cognition – experience supplies distinct concepts and proves their possibility. In order to highlight these roles (for experience), I will draw on both Wolff’s German and Latin logic

31

There is some reason to think that Wolff saw no difference between the two procedures. As H. W. Arndt puts it, in Wolff’s theory the “intensional” relationship between complex concepts and the simpler ones into which they are analyzed is “set in parallel with the extensional concept-pair of the general and the specific”; this parallelization “is so understood that the complex concept is at once contained in the simpler” one (Arndt 2000, 37). 32 The textual evidence that for Wolff all concepts are situated within a unique hierarchy is weak. In most of the discussions of containment relations cited by Anderson, Wolff merely stresses the importance of making concepts distinct and organizing them into species and genera (especially for purposes of syllogistic inference), without claiming that a unique hierarchy must result (cf. Anderson 2015, 86, n6). Anderson points out that Wolff does commit himself to a highest genus (ibid.), but it does not follow that concepts can be assigned to lower genera in only one way.

164

Katherine Dunlop

textbooks and the “Brief Instruction on Mathematical Method” (Kurzer Unterricht) that begins Anf. As we have seen, according to Wolff a concept is distinct when we can enumerate the marks by which objects are recognized to fall under it. Distinctness can be regarded as a stage or grade in the refinement of concepts. It is preceded by clarity: a concept is clear when it “suffices to distinguish the object to which it belongs; as when we know it is the very object which goes under this or the other name, and which we have seen in this, or the other place” (VGK I.9). (By contrast, a concept is obscure when we cannot determine whether an object thought to fall under it is identical to one encountered on another occasion.) So distinctness consists in an articulation or explanation of the ability possessed when a concept is clear. A distinct concept is in turn rendered adequate (vollständig) when our concepts of its marks are clear and distinct. Adequacy comes in degrees, “as the concepts of the characters of marks, of which [a concept] consists, may be anew analyzed or resolved into others” (VGK I.17). Analysis aims specifically at increasing adequacy (and is the only way to increase it, on the interpretation so far considered). Distinct concepts are also graded along another dimension, called completeness. A concept is complete (ausführlich) “when the characters or marks assigned are sufficient to distinguish the thing at all times from all other things”, and incomplete if it omits any of the marks required (at some time or in some circumstances) to distinguish the thing to which it applies from any other. 33 On Wolff’s view, concepts that are distinct and complete, “that is, of such a nature, as only to agree to individuals of the same species or genus, and consequently to be distinguishable at all times from all other things, that have any affinity with them”, are definitions (VGK I.36). Distinct and complete concepts are, more precisely, nominal definitions. Wolff follows a tradition that distinguishes nominal definitions, which instruct how words (or names, nomina) are to be used, from real definitions, which give the essence of things (res). 34 He follows Leibniz (whom he explicitly claims as a source) 35 in taking nominal definitions to “contain only the marks by which a thing is distinguished from others”. To be a real definition, by contrast, the judgment must make evident that the thing is possible. As we shall see, real definitions typically establish possibility of the robust sort that involves a cause sufficient to produce the thing. Wolff generally speaks of proving the possibility of a concept rather than of the thing it represents. This shift is licensed by his view that possibility consists in the absence of contradiction, with it assumed in the background that any contradiction contained in a thing itself will manifest at the conceptual level (as a pair of predicates that cannot be jointly ascribed). For Wolff, a putative concept that contains contradictory marks is really a notio deceptrix, which is “deceptive” precisely in that it presents itself as something

33

VGK I.15. My translation of “ausführlich” and “vollständig” as “complete” and “adequate”, respectively, corresponds to Wolff’s own use in PR of “notio completa” for a concept whose marks are sufficient to distinguish the object from every other in every circumstance (§ 92), and “notio adequata” for a distinct concept whose marks can be resolved (§ 95). 34 The tradition derives from Aristotle’s distinction between an account of what a name signifies and an account of what a thing is (Posterior Analytics 92b). A locus for the distinction in the early modern period is Arnauld and Nicole, Logic or the Art of Thinking (Part I, Ch. 12.) 35 VGK, Preface to the First (1712) edition.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

165

thinkable; in fact, in such a case we have no concept, but only words without meaning (termini inanes). 36 For the use of a concept in science, it is important that the concept’s definition be real. Wolff explains that the way in which the concept is acquired determines whether the nominal definition can stand as a real definition, or whether the concept’s possibility must be proved separately. He lists three ways of obtaining distinct concepts (Fig. 1), of which only one corresponds to analysis into higher concepts.

Figure 1: How distinct concepts are obtained and their possibility proved in Wolff92s VGK.

The first way presupposes representation of something that “contains not too many distinct things”. It consists in giving “special consideration” to these discernible contents, then “compar[ing] one with the other, and attentively examin[ing] their order and connection” (VGK I.19; cp. PR § 682). In PR, this method of concept-acquisition is described as “reflecting on” and distinguishing the parts in a perception (§ 716). “Reflection” might be thought to designate an intellectual faculty, but Wolff describes this way of acquiring concepts as “through the senses”, so for him their role in delivering the perception is paramount. Wolff claims that the possibility of a thing whose concept is acquired this way does not require proof, “for who can entertain a doubt of the possibility of a thing that really exists?” (VGK I.31). It is presumably the representation’s origin in perception that put its object’s existence beyond doubt. Wolff claims that we both arrive at the nominal definition of a triangle and are convinced of its possibility in this way, specifically “by actually perceiving that a space is enclosed in three straight lines” (KU-Anf.). The second way is to “seclude or select that which is common” to different things whose concepts are compared and “by this means form a new concept that applies to both”. Wolff’s example is that “on comparing the notion of a right lined triangle with that of a square, I find, that both are contained under right lines”, and thus form “the concept of a right lined figure, viz. that it is a space, contained under right lines” (VGK 36

PR § 38. Cf. Arndt 2000 and Kuehn 1997.

166

Katherine Dunlop

I.26). He explains that by leaving out more determinations, we can “ascend to notions still more general”, as by “omitting both the species and the number of sides”, we obtain “the concept of a plane figure in general” (VGK I.27). Similarly, from the concepts of man and beast (Vieh), we draw “the general concept of animal” (Tier), and from the concepts of animal and vegetable, we draw “the general concept of animate creature” (VGK I.29). This method of concept-acquisition is called “abstraction”. Because it yields concepts that rank higher in Porphyrian hierarchies (and thereby puts us in position to isolate the differences that characterize species), it is the analogue, in this scheme, of analysis. But note that even in this case, concepts derive their possibility from those below, rather than above, them. Wolff argues that because abstracted concepts “contain nothing but what is in the particular concepts, from which they are abstracted”, their possibility is as secure as that of the particular concepts (VGK I.32). So when the particular concepts are acquired by the senses, the possibility of concepts abstracted from them is guaranteed. 37 So far, it appears that Wolff countenances empirical methods for acquiring distinct concepts. Accordingly, discernment of containment relations is not opposed to – far less intended to replace – the discovery of empirical facts about objects. On the alternative interpretation I propose, we master the structure of our concepts at the same time that we discover empirical facts. It remains, however, to consider the way of obtaining distinct concepts that is most important for science. The third way of obtaining distinct concepts is to “determine what is not yet determined, or also to determine in another way what is already determined” in a given concept. In Wolff’s examples, the given concept is that “of a right-lined triangle, that it is a space enclosed in three straight lines”. Here the magnitude of the lines is not determined; the concept of equilateral triangle is obtained by determining that the three lines should be of equal length. Wolff then remarks that the concept of curvilinear triangle is obtained by determining the lines as curved, rather than as straight (VGK I.30). (Adding new determinations or substituting them for given ones appears bound to issue in either multiple hierarchies of generality, or a unified hierarchy that does not respect the division rules. Applying this procedure to the triangle, for example, yields a hierarchy of curvilinear figures that must be either separate from the hierarchy (to which the given concept belongs) of straight-lined figures, or combined with it; in the latter case, determinations such as “three-sided”, “four-sided” and so forth will occur on each of two divergent branches.) Wolff calls this method “determining according to our own election (Willkühre)”. Unlike the second method, it is not guaranteed to preserve the possibility of the concept on which it operates. For, Wolff argues, “our will (Wille) can make nothing possible”. He further cautions that “it is not enough that the determinations are possible in themselves. Rather, it is also required that they can exist (bestehen) alongside the others”. Wolff’s illustration of this point, which will be adapted by Kant to show that the concept of a possible thing must “agree with the formal conditions of an experience in general” (KrV A220 /B268), is that “it is equally possible for two lines to be either right or curved; but if you farther add that they enclose a space, or that they come together at both ends, this indeed answers in the second case, but not in the first” (VGK I.33). If the combined determinations are contradictory, then the attempt to form a concept has 37

Cf. Kuehn 1997, 233.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

167

failed. This procedure for forming concepts (which I call “arbitrary determination”) is the only opportunity for contradiction and empty expressions to enter the foundations of science, so the means of ascertaining the possibility of concepts formed in this way are of special importance for Wolff’s overall account.

4.2.

Proving the possibility of arbitrarily determined concepts

Wolff gives three ways in which the products of arbitrary determination are shown really to be concepts, i. e. to be possible. First, we can find by experience “whether a concept is possible” by “looking around” and attending to whether “we find anything in the world that agrees therewith” (VGK I.34). Wolff appears not to regard this as part of the method appropriate for science, i. e. the mathematical method; for he gives no indication that the possibility of a mathematical concept could be proved in this way. The second way is to show “how such a thing could come into being”, since “if we know how something could come into being, we may no more doubt as to whether it could be”. Wolff explains that Euclid “proves in this way that an equilateral triangle is possible when he shows how [such a triangle] can be described on any straight line.” (He then claims that “in the same way it becomes clear that a machine is possible when I correctly show how it is made.” We will shortly consider the significance of this comparison.) The third way is “to investigate whether something flows from the concept, of which we already know whether it is possible.” To justify this method, Wolff argues that “if impossible things flow from a concept, then neither can the concept itself be possible; but if only possible things flow from it, then it must itself be possible. For what flows from something else can be, because this other thing is” (VGK I.35). Wolff claims that this method shows a rectilinear two-sided figure (Zweyecke) to be impossible. In VGK, Wolff groups the latter two ways of ascertaining possibility under the heading of “proof”, in contrast with the first way, “by experience” (see Fig. 1). In PR, the second and third ways are classified as “a priori” means of forming definitions (PR § 734, §§ 720– 721). But in this period, talk of knowing something a priori primarily meant knowing it “from grounds”, specifically having insight into how its grounds make it true. 38 Since this insight is a kind of rational understanding, such knowledge involves the rational faculty, but it need not be a priori in the contemporary sense of being justified independently of experience. 39 I will argue that experience has a justificatory role in these cases.

4.3.

How real definitions are attained

The role of experience in justifying mathematical cognition shows itself clearly in Wolff’s account of how real definitions are obtained. The issue of obtaining real definitions is separate from that of ascertaining the possibility of distinct concepts (even though in showing their possibility, we show nominal definitions to be real), because we can acquire a real definition of something of which we have no distinct concept – indeed, of which we “know absolutely nothing”. According to Wolff, this happens when “we assume such things, with which [we are] already familiar, and carefully investigate what arises from 38 39

See Smit 2008. On this point, see Vanzo 2015 and Paccioni 2003.

168

Katherine Dunlop

their combination” (VGK I.51). We can then inquire whether the thing produced in this way is “already actually at hand” and called by some name. In case it is not, we presumably come to represent something at the same time that we ascertain its possibility. In this way the function of a real definition (proving the possibility of something) is fulfilled, but it is not so obvious how the more familiar function of definition (presenting the elements that comprise a concept) is fulfilled. Wolff’s idea may be that the concept thereby formed represents the thing as what results from a certain combination, so that these materials and the manner of their combination become elements of the concept. Wolff notes that this phenomenon occurs “in mathematics”, when we identify a curve the way in which it is constructed. If we then find that the resulting plane figure has a property already studied by geometers, 40 the possibility of a figure with this property is proved in the second way. While Wolff evidently regards this as part of usual mathematical practice, it does not appear to count as a logical or rational way of gaining knowledge. For Wolff claims that “here much depends on blind luck. Namely, if either fortuitously (ungefehr) or with design (mit Vorsatze) we combine such things together, of which we could not beforehand affirm, that they would yield us any new thing, only observing what might be the result” (VGK I.52; cf. PR §§ 735–6). That the combination “yields a new thing” is just the proof of possibility required for a real (as opposed to merely nominal) definition. Here, Wolff denies that its possibility is ascertained in any other way than through experience. Since Wolff denies specifically that its possibility could be ascertained in any other way “beforehand”, experience might be thought necessary only for the initial acquisition of the concept (leaving open that its possibility could be subsequently be ascertained rationally, e. g. by situating it in the “true hierarchy”). But the thrust of this passage is rather that no amount of prior information could, in principle, yield a rational proof of the “new” thing’s possibility. In KU-Anf., the arbitrary combination of “possible things” (which are here mathematical objects) is compared to the invention of machines in order to bring out the experimental character of the former. Wolff writes that one way to find real definitions is to “combine many possible things, which one has cognized, with one another, and thereby bring out a new thing, as if one were to combine the simple machines with one another, so that a new and complex machine emerges, of which one previously had no concept at all” (KU-Anf. § 23). Since here we antecedently had no concept at all of the result (of the combination), this method of finding its definition is obviously not rational or logical. Now Wolff does not explicitly deny that a real definition of the new machine could subsequently be derived by rational means, but he does not give any indication how such a derivation could be carried out. Wolff uses a comparison with machines to the same purpose in VGK, specifically in his account of how to obtain real definitions, which returns to the topic of proving the possibility of a distinct concept. Wolff claims that insofar as one considers the marks contained in the concept, “what is required for the formation of the thing will show itself”.

40

VGK I.53. A celebrated example is the cycloid, first known as the curve traced by the path of a point on the rim of a (circular) wheel that rolls (without slipping) along a straight line, and later recognized as a “tautochrone”, i. e. having the property that a body placed anywhere on (a completed cycle of) the (inverted) cycloid and accelerated only by gravity will reach the lowest point in the same time.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

169

For instance, we discover how steam is generated (namely, by heating water to “rarify” the air contained in it) from the nominal definition of steam (as “aqueous particles which collect high in the air”) and what is “known distinctly about water, air, and the ascent of bodies in fluids; namely, that there is much air in water, that [. . .] air rarifies with heat, that things specifically lighter ascend in fluids specifically heavier”. But it is much easier, Wolff claims, to grasp the procedure for generating a thing that has “a certain structure which can be well examined either with the naked eye or with magnifying lenses”. Here, we need only “eyes to see, attentiveness, and a ready and dextrous hand to analyze the thing”, rather than the prior knowledge and “deep reflection” needed to understand how particles of water are made to rise in air (VGK I.54). (In contrast to the other two passages, here Wolff explicitly distinguishes rational and empirical means of proving something’s possibility. But there is no indication that the rational means is superior to, or meant to supplant, the empirical one.) With this later passage in view, the comparison between the design of machines and the construction of geometrical figures in § 35 of Chapter I can be seen to reinforce the suggestion that the combinations by which figures are generated are learned through experience. This role for experience is also apparent in Wolff’s discussion of the two-sided plane figure. In VGK, the “impossible” consequence that “flows from” this concept is said to be that “two right lines may intersect each other in two points”. Wolff claims that the uniqueness of the lines’ intersection point is certain “from other considerations” (VGK I.35), but does not specify them. On his view, any such conclusion must ultimately be deducible from definitions, perhaps in conjunction with “indubitable experiences”. In his Latin metaphysics, Wolff concludes that a bilineum rectilineum is impossible because it contradicts “the truth that between two points can be contained no more than one straight line” (PP § 79) and it is an axiom that “there can be only one straight line between two points.” 41 This is therefore the principle that should follow immediately from definitions and entail (perhaps by further reasoning) that lines can intersect in only one point. But Wolff does not supply definitions from which it follows. 42 The above account of how we determine the possibility of combinations of known things, namely by “blind luck”, suggests another source for Wolff’s conviction that there can be only one straight line joining two points: namely, the failure of all attempts to construct multiple such lines. Wolff’s conviction can thus be seen to rest on experience, namely of how space constrains the construction of figures. This provides further evidence that knowledge of “how” things “come into being” can be (and even typically is) empirical. It also implies that the distinction between the second and third ways of proving arbitrarily determined concepts’ possibility is not sharp. Insofar as the impossibility of what “flows from” the rejected concept is known by experience, it shows that experience can enter into the third way of proving possibility.

41 42

Listed as an axiom in Anf., 129. I argue in Dunlop 2013 that it does not follow from the definitions Wolff gives.

170

Katherine Dunlop

5. Justifying the use of generalizations in syllogisms I have argued that for Wolff, even in mathematics experience functions to guarantee that “only those things are admitted as possible which truly exist and occur” (PD § 10). In particular, experience establishes the possibility of arbitrarily combined concepts. I have raised objections to the view that possibility is instead established by placing concepts in the “true” hierarchy. As I argued, Anderson does not grant experience any role in making concepts distinct. But a rationalist reading such as Anderson’s could perhaps concede such a role for experience, yet ultimately deny experience any place in the “order of justification”, specifically syllogistic demonstration, proper to scientific cognition. Anderson himself identifies “three main features” of Wolff’s view that attest his commitment to “the rationalist ideal of knowledge from concepts alone”: “the fundamental status of the principle of contradiction; the centrality and alleged fruitfulness of the method of conceptual analysis; and the theoretical importance granted to the syllogism” (Anderson 2015, 79–80). For these features to properly cohere, appeals to experience must be dispensable (so that the premises of syllogisms, as well as their conclusions, are justified by concept containment relations, “unpacked” in accordance with the principle of contradiction). In Part 5, I argue that the experience through which definitions are formed has a specific justificatory role that underlies Wolff’s account of their use in syllogisms. This involves a defense of Wolff’s view (as I understand it) against Anderson’s criticisms. In Part 6, I argue more directly against Anderson’s view that for Wolff, all empirical justification must be recast as rational, specifically as instantiating the principle of contradiction. Our focus now shifts from the ways definitions are shown to be real, to how they are shown to have the generality required of both real and nominal definitions. We saw in 3.2 that Wolff uses the example of discovering that wax is not “constantly” soft to illustrate how we can learn from experience whether a property is an attribute of a thing. In VGK, he gives a general methodology – illustrated by the same example – for ensuring that nothing is “taken into a nominal definition, but what at all times agrees with” the thing being defined. The rationale for transporting the wax from a warm place to a cold one is that “I must remove a thing from its present contiguity with some things to a contiguity with other things” to make it apparent “whether anything agrees with it only in certain circumstances”. Notably, Wolff seems to offer this as explication of how “we are carefully to inquire into the reason of this or the other notion agreeing to a thing”, and in particular whether the reason lies in the thing or without it (VGK I.42). So this is another instance of using “reason” to refer to properties which are found to obtain (under given circumstances) in experience. I will now argue that the role of experience in ensuring that nominal definitions contain only invariant properties also warrants their role in syllogistic argument. Anderson emphasizes that Wolff is “just as keen to insist on syllogistic reconstruction for empirical arguments as for mathematics” (Anderson 2015, 91). To illustrate the application of “geometrical” method to natural science, Wolff syllogistically proves that air has expansive force. He claims to have learned that air has expansive force “from experience: Namely, if I closely tie up a little air in a bladder (to prevent its escape), hang it under a glass receiver, and pump away the external air; the air in the bladder becomes expanded”

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

171

(VGK I.45). The argument by which Wolff formalizes this result can be condensed as follows: (P1) Whatever expands a bladder, upon removing the resistance, has expansive force; (P2) The air, upon removing the resistance, expands the bladder; (C) Therefore, the air has expansive force. Anderson observes that Wolff’s “empirical reconstruction contains no distinct step generalizing from particular experience”, such as the expansion of a balloon inside a vacuum jar, “to universal claim [such as] ‘Air expands when resistance is removed’”. He understands Wolff (correctly, I believe) as seeking to exploit the “standard rule that treats singular judgments as universal for purposes of inference, since they apply the predicate to the whole extension of the subject” (Anderson 2015, 92). Wolff explains (in a paragraph entitled “How universal propositions are acquired through experience”) that while propositions based on single (eintzele) things are singular “in and for themselves”, “we can very easily change them into universal propositions, if only we take exact notice of the circumstances in which something happened” (VGK V.15). He refers back to his earlier argument that the “reason for the agreement” of a predicate with a subject can be contained in the subject of a particular (besondere) proposition in the same way as in a universal proposition, namely, so that it must agree with every thing belonging to a species. This can happen if, specifically, “the condition is added”. For example, the particular proposition “Some stones warm, which themselves are warm” “becomes universal if I say: ‘All stones that lie a long time in the warmth, are warm’”. The predicate now agrees with every member of the class of stones that lie a long time in the warmth. I think Anderson is also correct that for Wolff, “what is essential to the weight-bearing role of the minor premise is [. . .] that it finds the correct general concepts for characterizing the experience in the first place” (Anderson 2015, 93), in particular, concepts that specify invariant features. For on Wolff’s view, as we have just seen, we can identify the determinations constantly possessed by things of a certain kind by varying the circumstances in and under which we observe the things. When we identify their invariant features in this way, we are in position to determine the conditions under which such things gain or lose their other properties. Propositions whose predicates express the properties and whose subject-terms incorporate these conditions are definitions (in the sense that they are framed with maximal generality) of the concept, and can be used as premises in syllogisms. The source of our warrant to treat these propositions as universal (i. e. as applying a predicate to everything in a certain class) appears to be just the process of observation by which we arrive at them. In the minor premise of Wolff’s syllogism, the condition (that the resistance is removed) is already made explicit in the subject clause. Anderson, however, finds Wolff’s account of the reasoning unsatisfactory. Anderson charges that the problem of generalizing singular judgments, which it appears to resolve, in fact reappears “as a difficulty about forming truly general empirical concepts which correctly capture” things’ essences. He objects, in particular, that Wolff’s “control requirements” on concept-formation are inadequate, which renders this “approach to settling worries about induction” “rather cavalier” (Anderson 2015, 93). By “control requirements”, Anderson refers to Wolff’s counsels that we should systematically vary the circumstances and environments of observation, and make sure experiments are repeated by ourselves or others (VGK I.42, V.6–7, V.12),

172

Katherine Dunlop

before concluding we have identified the “condition” under which a predicate holds. (This reflects Wolff’s view that definitions are not generally based on “particular” experiences, but rather on experience of an object in a variety of settings. 43) While Anderson may well be correct that Wolff underestimates the risk of error in generalizing from experience, it is important to see that this is not an in-principle difficulty for the project of justifying a concept’s use in a universal proposition by means of the experience by which we arrive at its definition. 44 For if Wolff’s precautions are not adequate, the prospect remains that stronger requirements would satisfy the concerns. A point on which I agree with Anderson is that the knowledge available to finite intellects is not just an “empirically grounded approximation” to a “fully demonstrative final system” of knowledge, but that a completed, comprehensive system of science is within the reach of (collective) human endeavor. Of course, I do not agree that within the final system predications must be based on the logical extraction of predicates from concepts, rather than being empirically warranted. Considering experience’s role within the system of science brings us to the important issue of whether Wolff subscribes (along with Kant and Leibniz) to the view that experience is never sufficient to grasp necessary truths. 45 Wolff thinks experience can not only show that properties belong to things only conditionally (as when the wax loses its softness), but also that properties belong to things under all circumstances, i. e. are “attributes”. Thus, he claims we may conclude that “hardness is an attribute of stone” on the grounds that wherever the stone is conveyed, “it still remains hard” (VGK V.6). This is very close to saying that we can grasp things’ essences through experience. In fact, however, Wolff distinguishes essential features from (mere) attributes on the grounds that the former are sufficient to explain the latter. One might also suppose that essential features hold of an object even in counterfactual situations, whereas mere attributes hold merely in all actual circumstances. I do not claim that attributes can be found through experience to have these characteristics, which would qualify them as essential. But I do think Wolff’s comparison between the generation of geometrical objects and the operation of machines helps to show how a constituent structure, which belongs inseparably to something (and even explains its other features), could be grasped through experience. Some of Wolff’s examples of how concepts are made distinct, and conditions are identified, through experience seem to presuppose that the having of properties is to be explained in a broadly mechanistic manner, in terms of how parts of certain shapes and sizes act (locally) on one another.

43

Arndt argues that in place of a method (Art) of inferring from a single case to the general case, Wolff has a “research strategy [. . .] based on the circumstance that the general case is always already examined and reflected in single cases, on account of the generality of the investigative set-up (Fragestellung)” (Arndt 1983, 33). 44 It might seem that Wolff cannot have this project, since he claims that only through understanding do we “have universal concepts and therefore universal cognition at all”; VGG § 286 (titled “The understanding brings us to universal cognition”). But in the preceding paragraph (§ 285) Wolff insists that “our understanding is never pure”, where cognition of the understanding is “impure” when it is “still united with the senses and imagination (§ 282). It has been argued that a crucially important exercise of “impure understanding” is the “simple apprehension” by which the understanding comes to represent features common to a number of (perceived or imagined) particulars, and thereby attains concepts of species and genera. See École 1986 and Paccioni 2003. 45 I thank an anonymous referee for prompting me to address this point directly.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

173

6. Experience and the Principle of Non-Contradiction We saw that Anderson finds three elements of Wolff’s view that “push in the direction” of holding that all truth is ultimately conceptual, so that (rational operations on) concepts are a sufficient basis for all knowledge. With respect to the first two (conceptual analysis and syllogistic inference), I have argued that distinct concepts and syllogisms are important as ways of systematizing, rather than as replacements for, information derived from experience. It remains to consider the third element, which is the apparent sufficiency of PNC as a basis for all knowledge. The first and third elements are interrelated: PNC suffices to determine the truth of all judgments (rather than only the falsity of contradictory ones) because analysis makes it possible to establish the truth of judgments whose subject- and predicate-concepts are not contradictory. As we saw in 3.3, if two concepts are not contradictory they must stand in a relation of direct linear descent (in a Porphyrian hierarchy). But this is just the containment of the predicate concept in the subject (or in the genera contained in the subject concept), which makes the judgment true. Wolff’s attempt to derive the Principle of Sufficient Reason (PSR) from PNC is wellknown (see Anderson 2015, 84–85), but the parallel Anderson finds between Wolff’s treatment of PSR and his treatment of experience is not as widely recognized. Central to Anderson’s interpretation are Wolff’s claims that through the PNC “a proposition that we experience is placed beyond all doubt”, and that experience “ultimately has [PNC] to thank for its certainty” (VGG § 10, § 391). According to Anderson, Wolff is claiming that “our knowledge, or certainty, through experience derives from” PNC (Anderson 2015, 81). Anderson discerns two lines of argument for this claim, and objects that both are circular. On the first line of argument, the certainty of Descartes’s cogito reasoning extends to all experience, through (implicit) reliance on PNC. Wolff claims that in the case of the cogito, certainty in our existence is inferred from the following premises: (1) We undeniably experience that we are conscious of ourselves and other things. (2) It is clear to us that whoever is conscious of himself and other things exists. (VGG § 5)

Wolff contends that the experience referred to in the first premise is certain in virtue of PNC, for when “we cognize that we are conscious of ourselves and other things, and take this to be certain, this occurs because it is in fact impossible for us to comprehend that we should be conscious of ourselves and at the same time not be conscious of ourselves”. Wolff then claims that “in all other cases we find that it is impossible for us to comprehend that something does not exist when it does”, and thus implicitly “acknowledge” the “universal proposition [known as PNC]: Something cannot at the same time be and also not be” (VGG § 10). Anderson objects that with respect to these “other cases”, “if I were not already certain that the something in question ‘is’, then there would be no impediment whatsoever to my thinking ‘that it was not’”. While it would be impossible for me to think both thoughts together, considering this impossibility “does nothing to improve my certainty about what I experienced in the actual case” (Anderson 2015, 82). The “leading idea” of the second line of argument is that “the possibility of a thing consists in its containing no contradiction in itself”. So when we experience things, the possibility that is vouchsafed through that experience is “inherited” from “consistency among their constituent marks” (Anderson 2015, 83). Anderson objects that this line of

174

Katherine Dunlop

argument, like the first, assumes the certainty of the experience in question, rather than showing it to be based on PNC. For whatever certainty we have that what we experience is “a thing”, rather than mistakenly represented as one, is not due to PNC. I think these criticisms may mistake the aim of Wolff’s argument. In taking Wolff to hold that “knowledge, or certainty, through experience derives from” PNC, Anderson elides an important distinction. Wolff need not assume at the outset that a belief based on experience (that something “is” or is “a thing”) is certain, but merely that it is knowledge. The role of PNC could then be to show it to be certain, by showing the impossibility of believing the opposite. Specifically, PNC shows the untenability of the conjunction to which we will be committed if we believe the proposition’s negation without giving up our assent to the proposition. To be sure, the untenability of this contradiction does not itself weigh in favor of accepting the proposition rather than its negation. But it does force us to choose, and experience supports the acceptance of the proposition, while nothing supports the acceptance of its negation. On this reasoning, the argument illustrates Wolff’s tendency to contend fussily for the obvious. 46 But it no longer begs the question. Additional reason to doubt that PNC plays the role Anderson attributes to it is that Wolff elsewhere suggests that PNC’s validity is grounded on experience. A paragraph of Wolff’s Latin metaphysics, entitled “Foundation of the Principle of [Non]-Contradiction”, argues that experience shows it to be “the nature of our mind” that we cannot judge at once both that something is and that it is not”. 47 Without taking time to examine what sort of “foundation” this comprises, we can say at least that if experience’s role in knowledge depends on PNC, there is also a dimension on which our entitlement to PNC rests on experience.

7. Conclusion On the interpretation presented here, the use of PNC is to rigorously express the warrant supplied by experience, in much the same way that the exhibition of containment relations in genus-species hierarchies formalizes empirical knowledge of how widely conditions hold. Neither kind of regimentation supplants empirical sources of knowledge. In closing, I briefly consider how it suits Wolff’s purposes to find roles for experience in mathematical and (formal) syllogistic reasoning. To defend the universal applicability of mathematical method, Wolff must show that it is suitable for natural science, in particular. The examples Wolff uses in PD to show the usefulness of philosophy (with respect to historical cognition) are primarily from “physics”, which Wolff defines as “that part of philosophy which treats of bodies” (PD § 59). (On this conception, physics includes botany and physiology as well as the study of atmospheric phenomena, minerals, and fluids.) If the mathematical method already gives experience a justificatory role, it is far easier to see how it could be appropriate for such disciplines. I have explained how experience can both show concepts to be possible, and show whether properties are attributes, by revealing the constituent structure of a thing (or 46 47

This tendency is vividly characterized in Beck 1969. PP § 27. Cf. Arndt 1983, 37, n. 48; Cataldi Madonna 2011, 285; and Kreimendahl 2007, 101.

Definitions and Empirical Justification in Christian Wolff’s Theory of Science

175

how it issues from a combination of simpler things). After noting that real definitions are easily found by grasping such structures, Wolff claims the structures are possessed by “all machines that are actually to be found” as well as by all plants and animals (VGK I.56). So far I have emphasized the role of experimentation, e. g. in combining primitives. But for Wolff, the experience through which we learn how a thing comes into being can consist in passive observation, rather than actively trying out combinations of things. He ends VGK’s chapter on concepts by noting that it is easy to acquire real definitions when “we are present with attention at the genesis or formation of a thing” (VGK I. 57). On this construal of experience’s role, mathematical cognition can be a model for natural sciences in which observation plays a larger role than experimentation, such as geology and meteorology. It is particularly apt with respect to biology, especially (even if coincidentally) Linnaeus’s classification of plants in terms of their sexual organs. For “the genesis or formation of a thing” can mean the entire process of reproduction, and if we can observe this in its details, we will also have identified traits that serve to place the thing in a genus-species hierarchy. 48

Bibliography Anderson, R. L. 2015. The Poverty of Conceptual Truth. Oxford: Oxford University Press. Arndt, H. W. 1983. Rationalismus und Empirismus in der Erkenntnislehre Christian Wolffs. In: Schneiders, W. (ed.). Christian Wolff 1679–1754. Hamburg: Meiner. Arndt, H. W. 2000. Zum Wahrheitsanspruch der Nominaldefinition in der Erkenntnislehre und Metaphysik Christian Wolffs. In: École, J. (ed.). Autour de la philosophie Wolffienne. Hildesheim: Olds. Beck, L. W. 1969. Early German Philosophy. Cambridge, Mass.: Belknap. Cataldi Madonna, L. 2011. The Eighteenth-Century Rehabilitation of Sensitive Knowledge and the Birth of Aesthetics. In: Munk, R. (ed.). Moses Mendelssohn’s Metaphysics and Aesthetics. Dordrecht: Springer. Coffa, A. 1982. Kant, Bolzano, and the Emergence of Logicism. Journal of Philosophy 79, 679–689. Dunlop, K. 2013. Mathematical Method and Newtonian Science in the Philosophy of Christian Wolff. Studies in History and Philosophy of Science 44, 457–469. Dunlop, K. 2014. Arbitrary Combination and the Use of Signs in Mathematics: Kant’s 1763 Prize Essay and its Wolffian Background. Canadian Journal of Philosophy 44, 658–685. École, J. 1986. “Du role de l’entendement intuitif dans la conception wolffienne de la conaissance”. Archiv für Geschichte der Philosophie 68, 280–291. Frängsmyr, T. 1972. Wolffianismens genombrott i Uppsala. Uppsala: Acta Universitatis Uppsaliensis. Hatfield, G. 1997. The Workings of the Intellect: Mind and Psychology. In: Easton, P. (ed.). Logic and the Workings of the Mind. Atascadero, Calif.: Ridgeview Pub. Co. Hogan, D. 2009. Three Kinds of Rationalism and the Non-Spatiality of Things in Themselves. Journal of the History of Philosophy 47, 355–382. Kreimendahl, L. 2007. Empiristische Elemente im Denken Christian Wolffs. In: Stolzenberg, J. / Rudolph, O.-P. (eds.). Christian Wolff und die europaïsche Aufklärung. Hildesheim: Olds. Kuehn, M. 1997. The Wolffian Background of Kant’s Transcendental Deduction. In: Easton, P. (ed.). Logic and the Workings of the Mind. Atascadero, Calif.: Ridgeview Pub. Co.

48

I thank R. Lanier Anderson, Eric Watkins, and several anonymous referees for helpful comments on earlier drafts of this paper.

176

Katherine Dunlop

Mayr, E. 1982. The Growth of Biological Thought. Cambridge, Mass.: Belknap. Paccioni, J.-P. 2003. Wolff, l’expèrience et la raison non pure. Revue Philosophique 3, 307–322. Peursen, C.-A. v. 1987. Christian Wolff’s Philosophy of Contingent Reality. Journal of the History of Philosophy 25, 69–82. Rudolph, O.-P. 2011. Christian Wolffs Ontologie also Wissenschaft des Möglichen. In: Fabbianelli, F. /Goubet, J.-F. /Rudolph, O.-P. (eds.). Zwischen Grundsätzen und Gegenständen (Wolffiana IV). Hildesheim: Olds. Schönfeld, M. 1998. Dogmatic Metaphysics and Tschirnhaus’s Methodology. Journal of the History of Philosophy 36, 57–76. Shabel, L. 2003. Mathematics in Kant’s Critical Philosophy. Routledge: New York and London. Shabel, L. 2006. Kant’s Philosophy of Mathematics. In: Guyer, P. (ed.). The Cambridge Companion to Kant and Modern Philosophy. Cambridge: Cambridge University Press. Smit, H. 2008. “Reason, Insight, and Apriority in Kant”. In: Rohden, V. et al. (eds.). Recht und Frieden in der Philosophie Kants: Akten des X. Internationalen Kant-Kongresses. Vol. 2. Berlin /New York: de Gruyter. Stang, N. 2016. Kant’s Modal Metaphysics. Oxford: Oxford University Press. Sutherland, D. 2010. Philosophy, Geometry, and Logic in Leibniz, Wolff, and the Early Kant. In: Dickson, M. /Domski M. (eds.). Discourse on a New Method. LaSalle, Ill.: Open Court. Vanzo, A. 2015. Christian Wolff and Experimental Philosophy. Oxford Studies in Early Modern Philosophy 7, 225–255. Watkins, E. (ed.). 2009. Kant’s Critique of Pure Reason: Background Source Materials. Cambridge: Cambridge University Press. Wolff, C. 1716. Mathematisches Lexikon. Leipzig: Joh. Friedrichs Gleditschsens seel. Sohn. Wolff, C. 1733. Von der Logick des Autoris insbesondere. Ch. 6 of Ausführliche Nachricht von seinen eigenen Schrifften. Frankfurt am Main.: Joh. Benj. Andrei und Heinr. Hort. Wolff, C. 1770. Logic or Rational Thoughts on the Powers of the Human Understanding. London: L. Hawes, W. Clarke and R. Collins. (Original: Wolff, C. 1754. Vernünftige Gedancken von den Kräften des menschlichen Verstandes. Halle Magdeburg.) Wolff, C. 1841. Christian Wolffs eigene Lebensbeschreibung. Wuttke, H. (ed.). Leipzig: Weidmann’sche Buchhandlung.

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy: A Study of Their Responses to the vis viva Controversy Huaping Lu-Adler, Georgetown University

Abstract This paper examines Du Châtelet’s and Kant’s responses to the famous vis viva controversy – Du Châtelet in her Institutions Physiques (1742) and Kant in his debut, the Thoughts on the True Estimation of Living Forces (1746–49). The Institutions was not only a highly influential contribution to the vis viva controversy, but also a pioneering attempt to integrate Leibnizian metaphysics and Newtonian physics. The young Kant’s evident knowledge of this work has led some to speculate about his indebtedness to her philosophy. My study corrects such speculations as well as misunderstandings of the Living Forces. This corrective result has implications for how to investigate Kant’s relation to the ever-evolving landscape of Leibniz exegeses.

1. Introduction My goal in this paper is to clarify the relation between Kant’s early philosophy and Émilie Du Châtelet’s work. I do so through a focused examination of their responses to the famous vis viva controversy – Du Châtelet in her Institutions Physiques (1742, second edition) and Kant in his first publication, the Thoughts on the True Estimation of Living Forces (1746–49). The fact that Kant repeatedly mentions Du Châtelet in his debut, coupled with recent studies of her as an influential and unique voice in the discourse on natural philosophy during the 1740s, suffices to make us curious. 1 There have indeed been speculations about the early Kant’s relation to Du Châtelet, but, as I shall explain shortly, a more grounded study of that relation is in order. An important part of this study is to understand what Kant might have sought to accomplish with the Living Forces, a question that has received competing answers. 2 Particularly controversial is how this work relates to what Martin Schönfeld calls Kant’s “precritical project,” defined by the ambition to find “a coherent philosophy of nature” and “to integrate Newtonian physics in a comprehensive and speculative framework” (Schönfeld 2000, 3). To Schönfeld, the Living Forces was not a bona fide part of this project, even though, as the starting point of Kant’s “precritical philosophy,” it would

1

Kant shows a keen interest in Du Châtelet’s dispute with Jean de Mairan (GSK 1: 45–46, 55, 67–68, 92–93, 130– 133), a well-known episode of the vis viva controversy. I discuss the episode in section 3. 2 See Adickes 1924, 65–144; Cassirer 1981, 26–32; Shell 1996, 10–30; Kuehn 2001, 86–95. I will also mention other commentaries below.

178

Huaping Lu-Adler

“cast a long shadow over Kant’s subsequent endeavors” and lead to the precritical project as an “indirect consequence” (Schönfeld 2000, 18–19). When writing his first book, Kant had not yet experienced the Newtonian conversion that would dominate his thoughts on nature for the rest of his life, and he had not yet given thought to the grand issues of metaphysics that would govern the precritical project. In this regard, the Living Forces occupied a position all on its own. (Schönfeld 2000, 18)

To Michael Friedman, by contrast, the Living Forces already “initiates a fundamental philosophical reconsideration of Newtonian physics which is then continued throughout the so-called pre-critical period.” The purported reconsideration centers on an attempt “to redefine the nature and method of metaphysics in light of the recent breathtaking advances in mathematics and mathematical physics” and, especially, “to revise the LeibnizianWolffian monadology in light of Newtonian physics” by, among other things, “import[ing] Newton’s second law of motion into the very heart of the monadology” (Friedman 1992, xi, xiii, 5). 3 However important it may be to clarify the early Kant’s relation to Newtonian physics, 4 it seems problematic to make this a key interpretative concern that determines the place of the Living Forces in Kant’s philosophical development. For one thing, it is the Cartesian, not Newtonian, physics that gets most of the attention in this text. For another, the more basic philosophical issue at play concerns the relation between metaphysics and natural science (physics) in general, regardless of whether one is a committed Newtonian in the latter area. 5 In that connection, we may very well describe Kant’s precritical project, as Schönfeld himself does at one point, simply in terms of a “reconciliation of the perspectives of natural science and metaphysics” (Schönfeld 2000, 17). Du Châtelet’s Institutions (Foundations), as we shall see, represents an unprecedented attempt at such a reconciliation. This fact, together with an observation of “the apparent overlap between topics treated by Du Châtelet and by the early Kant,” has led Katherine Brading to ponder about the connection between their philosophical outlooks. Kant’s first publication (1749) was his contribution to the so-called “vis viva controversy”, and this same topic occupies the final chapters of Du Châtelet’s Foundations as part of a public dispute. Kant is explicitly continuing this debate. [. . .] Reading on, the similarities seem much deeper and more important than this. Schönfeld’s (2000, Introduction) description of Kant’s precritical project could be a description of what Du Châtelet sets out to do in her Foundations. (Brading 2015, 28, n. 33)

While Brading cautiously suggests that “there is much work to be done on the relationship between Du Châtelet’s Foundations of Physics and Kant’s early philosophy” (Brading 2015, 28, n. 33), Ruth Hagengruber confidently asserts that Kant “dedicated” his debut to Du 3

There is in fact no clear textual basis for bringing up monadology here. Kant mentions monads just once, while considering whether striving force is “directed toward all regions” or “entirely indeterminate with regard to direction.” He prefers the latter view, citing G. E. Hamberger’s claim that “the substantial force of monads strives toward motion equally in all directions” (GSK 1: 26). But Kant does not insist that the substance with striving force be a monad. 4 The early Kant’s attitude toward Newtonianism may turn out to be more nuanced than how Schönfeld and Friedman each has portrayed it. See Watkins 2013. 5 I refer to “natural science,” “physics,” and later “mechanics” as though they are interchangeable concepts. Their differences are tangential to the purpose of this paper.

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

179

Châtelet’s work and even cites Johann A. Eberhard as later accusing him of “copying from her” – an accusation that would presumably be unsurprising at the time, if Du Châtelet’s work was indeed treated, “in Germany at least for a certain period,” as “part of the canon” on natural philosophy (Hagengruber 2015, 39). My analysis will reveal little, however, to encourage the thought that Kant’s Living Forces was indebted to Du Châtelet’s work in any philosophically meaningful way. All in all, Kant’s debut shows far less philosophical ambition in comparison with the Institutions, especially when it comes to reforming Leibnizian metaphysics in light of the advances in physics at the time. In what follows, I argue for this reading in three steps. I begin, in section 2, by considering the vis viva controversy that prompted Kant’s Living Forces. I present the controversy as a complex affair that implicated all three leading systems of the time, namely Cartesianism, Leibnizianism, and Newtonianism. I do so partly to shed a much-needed new light on the context of Kant’s first publication, highlighting the opportunity provided thereby for constructing a philosophical framework to integrate the best elements of the systems just mentioned. In section 3, I study how Du Châtelet seized that opportunity and rendered Leibniz’s metaphysics in such a way that it would not only be essentially compatible with Newtonianism but also underscore a most advantageous scientific methodology. My study centers on Du Châtelet’s treatment, contra her partner Voltaire’s, of the Principle of Sufficient Reason. Working from different interpretations of Leibnizian metaphysics, these two committed Newtonians would arrive at opposite conclusions about its relation to Newtonian physics. In section 4, I look at Kant’s attempt to resolve the vis viva controversy, giving special attention to his sundry remarks about (Leibniz’s) metaphysics. I then compare his and Du Châtelet’s responses to the opportunity of philosophical reform presented by the controversy. The comparison will show that the young Kant’s philosophical vision was much narrower than Du Châtelet’s. I then conclude by pointing out the implication of my study for a broader interpretative project in which one examines how Kant’s philosophical developments might have interacted with the ever-evolving history of Leibniz exegeses.

2. The vis viva controversy and the struggles to make metaphysics (ir)relevant to physics Kant saw the vis viva controversy as one of the greatest disputes that divided European thinkers (GSK 1: 16). Some commentators believe that the controversy virtually ended with Jean d’Alembert’s Traité de Dynamique (1743). Kant’s first publication is therefore under-informed and “bookish” (Polonoff 1973, 6) or, worse still, a “false start” and “thorough embarrassment” partly because “d’Alembert had already published a theory that effectively settled the debate three years before Kant turned his mind to it” (Schönfeld 2000, 18). From the eighteenth-century point of view, however, d’Alembert’s Traité did not have the effect of settling the debate in 1743. Leonhard Euler’s “De la force de percussion et de sa véritable mesure,” published in 1746 after being presented (in Latin) to the

180

Huaping Lu-Adler

Berlin Academy in 1744, was just one among many indications that the dispute remained “unresolved and hotly contested” (Laudan 1968, 132; also Hankins 1965 and Iltis 1970). More importantly, by then it had become clear that the controversy was never simply a technical one about how to measure force. Rather, implicated therein were also some of the most important and most divisive philosophical issues concerning physics – viz. what must be assumed about bodies (e. g. hardness) in order for certain laws of physics to be applicable, the relation between force and motion, God’s role in natural order, and scientific methodology. Debates on this last issue will in turn bring into sharp relief the need to manage the relation between metaphysics and physics and, for Leibniz’s followers in particular, to clarify his position on this subject. My following sketch of certain events pertaining to the vis viva controversy is meant to accentuate some of the philosophical issues just mentioned. Leibniz initiated the controversy in a series of publications on Cartesian mechanics. On the surface, it was about whether the “force” of a body in motion should be measured by mv, as the Cartesians did, or by mv2. At its root, however, this controversy was not just a mathematical dispute over the correct estimation of force but, as Carolyn Iltis puts it, “a fundamental disagreement as to the very nature of force itself,” with Leibniz attacking the Cartesian conception thereof as an “inadequate [. . .] description of the world” (Iltis 1971, 23, 32). An overview of the relevant texts will show that the disagreement went even deeper, reaching the point where a defender of either the Cartesian or the Leibnizian position would have to take a stance about whether metaphysical considerations are relevant to mechanics. At the center of Leibniz’s polemic against Cartesian mechanics is the law of conservation. The two sides agree on the principle that motive force must be conserved in nature, but disagree over the nature and measurement of this force. While the Cartesians equate it to the quantity of local motion and measure it just like the latter, namely by “the product of the body and its velocity [mv],” Leibniz sees a “big difference” between the two, so that “the one cannot be calculated by the other.” The forces that are conserved after the collision of two bodies with equal mass, he argues, “are proportional not to their velocities but [. . .] to the squares of their velocities.” That is, the conserved force in such cases must be mv2. After providing a mathematical demonstration for this law of conservation and placing it “among the immutable foundations of the science of mechanics,” Leibniz adds: the “ultimate reason” for this result is that “motion is not something absolute and real in itself” (PPL 296–297, 299–301). This remark points to a key difference between the Leibnizian and Cartesian brands of mechanics: they presuppose radically different metaphysical outlooks, especially concerning the nature of body in motion and the laws governing all corporeal motions. In Descartes’s metaphysics, motion has a twofold cause. The primary and “general cause” of all motions is God, who on account of his immutability and by “regular concurrence” conserves their total quantity. Meanwhile, each motion has a motive force, as “the particular cause which produces in an individual piece of matter some motion which it previously lacked” in accordance with the three laws of motion that follow from God’s immutability. Conceptually, then, motive force does differ from the motion caused thereby: the transfer of a body from one place to another is “opposed to the force or action which brings about the transfer.” Descartes prefers, however, to study motion without considering motive force. When he does talk about the latter, he does so in terms of its

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

181

effect and takes it to consist “simply in the fact that everything tends, so far as it can, to persist in the same state” according to the first law of motion (Descartes 1985, 216, 233, 240, 243). When Descartes speaks of laws of nature, he limits “nature” to matter, as mere extension, along with its qualities. In his view, the only “clear and distinct notions” we can obtain regarding the relevant corporeal qualities are those of shape, size, and motion, which are modified strictly in accordance with “the principles of geometry and mechanics.” In that connection, laws of nature are none other than laws of motion and enjoy the same kind of necessity as geometrical principles do, as they “follow inevitably from the eternal truths on which mathematicians have usually based their most certain and most evident demonstrations [. . . and] according to which God himself has taught us that he has arranged all things in number, weight and measure” (Descartes 1985, 92, 97, 288). Leibniz makes a decisive break with this Cartesian view in his “Specimen Dynamicum” (1695), arguing that “in corporeal nature besides the object of geometry, or extension,” there is also force. This force is either active or passive, and each of these is in turn either primitive or derivative. Primitive active force, as the “substantial form” or “first entelechy” of bodies, inheres “in all corporeal substance as such.” Primitive passive force, constituting the materia prima of bodies, represents their endowed capacity to resist penetration and motion. A derivative force is either a “dead force,” as mere “solicitation to motion” without actual motion, or a “living force,” which is “ordinary force combined with actual motion.” It is by these derivative forces that “bodies actually act and are acted upon by each another.” They alone are directly connected to determinate motions, in terms of which we must give specific causal explanations of all other material phenomena in accordance with laws of nature (PPL 436–438). As for primitive forces, though insufficient “to explain the phenomena,” they are “necessary [. . .] for philosophizing rightly.” Absurd consequences follow, Leibniz contends, if we understand bodies “in mathematical terms only” and strictly in accordance with “the bare laws of motion derived from pure geometry,” without any recourse to “metaphysical notions such as active power in form, or of passive power and resistance to motion in matter.” To avoid such consequences, we must also consider forces, as something inherent in bodies, and the relevant “metaphysical laws.” Only then will we have an adequate basis, which goes beyond “logical and geometrical axioms alone,” for determining truths about the corporeal nature, including the aforementioned law of conservation (PPL 436, 440– 441). Leibniz takes himself to have thereby found a middle ground between philosophers who invoke an active principle directly to explain natural phenomena and the ones whose view of nature leaves no place for any metaphysical consideration whatsoever. His strategy is to distinguish “immediate and particular efficient causes of natural things” and “the first and most universal efficient cause” (e. g. first entelechy), which pertain to mechanical laws and metaphysical reasons respectively. Although “mechanical laws are themselves to be derived in general from higher [metaphysical] reasons,” we must explain all specific corporeal phenomena in purely mechanistic terms (PPL 441). Now we turn to Newton. Although he did not explicitly reject vis viva in his publications, the rejection was widely perceived as implied – hence Du Châtelet’s impression that Newton “did not acknowledge forces vives, for the name of M. Newton is in itself nearly an objection” (FP 199). With the caveat that there is more in Newton’s writings that bears

182

Huaping Lu-Adler

on aspects of the vis viva controversy – especially on the relationship between forces and motions – than I can delve into here, 6 I shall focus on remarks that are suggestive of his general scientific methodology and view on the relation between metaphysics and physics, so as to pave the way for my later analyses of Voltaire’s and Du Châtelet’s positions on these subjects. 7 At the beginning of his Philosophiae Naturalis Principia Mathematica (first published in 1687; the third edition [1726; 1999] is used), Newton states: the quantity of motion is the product of quantity of matter and its velocity; by the “inherent force of matter,” vis inertiae, a body will remain at rest or in uniform motion along a straight line unless a motive force is impressed on it to alter that state; this force is proportional to the motion generated thereby in a given time (Newton 1999, 404–405, 407). But vis inertiae, as a merely passive force, can by itself neither bring about any motion nor preserve the same quantity of motion in the world. Newton therefore sees the need to introduce “active principles.” He says in the queries to the Opticks (first edition in 1704; the fourth edition [1730] is used): “the variety of Motion which we find in the World is always decreasing, [and so] there is a necessity of conserving and recruiting it by active Principles such as are the cause of Gravity” (Newton 1730, 375). While recognizing that “we meet with very little Motion in the World, besides what is owing to these active Principles,” Newton claims no knowledge about their causal mechanisms. He might stress one thing, though: they are far from Leibniz’s active forces. While the latter belong in Leibniz’s metaphysical category of primitive forces, Newton’s active principles are part of his physics. He considers these “not as occult Qualities, supposed to result from specific Forms of Things, but as general Laws of Nature, by which the Things themselves are form’d.” Their reality is proven not through metaphysical reasoning, but by their “manifest Effects” (Newton 1730, 375–377). Having nothing more to say about the active principles in question does not bother Newton. In his opinion, it suffices for a universal physics that he has discovered the “impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity” and shown that “gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.” Following the dictates of “rules for the study of natural philosophy,” especially the rule of admitting “no more causes of natural things [. . .] than are both true and sufficient to explain their phenomena,” Newton refrains from feigning hypotheses about the causal grounds of gravitational forces, hypotheses being whatever are “not deduced from the phenomena” (Newton 1999, 794, 943). As an example of this refrain, while stating that “the small Particles of Bodies [have] certain Powers, Virtues, or Forces, by which they act at a distance [. . .] upon one another for producing a great Part of the Phænomena of Nature” (this is part of the theory of universal gravitation), Newton professes no insight into how the gravitational forces may be performed – be it “by impulse, or by some other means unknown to me.” Accordingly, he resigns himself to using ‘attraction’ to “signify only in general any Force by which Bodies tend towards one another, whatsoever be the Cause,” and studying from natural 6

For a brief but helpful account of Newton’s complicated relation to the vis viva controversy, see Smith 2006, 35. On Newton’s treatments of forces, see Janiak 2008, 50–86. 7 For a more extensive and nuanced discussion of Newton’s views on the relation between metaphysics and physics, see Janiak 2008, 11–49, 163–78.

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

183

phenomena “what Bodies attract one another, and what are the Laws and Properties of the Attraction” (Newton 1730, 350–351). Fast forwarding to 1740s, we can see one reason as to why d’Alembert was in no position to end the vis viva controversy with his Traité. The preface to this treatise suggests a narrow, one-sided interest in mechanics as a (Cartesian) mathematical science, coupled with an eagerness to dodge metaphysical queries altogether. Mechanics owes its certainty to the “simplicity” of its object, he claims, namely “motion and its general properties.” If force may be intelligibly considered as one such property, it can only be “the quantity of motion” (mv). For we can have “no precise and distinct idea for the word ‘force’” except by “restricting this term to express an effect,” the effect being motion. Otherwise, the whole question of the measurement of force would come down to “a very futile metaphysical discussion” or, worse still, “a dispute of words (une dispute de mots).” For this reason, d’Alembert circumscribes “motive causes” and considers only the observable phenomena of motion produced thereby. He in fact “proscribe[s] entirely the forces inherent to the body in motion, obscure and metaphysical beings that can only strew darkness over a science clear by itself.” While feeling obliged to mention the accounts of motive cause by Leibniz and “a lady illustrious for her genius” (Du Châtelet), d’Alembert is abundantly clear in its “perfect uselessness for mechanics.” For mechanics is “more a science of effects than that of causes” (D’Alembert 1743, i, v, xvi–xvii, xix, xxi, xxiii). D’Alembert’s offhand dismissal of metaphysics begs the very question about its relation to physics that was implicated in the vis viva controversy from the start. Nor could his oftcited phrase “une dispute de mots” serve to simplify the controversy. This phrase, as Andrea Reichenberger has shown, had already been “widely-used” to portray the controversy as a “semantic dispute” without, however, thereby reducing it to “a pointless quibble over semantics.” The query about the nature of force or other related metaphysical issues did not and would not go away just because some found it inessential to mechanics. Rather, the protraction of the vis viva controversy suggests a need to scrutinize the metaphysics of the three leading natural philosophies of the day – the Cartesian, the Leibnizian, and the Newtonian (Reichenberger 2012, 158–159). 8 Thus, the vis viva controversy left its participants in the 1740s with an excellent opportunity to think deeply and systematically about the philosophical issues implicated therein. Du Châtelet would rise to this occasion as an independent, visionary thinker.

3. Between Leibnizian metaphysics and Newtonian physics: Du Châtelet contra Voltaire In 1741, an exchange took place between Du Châtelet and Jean de Mairan, then secretary of the Paris Academy. The exchange included De Mairan’s response to Du Châtelet’s criticism of his anti-Leibnizian arguments about force and her point-by-point rebuttal. Both documents were appended to the 1742 edition of her Institutions and its German trans8

Reichenberger also thinks “the common categorization between the Cartesian, Leibnizian and Newtonian school is oversimplified,” though, as can be shown from a “deeper look at the [vis viva] controversy” (Reichenberger 2012, 160). Part of what would complicate the matter, as she goes on to show, was Du Châtelet’s attempt to combine Newtonianism and Leibnizianism.

184

Huaping Lu-Adler

lation (1743). Details of Du Châtelet’s treatment of the vis viva controversy (in the final chapter of the Institutions) aside, what intrigues me is Reichenberger’s following characterization of her conciliatory approach: she carried out “a reformation of metaphysics as science” to provide the framework for integrating Leibnizian and Newtonian sides of the controversy. More specifically, Du Châtelet’s plan was to integrate “Leibniz’s vis viva theory into Newtonian mechanics” (Reichenberger 2012, 158). I defer to Reichenberger’s analysis for how this specific integration works and how a reformed metaphysics is supposed to ensure its feasibility. In what follows, I consider only Du Châtelet’s philosophical framework in its broad strokes, insofar as it is to bring Leibnizianism and Newtonianism together. 9 We saw earlier that Newton had little to say about the cause of attraction besides calling it an “active principle” and inferring its reality from manifest phenomena. What was to him a disciplined refrain from feigning hypotheses about this principle would, however, be viewed by many as a reason to reject his theory of universal gravitation. According to Judith Zinsser, Du Châtelet’s Institutions was to address this “principal weakness” of Newton’s theory in a way that her fellow Newtonians – including Voltaire, who popularized Newtonianism with his Elémens de la philosophie de Newton (1741, expanded edition) – had failed to do. 10 That is, it would offer “metaphysical, causal explanations for the phenomenon of attraction, how and why it worked as it did” and do so by “giv[ing] Newtonian mechanics the metaphysical foundations the Englishman had failed to sort out” (Zinsser 2009, 105). A different picture emerges, however, if we take a closer look at Voltaire’s defense of Newton and then read the Institutions in that connection. The disagreement between the two Newtonians runs deeper than Zinsser suggested, especially over the following questions. First, how far should we go inquiring about the causal grounds of natural phenomena? Second, how are we to interpret Leibniz’s metaphysics and its supposed relevance to physics? Third, more generally speaking, what counts as a proper “metaphysics” for physics and how are we to adjudicate between competing versions thereof? On Voltaire’s part, he defends Newton’s system against its Cartesian and Leibnizian critics respectively. He has a ready answer to the Cartesians: we are equally ignorant about the cause of Cartesian impulsion and that of Newtonian attraction. If the latter, as a “universal property” of matter, is dismissed as an “occult quality” in the sense of being a “real principle for which no reason can be given,” impulsion fares no better in this regard. Still, there is a sense in which attraction is not occult, i. e. not chimerical: Newton established it “by the most sublime and most exact mathematical demonstrations.” All things considered, then, we must be content with his discovery of “this visible attraction for which neither he nor any other philosopher could find the reason” (Voltaire 1741, 185– 188). A Leibnizian would criticize this contentment for violating the Principle of Sufficient Reason (PSR), by which we must “penetrate as far as possible into the heart of the causes.” Voltaire responds by denying PSR of its normative claim here. This principle, he contends, 9

I follow a common narrative in referring to Du Châtelet’s plan of merging Leibnizianism and Newtonianism. See Barber 1967, Hutton 2004, and Hagengruber 2012b, which represent varying accounts of Du Châtelet’s relations to Leibnizianism and Newtonianism respectively. 10 The 1741 edition of Voltaire’s Elémens has a newly added part on metaphysics.

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

185

cannot take us as far as it pretends to in our causal inquiries. Monadology is a case in point, which resulted from Leibniz’s quest for the sufficient cause of extended beings, a cause that must be other than extension (to avoid circular explanation). Taking Leibniz’s view to be that extended beings are literally “composed” of simple monads, Voltaire dismisses it as contradictory and absurd. Can one posit, he asks rhetorically, that “a drop of urine is an infinity of monads and that each of them has ideas, however obscure, of the entire universe”? Leibniz’s system is but a product of “sheer imagination,” then, in the labyrinth of which one wonders off following the thread of PSR only to “march methodically towards error” (Voltaire 1741, 62–65). Overall, Voltaire portrays Leibniz and Newton as having opposite methods for causal inquiries. Leibniz is said to have followed the dictate of PSR to investigate real causes for such phenomena as bodily motions and mind-body union – but to no avail. What has Leibniz “proved,” Voltaire asks, “by all these new efforts?” – That he had “a great genius,” for sure. But had he thereby “enlightened” anyone? Newton, by contrast, at least knew “how to doubt” and “hardly ever formed a judgment that was not founded on either mathematical evidence or experience.” His method of analysis, by which general conclusions are induced and tested on none other than experiential basis, is the only one appropriate for us to reason about objects in nature, while knowledge from first principles pertains strictly to God (Voltaire 1741, 21–25, 45–52; see Newton 1730, 380). As for Du Châtelet, she sees physics as an edifice that requires collective effort for its sound construction: while some lay the “foundations [. . .] by means of geometry and observations,” others, including her, “survey the plan of the building.” Her plan, as is often understood, is to put Newtonian physics on a proper metaphysical footing. Accordingly, she begins the Institutions with an exposition of core elements of Leibnizian metaphysics and gives PSR the central place, with which Leibniz is said to have “provided a compass capable of leading us in the moving sands of this science” (FP 123). To counter Voltaire’s anti-Leibnizian rhetoric, she must make clear that the metaphysics she is about to expound is not meant to indulge our runaway imagination but rather to guide our intellect in an ongoing quest to penetrate phenomena. She must also explain, or at least indicate, what constitutes a true metaphysics for physics and how to establish it as such. It is worth adding here that “metaphysics” was a shifting notion in the eighteenth century. On the original Aristotelian account, metaphysics is first philosophy in that it studies the first causes and first principles of things. In Wolff’s Philosophia Prima sive Ontologia (1736), only ontology or general metaphysics (as opposed to special metaphysics) is first philosophy properly so called. As a science of being qua being, it supplies immutable principles to all other sciences insofar as they are to be treated demonstratively (aka. scientifically). 11 Presumably, Du Châtelet was familiar with that conceptual scheme (she read Wolff’s Ontologia), and Voltaire would deny the possibility of a general metaphysics while allowing there to be some kind of special metaphysics for physics.

11

PP, Prœfatio; Prolegomena, §§ 1–9. See Lu-Adler 2018 for a relevant account of Wolff’s – as well as Kant’s – relation to “ontology,” a seventeenth-century invention. Wolff’s special metaphysics includes cosmology, psychology, and natural theology. I will not use ‘special metaphysics’ in Wolff’s limited sense, though. Rather, as it will become clear shortly, I am using this term in the loose sense of a metaphysics for a special domain of inquiry.

186

Huaping Lu-Adler

To be specific, Voltaire’s intention in the metaphysics part of the Elémens is to compare Newton’s metaphysics with Leibniz’s and show that the former alone is valid (Voltaire 1741, 73). This comparison presupposes that physics has its own metaphysics, although there may be good and bad versions thereof. This presupposition would eventually find its articulation in the popular Encyclopédie edited by d’Alembert and Denis Diderot. In the unassigned entry “Métaphysique,” metaphysics is identified as “the science of the reasons of things.” In this sense, “everything has a metaphysics” or, to borrow the terminology just introduced, there is a special metaphysics for any given science. There is no acknowledgement of general metaphysics, though, which would have to abstract from differences among various domains of inquiries and study being qua being. In fact, a metaphysics is “despicable” if it consists in “empty and abstract considerations about time, space, matter, and spirit.” It is altogether different, however, if considered “from its true point of view” (D’Alembert & Diderot 1765, 440). What this true point of view may be, the entry does not say. Presumably, what differentiates a good or true metaphysics from a bad or false one is not so much whether it treats subjects like space and time as how it treats them. Voltaire’s comparison of Descartes and Newton helps to illustrate this point: while the two share an account of “the first principles of matter” according to which there is an indifferent and uniform primary matter, Newton arrived at this system in a different way than Descartes did – not from abstract metaphysical principles, but on strictly mathematical and experiential grounds (Voltaire 1741, 50–51). Notably, the first chapter of Du Châtelet’s Institutions is on principles. Insofar as every science, being an interconnected system of knowledge, has “first principles” on which other truths depend, she argues, it is important to be “attentive to principles, and the manner in which truths result from them” (FP 124–125). It is not obvious what is meant by ‘principle’ here. As a then-standard practice, one could use this term to signify both things and propositions. For instance, on Kirsten Walsh’s analysis, the foundational principles of Newton’s system include both “ontic-principles,” which are “powers, forces, or dispositions that function as causes of phenomena” and are “foundational” due to this causal primacy, and “propositional-principles,” which are foundational as premises for the demonstration of other propositions (Walsh 2017, 196, 200). Voltaire’s reference to “the first principles of matter” was to ontic-principles. Du Châtelet also seems to have such principles in mind when, in a later chapter on the elements of matter, she talks about “the first principles of things” and refers to force as a principle of action (FP 168, 173). But the absolutely first principles – first not just relative to a specific science – introduced in chapter one of the Institutions seem to be neither ontic nor propositional in Walsh’s sense. They have three related characteristics. First, they are principles of human cognition (connaissance), as the title of the chapter suggests. Second, they are “self-evident.” Third, they are universal, in that we all “naturally follow” them in reasoning. There are two such principles: the principle of contradiction as the principle of all necessary truths, and PSR as that of all contingent truths. While geometry depends only on the former, natural sciences depend on PSR. Certain principles about nature follow from PSR. One is the principle of indiscernibles, which in turn “banishes from the universe all similar matter.” (Recall Voltaire’s claim about primary matter being uniform.) The other is the principle of continuity, which is “one of the most fruitful in physics” as in, for example, theorizing about optical phenomena, discovering and demonstrating “true laws

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

187

of motion,” and determining whether there are perfectly hard bodies in nature (FP 124, 128–138). These foundational principles are unmistakably Leibnizian. Unlike Voltaire, Du Châtelet does not treat their application to physics as a matter of reasoning from first principles. They do not figure as premises in deductive inferences about natural phenomena. Rather, they seem to serve the following functions. First, they provide standards for determining a special metaphysics for physics, which treats ontic-principles that are specific to physics, such as those of body and motion. (Du Châtelet’s remark about the principle of indiscernibles suggested this function.) Second, they limit what kind of hypotheses we can seriously entertain about possible causes of certain phenomena before subjecting them to experimental tests. Third, they (especially PSR) determine the boundaries of physics as a causal-explanatory science of natural phenomena. I shall briefly explain the last two, again by way of contrasting Du Châtelet’s approach with Voltaire’s. In Voltaire’s view, the only knowable cause of gravitation is God. Even then, we can only say that He is the cause, not how He has made gravitation work or why it works in such and such ways. For God created the universe and directs its course with “absolute liberty” and no particular reason. If one protests that “we must not resort to God in philosophy,” this principle is valid, Voltaire claims, only with respect to “things that must be explained by proximate physical causes” (Voltaire 1741, 6–7, 134; also 21–25). Du Châtelet disagrees. To her, physics is an unceasing human effort to gain an ever deeper understanding of nature. We are still in this science, she notes, “like this man blind from birth whose sight Chiselden restored.” The time may “never come entirely” that we see things with clarity, for “there are probably some truths not made to be perceived by the eyes of our mind.” But this limitation cannot and should not stop us from always trying to learn more and penetrate further. If physics is, as it were, “made for man” as a science that “turns upon the things that constantly surround us,” the human mind – with PSR as a natural principle by which we inquire about contingent matters – will not rest content until it finds a cause that contains “the sufficient reason for” the phenomena, namely the reason that “makes it possible for an intelligent being to understand why” they are the way they are (FP 116, 120, 131). More often than not, the requisite causal explanation can neither be straightforwardly induced from the empirical data at hand nor be deduced from already ascertained principles. The proper course to take is not to halt the inquiry by citing, as Voltaire did, our inability to be thoroughly certain about the true causes of natural phenomena. Rather, “one is obliged to be content with probable reasons to explain them.” That is, one must “frame hypotheses to explain the phenomena, the cause of which cannot be discovered either by experiment or by demonstration.” Hypotheses are essential to scientific progress in such cases. We just have to use them well, by making sure to develop our hypotheses in a methodical manner, so that they are (i) in line with PSR and other foundational principles identified so far, (ii) adequately informed by the relevant facts that we already know and by an analysis of the explanandum, and (iii) amenable to experimental tests, by which we can determine their degrees of probability (FP 147–149, 151). This account of scientific methodology gives a new significance to Newton’s refrain from speculating about the cause of gravitation. While Voltaire took it to suggest that, in principle, physics can only go so far in its causal inquiries, Du Châtelet has a different lesson to draw. To her, physics is a process of human endeavor that neither begins nor

188

Huaping Lu-Adler

ends with Newton. If he made important discoveries about gravitation based on the pathbreaking work done by his predecessors (especially in astronomy), ensuing generations of researchers must pick up where he left off. For everyone involved, successful discoveries come only from the audacity to conduct difficult inquiries with informed hypotheses, even if at times, when compelled by experimental evidence, one may have to abandon them and start all over again. For, in “seek[ing] the reason for [a phenomenon] by means of hypotheses, [. . .] the efforts made to find the truth are always glorious, even though they might be fruitless” (FP 152). In these terms, although there is no guarantee that we will ever identify the true cause of Newtonian attraction, we must still look for the most probable candidate through rigorous applications of the method of hypothesis. Here we have a case of how to make a principle of Leibniz’s metaphysics, PSR, pertinent to physics without affecting its status as a system of purely physical explanations (that is, no general-metaphysical principles play any direct explanatory role therein). Du Châtelet’s rendering of the principle may be seen as part of a considered apology for Leibniz’s metaphysics. Having situated it in the polemic context defined by Voltaire’s anti-Leibnizian rhetoric, I am skeptical about an old portrait that attributes her integration of Leibnizianism and Newtonianism partly to her being “less critical and more easily attracted [than Voltaire was] by speculative theorising.” Nor does it seem fair to treat her Institutions as just another example of “the difficulty [. . .] of establishing [within the context of eighteenth-century rationalism] any clear frontier between scientific knowledge and philosophical speculation” (Barber 1967, 209, 222). She in fact problematized, to say the least, the assumption that “philosophical speculation” – often an unflattering reference to metaphysical consideration – was so irrelevant to scientific inquiries that one must break free from it while pursuing scientific knowledge. On her reading, a Leibnizian principle like PSR points to a fundamental feature of human reason. This principle drives scientific progress, as it naturally propels us to seek sufficient-causal explanations of phenomena and do so indefinitely (since we can never be sure about having reached the end). Du Châtelet’s concern was only to rein in undisciplined exercises of this natural tendency by a proper method of hypothesis, which requires that the causal-explanatory inquiries proceed in lockstep with suitably designed experiments. By this analysis, Du Châtelet’s Leibniz exegesis partially resembles the mature Kant’s self-proclaimed “true apology” for Leibniz’s metaphysics, according to which PSR is not a principle “construed objectively (as a natural law),” but “a merely subjective one, having reference only to a critique of reason” (ÜE [1790], 8: 247–248, 250). 12 This resemblance, besides the fact that the early Kant evidently took interest in the Institutions, makes one wonder whether his philosophical outlook was somewhat inspired by Du Châtelet’s. We shall have a rough answer to this question after an overview of Kant’s remarks about (Leibniz’s) metaphysics in his first publication.

12

Kant characterizes PSR as one of the “three peculiarities” of Leibniz’s metaphysics, the other two being monadology and the doctrine of pre-established harmony (ÜE 8: 247).

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

189

4. Kant’s treatment of (Leibniz’s) metaphysics in the Living Forces Kant’s Living Forces exhibits a conciliatory, independent-minded posture similar to Du Châtelet’s. In the name of “the freedom of human understanding,” he ventures “to think nothing of the reputation of a Newton and a Leibniz, if it should oppose the discovery of truth, and to obey no persuasions other than the force of the understanding.” He portrays the vis viva controversy as an internal conflict of human reason “embodied differently in astute men.” To resolve it is then to “reconcile reason with itself [. . .] and to find the truth, which is never wholly missed by reason’s thoroughness (Gründlichkeit)” and requires only “a little absence of partisanship, and a brief balance of one’s intellectual inclinations” (GSK 1: 7–8, 149, 181). This attitude shapes how Kant deals with Leibniz’s metaphysics in the three-chapter treatise. In chapter one (GSK §§ 1–19), Kant indicates his support for the core tenets of the Leibnizian doctrine of living forces – that they are real, conserved in a physically interacting world, and measured by mv2 – and the basic metaphysical framework presupposed thereby. But he also finds it necessary to modify the doctrine to make it “certain and definitive.” To this end, he begins by clarifying the “metaphysical concepts” of force. He takes there to be an active force as such (vim activam überhaupt), an essential metaphysical force that inheres in a body and is the origin of all its motions (GSK 1: 17–19). 13 He then divides all corporeal motions into two kinds. The first, “free” motion, “has the property of conserving itself in the body to which it is communicated, and of persisting infinitely if no impediment opposes it.” The force expressed therein must then be a living force, as “an internal source of an intrinsically imperishable force that performs its action over time.” The second kind of motion requires only an external, dead force and “disappears as soon as this force ceases to sustain it.” This distinction differs from the original Leibnizian one: while the latter was cast in terms of whether motion is actualized (see section 2 above), Kant views the absence or involvement of actual motion as inessential and intends his new distinction to serve for his “main purpose of improving on the Leibnizian measure of force” (GSK 1: 28–30; see 1: 33–39). Kant ends chapter one by noting that “our metaphysics is [. . .] only on the threshold of a properly founded cognition (Erkenntniß)” and that a “merely metaphysical” contemplation cannot promise anything decisive or irrefutable. So, he decides to take a lengthy mathematical excursion in chapter two (GSK §§ 20–113) to examine the representative proofs that the Leibnizians so far have constructed for the doctrine of living force. This examination, Kant hopes, “may perhaps, through the application of mathematics, have more claim to persuasion” (1: 30, modified translation). Kant thereby signals a degree of sensitivity to the kind of anti-metaphysics sentiment that we saw earlier in d’Alembert’s disparaging reference to “futile metaphysical” considerations about force. As Kant subsequently puts it, the “Naturlehrer” of the day could reject a view simply for having a “metaphysical” basis (GSK 1: 61). Accordingly, while deeming it “evident that the very first sources of nature’s operations definitely have to be

13

I translate “überhaupt” as “as such” to reflect Leibniz’s conception of active force as “force in the absolute sense,” a primitive power that “endures in each and every corporeal substance.” A derivative force is an alterable modification of the primitive one (PE 252, 254). Kant follows Leibniz in treating active force as metaphysically prior to living force.

190

Huaping Lu-Adler

a subject of metaphysics,” he stands ready to offer “a method to please those who mistrust anything that has even the appearance of metaphysics and who consistently insist on experience as the ground of conclusions.” That is, he seeks to demonstrate the reality of living forces and its correct estimation from experiments and observations and do so “with mathematical precision” (GSK 1: 150; see 1: 176–179). The application of a proper method is key to Kant’s search for an “intermediate position which concedes that both parties [the Cartesians and the Leibnizians] are to some extent right” (GSK 1: 32). This method promises to resolve the vis viva controversy by revealing so-far-hidden errors on both sides: [it] allows one to decide in each case, by a general consideration of the principles on which a certain opinion is built and by a comparison of this opinion with the implications drawn from those principles, whether the nature of the premises really contains everything that the doctrines that are drawn as conclusions require. (GSK 1: 93)

In short, by this method Kant is to investigate whether the principles /premises of a proof are “sufficient and complete for the conclusion” that it is constructed to establish (GSK 1: 97). 14 Kant’s investigation reveals to him that the Cartesians and Leibnizians presupposed different conceptions in proving their respective theories about how to estimate force. Explicating those conceptions and their implications is Kant’s focus in chapter three (GSK §§ 114–163). He drives a wedge between mathematics and nature, which allows him to expel living forces from mathematics only to admit them into nature and to show that, while mv is the only true measurement of force in mathematics, mv2 alone is true of force in nature. The possibility of this resolution comes from a distinction between mathematical and natural bodies: mathematics defines its concept of body by means of Axiomatum, requiring of them that they be presupposed in its body, even though they actually prohibit and exclude certain properties from it, properties that are still necessarily found in bodies in nature; hence a body in mathematics is a thing utterly distinct from a body in nature, and something can therefore be true of the latter that still does not belong to the former. (GSK 1: 139–140)

Force is the differentiating property: while “mathematics admits force in the body only insofar as force was caused in it from the outside,” namely a dead force (mv), a body in nature has “an altogether different constitution.” This body has a living force, whereby it “bases its motion sufficiently on itself” and “will, on its own, preserve the motion that it has, freely, permanently, undiminished, and to infinity.” This force cannot be produced by an external cause but must “acquire determinations pertaining to the measure by the square from the inner source of the body’s natural force.” That is, it must be mv2 (GSK 1: 140, 143–145). Finally, just as Kant began chapter one with a measured endorsement of Leibniz’s metaphysics of nature, so does he conclude chapter three with an expression of indebtedness to Leibniz’s groundbreaking work in this area. “I could have done nothing,” he professes, “without the guiding thread of the splendid law of continuity, [. . .] which was 14

It is unclear whether this method is of the same kind as the one I mentioned in the preceding paragraph. Commentators have given radically different assessments of the significance of Kant’s references to “method” in the Living Forces (see Cassirer 1981, 27–28; Polonoff 1973, 60).

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

191

the only tool for finding the exit from this labyrinth” (GSK 1: 181). There is no room here to examine how the law of continuity might have helped Kant to find his way through the vis viva controversy (see 1: 37, 105, 145–146, 155–156, 166), to assess the quality of his mathematical arguments, 15 to see whether he has actually succeeded to resolve the controversy (most historians would say no), or to determine the degree of his adherence to Leibniz’s metaphysics (see Schönfeld 2000, 41–42). Now I return to the question about Kant’s connection to Du Châtelet. Notably, in the Living Forces, the only one of Kant’s pre-critical publications that contains references to Du Châtelet’s work, she figures primarily as a mathematical scientist taking Leibniz’s side of the vis viva debate. How Kant views the rest of her Institutions is hard to tell. If I was right to observe, at the end of section 3, a certain resemblance between Du Châtelet’s treatment of PSR and how Kant would interpret it several decades later, the Kant of the 1740s seems to have little to offer on this subject. And, while he shares her view that the principle of continuity is one of the most consequential Leibnizian-metaphysical principles for physics, he takes its legitimacy for granted in a way that she did not. More generally, although he is obviously aware of the anti-metaphysics tendency among the Naturlehrer, he is far less responsive than Du Châtelet was to the need to provide a systematic apology for Leibniz’s metaphysics or at least to clarify its relation to physics. Meanwhile, as what Hartmut Hecht claims to be an “established fact,” Du Châtelet – besides her mentor Pierre de Maupertuis and occasional correspondent Euler – played an instrumental role in the early developments of the exegetical approach examined in this paper, namely that of interpreting Leibniz’s philosophy “from a natural science point of view.” 16 This approach supposedly originated in the French-speaking parts of Europe before Du Châtelet et al. introduced it to German academic circles in the 1740s. Moreover, her Institutions has a pioneering feature not shared by her peers’ work: if Maupertuis and Euler were primarily concerned with specific “aspects of natural science,” she sought for “a systematic philosophy” to underscore the best scientific practices of the day (Hecht 2012, 61–62). Here, then, we see a most remarkable difference between Du Châtelet’s and the early Kant’s responses to the vis viva controversy. In section 2, I presented the controversy as an intricate philosophical affair that, from the start, involved not only specific metaphysical issues, such as the nature of body qua the subject matter of physics, but also the very relation between metaphysics and physics. As such, it presented later participants with an exceptional philosophical opportunity. If Du Châtelet used the occasion to transform Leibniz’s metaphysical system – or, perhaps more aptly, to uncover its true meaning – and thereby accommodate it to the best physics of the day, the younger Kant (born in 1724) was preoccupied with the technical aspects of the controversy. In this regard, 15

By one verdict, the Living Forces “consists for the most part of an excruciating enumeration of flawed objections to flawed arguments” (Schönfeld 2000, 20, with textual analysis at 36–55). 16 Euler’s contribution in this regard was a 20-page pamphlet, Gedancken von den Elementen der Cörper (1746), which by all accounts quickly proved to be “a volley in a metaphysical battle that Euler had much to do with initiating” (Wilson 1992, 410). It propelled intense debates not only over monadology, furthering the Voltaire-style objection that I mentioned in section 3, but also over the larger issue of how to interpret Leibniz’s metaphysics and its relation to physics (see Clark 1999, 438–444; Broman 2012). Kant’s Physical Monadology (1756) is typically understood as a response to the challenges raised in Euler’s pamphlet. If so, Kant’s response was almost a decade late – another case in point for what I am about to say at the end of this paper.

192

Huaping Lu-Adler

his approach was more like Maupertuis’s and Euler’s. The remarks about (Leibniz’s) metaphysics found here and there in the Living Forces, as I sampled them above, were still a far cry from the systematic reflections on its meaning and validity that would define his mature philosophy. So, in all likelihood, neither Du Châtelet’s innovative Leibniz exegesis nor her broader project of merging Leibnizian metaphysics and Newtonian physics got Kant’s attention in his earliest endeavor. If he was indeed aware of certain Naturlehrer’s hostility toward the Leibnizian-style metaphysics, we saw him mostly playing along, despite his belief otherwise. Although the opportunity was present, he was far from ready to initiate the grand project of redefining Leibnizian metaphysics in light of Newtonian physics that Friedman attributed to him, a description that indeed better captures Du Châtelet’s Institutions.

5. Conclusion My focus in this paper was to study how Kant’s first publication related to and compared with the Leibniz exegeses in its background, especially the unparalleled version submitted by Du Châtelet. I began by looking at the vis viva controversy behind Kant’s debut. It was a protracted historical event that involved many important philosophical subjects on top of complicated issues of mechanics. By 1740s, any serious participant in the controversy would be confronted with not only the relevant mathematical and mechanical problems but also certain issues fundamental to a modern philosophy of science, such as what makes a proper scientific methodology and how to manage the relation between metaphysics and physics. Partly for this reason, the controversy was still live when Kant entered the fray. It presented him with an opportunity to confront the fundamental issues just mentioned and do so in a systematic manner. In section 3, I took my cue from Reichenberger that Du Châtelet answered the said opportunity with a philosophical framework to bring together Leibnizianism and Newtonianism. I focused on how she made Leibnizian-metaphysical principles foundational to physics. I examined her treatment of PSR in particular, positioning it vis-à-vis Voltaire’s arguments that pitted Leibnizian and Newtonian approaches to physics against each other. In section 4, I overviewed Kant’s attempt to resolve the vis viva controversy. I gave special attention to his treatment of (Leibniz’s) metaphysics, which I then compared with Du Châtelet’s. In the final analysis, what Kant had to offer fell far short of her revolutionary initiative to reconcile Leibnizian metaphysics and Newtonian physics. In this way, I hope to have cleared out an interpretative space that sits between those who have read too much into Kant’s debut and those who have thought too little of it or basically ignored it. One take-away of my study is that Kant, who strived to be an independent thinker from the very start of his career, had to take in the evolving landscape of Leibniz exegeses on his own terms. If I was correct in suggesting that he did not materialize the opportunity provided by the vis viva controversy to develop a systematicphilosophical framework as Du Châtelet did, it was less a failure or lack of sophistication on his part than an indication that his early self was preoccupied with specific issues

Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy

193

within natural science. To a greater or lesser extent, the same may be said of Kant’s numerous publications on natural science throughout the 1750s and in much of the 1760s. Although he would insert suggestive philosophical reflections here and there in specialized treatises, he would not thereby disclose any resolution to construct a comprehensive philosophical system – with, say, a reformed Leibnizian metaphysics at its foundation and a thought-out account of scientific methodology – to go with Newtonian physics. 17 This kind of construction would be a later development, during the decade or so leading to the publication of the Critique of Pure Reason (1781), which Kant would eventually tout as “the true apology for Leibniz” in a polemic with Eberhard, a self-branded Leibnizian (ÜE 8: 250). Only then, having made his so-called critical turn, would he consider how his approach to metaphysics compared with trending Leibniz exegeses at the time and declare his own as the truly faithful one. Further explication of this interpretative hypothesis is the subject of another paper. 18

Bibliography Adickes, E. 1924. Kant als Naturforscher. Vol. 1. Berlin: de Gruyter. Barber, W. 1967. Mme du Châtelet and Leibnizianism. In: W. H. Barber et al. (eds.). The Age of Enlightenment, 200–222. Edinburgh: University of St. Andrews. Brading, K. 2015. Émilie Du Châtelet and the Foundations of Physical Science. URL: 〈http: // philsciarchive.pitt.edu/11610/〉 (accessed: July 30, 2017). Broman, T. 2012. Metaphysics for an Enlightened Public: The Controversy over Monads in Germany, 1746–1748. Isis 103, 1–23. Cassirer, E. 1981. Kant’s Life and Thought. Haden (tr.). New Haven: Yale University Press. (Original: Cassirer, E. 1921. Kants Leben und Lehre. Berlin: Bruno Cassirer.) Clark, W. 1999. The Death of Metaphysics in Enlightened Prussia. In: W. Clark et al. (eds.). The Sciences in Enlightened Europe, 423–473. Chicago: University of Chicago Press. D’Alembert, J. 1743. Traité de Dynamique. Paris. D’Alembert, J. /Diderot D. 1765. Encyclopédie. Vol. 10. Paris. Descartes, R. 1985. The Philosophical Writings of Descartes. Cottingham et al. (eds.). Cambridge: Cambridge University Press. Du Châtelet, E. 1742. Institutions Physiques. Amsterdam. Partial translation: Foundations of Physics (FP), in: Du Châtelet 2009, 115–200. Du Châtelet, E. 1743. Der Frau Marquisinn von Chastellet Naturlehre an ihren Sohn. Halle and Leipzig. Du Châtelet, E. 2009. Selected Philosophical and Scientific Writings. Zinsser J. (ed.), Bour /Zinsser (trs.), Chicago: University of Chicago Press. Euler, L. 1746a. De la force de percussion et de sa véritable mesure. Memoires de l’académie des sciences de Berlin 1, 21–53. Euler, L. 1746b. Gedancken von den Elementen der Cörper. Berlin: Haude & Spener. Friedman, M. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press. Hagengruber, R. (ed.). 2012a. Émilie Du Châtelet: Between Leibniz and Newton. Dordrecht: Springer. Hagengruber, R. 2012b, Emilie Du Châtelet between Leibniz and Newton: The Transformation of Metaphysics. In: Hagengruber 2012a, 1–59.

17 18

For a comprehensive and highly informative study that bears on this subject, see Laywine 1993. I thank Katherine Dunlop and an anonymous referee for their helpful comments on the first version of this paper. Whatever infelicities may remain in this revised version are solely mine.

194

Huaping Lu-Adler

Hagengruber, R. 2015. Cutting Through the Veil of Ignorance. The Monist 98, 34–42. Hankins, T. 1965. Eighteenth-Century Attempts to Resolve the vis viva Controversy. Isis 56, 281–297. Hecht, H. 2012. In the Spirit of Leibniz – Two Approaches from 1742. In: Hagengruber 2012a, 61–75. Hutton, S. 2004. Emilie Du Châtelet’s Institutions de physique as a Document in the History of French Newtonianism. Studies in the History and Philosophy of Science 35, 515–531. Iltis, C. 1970. D’Alembert and the vis viva Controversy. Studies in History and Philosophy of Science 1, 135–144. Iltis, C. 1971. Leibniz and the vis viva Controversy. Isis 62, 21–35. Janiak, A. 2008. Newton as Philosopher. Cambridge: Cambridge University Press. Kuehn, M. 2001. Kant: A Biography. Cambridge: Cambridge University Press. Laudan, L. L. 1968. The vis viva Controversy, a post-mortem. Isis 59, 130–143. Laywine, A. 1993. Kant’s Early Metaphysics and the Origins of the Critical Philosophy. Atascadero: Ridgeview. Lu-Adler, H. 2018. Ontology as Transcendental Philosophy. Forthcoming in: C. Fugate (ed.). Kant’s Lectures on Metaphysics: A Critical Guide. Cambridge: Cambridge University Press. URL: 〈https: // www.academia.edu / 33574392 / _ Kant _ on _ Ontology _ as _ transcendental _ philosophy.pdf> (Accessed: April 30, 2018). Newton, I. 1730. Opticks. 4th ed. London: Printed for William Innys. Newton, I. 1726. The Principia: Mathematical Principles of Natural Philosophy. Cohen /Whitman (trs.). 1999. Berkeley: University of California Press. (Original: Newton, I. 1726. Philosophiae Naturalis Principia Mathematica (3rd ed.). London.) Polonoff, I. 1973. Force, Cosmos, Monads, and Other Themes in Kant’s Early Thougt [sic.]. Bonn: Bouvier. Reichenberger, A. 2012. Leibniz’s Quantity of Force. In: Hagengruber 2012a, 157–171. Shell, S. 1996. The Embodiment of Reason. Chicago: University of Chicago Press. Schönfeld, M. 2000. The Philosophy of the Young Kant. Oxford: Oxford University Press. Smith, G. 2006. The vis viva Dispute: A Controversy at the Dawn of Dynamics. Physics Today 59, 31– 36. Voltaire. 1741. Elémens de la philosophie de Newton. London. Walsh, K. 2017. Principles in Newton’s Natural Philosophy. In: P. Anstey (ed.). The Idea of Principles in Early Modern Thought, 194–223. New York: Routledge. Watkins, E. 2013. The Early Kant’s (anti-)Newtonianism. Studies in History and Philosophy of Science 44, 429–437. Wilson, C. 1992. Euler on Action-at-a-Distance and Fundamental Equations in Continuum Mechanics. In: P. Harman /A. Shapiro (eds.). The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences, 399–420. Cambridge: Cambridge University Press. Zinsser, J. 2009. Foundations of Physics. Volume Editor’s Introduction. In: Du Châtelet 2009, 105–108.

Kant on the Existence and Uniqueness of the Best Possible World Gonzalo Rodriguez-Pereyra, Oriel College, University of Oxford

Abstract In the 1750s Optimism, the Leibnizian doctrine that the actual world is the best possible world, popularized by Pope in 1733 in his Essay on Man, was a hot topic. In 1759 Kant wrote and published a brief essay defending Optimism, Attempt at some Reflections on Optimism. Kant’s aim in this essay is to establish that there is one and only one best possible world. In particular, he argues against the claim that, for every possible world, there is a possible world better than it and against the claim that there are two or more equally good possible worlds that are better than all the rest. Although it is not clear why, Kant was later dissatisfied with his essay. In this article I shall reconstruct, discuss, and evaluate Kant’s arguments. My evaluation will be negative, and so I think Kant had reasons to be dissatisfied with his essay.

1. Introduction Leibniz famously defended the doctrine that the actual world is the best possible world, and that it was selected from all possible worlds by an omniscient, omnipotent, and maximally benevolent God. The claim that the actual world is the best possible world presupposes the existence and uniqueness of the best possible world, i. e. it presupposes that among the possible worlds there is one (existence), and only one (uniqueness), best possible world. Leibniz does not provide – at least not in the texts I know – much of an argument for the idea that there is a unique best possible world. Leibniz’s doctrines imply that God would choose only what is best and that he would not be able to choose between two equally good worlds. This suggests the following possible Leibnizian argument for the thesis that there is a unique best possible world: there is a world, and since God would choose only what is best and he would not choose between two equally good worlds, there is a unique best possible world. Something like that, for instance, can be extracted from The Confession of a Philosopher (CP 101). 1 But such an argument – as Leibniz himself says of the argument he is discussing in the passage from the Confession – would proceed from the effect and be a posteriori (CP 101). In previous work I have pointed out why this is not sufficient for Leibniz, and why it would have been important for Leibniz to provide an a priori explanation for the uniqueness of the best possible world, i. e. an explanation proceeding from the cause of possible worlds (Rodriguez-Pereyra 2014, 102). Here I shall limit myself to observe that the argument adumbrated in the previous paragraph is meant to establish that there is 1

I have asserted previously that in that passage from the Confession Leibniz was actually arguing for the uniqueness of the best possible world (Rodriguez-Pereyra 2014, 102). I do not think so any more. However, from what Leibniz said in that passage one can extract such an argument for the uniqueness of the best possible world.

196

Gonzalo Rodriguez-Pereyra

a unique best possible world, as opposed to be meant to establish why there is a unique best possible world. This is important, since according to Leibniz’s Principle of Sufficient Reason every truth must have a reason why it is so and not otherwise (PE 210, 217). In the 1750s Optimism, the Leibnizian doctrine that the actual world is the best possible world, popularised by Pope in 1733 in his Essay on Man, was a hot topic. 1755 was an important year for the debate on Optimism. It was the year of the tremendous earthquake in Lisbon, which produced several tens of thousands of deaths, and provoked Voltaire to attack the doctrine of Optimism in his poem on the Lisbon disaster. It was also the year when the Prussian Academy awarded its prize for an essay on the topic of the relationship between Pope’s proposition ‘Whatever is, is right’ and the system of Optimism, or of the choice of the best (the prize had been advertised in 1753). The winning entry was by Adolf Friedrich Reinhard, a follower of Crusius who became professor of law at the University of Bützow, and also a judge, but who also wrote on metaphysical topics. 2 1759 was another important year for the debate on Optimism, since that is the year of the publication of Voltaire’s Candide, whose full title was Candide, ou L’Optimisme. And 1759 was the year when Kant wrote and published a brief essay defending Optimism, Attempt at some Reflections on Optimism. In his little opuscule Kant is concerned almost exclusively with the proposition that there is one and only one best possible world, i. e. with existence and uniqueness of the best possible world. In my view, Kant’s little essay is a reply to Reinhard. My reason for taking Kant’s essay to be a reply to Reinhard’s is that Kant responds to objections made by Reinhard, and Reinhard, other than Leibniz, is the only person cited by Kant in his essay. Although not conclusive evidence for my claim, this is highly suggestive of it. But note that taking Kant’s essay to be a reply to Reinhard is not to take Kant’s essay to be a reply only to Reinhard, and so what I am claiming is compatible with Kant’s own claim, made in a letter to Lindner, that in his essay he was replying to Crusius (see AK 10: 22–23/TP lvi). 3 What are the objections made by Reinhard to which Kant responds in his essay? Among many other interesting points about Pope and Leibniz, Reinhard makes the important point that Leibniz’s system presupposes that there is a unique best possible world and argues that such a supposition cannot be upheld. Reinhard says for instance: I have made see, I believe, clearly enough, that the ideas we have of perfection, do not allow us to think that only one world is, all things considered, the most perfect of all possible; and that would suffice for overthrowing the System of Optimism, which could not subsist [consister] without such supposition. (Reinhard 1755, 35; see also Reinhard 1755, 29). 4

What are Reinhard’s reasons for doubting the existence and uniqueness of the best possible world? His main point is that there could be two different possible worlds that are

2

Reinhard’s prized piece is entitled ‘Le système de Mr Pope sur la perfection du monde, comparé à celui de Mr de Leibnitz, avec un examen de l’optimisme, pour satisfaire au problème proposé par l’Académie Royale des Sciences et Belles-Lettres de Berlin’. 3 In what follows I use the following two abbreviations: TP = Immanuel Kant. The Cambridge Edition of the Works of Immanuel Kant. Theoretical Philosophy, 1755–1770. Translated and edited by David Walford, in collaboration with Ralf Meerbote. Cambridge: Cambridge University Press, 1992; Z = Kant, I. ‘Ensayo de unas Consideraciones sobre el Optimismo’, translated, edited, and with an introduction by E. Zerbudis, Revista Latinoamericana de Filosofía, XXVI, 2, 2000, 1–16. 4 This is my translation.

Kant on the Existence and Uniqueness of the Best Possible World

197

equally perfect, since different possible worlds contain different realities and they might sum up to the same total degree of perfection (Reinhard 1755, 32). If that were the case, there might be two or more best possible worlds, i. e. two or more equally good worlds that are better than all the others. In that case there would be no unique best possible world. But he also claims that there is no greatest degree of perfection, since every degree of perfection, being finite, can be augmented. This suggests that there is no best possible world because there is always a better one (Reinhard 1755, 34). Thus this second claim is concerned with the existence rather than the uniqueness of a best possible world, but neither does Reinhard put the matter so clearly, nor does he press on the issue. 5 Kant is clearer than Reinhard in identifying and stating the arguments against the existence and uniqueness of the best possible world. 6 He argues that there is a unique best possible world, since it is not the case that either every possible world is worse than another or there are two or more equally good possible worlds that are better than all the rest. This argument, if it works, gives a reason, perhaps the reason, why there is a unique best possible world. Kant had argued for the Principle of Sufficient Reason in his Nova Dilucidatio of 1755, and in that work he distinguished between reasons that and reasons why. A reason why something is the case renders intelligible that which is the case, while a reason that something is the case is a reason that lets us know that it is the case (ND 1: 392 /TP 12). 7 Although it is not clear why, Kant was later dissatisfied with his essay (see TP lvi– lvii, Z 6). In what follows, I shall reconstruct, discuss and evaluate Kant’s argument. My evaluation will be negative, and so I think Kant had reasons to be dissatisfied with his essay. I like the idea that perhaps some of the criticisms I shall make to his argument were Kant’s own.

2. A Best Possible World Kant first argues for the thesis that there is a possible world than which no better possible world can be thought. This is what he says: If no world can be thought, beyond which a still better world cannot be thought, 8 the Supreme Understanding could not possibly have cognition of all possible worlds. Now, this latter claim is false, so the former claim must be false as well. The correctness of the major premise becomes apparent in the following way: if I can assert of any particular idea whatever, which can be made of a world, that the representation of a still better world is possible, then the same thing can

5

Blumenfeld 1975 discusses what Leibniz could say God would do if either of the existence or uniqueness conditions were not satisfied. 6 Roinila 2013, 383 speaks as if the arguments against the existence and uniqueness of the best possible world were Kant’s – my view is that, although Kant is clearer than Reinhard in formulating them, he took them from Reinhard. 7 For a discussion of Kant’s distinction between reasons why and reasons that in the Nova Dilucidatio see Schnieder 2017, 6–7. 8 The second occurrence of the word ‘thought’ is mine. The Walford translation has instead ‘imagined’ (TP 71). But the original text reads: “Wenn keine Welt gedacht werden kann, über die sich nicht noch eine bessere denken ließe [. . .]” (VBO 2: 30). Thus I see no reason for using the word ‘imagined’ rather than the word ‘thought’, and I see every reason for using the word ‘thought’ rather than the word ‘imagined’.

198

Gonzalo Rodriguez-Pereyra also be said of all the ideas of worlds in the Divine Understanding. Therefore, there are possible worlds which are better than all 9 those known by God, and God has not had knowledge of all possible worlds. I imagine that the minor premise will be admitted by every orthodox believer. My conclusion is that it is false to assert that no world can be thought, beyond which a still better world cannot be thought. Or, to express the same idea differently: there is a possible world, beyond which no better world can be thought. Admittedly, it does not, of course, follow from this that one among all the possible worlds must be the most perfect, for if two or more such possible worlds were equal in respect of perfection, then, although no world could be thought which was better than either of the two, neither of them would be the best, for they would both have the same degree of goodness (VBO 2:30 /TP 71–72).

Kant’s intended conclusion in this part of the argument is that there is at least one possible world such that no other possible world is better than it or, equivalently, that it is not the case that for every possible world there is a possible world better than it. But he never states the thesis in this way. Instead he says that his conclusion is that it is false that no world can be thought beyond which a still better world cannot be thought or, equivalently, that there is a possible world beyond which no better world can be thought. But this seems not to be the same as what I take to be his intended conclusion, since it seems that even if there is a possible world beyond which no better world can be thought, it might still be the case that there is no possible world such that no other possible world is better than it. In effect, that there is a limit to the thinkable goodness of possible worlds does not seem to guarantee that there is a limit to the goodness of possible worlds: one would still need to rule out the possibility of worlds whose goodness is unthinkable. But why think that his intended conclusion was the one I have attributed to him, rather than the one he explicitly stated? The evidence that what I have attributed to him is his intended conclusion is the last sentence of the quoted passage, where Kant concedes that it does not follow from what he has concluded that a possible world beyond which no better world can be thought must be the best one (“the most perfect”), for if there were two worlds which are worse than no one, neither of them would be the best. That is, he sees his argument so far as incomplete because it does not allow him to conclude that there is one and only one best possible world, not because it does not allow him to conclude that there is one and only one possible world beyond which no better world can be thought. I take this to be evidence that his intended conclusion in this part of the argument is that there is at least one possible world such that no other possible world is better than it, that is, there is at least one best possible world, and this is how I interpret him. But if so, is the gap between his stated and his intended conclusion salvageable? Note that what Kant gets committed to by what he says is that there is at least one possible world beyond which no better world can be thought by God. Now, if Kant is taking God as someone who can represent perfectly everything that is possible–and surely such capacity for perfect representation is included in God’s traditional characterization as omniscient–then if there is at least one possible world beyond which no better world can be thought by God, there is at least one possible world such that no other world is better

9

The Walford translation omits the word “all”, which appears in the original (“also sind bessere Welten möglich als alle, die so von Gott erkannt warden [. . .]”).

Kant on the Existence and Uniqueness of the Best Possible World

199

than it. This is what allows Kant to cross the bridge between his stated and his intended conclusion. 10 But let us examine Kant’s argument in more detail. The general structure of the argument is a modus tollens and can be stated as follows: 11 (1) If no possible world can be thought beyond which a better possible world cannot be thought, God does not have knowledge of all possible worlds (“If no world can be thought, beyond which a still better world cannot be thought, the Supreme Understanding could not possibly have cognition of all possible worlds”). (2) God has knowledge of all possible worlds (“Now, this latter claim is false”). (3) Therefore, there is at least one possible world beyond which no better possible world can be thought (“My conclusion is that it is false to assert that no world can be thought, beyond which a still better world cannot be thought. Or, to express the same idea differently: there is a possible world, beyond which no better world can be thought”). Kant does little by way of supporting the second premise: “I imagine that the minor premise will be admitted by every orthodox believer” is all he says. I shall say a little more about premise (2) later on, but the action is not in that part of the argument, since premise (2) can be granted in the context of an argument that does not question that there is such thing as all possible worlds and that God is omniscient. The premise that needs attention is premise (1), and Kant does say more about it. Kant says the following to support it: “[. . .] if I can assert of any particular idea whatever, which can be made of a world, that the representation of a still better world is possible, then the same thing can also be said of all the ideas of worlds in the Divine Understanding. Therefore, there are possible worlds which are better than all those known by God, and God has not had knowledge of all possible worlds.” (VBO 2:30 /TP 72)

For this to support premise (1), asserting of an idea of a possible world that the representation of a better world is possible must be connected with the possibility of thinking of a world better than the one represented by the idea in question. I think the connection is very simple. I take it that Kant is assuming that to represent a possible world is to think of a possible world, and so for the idea of a possible world to be such that the representation of a still better world is possible is for it to be possible to think of a world better than that represented by the idea in question. So, to say that I can assert of any particular idea whatever, which can be made of a world, that the representation of a still better world is possible, is to say that for every possible world represented by any idea whatever it is possible to think of a better possible world. Since it is clearly being assumed that every possible world has an idea, to say that I can assert of any particular idea whatever, which can be made of a world, that the representation of a still better world is possible, is to say that for every possible world it is possible to think of a better possible world. In other

10

It is interesting to note that in some texts of the pre-critical period Kant is more or less explicit in identifying possibility with conceivability, e. g. The only Possible Argument in support of a Demonstration of the Existence of God, where Kant speaks of “inconceivability or impossibility” (EmB 2: 77 /TP 123). 11 Ezequiel Zerbudis (Z 10, n. 10) has recognized the modus tollens form of the argument. Cf. Fichant 2009, 175.

200

Gonzalo Rodriguez-Pereyra

words, it is to say that no possible world can be thought beyond which a better possible world cannot be thought. Thus this is how I reconstruct Kant’s argument in support of premise (1): (4) If no possible world can be thought beyond which a better possible world cannot be thought, no possible world represented in the Divine Understanding is such that a better possible world cannot be thought (“[. . .] if I can assert of any particular idea whatever, which can be made of a world, that the representation of a still better world is possible, then the same thing can also be said of all the ideas of worlds in the Divine Understanding”). (5) If no possible world represented in the Divine Understanding is such that a better possible world cannot be thought, there are possible worlds which are better than all those known by God (“Therefore, there are possible worlds which are better than all those known by God”). (6) If there are possible worlds which are better than all those known by God, God does not have knowledge of all possible worlds (“[. . .] and God has not had knowledge of all possible worlds”). (1) Therefore, if no possible world can be thought beyond which a better possible world cannot be thought, God does not have knowledge of all possible worlds (“If no world can be thought, beyond which a still better world cannot be imagined, the Supreme Understanding could not possibly have cognition of all possible worlds”). Note that in his text Kant does not explicitly derive that God does not have knowledge of all possible worlds from the claim that there are possible worlds which are better than those known by God. Instead, what he says is compatible with deriving the conjunction of both claims from the idea that no world represented in the Divine Understanding is such that a better world cannot be thought. But since one of the conjuncts seems to be a consequence of the other, and the text does not rule out a reading in which the second conjunct is derived from the first, I have decided to represent the structure of Kant’s argument in this way. I shall come back to this at the end of the section. What to make of Kant’s argument? The argument is valid, since it is based on the transitivity of the conditional (clearly, the conditionals in Kant’s argument are stronger than the material conditional). Premise (4) is plausible, since the worlds represented in the Divine Understanding are worlds that can be thought of (by God), and so if no world can be thought beyond which a better world cannot be thought, no world represented in the Divine Understanding is such that a better world cannot be thought. There are problems, however, with premises (5) and (6). Consider the consequent of premise (5): there are possible worlds which are better than all those known by God. It is plausible that this means that there is at least one possible world not known by God which is better than every possible world known by God. But then premise (5) is false, since it is possible that for every world God knows, there is a better world that is also known by God. But perhaps what the consequent of (5) means is simply that for every possible world known by God, there is at least one possible world better than it, where this is meant to be consistent with God knowing all those worlds. Admittedly, this is a less plausible reading of the consequent of (5), but I would

Kant on the Existence and Uniqueness of the Best Possible World

201

not exclude it as a possibly intended reading. Thus, the consequent of (5) can mean either (a) or (b): (a) For every possible world known by God, there is at least one possible world better than it. (b) There is at least one possible world not known by God which is better than every possible world known by God. If the intended interpretation of the consequent of premise (5) is (a), premise (5) is plausible. For, plausibly assuming that every world known by God is represented in the Divine Understanding, if no world represented in the Divine Understanding is such that a better world cannot be thought, for every world known by God there is at least one world better than it. But nothing here entails that God does not know all possible worlds. Indeed, that for every world known by God, there is at least one world better than it, is consistent with God knowing all worlds, since, for instance, it is possible that God knows all the worlds in an infinite lineal series of possible worlds ordered according to the better-than relation. So, if the intended consequent of premise (5) is (a), and therefore the intended antecedent of premise (6) is (a), premise (6) is false. But if the intended interpretation of the consequent of premise (5) is (b), premise (6) is true. However, if the intended interpretation of the consequent of premise (5) is (b), premise (5) is false, for that no world represented in the Divine Understanding is such that a better world cannot be thought is consistent with there being no worlds not known by God, since it is possible that for every world God represents, he thinks of, and knows, a world better than it. Thus either interpretation of the consequent of premise (5) falsifies one of premises (5) and (6). If so, the argument for premise (1) must have at least one false premise. But this is not the end of the matter. For perhaps Kant thought that if no possible world can be thought beyond which a better possible world cannot be thought, the notion of possible world is indefinitely extensible, in the sense that for any possible worlds it is possible by reference to one, some, or all of them to identify a further possible world that is not one of them. 12 The idea behind Kant’s argument would be, on this interpretation, that for any possible worlds there will be a possible world that (a) is not one of them and (b) is better than all of them. I think the text affords little if any evidence that this is what Kant had in mind. But for the sake of completeness, I shall discuss whether Kant could provide an argument for premise (1) based on the indefinite extensibility of the notion of possible world. One way in which the idea of the indefinite extensibility of the notion of possible world can be cashed out is as the idea that there is no single entity, whether it is a set, a sum, or what not, that contains or collects all the possible worlds. Another way in which the indefinite extensibility of the notion of possible world can be cashed out is as the idea that there is no such thing as all possible worlds. The former idea is weaker than the latter, for even if there is no entity that contains or collects all possible worlds, there might still be such a thing as all possible worlds, while if there is no such a thing as all possible worlds, there is no entity that contains or collects all possible worlds. 12

This definition of indefinite extensibility for possible worlds uses plural reference and is inspired in Levey 2016, 404.

202

Gonzalo Rodriguez-Pereyra

Could Kant have used the weaker idea of indefinite extensibility, the idea that there is no entity containing or collecting all possible worlds to produce an argument for premise (1)? In that case, premise (1) would say that if no possible world can be thought beyond which a better possible world cannot be thought (because there is no entity containing or collecting all possible worlds, because for any collection of possible worlds there is a world outside the collection which is better than all the worlds in the collection), God does not have knowledge of all the possible worlds. But this is false, for God’s omniscience would make him know all possible worlds, even if they are not contained or collected in any single entity. Thus the argument for premise (1) so interpreted must fail somewhere. Premise (4) on this reading means that if no possible world can be thought beyond which a better possible world cannot be thought (because there is no entity containing or collecting all possible worlds, because for any collection of possible worlds there is a world outside the collection which is better than all the worlds in the collection), then no possible world represented in the Divine Understanding is such that a better possible world cannot be thought. I think this may be granted. But premises (5) and (6) keep their original meaning, and so the problem with the argument is the same as before: if the consequent of premise (5) is read as (a), premise (5) is plausible but premise (6) is false, and if the consequent of premise (5) is read as (b), premise (6) is true but premise (5) is false; so the argument for premise (1) must have a false premise. Thus, assuming that there is no entity containing or collecting all possible worlds does not make a difference to the cogency of Kant’s argument. Could Kant have used the stronger idea of indefinite extensibility, the idea that there is no such thing as all possible worlds, to produce an argument for premise (1)? In that case, premise (1) would say that if no possible world can be thought beyond which a better possible world cannot be thought (because there is no such thing as all possible worlds, because for any possible worlds there is a possible world that is not one of them and is better than all of them), God does not have knowledge of all the possible worlds. This is true, for if there is no such thing as all possible worlds, there is no such thing as knowledge of all possible worlds (cf. Levey 2016, 423). How could Kant’s argument support this thesis? Premise (4) would be claiming that if no possible world can be thought beyond which a better possible world cannot be thought (because there is no such thing as all possible worlds, because for any possible worlds there is a possible world that is not one of them and is better than all of them), no possible world represented in the Divine Understanding is such that a better possible world cannot be thought. Again, I think this may be granted. What about premise (5)? If (b) is the intended interpretation of its consequent, premise (5) is false if there is no such thing as all possible worlds. For that there is no such thing as all possible worlds, and therefore that there is no such thing as knowledge of all possible worlds, does not entail that there are worlds God does not know. Indeed, that there is no such thing as all possible worlds is compatible with God knowing any worlds there are. Thus if (b) is its intended interpretation, premise (5) is false, since it does not follow from the fact that no world represented in the Divine Understanding is such that a better possible world cannot be thought that there is at least one world not known by God, and therefore it does not follow from it that there is at least one world not known by God which is better than any world known by God.

Kant on the Existence and Uniqueness of the Best Possible World

203

What if the intended interpretation of the consequent of (5) is (a)? If no possible world represented in the Divine Understanding is such that a better possible world cannot be thought, then for every possible world represented in the Divine Understanding, and so for every possible world known by God, there is at least one possible world better than it, even if there is no such thing as all possible worlds. Thus if (a) is the intended interpretation of the consequent of premise (5), premise (5) is true, even if there is no such thing as all possible worlds. Now, if there is no such thing as all possible worlds, God does not have knowledge of all possible worlds. Then the consequent of premise (6) is true if there is no such thing as all possible worlds. Thus, if there is no such thing as all possible worlds (because for any possible worlds there is a possible world that is not one of them and is better than all of them), and the intended interpretation of the consequent of premise (5) is (a), premise (6) has both a true antecedent and a true consequent. Now, it is plausible to suppose that if the notion of possible world is indefinitely extensible, it is necessarily so. And if the way to cash out the indefinite extensibility of possible world is via the idea that there is no such thing as all possible worlds, then it is necessary that there is no such thing as all possible worlds. But then, if it is necessary that there is no such thing as all possible worlds, premise (6) has both a necessarily true antecedent and a necessarily true consequent when the consequent of premise (5) is interpreted as (a). Does this make premise (6) true on this interpretation? I doubt it. Even so, I think this is a powerful argument for premise (1). But there are two problems with attributing this argument to Kant. First, it is very unlikely that this is what Kant had in mind. For if he had something like this in mind, it is not clear why he did a detour via (5) and (6) to reach (1), when he could have more simply argued that if no possible world can be thought beyond which a better possible world cannot be thought, because there is no such thing as all possible worlds (because for any possible worlds there is a possible world that is not one of them and is better than all of them), then God does not have knowledge of all possible worlds, since if there is no such thing as all possible worlds, there is no such thing as knowledge of all possible worlds. Second, even if the above is a powerful argument for premise (1), with premise (1) so interpreted the argument from (1) and (2) to (3) is invalid. For on this interpretation premise (1) says that if no possible world can be thought beyond which a better possible world cannot be thought (because there is no such thing as all possible worlds, because for any possible worlds there is a possible world that is not one of them and is better than all of them), God does not have knowledge of all the possible worlds. As we saw, Kant supports premise (2) by appeal to orthodox belief. But what orthodox belief dictates is God’s omniscience, and God’s omniscience is compatible with him not knowing all possible worlds because there is no such thing as all possible worlds (cf. Levey 2016, 423). God’s omniscience requires that there are no possible worlds God does not know. Thus premise (2) must be understood as meaning that there are no possible worlds God does not know. But the consequent of (1), on this interpretation, is not incompatible with there being no possible worlds God does not know. Thus, premise (2) is not the negation of the consequent of premise (1). Therefore, using the idea that there is no such thing as all possible worlds to establish premise (1) renders the argument from (1) and (2) to (3) invalid.

204

Gonzalo Rodriguez-Pereyra

Thus either one of the premises (5) and (6) is false, or the argument from premises (1) and (2) to (3) is invalid. Either way Kant cannot derive his intended conclusion. As I noted above, Kant’s text can be read as deriving the conjunctive claim that there are possible worlds which are better than those known by God and God does not have knowledge of all possible worlds from the idea that no world represented in the Divine Understanding is such that a better world cannot be thought. But this reading is subject to similar difficulties to those affecting my preferred reading. Under the alternative reading, there would be no premise (6) and premise (5) would read as follows: (5*) If no possible world represented in the Divine Understanding is such that a better possible world cannot be thought, there are possible worlds which are better than all those known by God and God does not have knowledge of all possible worlds (“Therefore, there are possible worlds which are better than all those known by God, and God has not had knowledge of all possible worlds”) The first conjunct of the consequent of (5*) can be interpreted as (a) or (b). But if there is such a thing as all possible worlds, then no matter how it gets interpreted, (5*) is false, since that no world represented in the Divine Understanding is such that a better world cannot be thought is consistent with God knowing all possible worlds. If there is no such thing as all possible worlds, if the first conjunct of (5*) is interpreted as (b), premise (5*) is false, since it does not follow from the fact that no possible world represented in the Divine Understanding is such that a better possible world cannot be thought that there is at least one possible world not known by God which is better than any possible world known by God. If there is no such a thing as all possible worlds, if the first conjunct of (5*) is interpreted as (a), premise (5*) is true, but then the problem is that the argument from (1) and (2) to (3) is invalid, for the reasons already given. Thus not even on this alternative reading can Kant derive his intended conclusion.

3. Potential Infinite Note that I have been implicitly assuming that the series of ever-better possible worlds, if there is one, is actually infinite. But there is some evidence that in the opuscule on Optimism Kant thought that every multiplicity is at most potentially infinite. Indeed, he says: “Multiplicity [as such] is finite, though additions can nonetheless be made to it in thought without its thereby ceasing to be finite” (VBO 2: 32 /TP 74). Taking this seriously means that the collection of ever-better possible worlds is not actually infinite, but at most potentially so, that is, it is necessary that for every possible world x it is possible that there is a possible world y such that y is better than x, and it is not possible that for every possible world x there is a possible world y such that y is better than x. 13 Thus, the collection of ever-better possible worlds is not actually infinite, since there must be at 13

This is inspired in Linnebo and Shapiro’s characterization of the potential infinity of natural numbers (Linnebo / Shapiro 2017, 8). Two comments on the characterization of the potential infinity of the collection of ever-better possible worlds in the text: (a) according to this characterization, an actual infinity of ever-better possible worlds is impossible. But I take Kant’s saying that multiplicity as such is finite to commit himself to the impossibility of actual infinities, though of course the matter of what the intended force of the ‘as such’ was is debatable; (b) the characterization in question is meant to capture the potential infinity of the collection of ever-better

Kant on the Existence and Uniqueness of the Best Possible World

205

least one possible world such that there is no better world than it – but it is possible that there is a world better than it. Even if Kant thought that every multiplicity is at most potentially infinite, I can see no evidence in the passage quoted at the beginning of Section 2 that he is thinking of the infinite as potential infinite. On the contrary, the passage strongly suggests that he is thinking of the multiplicity of possible worlds in terms of the actual infinite. Indeed, if possible worlds are representations in the divine mind, and the divine mind includes actual representations of everything that is possible, the multiplicity of possible worlds must be an actual infinite multiplicity within the divine mind. Thus, I think that the argument we have discussed was conducted in terms of the actual infinite. But, for the sake of completeness, let us consider what would happen to the argument if it were formulated in terms of the potential infinite. In that case, the consequent of premise (5) would be ambiguous between the following two readings: (c) For every possible world known by God, it is possible that there is at least one possible world better than it. (d) It is possible that there is at least one possible world not known by God which is better than every possible world known by God. But the argument faces problems similar to the ones we saw before. For if the intended consequent of premise (5) is (c), premise (5) is plausible. But, obviously, nothing here entails that God does not know all possible worlds. So, if the intended consequent of premise (5) is (c), and therefore the intended antecedent of premise (6) is (c), premise (6) is false. Of course, it will be replied that if the argument is rephrased in terms of the potential infinite, the consequent of premise (6), and therefore the consequent of (1), will be not that God does not know all the possible worlds, but that it is not necessarily the case that God knows all the possible worlds. Fair enough; but even so, if the intended consequent of premise (5) is (c), premise (6) is false. For (c) is consistent with God necessarily knowing all the possible worlds. That is, that it is possible that there is at least one possible world better than any world known by God does not require that God does not possibly know that better world. Even that it is necessarily possible that there is at least one possible world better than any world known by God does not require that God does not possibly know that better world, and so it does not require that it is not necessarily the case that God knows all the possible worlds. But if the intended interpretation of the consequent of premise (5) is (d), premise (6) is true, at least when its consequent is understood to mean that it is not necessarily the case that God knows all the possible worlds. However, if the intended interpretation of the consequent of premise (5) is (d), premise (5) is false, for that no world represented in the Divine Understanding is such that a better world cannot be thought is consistent with it being necessary that God knows all possible worlds. Thus, reformulating the argument in terms of the potential infinite makes no difference to the cogency of Kant’s argument.

possible worlds, so the fact that such a characterization is compatible with an actual infinity of possible worlds provided it is not the case that each one of them is worse than some other one does not affect the correctness of the characterization.

206

Gonzalo Rodriguez-Pereyra

4. A Unique Best Possible World At the end of the passage quoted in section 2 Kant says that it does not follow from what he has argued that one among all the possible worlds must be the most perfect, for his argument has left open the possibility that two or more possible worlds could be equally perfect. To prove that this is not possible Kant says he will offer a reflection that seems new to him. Let me summarize the beginning of his reflection. He starts by saying that the absolute perfection of a thing is its degree of reality (cf. Reinhard (1755, 23) for whom perfection is the sum of reality found in a being). And he asserts that realities can never be distinguished from each other as realities. 14 For if things differ from each other, they differ in virtue of something which is present in one thing and not in the other. But the characteristic marks of realities are positive. Thus if two realities were to differ from each other as realities, there would be something negative in one of them that made possible their distinction, but then those realities would not have been compared as realities. Thus, Kant concludes, realities differ from each other only in virtue of the negations, absences, and limits attaching to one of them, that is, realities differ from one another not in respect of their quality but in respect of their magnitude or degree (VBO 2: 31 /TP 72–73). Then Kant says the following: 15 Therefore, if things differ from one another, they always do so only through the degree of their reality, and different things can never have the same degree of reality. Hence, two different worlds can never have the same degree of reality either; that is to say, two equally good, equally perfect worlds are not possible. Mr. Reinhard says in his prize essay on Optimism: one world could well have precisely the sum of realities, albeit of a different kind, as the other, and then there would be different worlds and yet of equal perfection. But he is mistaken in thinking that realities of equal degree could be distinguished from each other with respect to their quality (qualitate). For, to say it again, suppose they could, there would then be something in one that is not in the other, they would thus differ from each other through the determinations A and not A, one of which is always a genuine negation, and consequently they would differ from each other through their limits and degree, but not through their quality [Beschaffenheit]; for negations can never be counted among the qualities [Qualitäten] of a reality, but they limit it and determine its degree. This consideration is abstract and may well need some clarifications, which I reserve, however, for another occasion. (VBO 2: 31).

Thus Kant gives first an argument that it is not possible that there are two equally perfect possible worlds, and then considers and replies to an objection. Since Kant does not modalize all of the relevant statements, his argument will not support his thesis that it is not possible that there are two equally perfect possible worlds; so let us ignore the

14

The German reads: ‘Nun behaupte ich, daß Realität und Realität niemals als solche können unterschieden sein.’ (VBO 2: 31). The Walford translation has: ‘I now assert that reality and reality as such can never be distinguished from each other.’ (TP 72). I find this less than absolutely clear since it can be read as suggesting that what can never be distinguished from each other are reality and reality as such. What the German text clearly indicates is that two realities can never be distinguished as such, i. e. as realities. This is confirmed by what Kant says later in the text, when he speaks of comparing realities as realities (‘als Realitäten’ VBO 2: 31). 15 The following passage is my translation, since the Walford translation, though actually favouring my interpretation of this passage, was too unfaithful to the original text on one point. I also consulted the Zerbudis Spanish translation, which is characteristically faithful to Kant’s text.

Kant on the Existence and Uniqueness of the Best Possible World

207

way in which he actually formulates the conclusion of his argument and let us use as the conclusion of his argument the thesis that there are no possible worlds that are equally perfect. His argument is based on the equation of perfection with degree of reality and the claim that no things can have the same degree of reality. It can be formulated thus: (7) The perfection of a thing is its degree of reality. (8) No two things have the same degree of reality. (9) Therefore, no two possible worlds are equally perfect. Kant asserts (7) in the part of the text I summarised and he asserts (8) and (9) in the passage quoted above. This argument makes clear the correct interpretation of Kant’s assertion that the perfection of a thing is its degree of reality. This must be understood as meaning that the degree of reality of a thing is how perfect that thing is. That is, the degree of reality of a thing is its degree of perfection. This entails that if two things are equally perfect, they have the same degree of reality. But even interpreting premise (7) in this way the argument remains invalid and needs at least two additional premises. One is the additional intermediate conclusion, which follows from (7) and (8), that no two things are equally perfect. The other one is the premise that possible worlds are things. These two premises would allow Kant to derive the conclusion that no two possible worlds are equally perfect. But one should grant these premises to Kant and assume them as implicit in his argument, which is what I shall do. Even with these extra premises, there is still a problem. For premise (8) is in need of support. Indeed, why could it not happen that two things have different perfections but which add up to the same degree of perfection? This is basically Reinhard’s point. Indeed, Reinhard points out that there could be two worlds which have different realities but which add up to the same degree of reality, and such worlds would be equally perfect (Reinhard 1755, 32). Kant has an answer to Reinhard’s point. His answer is that Reinhard’s point presupposes that realities of equal degree can differ with respect to their quality, but if this were the case, there would then be something in one that is not in the other, and so something in one of them would be a negation, but negations are not qualities of a reality but rather determine its degree, consequently realities would differ not with respect to their quality but with respect to their degree. Thus Kant is arguing a point he made before, namely that realities differ only with respect to their degree, and therefore there are no two realities of equal degree. A crucial point in Kant’s reply is the idea that negations are never qualities of a reality but instead they determine its degree. Kant himself acknowledges that this may well need clarification, but he does not provide it. The claim that negations are not qualities of a reality, which is entailed by his assertion that all the characteristics of realities are positive, seems to conflict with his claim that things in general, and realities in particular, differ from each other through a negation that is in one but not in the other. But as Kant explains in his Attempt to introduce the Concept of negative Magnitudes into Philosophy, negations are lacks, and they do not require a positive ground in the thing of which they are negations, but merely the lack of such a ground (VBnG 2: 178 /TP 217). Thus the sense in which a negation is in a thing is that the thing lacks that of which the negation is a negation. So the claim that realities differ from each other through a negation that is in one but not in the other does not conflict with the assertion that all the characteristics of realities are positive. Negations are not qualities of realities because they are lacks of

208

Gonzalo Rodriguez-Pereyra

qualities, but by being lacks of qualities they limit those realities – they mark what does not belong to those realities – and thereby determine their degrees – they fix how much reality they contain. 16 I hope this clarifies a bit the claim that negations are never qualities of a reality but instead they determine its degree. But there is a problem with Kant’s reply that is independent of the precise meaning of this point. This is that establishing that there are no two realities of equal degree is not sufficient for establishing that no two things can have the same degree of reality. For two things – let them be two possible worlds – could have the same total degree of reality even if the realities of one were of different degree from the realities of the other; such worlds would be equally perfect. To give a simple example: imagine a world having two realities, one of degree 3 and one of degree 6, and another world having two realities, one of degree 4 and one of degree 5. The degree of reality of both these worlds is 9. Since they have the same degree of reality, they have the same degree of perfection, and therefore they are equally perfect in the relevant sense: neither is more perfect than the other. But nothing Kant says in his essay rules out the possibility of two possible worlds having the same degree of perfection by one of them having realities of a different degree than those of the other. Therefore Kant has not established premise (8) and thus he has not established that there are no possible worlds that are equally perfect. 17

5. Perfectly Similar Worlds There is another problem with premise (8), a problem Kant does not consider. For premise (8), together with the implicit premise that possible worlds are things, rules out worlds that are perfectly similar, since such worlds would have the same degree of reality. But might there not be two perfectly similar worlds? Kant seems to have a reason why not. For he says that “if things differ from each other, they differ in virtue of something which is present in one thing and not in the other” (VBO 2: 31 /TP 72). If this is meant to rule out perfectly similar worlds, it must mean that there will always be some difference – other than one depending on their numerical identities – between two worlds. But this answer commits Kant to some version of the Principle of Identity of Indiscernibles. And this is problematic since in the Nova Dilucidatio of 1755 Kant rejected the Principle of Identity of Indiscernibles (ND 1: 409–410 /TP 35–36). Indeed, he also rejected

16

One should not confuse negations with negative characteristics. Indeed, in the Attempt to introduce the Concept of negative Magnitudes into Philosophy Kant is very explicit that negative magnitudes are not negations of magnitudes but they are instead something truly positive (VBnG 2: 169 /TP 209). But the concept of negative magnitude, unlike the concept of negation, plays no role in the Attempt at some Reflections on Optimism. 17 Admittedly, my example assumes that the degree of reality of a world (or of a thing in general) is the sum of the degrees of its realities. There might be alternative models of how the degree of reality of a world is determined by the degrees of its realities. For instance, if the degree of a reality is always a prime number, and the degree of reality of a world is the multiplicative product of the degrees of its realities, no two worlds can have the same degree of reality, assuming that every two realities differ with respect to their degrees (I owe this example to Martin Pickup). But the simple additive model is the one that seems to be presupposed by Reinhard, and Kant does not question it.

Kant on the Existence and Uniqueness of the Best Possible World

209

it, for appearances, in 1781 in the Critique of Pure Reason (KrV A 264 /B 320). 18 Did Kant change his mind about this principle around 1759 and then change it again at some point before 1781? Or did he not realise in the essay on Optimism that he was committing himself to something to which he was not entitled? Or is there no incompatibility between what Kant rejected in 1755 and what he accepted in 1759? Now, what Kant rejected in the Nova Dilucidatio was the proposition that there are no perfectly similar substances, while what he seems to be committing himself to in the essay on Optimism is the proposition that there are no perfectly similar possible worlds. Thus, one might think, there is no contradiction between what he rejects in 1755 and what he commits himself to in 1759. But I do not think this is the proper answer to my questions above. For in the essay on Optimism his use of ‘things’ (‘Dinge’), when he says that ‘if things differ from each other, they differ in virtue of something which is present in one thing and not in the other’, seems to be very general and include not only worlds but also substances and realities. Even so, I think there is no contradiction between the Nova Dilucidatio and the Attempt at some Reflections on Optimism on this issue. In the Nova Dilucidatio Kant says: The complete identity of two things requires 19 the identity of all their characteristic marks or determinations, both internal and external. Is there anyone who has excluded place from this complete determination? Accordingly, no matter how great the agreement of things in respect of their internal characteristic marks, things which are distinguished at least in virtue of place are not one and the same thing at all. (ND 1: 409 /TP 35). 20

Thus, what Kant is rejecting in the Nova Dilucidatio is the version of the Principle of Identity of Indiscernibles according to which there are no two things that are internally perfectly similar – that is, he rejects the principle that no two things share all their internal characteristics. But he requires for the identity of two things the complete identity of all their characteristics, both internal and external. This is why two things can differ with respect to place only. But this seems to entail that there can be equally perfect worlds, which is what he is arguing against in the essay on Optimism. For if two things can differ with respect to place only, then there can be equally perfect things, since two things that differ only with respect to place are equally perfect. But then two worlds that differ only in that in them things otherwise perfectly similar occupy different places would be equally perfect. That is, consider a world W where there are two things A and B that are otherwise perfectly similar and that differ only with respect to place. Now consider a world W* whose only 18

Although what Kant rejects in the first Critique is a version of the Principle of Identity of Indiscernibles restricted to appearances, this by itself does not constitute a great difference between Kant’s positions about the Principle of Identity of Indiscernibles in the Nova Dilucidatio and the first Critique, since in both these works he takes difference of spatial position to ground numerical difference no matter how otherwise similar the numerically different things might be. Thus in both works he accepts that there can be things that differ only with respect to spatial position but are otherwise perfectly similar. But this is not the place for an exhaustive comparison of Kant’s thought on the Principle of Identity of Indiscernibles in the Nova Dilucidatio and the first Critique. 19 The word here is ‘requiritur’. The Walford translation has ‘demands’. This is not inappropriate, but I think ‘requires’ is more apt, especially given the point I shall make at the end of the section when assessing Kant’s potential rebuttal of the objection based on perfectly similar worlds. 20 Note that when in this passage Kant speaks about ‘things’ (“Ad perfectam duarum rerum identitatem [. . .]”) he is clearly speaking about physical substances, since he is speaking about things that differ in relation to place.

210

Gonzalo Rodriguez-Pereyra

difference with W is that in W* the thing A occupies the place B occupies in W and B occupies the place A occupies in W. Such worlds W and W* would be equally perfect. But what Kant says in the Nova Dilucidatio entails that such pairs of worlds are not possible: Let A occupy the place of B. Since A does not differ from B at all in respect of internal characteristic marks, it follows that in occupying its place, it will be identical with it in all respects, and what was previously called A will now have to be called B; and that which bore the name B beforehand will now, having been transferred to the place of A, have to be called A. For this difference of characteristics indicates a difference only of places. (ND 1: 409 /TP 35–36). 21

Clearly Kant is not saying that a thing A, internally perfectly similar to a thing B, cannot move into B’s place. Apart from the obvious absurdity of such a claim, moving into B’s place would not make A have all the same internal and external characteristics, since it would still keep historical properties, like having been located at place P, which B would not have. Kant is making a point about whether the world could have been exactly as it is except that A would have occupied B’s place and vice versa. And what Kant says in this passage suggests that for him there is no pair of worlds like W and W*. What he is saying is that in a world like W* the characteristics of A(B), both internal and external, would be exactly the same as the characteristics of B(A) in a world like W, and so, in fact, what occupies in W* the place of A in W is A and similarly what occupies in W* the place of B in W is B. Why is it that in a world like W* the characteristics of A(B), both internal and external, would be exactly the same as the characteristics of B(A) in a world like W ? A(B) in W* occupies the place B(A) occupies in W, and so A(B) has in W* the external characteristics that depend on place that B(A) has in W. But since A and B differ only with respect to place in W, all their internal characteristics, and those external ones that do not depend on place, remain the same in W*. Therefore in W* the characteristics of A(B), both internal and external, are exactly the same as the characteristics of B(A) in W. And if this is the case, Kant argues in the passage quoted above, what occupies in W* the place of A in W is A and similarly what occupies in W* the place of B in W is B. But if this is the case, it is plausible to argue, there is absolutely no difference between W and W*, and so W and W* are one and the same world rather than two perfectly similar worlds. Thus, in general, no other possible world is generated just by permuting the spatial locations of things that differ only with respect to place in a given world. A similar consideration would lead to the conclusion that no other possible world is generated just by permuting the temporal locations of things that differ only with respect to time in a given world. And I think it is plausible to suppose that Kant would want to generalize this conclusion to all external characteristics (supposing he would admit external characteristics not depending on space and time). That is, no other possible world is generated just by permuting the external characteristics of things that are internally perfectly similar in a given world. Now, if possible worlds can only differ with respect to the characteristics things have in them and not with respect to the things that exist in them, what Kant is saying entails that there are no perfectly similar worlds.

21

I have omitted from the translation a couple of uses of a Greek particle. This does not change the sense of the passage; on the contrary, it makes it even more transparent.

Kant on the Existence and Uniqueness of the Best Possible World

211

Kant did not consider, in the essay on Optimism, the possibility of an objection to premise (8) based on the possibility of perfectly similar worlds, which have the same degree of reality. Nevertheless, what Kant says in the Nova Dilucidatio puts him in a position to defend premise (8) from such an objection, since it puts him in a position to reject, given certain assumptions, perfectly similar worlds. What I have done here is to explain such a potential rebuttal. But it is really interesting that what puts him in a position to reject perfectly similar worlds are the considerations he made in the course of rejecting the Principle of Identity of Indiscernibles! But we should assess Kant’s potential rebuttal: is it successful? There are two problems with it. First, it depends on his claim that A, which does not differ internally from B, could not occupy B’s place in an otherwise perfectly similar world, since in that case it would not differ at all from B, neither internally nor externally. And Kant seems to base this point on his claim that the identity of two things requires the identity of all their characteristics, both internal and external. But this consists of at least one non sequitur. Kant’s claim that the identity of two things requires the identity of all their characteristics entails that the identity of all their characteristics is necessary for the identity of A and B, not that it is sufficient for their identity. But when he argues that A, which does not differ internally from B, could not occupy B’s place, since in that case it would not differ at all from B, neither internally nor externally, Kant seems to be assuming that the identity of all their characteristics is sufficient for the identity of A and B. If Kant was indeed arguing like this, he committed a non sequitur. But perhaps Kant was not basing his point about A and B on his claim that the identity of two things requires the identity of all their characteristics. Perhaps Kant was independently assuming that the identity of all their characteristics is sufficient for the identity of A and B. This is indeed a possibility left open by the text. But there is another non sequitur (which would still be there anyway). This is that even if the identity of all their characteristics is sufficient for the identity of A and B, it does not follow from there that A, which happens not to be identical to B, could not have had all of the characteristics of B. In making this transition Kant seems to have invalidly jumped from the proposition that if x and y have all their characteristics in common then x and y are numerically identical to the proposition that having the characteristics y has is necessarily (or at least counterfactually) sufficient for being y. 22 The second problem with Kant’s potential rebuttal is that it works only if one assumes that possible worlds can only differ with respect to the characteristics things have in them and not with respect to the things that exist in them. If there are possible worlds such that no thing exists in both of them, then Kant’s considerations in the Nova Dilucidatio do not touch the possibility of two worlds such that no things exist in both of them but such that to every thing in either of them there corresponds an internally perfectly similar thing in the other. Such worlds would be perfectly similar in the sense that matters. More importantly, they would be equally perfect. For the perfection of a thing does not depend on external characteristics like time and place, and so internally perfect things are equally perfect. But then worlds such that to every thing in either of them there corresponds an internally perfectly similar thing in the other would be perfectly equal.

22

For a different objection to Kant’s argument see Southgate 2013, 411, n. 22.

212

Gonzalo Rodriguez-Pereyra

Thus, Kant did not consider an objection to premise (8) based on perfectly similar worlds. Had he considered it, he might have used material from the Nova Dilucidatio (material from his rejection of the Principle of Identity of Indiscernibles in that work!) to rebut it. But such a rebuttal would have been unsuccessful.

6. The Greatest Degree of Reality After having argued that there is one and only one best possible world, Kant considers an objection to his view. The objection is that, in the same way in which one can add units to a number without thereby ever producing the greatest number, one can add realities to the sum of realities in a world without thereby reaching the most perfect world (this is reminiscent of a point by Reinhard [1755, 34]). If so, there is no best possible world, since for every possible world there is a better one, in the same way that for every number there is a greater one. This is Kant’s reply to the objection: No greatest number is possible at all, but a greatest degree of reality is possible, and it is to be found in God. Let us examine the first reason why, in the argument under consideration, the concept of number is erroneously employed. The concept of a greatest finite number is the abstract concept of multiplicity as such. Multiplicity is finite, though additions can nonetheless be made to it in thought without it thereby ceasing to be finite. In this case, therefore, the finitude of the magnitude does not impose any determinate limits, but only such as are general. For this reason, the predicate ‘greatest’ cannot belong to any such finite number, for no matter what determinate plurality one thinks, every such finite number can be increased by addition without its finitude being thereby diminished. The degree of reality of a world is, on the other hand, something which is completely determinate. The limits which are set upon the greatest possible perfection of a world are not merely general but fixed by a degree which must, of necessity, be lacking to it. Independence, self-sufficiency, presence in all places, the power to create, and so on, are perfections which no world can possess. This present case is not like that of mathematical infinity, where the finite is connected, in accordance with the law of continuity, with the infinite by means of a constantly continued and ever possible augmentation. In this present case, the disparity between infinite reality and finite reality is fixed by means of a determinate magnitude, which constitutes their difference. The world, which finds itself at that point on the scale of beings which marks the start of the chasm containing the measureless degrees of perfection which elevate the Eternal Being above every creature – this world, I repeat, is, of all which is finite, the most perfect. (VBO 2: 32–33 /TP 74).

What Kant is saying is that there is a disanalogy between numbers and possible worlds. The reason why the perfection of worlds cannot be indefinitely increased is that there is a greatest perfection, which is found in God. Thus, although one can always add units to a number to get a greater number, one cannot always add perfections to a world, since some perfections, like independence, self-sufficiency, presence in all places, the power to create, and so on, cannot belong to a world – they can only belong to God. Thus, Kant thinks, there must be a world that is the most perfect of all. But all this shows is that no world can be as perfect as God is, something those who doubt that there is a most perfect world need not reject. Indeed, even if there are some perfections that cannot be had by worlds, nothing Kant says shows that there are not infinitely many perfections that worlds can have, in which case it still needs to be shown that worlds cannot be ordered in a hierarchy such that for every world there is another

Kant on the Existence and Uniqueness of the Best Possible World

213

world with one extra perfection. And note that such an infinite hierarchy could be such that the distance in perfection between any world and God is always greater than a certain fixed amount (in this case the limits set upon the most perfect possible world would be “fixed by a degree which must [. . .] be lacking to it”, though of course there would be no determinate magnitude which would constitute the difference between the perfection of God and that of the most perfect world, since in this case there would be no most perfect world). Thus Kant has not properly met the objection he was considering.

7. Three Reflections on the Arguments Before concluding, let me briefly discuss three issues about Kant’s project in his opuscule. The first is whether, had his arguments been successful, he would have shown why there is one and only one best possible world. He considered two ways in which there would not be one and only one best possible world: (a) all the possible worlds forming a series in which each world is worse than another one and (b) there being two or more equally perfect possible worlds that are better than all the rest. If condition (a) obtains, then there is no best possible world; if condition (b) obtains, then there is no unique best possible world. On the face of it, there are two other ways in which there would be no best possible world. The first one is: (c) no possible world is better than any other – they are all equally good (or equally bad). This is a possibility Kant did not consider, but it is not difficult to imagine that he would have tried to rule this out by means of the same considerations with which he tried to rule out the possibility of there being two or more equally perfect possible worlds that are better than all the others. The second way in which there would be no best possible world is: (d) there are two or more groups of possible worlds, such that worlds from different groups are incommensurable with each other, i. e. worlds from different groups are neither better than, nor worse than, nor as good or as bad as, each other (it is left open whether for any or all of the groups there are any worlds that are the best in that group). Kant did not consider this possibility and I do not know what he would have said about it. The second issue I will raise is whether Kant was aware that his arguments would provide reasons why there is one and only one best possible world rather than merely reasons that there is one and only one best possible world. Interestingly, Kant does not seem to see his arguments as giving a reason why there is one and only one best possible world. In effect, near the end of his essay on Optimism, he proposes another argument to arrive at ‘the same truth’, namely that there is a unique best possible world because God created a world and therefore this world must be the best one, since to have decided to create it he must have judged it to be the best one and God’s judgement never errs (VBO 2: 33–34 /TP 75). He even recommends this argument. But this argument, which is similar to the argument that can be extracted from Leibniz’s Confession of a Philosopher, establishes (if it works) that there is a unique best possible world, but not why there is a unique best possible world; thus, it is likely that Kant did not see his arguments in the opuscule on Optimism as establishing why there is a unique best possible world, since otherwise he would likely have seen that the argument that there is a unique best possible world because God created a world and so God, who never errs, must have judged it to be the best, cannot really play the role of his other arguments in his essay.

214

Gonzalo Rodriguez-Pereyra

The third issue I will raise is the relationship between the arguments in the opuscule on Optimism and what Kant briefly says about the existence and uniqueness of the best possible world in his later work, The only Possible Argument in support of a Demonstration of the Existence of God, of 1763. As I interpret it, in this work Kant argues that since God contains the grounds of all possibility, there cannot be anything possible that does not harmonize with its ground. But if there were no unique best possible world – whether because there were no best possible world or because there were more than one best possible world – there would be a conflict between what possible worlds are like and the possibility of God, the most perfect being, rationally choosing and creating a world (EmB 2: 153–154 /TP 193–194). Thus, Kant says, the possible worlds cannot contain any source of embarrassment to the rational choice of the Supreme Being (EmB 2: 153 /TP 194). An analysis and assessment of this argument is beyond the scope of this paper. But let me just say that although it is different from any of the arguments found in the opuscule on Optimism, it seems to be, however, related to the argument from that opuscule that I considered in the previous paragraph since it seems to presuppose that God has chosen a possible world. Indeed, Kant explicitly says that when considering the question of the existence and uniqueness of a best possible world it is difficult, if not impossible, to arrive at an answer simply by considering possible things (EmB 2: 153 /TP 193). The argument, like the one considered in the previous paragraph, seems to contain an empirical element, namely the existence of an actual world.

8. Conclusion Kant tries to show why there is a unique best possible world, but his arguments, as I have tried to show, do not seem to succeed. One of the arguments against the claim that there is no best possible world is based on Kant’s idea that if there were no best possible world because for every world there is a better one, then God would not know all possible worlds. But this argument was shown either to be invalid or to have a premise that depends on an unsound argument. Later, in Section 6, I discussed Kant’s rejection of an objection to his claim that there must be some world that is the best possible one. The objection is that to any given world one can add more perfection and thereby get a better possible world. Kant’s reply is that one cannot always add perfections to a world, since some perfections can only belong to God. But that there are some perfections that can only belong to God does not mean that there are not infinitely many perfections that worlds can have and, if that is the case, it might well be that for each given world there is another one that differs from it only in having one more perfection, in which case there would be no best possible world. Thus Kant did not deal with the objection satisfactorily. Kant also argues against the claim that there is no unique best possible world. Essential to Kant’s argument is the idea that there are no two realities of the same degree. But this leaves open the possibility that two worlds have the same total degree of reality even if the realities of one were of different degrees from the realities of the other. But such worlds would be equally perfect. And there is no reason why there could not be equally perfect worlds that are better than any other worlds. Thus Kant’s argument does not establish that there is a unique best possible world. I also argued that although Kant did

Kant on the Existence and Uniqueness of the Best Possible World

215

not consider an objection based on perfectly similar worlds, he might have used material from the Nova Dilucidatio to rebut it, but such a rebuttal would have been unsuccessful. In the last section I pointed out that Kant’s argument is incomplete in the sense that there are at least two other ways in which there would be no best possible world that Kant did not consider. In one case – the case in which there are incommensurable worlds – it is not at all clear what he would have said about it. I also pointed out that Kant does not seem to have seen his arguments as giving a reason why there is one and only one best possible world, since at the end of his little essay he fails to distinguish clearly between his argument and the Leibnizian argument that only establishes that there is a best possible world. I finished with a brief comparison between the Leibnizian argument Kant brings up near the end of his essay and the argument for the claim that there is a unique best possible world in The only Possible Argument in support of a Demonstration of the Existence of God. 23

Bibliography Blumenfeld, D. 1975. Is the Best Possible World Possible? The Philosophical Review 84(2), 163–177. Fichant, M. 2009. Le Principe de la Théodicée et le Concept de Grandeur Négative. In: P. Rateau (ed.), L’idée de Théodicée de Leibniz à Kant: héritage, transformations, critiques. Stuttgart: Steiner. Levey, S. 2016. ‘The Paradox of Sufficient Reason’, The Philosophical Review 125, 397–430. Linnebo, Ø., /Shapiro, S. 2017. Actual and potential infinity. Noûs, DOI: 10.1111 /nous.12208, 1–32. Reinhard, A. F. 1755. ‘Le système de Mr Pope sur la perfection du monde, comparé à celui de Mr de Leibnitz, avec un examen de l’optimisme, pour satisfaire au problème proposé par l’Académie Royale des Sciences et Belles-Lettres de Berlin’. In: Dissertation qui a Remporté le Prix Proposé par l’Académie Royale des Sciences et Belles-Lettres de Prusse, sur l’Optimisme, avec les Pieces qui ont Concouru. Berlin: Haude et Spener. Rodriguez-Pereyra, G. 2014. Leibniz’s Principle of Identity of Indiscernibles. Oxford: Oxford University Press. Roinila, M. 2013. Kant and Leibniz on the Singularity of the Best of All Possible worlds. In: Bacin, S. et al. (eds.), Kant und die Philosophie in weltbürgerlicher Absicht. Akten des XI. Kant-Kongresses. Vol. 5. Berlin /Boston: de Gruyter. Schnieder, B. 2017. The PSR in Kant’s Nova Dilucidatio. unpublished. Southgate, H. 2013. Kant’s Critique of the Identity of Indiscernibles. In: Bacin, S. et al. (eds.), Kant und die Philosophie in weltbürgerlicher Absicht. Akten des XI. Kant-Kongresses. Vol. 5. Berlin, Boston: de Gruyter.

23

Thanks to Paul Audi, Ralf Bader, Earl Conee, Damiano Costa, Natalja Deng, Ghislain Guigon, John Heil, Nick Jones, John Komdat, Jessica Leech, Øystein Linnebo, Fraser MacBride, Adrian Moore, Kevin Mulligan, Martin Pickup, Jannai Shields, Peter Simons, Edward Wierenga, Alastair Wilson, Ezequiel Zerbudis, an anonymous referee, and audiences in Geneva and Rochester for comments on a previous version of this paper.

The Canon Problem and the Explanatory Priority of Capacities Timothy Rosenkoetter, Dartmouth College

Abstract This paper offers a novel solution to the long-standing puzzle of why the Canon of Pure Reason maintains, in contradiction to Kant’s position elsewhere in the first Critique, both that practical freedom can be proved through experience, and that the question of our transcendental freedom is properly bracketed as irrelevant in practical matters. The Canon is an a priori investigation of our most fundamental practical capacity. It is argued that Kant intends its starting point to be explanatorily independent of transcendental logic and the ontic more generally, an independence that would be compromised if transcendental freedom were included in that starting point, even in a mode of supposition. In a different sense, however, practical reason precisely is dependent on the ontic: it can be realized only in beings. This species of dependence is used to explain the puzzling claim that practical freedom can be experienced.

1. Introduction: The Canon Problem Among the many interpretative puzzles of the Critique of Pure Reason, one stands out because we find Kant making what appear to be plainly contradictory statements about an issue of almost unparalleled importance to his project. The “Canon problem”, as it has come to be known, can be divided into two parts. 1 In each part, one side of an apparent contradiction is found in Section 1 of the Canon of Pure Reason, while Kant commits himself to the other side in the Transcendental Dialectic (and to some extent throughout the rest of the Critique): (E+) The Canon advances the experience thesis, telling us that “practical freedom can be proved through experience” (A802); it can be cognized “through experience, as one of the natural causes” (A803). 2 (E–) The Transcendental Dialectic, by contrast, tells us that “practical freedom” cannot be realized without transcendental freedom (A534). Yet because it is a mere idea transcendental freedom can never be proved through experience. Hence, the Dialectic denies the experience thesis. 1

Dieter Schönecker devotes an entire book (2005) to the Canon problem and has given it that name. I also follow him in dividing it into the two sub-problems that I label “(E)” and “(B)”. 2 A- or B-citations without further attribution refer to the Critique of Pure Reason. I include B-pagination only in cases in which the passage was added in the B-edition. Citations of the form “(#:###)” refer to the volume and page number of Ak. In cases in which a quotation from Ak. is a Reflexion, its number is included (“R. ####”) along with volume and page number for ease of identification. I have generally followed the Cambridge Edition translations, though I modify them when necessary without noting changes in each instance.

The Canon Problem and the Explanatory Priority of Capacities

217

(B+) The Canon asserts the bracketing thesis, viz., that it is appropriate when treating practical freedom to bracket the question of whether there is transcendental freedom: “the question about transcendental freedom concerns merely speculative knowledge, which we can set aside as quite indifferent if we are concerned with the practical (um das Praktische) [. . .]” (A803 f.). (B–) The Dialectic treats the question of transcendental freedom as “the real moment of the difficulties” surrounding morality, which is a sub-domain of the practical (A533). Bracketing would plainly be a mistake, since “the abolition of transcendental freedom would also simultaneously eliminate all practical freedom” (A534). There is a considerable history of patchwork theorists using the Canon problem to support their contention that the Critique is a mélange of texts from different time periods. These interpreters read the entire Canon-chapter as a pre-Critical remnant. 3 Less drastically, others hold that the Dialectic and the Canon are using the same terms for two different concepts. On this resolution, what matters for the Dialectic is an idea that can be disambiguated as “transcendental-practical freedom”, while the Canon is instead concerned with a fully naturalized concept of agency, which can be furnished with corresponding intuitions and thus is not an idea. 4 A third, more extreme option is to avoid exculpations altogether and simply observe that for some reason Kant made an egregious mistake in the Canon. The lengthy history of work on the Canon problem falls largely into one of these three camps. 5 An implication of all three readings is that the puzzling claims of the Canon are irrelevant to Kant’s moral philosophy after 1781. Against the background of this reception it is natural to view the Canon’s statements regarding practical freedom as an aberration of some kind – either as a temporary phase, an expositional oversight, or an outright mistake – which Kant manages to correct by the time of the Groundwork (1785). Moreover, on all three of these approaches the Canon problem appears to be a narrowly textual problem – a legitimate puzzle, to be sure, but one that is likely to interest only those who seek to reconstruct all of the twists and turns on the road to Kant’s mature position in moral philosophy. Unlike many of the curves in that road, this one just happens to be found in the first Critique. This paper will propose a new solution to the Canon problem. At the same time it will challenge the largely unspoken assumption that it is no more than a ‘details problem’, of interest to just a fraction of Kant’s readers. 6 What commends the Canon problem even 3

Commentators who adopt exemplary patchwork interpretations include Carnois 1987, 29, and Heimsoeth 1966, 753. Schönecker has compiled a lengthy list of interpreters who mention the apparent contradiction without offering any specific resolution (2005, 6 f.). Schönecker’s book provides an exhaustive overview of existing secondary literature. 4 Schönecker calls this a “tempered patchwork theory” (2005, 173). As Schönecker recognizes, while it solves the first part of the Canon problem, it leaves the second part untouched. Other proponents include Allison 1990, 54 ff.; and Willaschek 1992, 92. 5 A fourth major approach – the praxis approach – argues that the apparent contradiction can be resolved merely by distinguishing between theoretical and agential perspectives, which are adopted in the Dialectic and the Canon, respectively. § 4 will offer an argument against this approach. 6 To be clear, I am not suggesting that the Canon problem would be justly ignored, were it a details problem. Here I attempt merely to identify an assumption that I believe is in no small measure responsible for the relative

218

Timothy Rosenkoetter

to those with no particular interest in Kant’s mature moral theory is the light it can shed on his conception of proper philosophical method quite generally. What has made the Canon’s claims regarding practical freedom seem so problematic, I will contend, has been a failure to read them in light of Kant’s remarkable views on the lengths to which we must go to avoid “dogmatism”, his term for philosophy that endeavors to make progress “without an antecedent critique” of the capacity of pure reason. 7 Kant names Wolff as the figurehead for dogmatism in this well-known passage from the new B-edition (1787) Preface to the Critique. Kant’s charge, in simple terms, is that Wolff erred in looking to ontology to provide ultimate explanations. Dogmatism results when philosophers fail to recognize that transcendental philosophy, not ontology, is First Philosophy. Though my controlling aim is to make sense of Kant’s decisions during the composition of the first Critique, this paper will draw on the Groundwork’s criticism, four years hence, of the specific shape that Wolff’s dogmatism takes within practical philosophy. In the course of introducing the inquiry that Kant takes to be the key to the Groundwork’s manifold innovations, its Preface warns against assuming that metaphysics of morals is just another version of “the celebrated Wolff’s propaedeutic to his moral philosophy [. . .] what he called general practical philosophy”. 8 The Analogy Passage (as we can label the entire ensuing paragraph) develops an analogy between “transcendental philosophy” and metaphysics of morals. 9 We are told that metaphysics of morals (MM) stands to general practical philosophy (GPP) 10 as transcendental logic (TL) stands to traditional, general logic. The particular way in which Kant arrives at TL through a modification of general logic will assume importance below (§ 4), as we will see that Kant follows the same steps when introducing MM. For now, what is important is that though neither general logic nor GPP is itself ontology (or one of the branches of special metaphysics build thereupon), Kant believes that the tradition’s failure to hit upon, and then actualize, TL and MM has allowed it to remain wedded to the assumption that ontology and special metaphysics provide the foundation for philosophy. Kant intends to offer an alternative. Among the Analogy Passage’s specific criticisms of GPP is that it “does not judge at all about the origin of all possible practical concepts, whether they occur only a posteriori or a priori as well” (GMS 4:391). The clear implication is that any properly non-dogmatic foundation for practical philosophy must provide an account of the pure origin of the

7 8

9

10

neglect of the problem – viz., that it can be safely ignored by those who are primarily interested in Kant’s mature views – despite the presence of a stark contradiction on a central issue. B xxxv, the entire phrase is italicized in the original. GMS 4:390. It is easy to see why Kant was worried that the innovative nature of his foundational inquiry would be missed. As Schwaiger has noted, Baumeister, Knutzen, and Meier had used some version of “metaphysics of morals” to designate their versions of Wolffian general practical philosophy (Schwaiger 2001, 54), and Frobesius, Gottsched, and Reimarus had adopted related labels (Schwaiger 2007, 222). Kant uses the phrase “transcendental philosophy” rather than “transcendental logic” (GMS 4:390). However, the description provided matches precisely the Critique’s definition of the latter (A55–57). GPP is a partially empirical science containing the general truths common to the three branches of Wolff’s practical philosophy, namely: (1) politics, which considers the duties of citizens; (2) economics, which treats the duties that arise from membership in smaller social units; and (3) ethics, which covers the duties that bind individuals simply as such (cf. Discursus praeliminaris de philosophia in genere, §§ 62–68). Though natural law likewise belongs to practical philosophy, it is not defined extensionally, as are the three branches above (cf. § 68). This background is provided so that the reader has a better sense of the subject matter of GPP. It will not play any role in the argument below.

The Canon Problem and the Explanatory Priority of Capacities

219

central practical concepts, as transcendental logic had done for the central concepts of ontology. The Analogy Passage does not name the practical concepts in question. This paper will offer a positive and a negative proposal. Positively, I will argue that the practical concepts whose origin Kant traces to our practical capacity are 〈good〉 and 〈bad〉. 11 Negatively, I will argue that the concept 〈cause〉, and a fortiori 〈uncaused cause〉 (i. e., 〈transcendental freedom〉), are not among the concepts whose origins are traced within foundational practical inquiry. The payoff in resolving the Canon problem is as follows. If Kant intends practical critique to be explanatorily independent on the model of theoretical critique, it will follow that any attempt to place the question of our transcendental freedom at the foundation of practical philosophy would amount to a variety of dogmatism. In simple terms, to conceive of our practical capacity first of all as transcendentally free – even if this is not put forward as certain, but merely assumed – is to ground the critique of our practical capacity upon an ontological property. If it can then be shown that the Canon chapter is Kant’s first sketch of a properly critical foundation for practical inquiry (soon to be followed by the Groundwork), while the passages supporting (B–) in the Transcendental Dialectic are taking up an ontological standpoint, a resolution to the bracketing half of the Canon problem is forthcoming. The next section (§ 2) will begin by asking precisely what Kant rejects in Wolff’s method. This will open the way to seeing that something that Kant pointedly treats as a “capacity” rather than ontologically (viz., “the synthetic unity of apperception”) stands at “the highest point” within “transcendental philosophy”. 12 In part because the Analogy Passage treats the foundational practical project as an undertaking that is parallel to the foundational theoretical project – rather than belonging within it or being built upon it – we should not be surprised to find Kant likewise eschewing ontological questions within the former. § 3 will make a preliminary case for this hypothesis, while § 4 will test it against the text of the Canon. The one complication that we have yet to preview concerns an asymmetry between the objects (or objective properties) that theoretical and practical critique make intelligible. Simply put, the property that practical critique enables us to understand (goodness) can only be realized in beings. However, the reverse relation – that being can only be realized in goods – is not the case. § 3 will flesh out this asymmetry, while § 4 will show how it can help us make sense of the Canon’s espousal of the experience thesis, (E+). Crucially, though, this dependence with respect to realization – realization dependence, I will call it – is consistent with the independence of practical critique, which is the lynchpin for (B+). That is, the fact that goods are always also existing goods does not render incoherent Kant’s project of tracing “the origin of all possible practical concepts” (GMS 4:391) within the confines of practical critique, without thereby borrowing from ontology (or even, I will argue, theoretical critique).

11 12

Angle brackets will be used to mention concepts. B134ft. This footnote does not contain direct evidence that Kant declines to treat the synthetic unity of apperception, in particular, ontologically. For that case, see § 2.

220

Timothy Rosenkoetter

2. Pedagogical and Explanatory Priority Kant characterizes critique quite generally as “propaedeutic (preparation), which investigates the capacity of reason in regard to all pure a priori cognition”. 13 Should there be distinct instances of critique, they will presumably be distinguished by their study of different capacities (or different uses of a single capacity). Kant contrasts critique (including logic 14) with object-directed or “material” investigations, for which he often uses the term “doctrine”. 15 It is abundantly clear that Kant claims some sort of priority for a priori investigation of the subject’s capacities – “critique” in the sense I will be using it – over these object-directed investigations, including ontology. Regrettably, though, Kant is vague on the precise nature of this priority. Wolff’s position, which is also the dominant position among Kant’s contemporaries, is that the investigation of the subject’s capacities has pedagogical priority over ontology and the branches of special metaphysics. For Wolff logic is that part of philosophy that teaches us to use our cognitive capacity to attain truth and avoid error, while practical philosophy (and its foundational sub-discipline, GPP) teaches us to use our appetitive capacity to choose the good and avoid the bad. 16 Though these two capacity-directed investigations are first in the order of instruction, object-directed ontology is the proper object of investigation once one has graduated from pupil to philosopher. 17 Ontology’s subject matter encompasses these capacities, since its purview includes all beings. It provides the basis for the branches of special metaphysics – natural theology, psychology, and physics – which are distinguished from one another by their non-coincident extensions within the set of all beings. Thus, though theology and psychology do not share any subject matter, the same cannot be said if we compare psychology pairwise with either logic or GPP. Since our cognitive and appetitive capacities belong to the soul, the object of psychology, any results established by logic or GPP also fall within the purview of psychology, though psychology might well express them differently and emphasize different points. 18 Wolff argues that when we follow the proper method in philosophy – “demonstrative method” or “method of proof” – ontology must precede the branches

13 14

15

16

17 18

A841, italics elided; cf. A xi (A-only). Transcendental logic belongs to critique. There may be a relaxed sense of “critique” that also encompasses pure, general logic, since Kant defines it by recourse to capacities (cf. A52) and denies that it is a “material” investigation that “considers some object” (GMS 4:387). However, his more standard practice is to treat them as separate. Compare, for instance, the contrast of the “logician” (read: pure general logician) with the philosopher at A839 with the placement of critique within philosophy at A841. “The critique of the faculties of cognition with regard to what they can accomplish a priori has, strictly speaking no domain (Gebiet) with regard to objects, because it is not a doctrine [. . .]” (KU §III, 5:176). From the flowering of the Critical period (1769): “The science of cognition considered subiective is critique; the science of cognition considered obiective is doctrine” (R. 3964, 17:368). The first Critique itself contrasts “a mere analytic of pure understanding” with “ontology, which presumes to offer synthetic a priori cognitions of things in general (von Dingen überhaupt) in a systematic doctrine (e. g., the principle of causality) [. . .]” (A247, second italics added). Thus, in defining logic by recourse to a capacity Kant is following the standard line of his day. Cf. Discursus praeliminaris §§ 60–62; §§ 69–70. Discursus praeliminaris § 88, § 91. Not merely psychology, but also ontology, must be consulted in order that the various claims of logic can be proved from “principles” (Discursus praeliminaris §§ 90–91). This is because logic contains the rules for cognizing every kind of being, and ontology contains principles that are true of all beings. Similarly, Wolff

The Canon Problem and the Explanatory Priority of Capacities

221

of special metaphysics, while logic is subsumed within psychology, since only with this ordering do we begin with definitions of the most fundamental concepts and build up from there. 19 The Wolffian rationale for a science of logic – to focus for the moment on just one of the capacity-directed undertakings – is, accordingly, to be found in the needs of students. It is entirely appropriate that we study logic before attempting ontology or psychology, since we use our cognitive faculty to seek truth when pursuing ontology. Given the difficulties we as a matter of fact experience in judging the true and avoiding error, it makes sense to prepare for the rigors of properly ordered philosophy with a preparatory science that acquaints us with our cognitive tools, thereby sharpening them. Yet modest psychological improvements brought about by some other means (medicine or God’s intervention, let’s suppose) would gradually eat away at the need for logic, and sufficient improvements would make logic superfluous. There can be no serious doubt that Kant rejects what he sees as Wolff’s trivialization of capacity-directed inquiry. 20 To fail to undertake critique and see our way clear to erecting a transcendental logic is to rest content with dogmatism, and Kant shows no signs of believing that the reasons for avoiding dogmatism wax and wane in response to changes in our level of cognitive ability. This is already a significant datum: Kant believes that it is essential that we undertake a preparatory investigation of our cognitive capacities, while rejecting a primary consequence that would follow if his rationale for this propaedeutic were merely pedagogical, viz., that critique is in principle dispensable. I will assume here that Kant takes critique to enjoy a species of explanatory priority with respect to the doctrine built upon it. Kant does not begin with critique merely in order to train himself (and us) to grasp the genuine explanation that is provided by the metaphysics of nature. On the contrary, that doctrine will suffer from explanatory gaps if it is not properly grounded in critique. Though there are important questions to be asked about the precise nature of this explanatory priority and why Kant thinks that critique enjoys it, the particular focus of this paper dictates that those questions be left for another occasion. 21 What will, in contrast, be directly relevant below is that Kant

argues that ontology and psychology – as well as natural theology – are prior to practical philosophy (including GPP) in the order of demonstration, as opposed to the order of instruction (§ 92). 19 Discursus praeliminaris § 87, §§ 90–91. In § 73 Wolff makes explicit that without ontology philosophy could not be ordered according to the demonstrative method. 20 Kant’s disagreement with Wolff concerns the proper role of capacity-directed inquiry (i. e., critique in the broad sense). This disagreement extends to transcendental logic as an instance of the latter, even though Wolff lacked any conception of that species of logic. My focus here will be on transcendental logic, since it, rather than pure, general logic, is the species of logic to which Kant compares his foundational practical inquiry in the Analogy Passage. That said, already in the case of pure, general logic Kant would argue, in my view, that what it contributes cannot be replaced by demonstratively more basic principles in an object-directed science. In particular, ontology cannot do justice to the principle of contradiction by treating it as the most general truth. 21 An underappreciated element of the case for critique’s explanatory priority is its provision of an informative account of the meanings of concepts that play a central role in Wolffian ontology. Elsewhere I argue that it is only by tracing the semantic origin of 〈existence〉 to our capacity to judge that Kant has non-arbitrary grounds for rejecting competing proposals for that concept’s meaning, such as Baumgarten’s claim that it includes 〈complete determination〉 (cf. Rosenkoetter n.d.). This is just one prominent example of a pattern that should hold for all of the categories and predicables (cf. A82), regardless of whether Kant discusses the cases singly. Without critique the philosopher is condemned to pursue ontology blindly, guided by ordinary language,

222

Timothy Rosenkoetter

recognizes relations of explanatory priority within critique itself. This is clearly what Kant has in mind in the Metaphysical Deduction, where the logical functions of judgment are offered as explanations for why the categories have the particular content that they do, though not the reverse. 22 So that we can gain information about how Kant might view an analogous practical case, it makes sense to identify the point of maximum explanatory priority for the theoretical use of the understanding. His answer is famous: “the synthetic unity of apperception is the highest point to which one must affix all use of the understanding [. . .]” (B134). In § 15, as he prepares to introduce the reader to this highest point, Kant offers an argument that clearly records his objections to using the categories in order to explain the unity that is constitutive of pure apperception. Kant argues, in particular, that it would be circular to use the category 〈unity〉 in an attempt to account for apperception. The reason is that apperception itself figures in Kant’s account of the meanings of the categories. More specifically, apperception figures in Kant’s explanation of the functions, and the functions are themselves used to explain the categories. 23 So though Kant routinely uses the phrase “unity of apperception”, the unity in question is not categorial. It is a unity that is explanatorily prior to any category. Presumably, this same argument will apply to any category or predicament that one might be tempted to predicate of the synthetic unity of apperception, including 〈substance〉 and 〈cause〉. This is potentially significant because insofar as a subject’s possession of self-consciousness includes the awareness that “I, myself, am responsible for my assertions”, this might be thought to entail that 〈I think〉 contains both 〈substance〉 and 〈uncaused cause〉 (i. e., 〈transcendental freedom〉). § 15’s remarks concerning unity imply that it is not by virtue of 〈I think〉 containing the categories 〈substance〉 and 〈cause〉 (however modified through iteration and negation) that original apperception includes awareness of responsibility for one’s assertoric judgmental acts, if indeed it does. This is important in the current context because it is eminently plausible to take the passages supporting (E–) in the Transcendental Dialectic to suggest that 〈practical freedom〉 contains 〈transcendental freedom〉. 24 Yet if the Canon occupies a position of explanatory priority that is relevantly similar to what we find at “the highest point” of “transcendental philosophy” (B134), we will have a ready explanation for why Kant believes that the question of transcendental freedom is appropriately bracketed (i. e., (B+)), at least initially.

prejudice, and whim as she adjudicates proposals for what concepts such as 〈substance〉, 〈cause〉, and 〈reality〉 mean. 22 Cf. B131; and Longuenesse 1998, 201. It was open to Kant to adopt a holistic picture that eschews these asymmetric relations, in which case the categories would explain the functions just as much as the reverse. Yet it is clear that he rejects this picture. Though as students of reason we might initially find it easier to identify the functions by beginning with a list of what we take to be important metaphysical concepts and working backwards to the functions, this reflects our inferior epistemic position. 23 Cf. B130 f. For further explication of this argument, cf. Rosenkoetter 2014, 61–63. 24 Cf. “[. . .] reason creates the idea of a spontaneity, which could start to act from itself, without needing to be preceded by any other cause that in turn determines it to action according to the law of causal connection. [¶] It is especially noteworthy that it is this transcendental idea of freedom on which the practical concept of freedom is grounded [. . .]” (A533). One way a concept can be grounded on a second concept is if the first concept contains the second concept, as 〈F&G〉 contains 〈F〉.

The Canon Problem and the Explanatory Priority of Capacities

223

It is worth looking at a final, relatively well-documented case of Kant’s reluctance to allow the categories to be included within original apperception. Regardless of whether original apperception includes awareness of responsibility for judgmental acts of assertion, Kant clearly believes that it includes awareness of one’s own existence: “the ‘I think’ [. . .] contains within itself the proposition ‘I exist’” (B422 f.). Yet “here existence is not yet the category” (ibid.). That is, the intensional content that one ascribes to oneself simply by virtue of possessing original unity of apperception (we can call it 〈existence–〉) does not include the category 〈existence〉, though it is evidently bears a close enough relation to the category that Kant deems it appropriate to use the word Existenz to denote it. Beyond providing further confirmation of the pattern under discussion, this is significant because Kant holds that existence (i. e., what is thought using the category) belongs to the individuals that jointly constitute nature. 25 I propose that in declining to attribute existence to original apperception Kant is acknowledging the fact that this apperception, as original, belongs to critique rather than doctrine. His use of 〈existence–〉 is part of a general effort not to corrupt the explanatory priority of “the highest point” of “transcendental philosophy” (B134; cf. A346). This is consistent with holding (as I assume Kant does) that original apperception can only be realized in existent things, i. e., the beings that are studied in the doctrine of nature or else fall outside of that doctrine by virtue of being things in themselves. 26

3. Independence of Critique and Realization Dependence Does Kant take the explanatory priority of capacities to apply not merely to the theoretical project, but also to the practical project? This is a question of first importance for understanding his philosophy. In order for practical critique to enjoy explanatory priority it cannot help itself to concepts and principles from the doctrine that it grounds. In addition, we should be open to discovering relations of explanatory priority within practical critique itself. Yet neither of these claims speaks to the question that might hold the key to resolving the Canon problem. Does practical critique help itself to concepts or principles from theoretical critique and the doctrine founded upon it? It is natural to approach this question with two starkly contrasting alternatives, independence and dependence. The first of these can be motivated by considering that the 25

“Nature is the existence of things, insofar as that existence is determined according to universal laws” (P § 14, 4:294; cf. A160; MAN 4:467). 26 It is natural to worry that no matter how determined Kant is to avoid circularity, he cannot simply will a new concept, 〈existence–〉, into the conceptual landscape. The situation is made worse by the fact that this concept must bear some privileged relationship to 〈existence〉. Presumably, a wholly unrelated concept plucked from elsewhere will not do. I would suggest that the relation that categories bear to the functions of judgment provides some grounds for optimism. 〈Existence–〉 and the category might both result from operations on the assertoric function, though each from a somewhat different operation (cf. Rosenkoetter n.d.). As I argue in Rosenkoetter 2018, Kant takes the category of existence to be truly predicated of individuals only if they belong to an ordered whole. A dertiminate individual such as Kant does belong to such a whole, and insofar as Kant considers this individual self-consciously the category is appropriately used. In contrast, in undertaking critique one ascends a chain of explanatory conditions, such that the I of original apperception is no longer any determinate individual. It is not posited absolutely within an ordered whole, but is rather explanatorily prior to that whole.

224

Timothy Rosenkoetter

central claims of theoretical critique would still make sense even if Kant had never conceived of practical critique. 27 Perhaps practical critique is independent in this sense. Alternatively, practical critique might be dependent by virtue of helping itself to concepts that receive their explanation within theoretical critique or doctrine. This is indeed suggested by the twin facts that the “will is a kind of causality” and that the category 〈cause〉 is explained by theoretical critique (GMS 4:446, italics elided). This result would not imply that practical philosophy lacks a clearly delineated subject matter. Nor would it necessarily constitute a defect. Once combined with further plausible assumptions it would, however, entail that at its most basic level practical philosophy is the study of a particular type of cause, and thus a branch of theoretical philosophy in the widest sense. 28 For those who take their cue from Kant’s tendency to treat theoretical and practical critique as coeval this news might come as a surprise. 29 My hypothesis is that Kant insists on the independence of practical critique. What is explanatorily basic in practical critique is just the capacity to represent some x as good or bad, a capacity that is properly formulated using no ontic concepts, including 〈cause〉 and 〈existence〉. Familiarity with the ontic objects that receive their explanation in theoretical critique – whether these objects are phenomena or things in themselves – cannot be used to bootstrap oneself into possession of 〈good〉 and 〈bad〉. This is no more legitimate than supposing that a practical concept can explain the content of 〈cause〉 or 〈existence〉. Hence, at its most fundamental level practical critique is independent of theoretical critique. 30 Yet given that theoretical critique first enables us to understand what it is for something to be and to be a cause or effect, it is clear that anything accomplished by practical critique must in some way build upon the results of theoretical critique. After all, anything that is good or bad is a being that is good or bad; and anything that I ought to do is something that I ought to cause to occur. I propose that the doctrine founded upon theoretical critique encompasses all that there is, without equipping us to understand 27

This is not to deny that there is one capacity (reason), which allows for a theoretical and a practical use. That is a different matter. I am assuming only that theoretical critique does not borrow its most basic concepts or principles from the two remaining critiques. Even when the Canon chapter argues that our speculative interest in the soul, the world, and God is insufficient to explain why these ideas have dominated traditional metaphysics, Kant does not suggest that the original source of those concepts (or reason’s concomitant orientation toward the unconditioned) is practical (cf. A797–800). 28 This is a consequence of the view proposed by Tolley 2012. 29 Both the taxonomy of philosophical sciences that opens the Groundwork (4:387 f.) and the Analogy Passage – texts in which Kant is endeavoring to situate his practical project – treat theoretical and practical inquiry as standing alongside one another, rather than being governed by an inclusion or presupposition relation. The taxonomy’s two material sciences are distinguished by their objects, the ontic (what “happens”) and the deontic (what “ought to happen”). No hint is provided that their subject-matters overlap in any way (cf. GMS 4:427). This should be read in light of Kant’s unambiguous and positive insistence four years earlier on the non-overlapping nature of “is” and “ought” (cf. A547). 30 One source of resistance to this proposal is that the Critique of Practical Reason describes the categories of freedom, which seem like a good bet to be explanatorily prior relative to much else in practical philosophy, as “modi of a single category, namely that of causality” (5:65). Though strictly speaking I make no claims in this paper to capture Kant’s position after the Groundwork, the second Critique’s presentation of the categories of freedom can just as well be taken to support my proposal. To wit, Kant labels them “the categories of freedom with respect to the concepts of the good and bad”, and 〈good〉 and 〈bad〉 do not appear as categories (5:66). That is, it appears that these two concepts are in some way explanatorily prior to the categories of freedom.

The Canon Problem and the Explanatory Priority of Capacities

225

all of the properties that its objects (beings) instantiate. Kant holds that goodness and badness can only be grasped philosophically through practical critique, which is accomplished by tracing practical concepts to their origins. Causal properties are not explained by practical critique, and this holds just as much for uncaused causality as it does for the causal powers found in nature. Our grasp of 〈transcendental freedom〉 is limited by the fact that it lacks a schema. However, to the extent that we are able to grasp transcendental freedom, theoretical critique is sufficient for that task. In contrast, theoretical critique has nothing to tell us about what 〈good〉 and 〈bad〉 mean or what role they play in our agency. 31 This rough sketch is sufficient to make a summary of my proposed solution to the Canon problem intelligible. Recall that two features of the Canon stand in apparent contradiction to the Transcendental Dialectic (along with many other passages throughout Kant’s works): (B+) Kant’s insistence that it is appropriate for the Canon to bracket the question of transcendental freedom, and (E+) his assertion that practical freedom can be proved through experience. It is natural to assume that both can be traced back to a common factor: if, for whatever reason, Kant has determined that the supersensible species of freedom needs to be bracketed, that leaves him with no way to consider freedom except insofar as it can be experienced. To judge from the secondary literature, the assumption that a common factor explains (B+) and (E+) is nearly universal. 32 The next section will depart from that consensus by tracing each to a separate factor. What explains (B+) is Kant’s ambition to furnish an explanatorily fundamental characterization of the practical capacity. Here it is independence that Kant is after. In particular, if what is most explanatorily basic in practical critique is merely the subject’s possession of 〈good〉 – and not concepts of beings – then there will be at least some portion of that critique in which 〈transcendental freedom〉 is appropriately bracketed. Of course, there is no reason to expect that this bracketing of transcendental freedom will be appropriate to theoretical critique or ontology, which makes room for (B–). While it is the independence of practical critique that has the potential to defuse the apparent contradiction regarding the bracketing thesis, it is the fact that our capacity to will is dependent on nature for its realization that explains why Kant feels the need to assert the experience thesis in the Canon. My suggestion will be that while what it means to subsume an x under 〈good〉 cannot be explained by any ontic facts (either natural or supernatural), nor by anything that belongs to theoretical critique, there is still a need to explain how this subsumption presupposes, and is realized in, beings and the “order of nature”, which have received their explanation in theoretical critique. 33 No such explanation would be needed if practical reason had objects that were only goods, without also being existents (or possible existents). Nor is such an explanation needed

31

Henceforth, I will focus solely on 〈good〉, as is Kant’s habit. The fact that Kant sometimes includes both concepts on a par leads to potentially fruitful conjectures regarding their semantic origins. It is noteworthy that we have both pleasurable and painful feelings, whereas there is no parallel contrast among intuitions. This might explain why none of the theoretical categories come in pairs that are formally similar to 〈good〉 and 〈bad〉. 32 Two important examples are Allison 1990, 58 f, and Schönecker 2005. 33 A549. This order consists in the fact that the principles of the three analogies of experience obtain (see A145’s “time-order”, A189 ff. passim, esp. A201).

226

Timothy Rosenkoetter

in theoretical critique, since goodness is dependent on the ontic realm for realization, without the reverse being true.

4. The Canon of Pure Reason The evidence adduced thus far concerns critique, taken in the broad sense of a capacitydirected inquiry. The first question that we need to ask as we turn to the Canon itself is whether there is reason to think that the above results concerning critique apply to that text. Once we approach the chapter with this focus, we see that Kant is quite explicit in tying the very notion of a canon to the consideration of capacities and their use. We are told in the chapter’s Preamble that a canon is the set of the a priori principles for “the correct use” of a cognitive capacity (A796). Kant reminds readers that by this point in the Critique they have already encountered two canons. The analytic portion of pure general logic contains a priori principles for the correct use of the understanding and reason, though only with respect to form. 34 The analytic portion of transcendental logic (the Transcendental Analytic) is the canon of “pure understanding”. 35 Kant then asserts that there is no correct theoretical use of pure reason, since this use is thoroughly dialectical. 36 So if there is to be a canon of pure reason, it can only concern the practical use of that cognitive capacity. We will return to the notion of a canon later in this section in order to specify its relation to use. For now, let’s note that given the care with which Kant clarifies the concept in this Preamble, it would be natural for him to assume that his readers have been primed to recognize parallels between the canon of pure reason and one or both of the logics that he declares to be canons. Canons are individuated by the capacities whose use they treat. The Canon-chapter and its Preamble are unambiguous that it is the canon of pure practical reason. Yet soon there is a proliferation of capacities, as Kant uses four names for capacities in the two dense paragraphs that conclude Section 1 (A801 ff): “practical reason”, “practical freedom”, and “free choice (Willkür)”, along with a single mention of “will (Wille)”. One might at first wonder whether Kant is merely using these as different labels for a single capacity, yet this is made doubtful by sentences that seem to be intended precisely to distinguish them. A close look at the functional roles that Kant assigns to each capacity in these key paragraphs will clear matters up. 37 However, it is worth anticipating a central result at the outset: the canon in question is a canon of pure practical reason, as Kant has indicated starting in the Preamble (A797), rather than a canon defined by a distinct capacity, which Kant might be using one of the other three terms to denote. First of all, Kant is quite clear that practical reason determines free choice: “[. . .] a capacity of choice [. . .] which can be determined independently of sensible impulses, thus through motives (Bewegursachen) that can only be represented by reason, is called free 34

A796; cf. A53; A131; and GMS 4:387. A796, which italicizes “understanding” for didactic reasons. Cf. A63, A131. 36 A796; cf. A131 f. 37 I will resist the temptation to draw evidence from later works such at the Metaphysics of Morals, given that part of what is in question is whether Kant’s position in the Canon chapter diverges from those later works. Fortunately, there is already enough to go on in the 1781 text alone. 35

The Canon Problem and the Explanatory Priority of Capacities

227

choice (freie Willkür) [. . .]” (A802). I take Kant to be implying that these motives cannot be represented by free choice. Something other than free choice – namely, practical reason – enables us to represent something so that it is a motive. It does this by enabling us to represent it as good. When the quoted passage is examined in isolation Kant seems to be limiting the motives in question to moral motives. However, this natural interpretation is rendered untenable by the general scope of “practical freedom” as it is treated later in the paragraph. After asserting that “practical freedom can be proved through experience”, Kant explains: For it is not merely that which stimulates the senses [. . .] that determines human choice, but we have a capacity to overcome impressions on our sensory capacity of desire by representations of that which is useful or injurious even in a more remote way; but these considerations about that which in regard to our whole condition is desirable, i. e., good and useful, depend on reason. (A802)

Practical freedom is actualized not merely when we are motivated by the moral law, but also when we resist snacking in order to be hungry for a tasty meal. Next we face the question of whether “practical freedom” is to be distinguished from both practical reason and free choice or, alternatively, is to be identified with one of them. Whatever is decided should be consistent with the fact that it is practical freedom, rather than reason or free choice, that the experience thesis tells us “can be proved through experience” (A802). The answer, I suggest, is that practical freedom is the capacity that is actualized whenever reason determines free choice. Moreover, if we assume that Kant is using “will (Wille)” as a synonym for “free choice” in its single occurrence, then this is precisely what we are told in the chapter’s second and final assertion of the experience thesis, (E+): “We thus cognize practical freedom through experience, as one of the natural causes, namely a causality of reason in the determination of the will [. . .]” (A803). This fits the fact that what we first explain in natural causal terms when we observe the difference between a hyena and a human being when they are offered a snack is that something other than immediate sensible impulses is causing the human to decline the food. Kant is just observing that the best empirical causal explanation will posit practical reason as a cognitive capacity and free choice as an executive capacity. What we cognize through experience is that the former sometimes causes the latter, at least in human beings. It should be clear that practical reason, free choice, and practical freedom are merely different aspects of what could also, in contexts that require less specificity, be treated as a single capacity. 38 Part of what makes it convenient and natural to fuse them into a single capacity is the way that their tasks are intertwined. First, practical reason is not practical unless it determines free choice. Second, free choice is not free (but merely animal) if it is not determined by practical reason. Finally, the term “practical freedom” simply picks out the causal relation that obtains between the two, a relation that must be present if they are to be actualized as the capacities that they are. Given how natural it would have been to treat these three aspects as a single capacity, we might ask why Kant bothers to distinguish them here (albeit not in a way that any casual reader is likely to track). I wish to suggest that Kant’s goals in the Canon supply him with two reasons to distinguish practical reason from practical freedom and free 38

See the reference to “freedom in general (überhaupt)” at A807 for an example.

228

Timothy Rosenkoetter

choice. First, it is important for Kant to be precise about the capacity whose canon is being considered, in part so that readers see that the Canon is not merely rehashing material that already received its systematically appropriate explanation elsewhere in the Critique. As the Preamble notes, the Transcendental Analytic is the canon of pure understanding. By this point in the Critique it has already traced the origin of 〈cause〉 to pure understanding. Kant can only be fully clear that the present canon is a canon of pure practical reason if he distinguishes it from both free choice and practical reason’s causal influence on free choice (i. e., practical freedom). A canon of practical freedom would be a canon of reason and understanding. 39 Second, by distinguishing practical reason from free choice and practical freedom Kant makes it easier to clarify how practical reason is realized in the ontic realm. I’ll take these points in reverse order. It seems at first glance as if the second reason militates not only in favor of isolating practical reason from free choice and practical freedom but also in favor of specifying whether practical reason is a transcendentally free cause. After all, whatever the answer, this will help to fill out the picture of how practical reason is embedded in the ontic realm. Yet we know that Kant brackets that question in the Canon. Can we make sense of this? Upon closer inspection there is a crucial difference between the cases. In asking whether we are transcendentally free, we are asking whether practical reason itself is caused or uncaused. 40 An answer to that question is not required in order to gain the most basic conception of how practical reason is embedded within the ontic realm. Consider by way of contrast that practical reason is the capacity to represent “that which in regard to our whole condition is desirable, i. e., good and useful” (A802). In order to represent a tasty meal as good, I must be able to represent a tasty meal. In order to represent my cooking that meal as good, I must be able to represent my causing changes to the natural world. So in order to have any grasp of what it is that practical reason enables us to do, we need to understand that the use of this capacity is building upon a prior account of nature, an account that is grounded in theoretical critique. If we did not understand how practical critique builds upon the account of nature provided in the Transcendental Analytic, it would be natural to assume that we use “practical concepts” (A801) to represent a species of object wholly different from the objects of nature. 41 We would then need to ask a series of questions. Is there more than one good? How are goods individuated? Could there be a science whose object is the union set of beings and goods? In sum, we would not understand that natural states of affairs and natural actions are always in

39

Recall that pure, general logic is a canon of both understanding and reason, though only with respect to their form (A796). It is clear from this discussion that neither the Transcendental Analytic nor the present canon is a canon of two capacities. 40 “We thus cognize practical freedom through experience, as one of the natural causes, namely a causality of reason in the determination of the will, whereas transcendental freedom requires an independence of this reason itself (with regard to its causality for initiating a series of appearances) from all determining causes of the world of the senses [. . .]” (A803, italics added). 41 It is difficult to fathom what this would even amount to. It is not sufficient to point to the following. At first glance a good will might seem to be wholly different from any object of nature, since no agent is perfectly moral. This proposal loses sight of the fact that it is impossible to will without willing to do something, and these are intentions to act in nature. Of course, an absolutely good will has as its principle to act only on maxims that pass the universalization tests (GMS 4:447), yet these maxims contain ends and act-types that would be simply unintelligible apart from our prior understanding of nature.

The Canon Problem and the Explanatory Priority of Capacities

229

principle available to be represented as goods. 42 In contrast, for all of the importance that Kant attaches to the question of our transcendental freedom, the Canon’s bracketing of transcendental freedom does not lead us to lose all conception of what practical reason does and how it is connected to beings. In addition to concentrating on the fact that practical reason represents objects of nature as good, as I have just done, it is possible to focus on the fact that practical reason is able to determine free choice to action. This is a second, equally important piece of background knowledge that is essential if we are to understand how the canon of pure reason builds upon the canon of pure understanding, while still remaining independent qua critique. It is this second piece of background knowledge that Kant is calling attention to when he asserts the experience thesis. With this better understanding of the context we can now see that, contrary to what one might expect upon reading the isolated quotation (“practical freedom can be proved through experience”), Kant’s primary concern is not whether we can be certain that we have this capacity (though he does not have the slightest doubt that we do). Nor is Kant focused on the fact that the evidence for practical freedom is to be found in appearances, as opposed to in the supersensible. 43 Kant’s overriding goal here is instead to make intelligible precisely which capacity defines the canon of pure reason, and he aims to do this by making it stand out in relief from that which will not be playing that grounding role, viz., the causal effect that practical reason has upon free choice. In other words, Kant is pointing to practical reason’s causality in the determination of free choice and in effect telling us: “That is just an instance of ordinary causation, which was already explained by the canon of pure understanding and treated in the Analogies of Experience. Moreover, it is part of ordinary experience to posit a capacity that plays the causal role of practical reason, since human choice is not always determined by what is immediately enticing”. The introduction of the term “practical freedom” (and the related term, “free choice”) has allowed Kant to separate out the causal effects of practical reason’s use. This allows Kant to concentrate on what remains, which receives whatever explanation it admits of in this canon, rather than in the canon of pure understanding. What is it, then, which remains and serves as the explanatory ground for this new canon? My proposal, as noted above, is that practical reason in the relevant sense is the capacity to subsume some x under the concept 〈good〉. Textual support for this can be found at two points in the famous paragraph that spans A802. First, we are told that “considerations about that which in regard to our whole condition is desirable, i. e., good

42

In this paper I will remain agnostic on the difficult issue of whether all goods are actions of the subject (cf. Engstrom 2009 for an important interpretation that embraces this). Though I regard this as possible, it is striking that if this is Kant’s position in 1781, A802 f. gives the unsuspecting reader little indication of this presumably important commitment. One gets the impression from this pivotal discussion that the tasty meal itself can be a good, as opposed to the act of eating the tasty meal. 43 Allison misunderstands the experience thesis in precisely this way, combining it with a praxis approach (cf. n. 5) in the final lines: “what we experience is the ‘appearance’ or ‘sensible schema’ [A546] of a capacity to determine ourselves to act on the basis of reason [. . .] Since [Kant] holds that, at bottom, such a capacity is ‘merely intelligible’ [A546], Kant can hardly claim that we can certify empirically that we possess it [. . .] All of this is beside the point, however, given the practical concern of the Canon. Since his concern is merely to determine what we, as putative rational agents, ought to do, speculative questions [. . .] do not arise. For this purpose, we need only be reminded that we at least appear to have [. . .] arbitrium liberum” (1990, 59).

230

Timothy Rosenkoetter

and useful, depend on reason” (A802). I would suggest that Kant includes “desirable” and “useful” in order to conversationally suggest that reason represents mundane objects such as tasty food as good. His point is not that there are three distinct concepts whose origins can all be traced to reason. Second, and with considerably more precision, Kant writes that reason “yields laws that are imperatives, i. e., objective laws of freedom, and that say what ought to happen, even though perhaps it never does happen, and that are thereby distinguished from laws of nature, which deal only with that which does happen, on which account the former are also called practical laws” (A802). The Groundwork tells us that “all imperatives are expressed by an ought, and by this indicate the relation of an objective law of reason to a will that according to its subjective constitution is not necessarily determined by it (a necessitation). They say that to do or to omit something would be good [. . .]” (GMS 4:413). Thus, if we can depend on continuity in Kant’s views on imperatives between 1781 and 1785, imperatives can be restated as indicatives that predicate goodness of some x. 44 The two key passages from A802 agree: practical reason is the capacity to judge 〈x is good〉. A further source of support for this hypothesis can be introduced if we recall that the Canon’s Preamble denies the possibility of a canon of theoretical reason on the grounds that it has no correct “speculative use”, since that use is thoroughly dialectical. 45 It might at first seem that Kant is unfairly minimizing the achievements of the Transcendental Dialectic. After all, though the use is not speculative, theoretical reason admits of a correct regulative use in directing the understanding toward certain goals in theory construction. 46 Thus, it might seem that Kant has illegitimately narrowed his consideration of reason’s fruits to the speculative in an effort to motivate his decision to restrict the canon of pure reason to pure practical reason. This diagnosis results from a failure to appreciate that Kant intends “use (Gebrauch)” in a narrow, technical sense in his definition of canons as containing “a priori principles of the correct use” of a capacity (A796). In this narrow sense, one “uses” a concept only when an object is subsumed under it. This would explain why under theoretical reason Kant considers only reason’s speculative use: a theoretical judgment that subsumes an object under an idea is by definition speculative. The hypothesis that Kant intends the narrow, technical sense of use in his definition of canon also fits the evidence concerning Kant’s willingness to attribute canon-status to the Transcendental Analytic. One question that the Transcendental Analytic considers is whether the categories might admit of a “transcendental use”, in which “things in general (Dinge überhaupt)” (i. e., things that are not restricted to particular forms of sensibility) are subsumed under the categories (A246). Kant denies this possibility, stating that the categories have “merely transcendental meaning (Bedeutung)” (A248). What salvages the Transcendental Analytic’s status as a canon is the fact that with the help of the power of judgment the categories can be given an “empirical use” (A246), whereby objects of

44

The quoted passage is prior to the dichotomous and tripartite divisions that Kant effects among imperatives. Thus, there is every reason to think that an imperative concerning a wholesome meal can also be restated without loss of meaning using the predicate 〈good〉. 45 A796. “A theoretical cognition is speculative if it pertains to an object or concepts of an object to which one cannot attain in any experience” (A634 f.). The contrast concept is a cognition of nature (Naturerkenntnis). 46 Cf. A642 ff.

The Canon Problem and the Explanatory Priority of Capacities

231

possible experience are subsumed under them. It is for this reason that when Kant is being precise he states that “understanding and the power of judgment have [. . .] their canon of objectively valid, and thus true, use in transcendental logic”. 47 The subsumption of objects of experience under the categories requires schemata, and thus the power of judgment. All of this is relevant in the present context because there is some reason to expect that the canon of pure reason will have the same basic structure as the canon of pure understanding. Not every element of critique warrants the title “canon”. Even sections of the Critique such as “On the regulative use of the ideas of pure reason” (A642 ff.), which give us “a priori principles” (A796) for correctly employing a capacity, do not qualify as canons. So there is reason to expect that the present canon will furnish a priori principles for subsuming objects under concept(s). Given our results above concerning practical reason, there is then reason to expect that this canon will furnish a priori principles for subsuming objects under 〈good〉. However, since it is a canon of pure practical reason, we should expect that it will furnish principles of subsumption whose ultimate justification is pure. Not only is 〈good〉 an a priori concept. We should expect that some facts about which objects are properly subsumed under that concept can be determined a priori. In order to see whether the Canon meets these expectations, we need to examine its shift from consideration of practical reason’s general use to the “correct use of pure reason” (A797, italics added). While Section 1 of the Canon-chapter had considered the full array of goods that might serve as “motives” (e. g., tasty meals), Kant reports in Section 2 that he will now assume “that there are actually pure moral laws, which determine completely a priori (without regard to empirical motives (Bewegungsgründe), i. e., happiness) the action and omission (Tun und Lassen), i. e., the use of freedom, of a rational being in general [. . .]” (A807, second italics added). Though Kant does not make it especially easy for his readers to see this, the moral law allows us to subsume individual actions under the concept 〈good〉. 48 Crucially, the moral law itself is said to be “pure”. In contrast to the merely empirical justification for subsuming 〈tasty meal〉 under 〈good〉, the moral law is able to provide pure justification for various subsumptions. What we see in this progression from Section 1 to Section 2 of the Canon matches what the Analogy Passage would lead us to expect. Recall that there Kant tells us that MM stands to GPP as TL stands to traditional, general logic. This allows us to look to the progression from general logic to TL for guidance as how Kant should introduce MM. If the Critique’s Canon is Kant’s first draft for practical critique, the pattern should apply. When we examine the relation of pure, general logic to TL we find two important features. First, there is a single capacity that is treated by both pure, general logic and TL, viz., the capacity of thought. Accordingly, Kant already introduces pure, general logic by reference to that capacity (cf. A51 f.). Second, Kant introduces TL by proposing a logic that contains “merely the rules of the pure thinking of an object” (A55). We find the same elements in the Canon’s progression from Section 1 to Section 2. Section 1 introduces practical

47

A131, italics added. Cp. “Now to the use of a concept there also belongs a function of the power of judgment, whereby an object is subsumed under it [. . .]” (A247). 48 Once viewed in combination with the Groundwork’s uses of “good” in connection with morality (cf. GMS 4:414; 4:447), this accords with the assertion that “one must be able to will that a maxim of our action become a universal law: this is as such the canon of judging it morally” (GMS 4:424).

232

Timothy Rosenkoetter

reason quite generally as the capacity to subsume objects under 〈good〉, including tasty meals. Had it been consonant with his goals, Kant could at this point have offered the hypothetical practical principle as as an a priori principle of the correct use of practical reason, though it would have been “a canon [. . .] only as far as form is concerned, since it abstracts from all content” (A796). What was impossible at this point was to offer a priori principles that do not abstract from content. For that he needed to progress to Section 2’s consideration of what we can cognize purely about which objects are good. In sum, what we find in the progression from Section 1 to Section 2 is a treatment of practical reason that bears striking parallels to the progression that leads from pure, general logic to TL. Just as important as what we find in this progression is what we do not find. There is, namely, no hint that the shift from presenting the general use of practical reason in Section 1 to a consideration of the use of pure practical reason has been accompanied by a narrowing of the capacity definitive of the canon to transcendentally free practical reason. There is simply no mention of transcendental freedom. What has changed is the cognitive relation that practical reason bears to its objects, whether they are tasty meals or actions that are universalizeable. This relation is characterized in terms that are thoroughly familiar from the analogous case of the understanding and its objects. A representational capacity can relate to its objects empirically; or it can have pure representations of them.

5. Conclusion In closing it will be instructive to compare the present interpretation with the praxis approach, which claims to resolve the Canon problem simply by supposing that practical questions are the questions that agents face when they ask, “What ought I to do?” 49 According to this approach, while the Dialectic and many other portions of the Critique are interested in reconstructing what is the case, the Canon adopts the perspective of an agent who is deciding what to do, as is plausibly indicated when Kant explains that “this problem [i. e., the problem of transcendental freedom] does not belong to reason in its practical use” (A803). The reconstruction provided above allows us to see that proponents of the praxis approach have neglected a possibility. According to the present interpretation, what is at issue in the Canon is not mere praxis but a theory of praxis. Crucially, it is a theory which has the idiosyncratic structure of critique, which requires that factors that are dependent on the explanatory ground not be used, circularly, in an attempt to explain that very ground. This interpretation has the advantage that it is in principle consistent with allowing that the question of transcendental freedom is appropriately posed at some point in Kant’s practical theory. The mere fact that Kant conceives of practical critique as having an independent foundation does not mean that it cannot draw on theoretical results at any subsequent point. The praxis approach, in contrast, will be constrained by its separation of the agential perspective from the project of ontic explanation. A second difference between the praxis approach and the present interpretation draws on the results concerning original unity of apperception in § 2. The praxis approach should lead us to expect that the Canon chapter will revolve around the same concept 49

See Beck 1960, 190; Timmermann 2003, 140–144; and Allison 1990, 59.

The Canon Problem and the Explanatory Priority of Capacities

233

as do Kant’s speculative (ontic) treatments of moral agency, while merely adopting a different attitude toward that concept. On this view, the notion of agency that is decisive for the Canon involves transcendental freedom; it is simply that the agent who needs to decide what to do can (and must) assume that she is transcendentally free. In the practical perspective an agent takes a different attitude – an attitude of assumption or supposition – toward the same concept. What this misses is the fact that the Canon does not introduce the concept 〈transcendental freedom〉 to describe the use of practical reason that occurs when we are motivated by the moral law (A807). Instead, the Canon investigates our capacity to use 〈good〉, the justification for which can be either empirical or pure. The Canon’s failure to accord with the praxis model mirrors what we found in § 2 in the case of pure apperception. Just as the Canon does not tell us that because we cannot be certain that we are transcendentally free we must assume it, so theoretical critique does not tell us that because we cannot be certain that we exist (i. e., the category), we must make do with merely assuming it. Kant instead introduces a different content entirely, 〈existence–〉. His use of this concept is provisional. At some point – at the latest by the point at which theoretical critique provides a proper grounding for doctrine – Kant will have no qualms about using the category to judge that thinking beings exist. Similarly, it is not a consequence of my argument that practical critique is at no point properly concerned with the question of whether practical reason is transcendentally free. Yet we should take care not to assume that practical critique begins with this concept. What I have tried to show here is that the hypothesis that practical critique makes its beginning solely with the concept 〈good〉 can explain Kant’s otherwise puzzling choices in the Canon. 50

Bibliography Allison, H. 1990. Kant’s Theory of Freedom. Cambridge: Cambridge University Press. Carnois, B. 1987. The Coherence of Kant’s Doctrine of Freedom. Booth (tr.). Chicago: University of Chicago Press. Beck, L. W. 1960. A Commentary on Kant’s Critique of Practical Reason. Chicago: University of Chicago Press. Engstrom, S. 2009. The Form of Practical Knowledge. Cambridge: Harvard University Press. Heimsoeth, H. 1966. Transzendentale Dialektik. Berlin: de Gruyter. Kant, I. The Cambridge Edition of the Works of Immanuel Kant. Guyer, P. /Wood, A. (eds.). Cambridge: Cambridge University Press. Longuenesse, B. 1998. Kant and the Capacity to Judge. Wolfe (tr.). Princeton: Princeton University Press. Rosenkoetter, T. 2014. Kant’s Three Transcendentals, Explanation, and the Hypothesis of Pure Apperception. In: Altman, M. (ed.). The Palgrave Handbook of German Idealism. London: Palgrave. Rosenkoetter, T. 2018. Toward a Specification of Kant’s Concept(s) of Existence. European Journal of Philosophy 26, 1141–1147.

50

This paper has benefited greatly from the close attention of an anonymous reviewer, Samuel Levey, and Katherine Dunlop, for which I thank them. Time pressures made it impossible to address some of their questions. I hope to do this in future work.

234

Timothy Rosenkoetter

Rosenkoetter, T. n.d. A response-dependent account of the meaning of the categories. Unpublished manuscript. Schönecker, D. 2005. Kants Begriff transzendentaler und praktischer Freiheit. Eine entwicklungsgeschichtliche Studie. Berlin: de Gruyter. Schwaiger, C. 2001. Die Anfänge des Projekts einer Metaphysik der Sitten. Zu den wolffianischen Wurzeln einer kantischen Schlüsselidee. In: Gerhart, V. (ed.). Kant und die Berliner Aufklärung. Vol. II. Berlin: de Gruyter. Schwaiger, C. 2007. Christian Wolffs Philosophia practica universalis. Zu ursprünglichem Gehalt und späterer Gestalt einer neuen Grundlagendisziplin. In: Stolzenberg, J. (ed.). Christian Wolff und die europäische Aufklärung. Akten des 1. Internationalen Chr.-Wolff-Kongresses. Vol. 3. Hildesheim: Olms. Smith, N. K. 1992. A Commentary to Kant’s “Critique of Pure Reason”. Atlantic Highlands, NJ: Humanities Press. Timmermann, J. 2003. Sittengesetz und Freiheit: Untersuchungen zu Immanuel Kants Theorie des Freien Willens. Berlin: de Gruyter. Tolley, C. 2012. The Generality of Kant’s Transcendental Logic. Journal of the History of Philosophy 50, 417–446. Willaschek, M. 1992. Praktische Vernunft. Handlungstheorie und Moralbegründung bei Kant. Stuttgart: Metzler. Wolff, Ch. 1997. Discursus praeliminaris de philosophia in genere. Gawlick, G. /Kreimendahl, L. (eds., trs.). Stuttgart: Frommann-Holzboog.

The Category of Substance Stephen Engstrom, University of Pittsburgh

Abstract This paper considers a principal concept of metaphysics – the category of substance – as it figures in Kant’s critical program of establishing metaphysics as a science. Like Leibniz, Kant identifies metaphysical concepts through logical reflection on the form of cognitive activity. He thus begins with general logic’s account of categorical judgment as an act of subordinating predicate to subject. This categorical form is then considered in transcendental logic with reference to the possibility of its real use. Transcendental reflection reveals that the categorical form, in its potential for such use, constitutes the category of substance and accident, representing a first real subject and a determination of its existence. But to qualify for objective, scientific employment, metaphysics’ concepts must admit of real definitions, which show their objects to be possible, and such possibility, pace Leibniz, can be established only in relation to possible experience. Thus, relying on his doctrine of the schematism, Kant shows the category to figure constitutively in experience, as the ground of the first law of nature, that in all change substance persists.

From antiquity up to the time of the great speculative systems of the modern era, philosophy marked off from its other areas of inquiry a primary field of study, under the name of first philosophy, or metaphysics. This preeminent discipline was devoted to the knowledge of first principles and aspired to be a science in its own right, ruling over human knowledge as a whole and providing the foundation for all the other sciences. Yet in fact metaphysics was chronically plagued by controversy and contention, and ever since Kant’s famous critique of this putative science, philosophy has in the main turned away from metaphysics in favor of other inquiries, focusing much of its attention on a succession of questions that have arisen in connection with developments in the special sciences. Many factors have contributed to this turn, including the profuse and explosive growth of the special sciences themselves, which has made them objects of emulation for philosophy. But to the extent that Kant’s criticism has played a role in the eclipse of traditional metaphysics, we have reason to reconsider this outcome. For Kant’s intention was never to do away with metaphysics, but rather to secure, through critical reflection, the conditions under which it can establish itself as a science. Such reconsideration would be timely. Recent decades have seen signs of reawakening interest in this field, yet the revival has occurred in relative ignorance of metaphysics’ troubled history. It may therefore serve us well, if we care to avoid retracing missteps of the past, to recall that history, and in particular Kant’s critical reflections on how a scientific metaphysics can be established. A full reconsideration would of course lie well beyond the reach of these few pages. But a more limited investigation may still be of use, for purposes of illustration. I shall take up one principal concept of metaphysics – the category of substance – and consider it as it figures in Kant’s critical reconstitution of traditional first philosophy as transcendental philosophy. When so considered, this

236

Stephen Engstrom

concept can be recognized as the ground of a principle of knowledge, a principle that constitutes the first law of nature.

1. Approaching the concept of substance 1.1

Demarcating the science of metaphysics

Kant shares the traditional metaphysician’s recognition that first philosophy, as a science of the principles of knowledge, cannot be dependent on or beholden to any special science. The concepts of metaphysics must be fundamental to all such sciences, being already in play in absolutely all knowledge of things and hence even in the primordial, prescientific use of the human cognitive capacity in common experience. This recognition informs the approaches taken by the great metaphysicians of history. It can be seen for instance in Aristotle’s respect for commonly accepted opinions in his investigation of first principles, in Descartes’s decision to conduct his meditations on first philosophy not in the jargon of the schools but in terms intelligible to ordinary men of good sense, and in Leibniz’s conviction that we find the primitive concepts and truths of metaphysics naturally within ourselves. 1 Kant is particularly scrupulous in this regard. His investigation of the possibility of scientific metaphysics is to rest solely on reason, the capacity to know from principles. 2 The only science presupposed is logic, or more precisely what he calls pure general logic, a merely formal science, constituting a canon for all use of the cognitive faculty. And while he accepts the spirit of the traditional characterization of metaphysics as “the science of the first principles of human knowledge”, he insists on a precise demarcation of this science from other knowledge, delineating it as the system of pure material rational knowledge from concepts: as a system, it differs from common, prescientific knowledge; as pure, it contains no empirical knowledge; as material, it is distinguished from general logic; and as knowledge from concepts rather than from the construction of concepts, it counts as philosophical and is marked off from all mathematical and other technical knowledge. 3 And he strictly adheres to the insight, emerging from his critical investigation, that

1

Descartes goes so far as to say that his principles, with the sole exception of the proposition relating to God’s existence, “have been known for all time and indeed accepted as true and indubitable by everyone” (IXB 10, cf. 12–13 [I 184, 185]). (References to Descartes’s writings cite volume and page of AT, followed by parenthetical reference to volume and page of CSM(K).) Similarly, but more circumspectly, Leibniz responds to Locke’s criticism of the argument from universal consent by observing that while general acceptance cannot establish the certainty of innate principles, it is still a sign that a principle has such a status, and that such principles are known by all in the sense that, even if they are not always explicitly recognized, everyone uses them all the time (NE 75–76). 2 See P 4:274. 3 See KrV A837-844 /B865-872, GMS 4:387–388. The quoted characterization of metaphysics is a formulation offered by Kant (KrV A843 /B871), which reproduces verbatim the definition presented in § 1 of Baumgarten’s Metaphysica, the textbook Kant used in his lectures on metaphysics (“Metaphysica est scientia primorum in humana cognitione principiorum”). Baumgarten’s definition is in turn essentially the same as the characterization provided in Descartes’s Principles of Philosophy (IXB 16 [I 187], VIIIA 5 [I 193]), which is broadly similar to the traditional Aristotelian conception. Aristotle spoke of first philosophy, or wisdom, as the knowledge of first principles, and some of his descriptions suggest that it could be characterized as the science of the first

The Category of Substance

237

metaphysical concepts can be certified as valid only for immanent use, in experience, and only through an exhibition of them as conditions of its possibility.

1.2.

Reflection and the concepts of metaphysics

It might at first be suspected that a putative science that confines itself to concepts already at work in common experience would find itself hopelessly mired in a confused mass of impressions and obscure opinions. But the fact that ordinary thought can be confused and inarticulate does not preclude the possibility of explicating it through reflection and analysis – that is, through a certain skilled attention, for which natural aptitude and extensive practice may be required. Both Leibniz and Kant rely on such reflection, and in carrying out their analysis both employ a modal criterion, namely necessity, to distinguish from empirical representations certain concepts, which, originating in our cognitive capacity, are suited to figure in the first principles of knowledge (NE 51, 83–84; KrV B1-4). According to Leibniz, it is through the thought of oneself that one comes by the concept of substance, along with other concepts of metaphysics. The thought of myself, who perceive sensible objects, and of my own action which results from it, adds something to the objects of sense. To think of some color and to consider that I think of it – these two thoughts are very different, just as much as color itself differs from the ego who thinks of it. And since I conceive that there are other beings who also have the right to say ‘I’, or for whom this can be said, it is by this that I conceive what is called substance in general. It is the consideration of myself, also, which provides me with other concepts in metaphysics, such as those of cause, effect, action, similarity, etc., and even those of logic and ethics. Thus it may be said that there is nothing in the understanding which has not come from the senses, except the understanding itself, or the one who understands. (On What is Independent of Sense and of Matter [PPL 549])

What exactly Leibniz has in mind here is not immediately apparent, though it seems reasonably clear that he means in part to be espousing a version of a traditional innatist view, in opposition to empiricism. Yet Locke and other empiricists also speak of reflection as one of the powers of the mind, and some care is needed to distinguish the reflection Leibniz intends from what such empiricists have in view. Locke assimilates reflection to sensation, classifying these powers as the two sources of our simple ideas, which make up all the materials of our knowledge. In the case of reflection, the ideas acquired are of the mind’s own operations, beginning with perception, and Locke says explicitly that these ideas, like those of sensation, are passively received (An Essay Concerning Human Understanding [henceforth Essay] II.i.24-25, xii.1). Leibniz demurs here, on two points. He is puzzled by Locke’s claim that in reflection’s reception

principles of knowledge (e. g. Metaphysics I.2, 982b2-4), though he never, so far as I know, called it the science of the first principles of human knowledge. (References to Aristotle’s works normally cite book and chapter numbers, followed by the standard Bekker page and line numbers.) Over the course of his investigation, he further characterized metaphysics as concerned with being qua being and with substance. Kant’s demarcation leaves open the possibility of a practical as well as a theoretical metaphysics. In their practical use, metaphysics’ categories concern, not the object of theoretical knowledge, but the subject of practical knowledge (the concept of substance, for instance, grounds the concept of a person); but here I leave such use aside.

238

Stephen Engstrom

of simple ideas the mind is “wholly passive”. 4 And he opposes Locke’s implicit suggestion that reflection can have something passive as its object. Noting that perceptions can be unconscious, Leibniz maintains that the proper object of reflection is not perception generally, as Locke holds, but specifically thought: “thoughts are actions”, Leibniz states; while “beasts have perception”, “they don’t necessarily have thought, that is, have reflection or anything which could be the object of it” (NE I.i.26, 86, NE II.ix.1, 134). Later, he elaborates: So ‘understanding’ in my sense is what in Latin is called intellectus, and the exercise of this faculty is called ‘intellection’, which is a distinct perception combined with a faculty of reflection, which the beasts do not have. Any perception which is combined with this faculty is a thought, and I do not allow thought to beasts any more than I do understanding. So one can say that intellection occurs when the thought is distinct. (NE II.xxi.5, 173)

Since Leibniz restricts the term ‘faculty’ to active powers, 5 his mention of “a faculty of reflection” indicates that he supposes that the reflections in which we are conscious of our thoughts are just as much actions as are those thoughts themselves. The foregoing considerations do not entirely rule out the possibility that Leibniz holds that the way in which the reflecting mind comes by its concept of substance is through an immediate intellectual apprehension or “internal experience” of itself, a representation of itself in which the representation of substance can be found, and from which it can be extracted by analysis. 6 Such a position would be tantamount to a doctrine within traditional rational psychology, the ostensible science criticized in Kant’s Paralogisms of Pure Reason. But since Leibniz conceives of substance not simply through the idea of independent existence, as Descartes and Spinoza do, but in terms of a capacity to act, some of what he says about reflection can be understood as at least suggestive of the thought that the concept of substance is understood, not through the operation of a passive intellect, but in an active self-consciousness internal to the mind’s own activity. Such a thought 4

NE II.i.25, 119. Leibniz’s puzzlement may stem at least in part from the thought that reflection involves the mind’s act of turning its attention to its own operations, as Locke elsewhere acknowledges. 5 NE II.xxi.1, 169. As does Kant: ApH 7:140. 6 At NE I.iii.18, 105 Leibniz seems to suggest that our finding the idea of substance within ourselves is related to our being substances: “It is my opinion that reflection enables us to find the idea of substance within ourselves, who are substances” (at I.i.23, 85–86 a similar point is made regarding the idea of being). A more explicit expression of this view seems to be discernible in the following fragment: “That we are not substances is contrary to experience, since indeed we have no notion [notitiam] of substance except from the intimate experience of ourselves when we perceive the I [to Ego], and on that basis we apply the term ‘substance’ to God himself and other monads” (Grua 2.558; quoted in Jolley 1984, 123). In another similarly explicit passage, Leibniz writes, “It is very true that our perceptions or ideas come either from the exterior senses, or from the internal sense, which can be called reflection: but this reflection is not limited to just the operations of the mind, as is said [by Locke] [. . .] it goes as far as the mind itself, and it is in perceiving [the mind] that we perceive substance” (NE 14; quoted in Wilson 1999, 377). See also Discourse on Metaphysics § 27: “So the expressions which are in the soul, whether conceived or not, can be called ideas, but those which are conceived or formed can be called notions or concepts. But in whatever sense they are taken, it is always false to say that all of our notions come from the senses which are called external; for the notions which I have of myself and of my thoughts, and, consequently, of being, of substance, of action, of identity, and of many others, come from an internal experience” (PPL 321). There is some indication that by ‘internal experience’ Leibniz has in mind the self-awareness described in Descartes’s Second Meditation, for in his response to Locke he gives as an example of what is needed for the conception of “the same thing” that we find in the notion of “pure subject in general” the recognition that “it is the same thing which understands and wills, which imagines and reasons” (NE II.xxiii.2, 218, cf. IV.ii.1, 367).

The Category of Substance

239

would anticipate Kant’s account, according to which the intellect understands itself in such self-consciousness rather than through the receptivity of inner sense or through the putative power of rational intuition invoked by the dogmatic metaphysician. When Kant adopts Leibniz’s term apperception, he gives no sign that he means to depart from Leibniz’s usage. And as we noted, both Kant and Leibniz regard our consciousness of necessity in our thought and knowledge as a mark by which the intellect’s contribution can be distinguished. So there is some basis for surmise that a certain way of understanding Leibniz’s suggestion that we have the concepts of metaphysics through reflection on ourselves serves as an inspiration for the approach Kant takes in developing his account of the categories. But before turning to Kant, a few further comments are in order regarding the different approaches taken by Locke and Leibniz, since Kant cites these thinkers as foils in articulating his own position.

1.3

Two perspectives on substance: Locke and Leibniz

In his account of how we come by the notion of substance, Locke states that when we notice several simple ideas going constantly together, we presume them to be united in one subject, accustoming ourselves to suppose a substratum wherein they subsist, which we call substance. From this account he concludes that we have no distinct idea of pure substance in general, but only a supposition of an unknown support of the qualities that directly or indirectly produce ideas in us, qualities we speak of as its accidents. In responding to this account, Leibniz denies that there is anything problematic in our thought of substance: “we have no need”, he writes, “to ‘accustom’ ourselves to it or to ‘suppose’ it; for from the beginning we conceive several predicates in a single subject, and that is all there is to these metaphorical words ‘support’ and ‘substratum’”. And he argues that Locke’s conclusion that the idea of substance is “empty and sterile” is a creature of Locke’s own implicit analysis, which has stripped away all of the attributes. 7 Underlying this disagreement, we can find a noteworthy difference in the vantage points from which Locke and Leibniz consider the notion of substance. Locke’s perspective is reflected in his often-cited remark that if we are asked what is the subject in which color or weight inheres, we will have nothing to say but the solid extended parts, and if pressed to say what the solidity and extension inhere in, we will be in a position like that of an Indian philosopher who, when subjected to a similar interrogation, answered that the world rested on an elephant, which in turn stood on a giant tortoise, supported by something, he knew not what. Leibniz, in contrast, says that from the beginning we conceive several predicates in a single subject. Thus unlike Locke, who represents us as first thinking of qualities that are implicated by the passivity of our reception of simple ideas and then, out of a kind of need, supposing a substratum to support those qualities, Leibniz draws our attention to the constitution of the act of predication, in which thought of a subject is presupposed. So whereas Locke thinks of substance as the last subject of inherence, something beyond the reach of our ideas, which we cannot know, Leibniz thinks of it as the first subject of predication, something we must know insofar as we

7

NE II.xxiii.1-2, 217–218. For Locke’s account, see Essay II.xxiii.1-2.

240

Stephen Engstrom

know anything at all. 8 This difference reflects the presence of two relations – one logical, the other real – long recognized in traditional thinking about substance. According to Aristotle’s account, substance in the primary sense is distinguished from and related to both things that are predicable of it (predicates or attributes) and things that inhere in it, or are in it but not as parts (accidents, modes, or affections). 9 In many cases one and the same thing may bear both relations to substance, as whiteness does to this body, the chalk I see on the table, but as Aristotle points out, these relations do not coincide. Extension, for example, is predicable of the chalk, but does not inhere in it; and something may inhere in the chalk without being predicable of it, for instance its own individual whiteness. Leibniz focuses on the first of these relations, Locke on the second. This difference in perspective is rooted in a broader difference in approach. Locke is attempting to show how, starting from experience, which provides, he says, “the materials of Reason and Knowledge”, we can, without reliance on innate principles, acquire all the knowledge we have. His point of departure for investigating how we come by the notion of substance accordingly lies in the consideration of experience, which, as he conceives of it, is characterized by the passivity of the mind’s reception of the ideas that make up the materials of knowledge, which he identifies as its simple ideas. The passivity of that reception points to active powers distinct from the ideas – certain “qualities”, as Locke calls them – and substance is accordingly conceived as the supposed common subject of inherence that supports and unites certain qualities that are first conceived as the powers acting to produce such passively received simple ideas as are noticed to go together in our experience. Since Locke includes among the powers whereby the mind passively receives its simple ideas not only sensation but also reflection, he treats sensation and reflection as on a par in this regard and does not consider any contribution that might arise from a self-conscious act of the intellect. 10 Leibniz on the other hand is interested in exhibiting the role in cognition that is played by ideas and principles recognized in the intellect’s reflection on its own purely intelligible activity. He thus understands reflection differently from Locke, as the intellect’s active power to conceive its own ideas, and he accordingly maintains that “reflection enables us to find the idea of substance within ourselves, who are substances”. 11 And since as we saw he holds the concepts of logic as well as those of metaphysics to be provided by the consideration of oneself, he likewise takes logic’s concept of a subject of predication to be understood through self-consciousness or apperception. Thus in his remark that “from the beginning we conceive several predicates in a single subject”, Leibniz foregrounds predication rather than inherence, calling attention to a logical operation of the intellect, at once an action and a logical relation. 8

This is not to say that Locke is unaware of the possibility of conceiving of substance as the first subject of predication; he seems to hold that once the indistinct idea of substance in general has been framed, it can be used in this way (see Essay II.xii.6). 9 Categories 2 and 5. 10 Locke does speak of a “reflex Act of Perception” (Essay II.xxvii.13), but since he holds that “the Mind is wholly Passive in the reception of all its simple Ideas”, whether of sensation or of reflection (Essay II.xii.1; cf. II.i.25), the “Act” that figures in a reflex act of perception is evidently the act of reflection (the mind’s turning of its attention back onto itself), as distinct from the reception of a simple idea of reflection, in which the mind is “wholly Passive”. 11 NE I.iii.18, 105; cf. I.i.23, 85: “intellectual ideas, or ideas of reflection, are drawn from our mind”.

The Category of Substance

241

Leibniz acknowledges that Locke’s notion of “pure substance in general”, precisely on account of the abstraction involved in framing it, must be empty of all specificity, containing merely the notion of a substratum (whether conceived as last subject of inherence or as first subject of predication), which serves as “the same thing” to which several qualities or attributes belong, the ground of their unity. But he nevertheless maintains that “this conception of substance, for all its apparent thinness, is less empty and sterile than it is thought to be. Several consequences arise from it; these are of the greatest importance to philosophy” (NE II.xxiii.2, 218; cf. II.xiii.20). Although Leibniz does not here identify the consequences he has in mind, we may surmise from what he says elsewhere that he is thinking of consequences that will flow from a real definition. He clearly holds that the logical concept of substance does not by itself amount to such a definition. In explaining at one point what an individual substance is, he says, “It is of course true that when a number of predicates are attributed to a single subject while this subject is not attributed to any other, it is called an individual substance. But this is not enough, and such a definition is merely nominal” (Discourse on Metaphysics § 8 [PPL 307]). Nominal definitions, he holds, “contain only marks for discerning one thing from others” and merely provide a property coextensive with the concept they define; real definitions, in contrast, are ones “through which the possibility of the thing is ascertained” (Meditations on Knowledge, Truth, and Ideas [PPL 293; cf. PPL 230–231, 319]). Leibniz’s thought, then, appears to be that although the nominal definition, imperfectly registered in Locke’s account, is a thin concept, logical reflection can reveal it to be purely intellectual, thereby enabling further reflections which may lead to a real definition from which consequences “of the greatest importance to philosophy” will flow. And this does appear to be the path Leibniz follows. He holds that the concept of substance that we have from ourselves, when properly analyzed and purified through the removal of limitations, yields the notion of an absolutely perfect being, and if by such reflections a real definition of such an individual can, as Leibniz supposes, be achieved – one that, by making evident the consistency of all the perfections understood in this concept, shows such a substance to be possible – then necessary existence too can be established, insofar as existence is one of those perfections, the perfection of possibility itself. Relying on this momentous conclusion, Leibniz elaborates a metaphysical system of the created world, grounded in an account of divine nature, on which divine will, in perfect accordance with unlimited divine understanding, creates the most perfect world possible.

2. Immanent metaphysics: substance and the first law of nature Like Leibniz, Kant proceeds from nominal to real definitions in treating the categories of metaphysics, framing his nominal definitions in purely logical terms. 12 Kant’s path differs from Leibniz’s, however, in that his adherence to a mode of reflection consistent 12

Some caution is in order in speaking of Kant as dealing in definitions. Kant emphasizes that a chief respect in which reason’s use in philosophy differs from its use in mathematics is that only the latter science can provide definitions strictly so called. Because philosophy deals with concepts that are given a priori, it cannot ensure with apodeictic certainty the completeness required for a definition: “strictly speaking, no a priori given concept can be defined, for example substance, cause, [. . .]” (KrV A728 /B756). Recognizing the long tradition of philosophical usage, however, Kant allows that we may speak of definitions in philosophy, provided that the

242

Stephen Engstrom

with the possibility of a scientific metaphysics requires not only a starting point in the intellectual self-consciousness of logical reflection, but also an understanding of reality and of real definition consistent with the limits of possible experience. Remaining within the ambit of our self-conscious cognitive activity, Kant’s reflection leads directly from logic to an immanent metaphysics. Through a radically internal, hylomorphic analysis of human, discursive knowledge, he is able to show that such knowledge, though dependent for its actuality on affection by an independently existing object, is nevertheless selfdetermining and hence so related to its object that the object must conform to it. 13 He can thus move from a logical to a real definition by relying, not on a speculative doctrine of an infinite, intuiting intellect whose knowledge creates – or is absolutely productive of – the objects it knows, 14 but rather on an account of our finite, discursive intellect as a faculty whose knowledge constitutes – or is productive in respect of the form of – the independently existing objects it can know. This distinction between finite and infinite knowledge brings with it a corresponding distinction between their objects, in that according as an object does or does not exist through the knowledge of it – according, that is, as the knowledge of it and the ground or cause of its existence are identical or distinct – it is either a thing in itself (noumenon) or an appearance (phenomenon). 15 Following this “Copernican” path, Kant develops his account of substance by first articulating the logical concept of it, derived from the form of a categorical judgment. From there he advances, in a second step, to an account of how this concept can generate a sensible representation – a “schema” – of its object as the permanence of the real in time, putting himself in a position to frame a real definition. He can then, in a third step, prove a priori the possibility of the object of the resulting “realized” concept by showing, in his first “Analogy of Experience”, that the use of this concept is a formal condition of the possibility of the experience of objective change, a condition that constitutes the first principle of all knowledge of contingent things (things that come to be and pass away) and thereby also, in accordance with the Copernican way of thinking, the first and highest explanations offered under this name are not confused with the strictly so-called definitions of mathematics. Mathematical definitions, he says, are synthetically established constructions of originally made concepts, and as such they make the concepts they define; philosophical definitions, in contrast, are established analytically through dissection, the completeness of which is never apodeictically certain, and they are accordingly merely expositions of given concepts, serving only to explain or to elucidate them, or to make them distinct (A370 / B758, L § 104). Partly with an eye to this difference, Kant declines to present definitions of the pure categories, but he does not deny that he possesses them (A82-83 /B108-109; cf. A241), and from his various discussions of individual categories it is usually possible to derive at least a rough idea of what he would have included had he offered nominal definitions; real definitions are touched on in the first and third chapters of the Analytic of Principles. (For the case of the category of substance, see esp. A147 /B186, A242-243/B300-301.) 13 Limitations of space preclude detailed consideration here of this “Copernican” account of cognition’s relation to its object; I offer a fuller treatment in Engstrom 2017. 14 KrV B72; cf. B138-139. In Leibniz’s striking comparison, “all the other substances depend on God as our thoughts emanate from our substance” (Discourse on Metaphysics § 32 [PPL 324]). 15 This distinction is, as Kant says, transcendental rather than empirical. It is therefore not to be confused with the distinction between thing in itself and appearance as ordinarily understood. Although the objects of our discursive knowledge are phenomena, this does not prevent us from distinguishing these objects themselves, that is, the objects knowable in experience, from the appearance of them in bare perception (i. e. senseperception: Wahrnehmung) (see KrV A45-46 /B62-63). The appearance apprehended in bare perception is a mere appearing and as such may change with change of position, condition, or perceiver, while the object itself (the phenomenon) remains the same for oneself and for everyone.

The Category of Substance

243

law of nature, namely that in all change among appearances, substance, as permanent, persists. In what follows, I consider these steps in order.

2.1

From the form of categorical judgment to the category of substance

As we noted, both Leibniz and Kant hold that we come by the concept of substance through reflection. Though our consideration of Leibniz’s understanding of reflection left important questions unresolved, we can characterize reflection in Kant’s understanding of it as the attending, in conscious activity, to that same activity and in the first instance to what, marked out by its necessity, belongs to the activity’s form. 16 The reflection carried out in logic, as Kant conceives of it, concerns the conscious activity of thinking and knowing, seeking to expound wholly a priori the form of knowledge. Since this form, considered as potentiality, constitutes the faculty of knowledge, or the understanding (including reason), logic is “a self-knowledge of understanding and of reason”; in this selfknowledge, the understanding is expounded first “solely according to form” in general logic and then “in respect of its material use” in transcendental logic. 17 Here two points should be noted at the outset, as they inform the self-knowledge articulated in logical reflection and so furnish context for thinking about the categories. One concerns knowledge in general, the other is specific to our theoretical knowledge. First, we recognize that knowledge is not a process or event, but a self-conscious activity constituted by a certain unity of consciousness: not merely the unity of thought, which may be arbitrary, but a self-consciously determinate and hence self-sustaining unity, lying in a self-agreement grounded in the at least implicit understanding that knowledge must agree with knowledge. So far as this activity understands itself to be material knowledge, or knowledge that – unlike the formal self-knowledge articulated in logical reflection – is a conscious representation of objects, or of things that can exist, or have actuality outside the knowledge of them, it necessarily understands itself to be in agreement with its objects, in that it is in such conscious representation itself that the latter are first conceived and understood. And since material knowledge, as knowledge, understands itself to be in self-sustaining agreement with itself, it understands its agreement with its objects to be nonaccidental, and the objects to be essentially knowable. From this understanding it can be seen that those objects must agree with one another. For however much more they may contain than is represented in a given subject’s actual knowledge of them, they are nevertheless, as knowable things, nothing but what the complete knowledge of them would represent them as being. Knowledge thus includes originally and from its own self-understanding a representation of its objects – knowables – as in thoroughgoing agreement. Second, we also recognize that insofar as our material knowledge is theoretical, or in other words knowledge of reality, or of objects that exist independently of that knowl16

In reflection, then, consciousness can become explicitly conscious of itself. Although Kant does not characterize reflection in exactly the terms used here, reflection must be constituted as here described if it is to be, as Kant holds it to be, the birthplace of the generality of representation that constitutes the form of a concept (see L §§ 5–6, KrV A260 /B316). 17 L 9:14. Kant correspondingly distinguishes two types of reflection, logical and transcendental (KrV A260-263 / B316-319). It is to be noted here that the self-knowledge figuring in logical reflection is not merely of one individual subject, but of the understanding itself, shared by all.

244

Stephen Engstrom

edge, it is limited. 18 Such objects can be the theoretically knowable objects they are only insofar as we stand in a certain passive relation to them by possessing, in our capacity to know, a receptivity through which they can, by modifying our consciousness, affect us in a way that enables us to come to know them. Hence our knowledge, so far as it is acquired in this way, comes to be, and so stands between complete ignorance and complete, unlimited knowledge. Yet the self-consciously self-sustaining character of this knowledge entails that it cannot be a mere effect of objects upon us, but must rather be the self-conscious actualization of a spontaneous capacity, the faculty of knowledge. Our knowledge, then, is finite, being dependent for its actuality on affection by its objects, yet grounded in a spontaneous capacity, through which it begins in an understanding of its objects as knowable though not already actually known. It is thus discursive, springing from concepts, or general and hence partial representations. As knowledge from concepts, it constitutes a kind of development, 19 in which the concept or knowledge of an object through which we understand it as knowable is enlarged, or grows, in that further concepts are combined with it, or integrated into it, in acts of synthesis carried out by the understanding to secure and to extend the determinate unity of knowledge. Logic reflects on the form of this discursive cognitive activity with a view to articulating the understanding’s function of securing the unity of knowledge in the face of the diversity of representation that knowledge contains through its dependence for its actualization on affection by the object. The function by which this discursive unity is secured is judgment, a synthesis, or combination, of conceptual representations. Now as I just mentioned, we know in advance that knowledge secures its own unity and that its object must therefore have unity as well, so we can anticipate, as Kant does, that the system of basic forms of judgment expounded in logic will provide a “guiding thread” for identifying the fundamental functions that secure this unity and thereby furnish the basic concepts of the object of knowledge, concepts that Kant refers to as “pure concepts of the understanding” and in honor of Aristotle calls “categories”. The function that grounds the category of substance lies – as we have here to explain – in judgment’s most basic form, that of categorical judgment, a combination of two concepts. This combination can be variously modified, for instance in respect of quantity as universal, particular, or singular, and in respect of quality as affirmative, negative, or infinite. But we may for now leave the modifications aside and focus directly on the relation between the concepts in the primary, affirmative case. As is indicated by his talk of forms of judgment, Kant relies on a hylomorphic analysis of judgment and knowledge. Such an analysis is suited to the discursive character of theoretical knowledge as the work of a cognitive capacity that is spontaneous yet dependent for its exercise on enabling conditions of receptivity. In the Jäsche Logic it is stated that every judgment has both matter, which lies in the representations combined or related in it, and form, or the determination of how they are united in one consciousness; it is also stated that in a categorical judgment the matter comprises the two aforementioned

18

There is another species of material knowledge, one with which we are not here concerned, namely practical knowledge, whose object – the good – depends on such knowledge for its existence. 19 I am thinking here of material in contrast to merely formal (L § 37n1) development (Entwickelung) (cf. L § 36n1, where a similar distinction is drawn with respect to the augmentation of knowledge).

The Category of Substance

245

concepts, designated as subject and predicate, whereas the form, or determination of their relation, lies in the copula. 20 This analysis might give the impression that the two concepts, as the materials combined, are to that extent on a par in the roles they play in the judgment. And it is indeed true that every concept, in virtue of its form as a general representation, is in itself suited to serve either as predicate or as subject. But as is already indicated by logicians’ employment of distinct terms to designate these concepts, these roles are different; to speak of a subject or a predicate is to speak of a concept in a certain use. A familiar sign of the difference is that the operation of simple conversion, when applied to a universal affirmative or a particular negative judgment, does not yield an equivalent judgment. Although the concepts combined in the judgment all bodies are divisible contain nothing in their form as general representations that prevents their roles from being reversed (all divisibles are bodies), such an operation can constitute a valid inference only under a restriction of quantity (some divisibles are bodies), and as a result the iteration of the operation (some bodies are divisible) will not return us to the original judgment. 21 The function of the copula is not, so to speak, commutative. We can take a step toward clarifying the asymmetry by noting further hints and indications in the texts. It is stated in the Logic that in a categorical judgment the predicate is subordinated to the subject, and in the Critique Kant contrasts subject with “mere predicate” and ascribes a “logical precedence” to a subject that is not also a predicate. 22 These

20

L § 18, § 24; cf. KrV A266 /B322. In logical contexts, Kant standardly employs ‘subject’ and ‘predicate’ to refer to the concepts in use in a categorical judgment, but on occasion, particularly in contexts where the category of substance is in play, he will employ these terms to refer to what is thought through the subject and predicate concepts in such use (e. g. at A147 /B186-187, B233, A205 /B250). I shall allow myself a similar freedom, while seeking to ensure that the intended sense is always clear (for instance by speaking of a real as opposed to a logical subject). 21 Cf. KrV B128–129, L §§ 51–53. 22 L § 23, KrV B129, A242-243 /B300-301 (see also L § 60, where the condition of the objective unity of consciousness of the manifold of cognition in a categorical judgment is identified as “subject of the inherence of marks”). Two comments: (i) The statement in L § 23 that in a categorical judgment the predicate is subordinated (untergeordnet) to the subject might seem to conflict with the account of judgment set out in the metaphysical deduction, where Kant says, “All judgments are accordingly functions of unity among our representations, where instead of an immediate representation a higher representation, which comprehends this and others under itself [unter sich begreift], is employed for the knowledge of the object” (A69 /B94). In this statement, Kant appears to be suggesting that in every affirmative categorical judgment (negative judgments have only a secondary status and are not here under consideration: cf. B149) the predicate is related to representations contained under it. And while he does not here speak explicitly of subordination, he did speak of an ordering of diverse representations under a common one (unter [. . .] ordnen) in his earlier characterization of function (A68 /B93), and we find ‘subordination’ (Subordination) used in other places (e. g. L § 29n). Because in all such cases the subordination is a matter of the predicate’s containment in another representation, which it therefore contains under itself, such subordination might be called “subordination in content”, or “analytic subordination”, a relation pertaining to concepts in themselves, independently of their use in judgment. Despite initial appearances, however, the metaphysical deduction’s account of judgment in terms of such subordination is not in conflict with the characterization in L § 23 of categorical judgment in terms of the subordination of predicate to subject. As will be explained in what follows, the subordination mentioned in § 23 pertains to the use of the concepts serving as subject and predicate and might accordingly be called “subordination in use”, or “synthetic subordination” (if ‘synthetic’ is understood broadly, as signifying the synthesis grounding not only synthetic but even analytic judgments; cf. B131n). Thus categorical judgments involve not only an analytic subordination of representations to the predicate, but also a synthetic subordination of the predicate to the subject. (For discussion of Kant’s

246

Stephen Engstrom

remarks suggest a certain priority of the subject to the predicate in judgment and knowledge. Such priority comports with the foregoing characterization of discursive knowledge as lying in a development of concepts, and it fits with our reflective understanding of categorical judgment as containing two moments: (1) the use of a concept as subject, to think of an object, bringing into use an understanding of what it is; and (2) the use (together with [1], in a single act) of a concept as predicate, to assert – or to think in the determinate, self-sustaining way that constitutes an act of knowledge – something in respect of the object thought of in (1). These are moments, not stages in a process; their order is not a succession in time. The first provides a ground for the second, a condition of its possibility; whereas the second is not reciprocally a condition of the possibility of the first. A categorical judgment can accordingly be regarded as lying, strictly speaking, in the assertion of what is thought through the use of the concept serving as predicate, 23 for in that assertion the use of the concept serving as subject is consciously presupposed. 24 The judgment is therefore an act in which another act, namely the use of the concept serving as subject, is contained, as the inner condition enabling the assertion of what is thought through the use of the concept figuring as predicate. 25 The second moment, which constitutes the judgment, is thus an act that lies in a development of the act serving as its ground. This order is integral to categorical judgment in general, whether synthetic or analytic. In a synthetic judgment, the use of the one concept as predicate is conditioned by the use of the other as subject. Although the concept divisible can be used independently of the concept body, its use in all bodies are divisible is dependent on and hence subordinate account of judgment in terms of subordination to the predicate, see Longuenesse 1998, 86–90. Longuenesse notes that L § 23 is concerned with subordination in a sense other than that of subordination to the predicate, and although she does not explore it in detail, she describes it as “subordination of the assertion to its condition” (1998, 93–94), drawing on language employed in the Logic’s characterization of the major premise of a syllogism (L § 58n, § 60). If I have understood her, this description is in agreement with the idea of synthetic subordination that I will be spelling out here.) (ii) The subordination of predicate to subject differs from the subordination of consequent to ground in a hypothetical judgment (L § 23); while a predicate is no less dependent on its subject than is a consequent on its ground, it does not constitute a separate judgment in its own right. (Cf. A414 /B441, where Kant similarly distinguishes the subordination of accident to substance from subordination in the strict and proper sense, which is found in the relation of effect to cause.) 23 See KrV A322 /B378, where “predicate” is glossed as “assertion in general”. Kant does not explicitly mark the now familiar distinction between predication and assertion (Geach 1965), but by distinguishing modalities of judgment he is able to accommodate non-assertoric predication, for instance in compound judgments (A74-76 / B99-101). 24 Similarly, Kant identifies a syllogism with its conclusion: a syllogism is “a judgment by means of the subsumption of its condition under a universal rule (major premise)” (KrV A307 /B364; cf. L § 56). 25 This two-moment explication of the subordination of predicate to subject may call to mind Frege’s analysis of a singular proposition into two heterogeneous parts – a proper name (or singular term), which is grammatically complete, and the remainder, a predicate, which is grammatically incomplete, needing supplementation by a proper name to yield a proposition (Frege 1891, 17–18); see also Strawson 1959, chaps. 5–6, esp. pp. 137–153, 186– 189. But despite the similarity, the moments of an act of judgment are not to be assimilated to the components of a Fregean proposition. It may seem, for instance, that, like the Fregean analysis, the two-moment explication dispenses with the copula, but in fact the copula figures in the two moments as the judgment’s principle of unity, though it will not be fully explicit until we advance from the present account, which belongs to general logic, to the analysis of synthetic judgment available in transcendental logic.

The Category of Substance

247

to the latter’s use. Were no concept used as subject, no assertion would be possible; and were a different concept used (e. g. space), a different use of divisible would be entailed. In the case of an analytic judgment, such as all bodies are extended, the same points hold. 26 But there is of course an important difference between the cases, which is at least implicitly understood in the act of categorical judgment. Where the concept used as subject already contains the concept employed as predicate, it cannot be determined, or enlarged, through the predication; where there is no such containment, the determination of the concept (in its use as subject of the judgment) 27 is possible. In both cases the subject concept is developed, but in the one case the development is only formal, consisting in clarification and articulation, while in the other it is material, lying in determination and growth. This difference implies that in the latter case but not the former the predication depends for its possibility on more than the use of the subject concept. Whereas the possibility of the predication constituting the analytic judgment all bodies are extended is contained wholly within the use of the subject, the corresponding possibility in the case of the synthetic judgment all bodies are divisible consciously depends not only on the use of the subject but also on a further condition, lying outside it. We may call it a material condition, since the dependence is conscious. Hence while the subordination of the predicate to the subject that constitutes the categorical form of judgment does not, just as such, depend on a material condition, it does depend on such a condition if the judgment is synthetic. Synthetic judgment thus constitutes the material use of the form, or logical function, of categorical judgment; and in theoretical knowledge strictly so called, such use is equally its real use, or use in knowledge of the real, of what exists independently of that knowledge. 28 This brings us to the category of substance. For as will be further explained below, the logical form in

26

Cf. KrV B131n. I am thinking here of analytic judgments as standardly characterized (A6-7 /B10-11). I leave to the side other forms, such as particular judgments in which the subject is contained in the predicate (cf. L § 21n5), for instance some extended things are bodies, which, though synthetic according to the standard characterization, is obtainable analytically, by conversion per accidens, from the analytic judgment all bodies are extended. 27 I add this qualification in view of the difference between a concept considered in its use as subject of a judgment and a concept considered in abstraction from such use. Considered in the latter way, a concept is fixed; considered in the former, as a concept of an object, it can be determined and enlarged through synthetic judgments in the growth of knowledge, as happens in an advance from a nominal to a real definition. This difference is of course idle in the case of analytic judgments. 28 Again, I leave aside the practical material use of the logical function. And I say “theoretical knowledge strictly so called” because I am also leaving aside such theoretical use as figures in mathematics. In pure mathematics, according to Kant’s account of it, the use of this function, though material, does not count as a real, theoretical use in the strict and primary sense. For the material condition on which its employment depends in mathematics does not include sensation, or the affection of consciousness by independently existing objects, but lies merely in space and time as original, formal intuitions, which rest solely on the unity of consciousness and the forms of human sensibility (thus, as Kant observes, while the figures studied in pure geometry count as objects within this science, they are absolutely speaking only the forms of objects of full-fledged theoretical knowledge); mathematical knowledge nevertheless counts as theoretical in a broad sense in that, owing to the relation its possibility bears to the possibility of theoretical knowledge in the strict sense, it is necessarily applicable to the objects of such knowledge (cf. KrV B146-148, A223-224 /B271). Our concern here is not with mathematical knowledge but with theoretical knowledge that is philosophical and in particular metaphysical, where the material and the real use of the categorical form coincide.

248

Stephen Engstrom

its potential for material and real use constitutes a category, one of the understanding’s original “concepts of an object in general”. 29 Before we turn to the category of substance, however, we need to revisit our initial consideration of the categorical judgment, in which we distinguished two moments, first a use of the concept serving as subject, second the assertion constituting the judgment. Because in that consideration it was necessary to abstract from the difference between synthetic and analytic judgment, the material condition just mentioned was ignored. To articulate the moments integral to the real use of the categorical form, we must advance from logical to transcendental reflection, taking into account not only the general form of categorical judgment, but also the understanding’s conscious reliance on that material condition in the synthetic judgment in which the real use of the categorical form consists. Judgment of this sort understands itself to be theoretical knowledge, knowledge of an independently existing object. Since such knowledge is of an object, it consists in representation, or in the exercise of a capacity to know that is a capacity to represent. And since the object of this knowledge exists independently of the knowledge of it, this capacity to represent must possess a receptivity through which the object, by modifying consciousness, can affect the subject in a way that enables knowledge. This knowledgeenabling affection is registered in immediate representations of objects – intuitions – that are marked by consciousness of their dependence on affection from without and as such count as empirical intuitions, intuitions figuring in perception. Representations thus dependent on affection belong to the receptivity – or, to use the more familiar traditional designation, the sensibility – of the judging subject’s capacity to know, and as such they provide the material condition on which judgment that understands itself to be theoretical knowledge consciously relies. In transcendental reflection, these sensible representations are considered only in their general character, as understood in the consciousness integral to all theoretical knowledge. Such knowledge has two aspects, in that as knowledge it is constituted by unity of consciousness, yet as theoretical it is of independently existing objects. It accordingly involves an at least implicit recognition of two corresponding aspects in the sensible representations that constitute its material condition, aspects that render them suited to enable such knowledge. On the one hand, these intuitions have a common form, in that they are all modifications of a common receptivity belonging to a single capacity to know and so allow of being ordered together in accordance with the synthetic unity requisite for any representation of theoretical cognition’s object. Thus the spontaneity of that same capacity – the spontaneity that, in its discursive exercise, constitutes a capacity to think and to judge – is able to determine sensible representation in respect of the latter’s form through synthetic activity in accordance with its unity of consciousness and thereby to secure synthetic unity in sensible representation itself. According to Kant’s well-known account, this form is two-fold, in that human sensibility, being divided into outer and inner sense, allows its representations to be ordered respectively in space and in time. On the other hand, intuitions also have matter to the extent that they are empirical, or marked by consciousness that includes awareness of their dependence on affection from without, or on sensation. This empirical consciousness constitutes perception, and it

29

KrV B128; the categories are explicitly identified with the functions of judgment at B143, P 4:324.

The Category of Substance

249

makes possible the spontaneous representation, in judgment, of something real, existing independently of cognition’s own conscious activity. In short, then, the material use of the categorical form consciously relies on intuition, or sensible representation, and insofar as it is also a real use, constituting theoretical knowledge strictly so called, the intuition on which it relies is empirical, or sensationinvolving. Now insofar as such knowledge relies on this sensible condition, the predicate figuring in it can be – and indeed is – understood to be external to (not contained in) the subject, and on account of the consciousness of this externality the real use of the categorical form must include not just two moments but three, in that the final moment is conditioned by two acts, not one. The first two moments are preparatory and constitute the materials – first the subject and then the predicate – and the third secures and extends the synthetic unity of theoretical knowledge in a single act comprising both a positing use of the subject and a determining use of its predicate. We thus have (i) the use of a concept S – an understanding of what (an) S is – as subject for a possible synthetic judgment, a use constituting the possibility of positing S (e. g. in the recognition, through perception, of this S); (ii) the use of a concept P (external to S) – in a comparison with S as used in (i) – as predicate for a possible synthetic judgment, that is, for a possible determining of S (in its use as the judgment’s subject); and (iii) the assertion (the use of the copula, or categorical form), lying in the joint actualization of (i) and (ii) (i. e. their joint use in a single act, the actual judgment), constituting the determination of S (in its use as subject) through the use of P and thereby the determinate representation of the posited S as P. The moments are presented here in their order of dependence: the second on the first, the third on the second. 30 In addition, the first and the second each depend on their own distinct sensible conditions, which enable respectively the use of the subject and the use of the predicate; these conditions lie in intuition so far as the judgment constitutes material knowledge, or knowledge of an object, and in empirical intuition so far as it constitutes knowledge of reality, or of an existing object. 31 A few points about these moments bear noting, on account of their relevance to the discussion to follow. First (re [i]), since the representation used in the act of positing is a concept, or general representation, it is of course understood to be determinable, but its generality is equally recognized as allowing the positing to be modified in respect of

30

If we bear in mind that the first moment presupposes a concept (an understanding), we can partially express the dependencies figuring in these moments by saying that understanding what S is grounds the possibility of supposing that S is, which grounds in turn the possibility of determining how S is. 31 In accordance with the two aspects of these sensible conditions – formal (intuition) and material (sensation) – two grades can be distinguished in the act of sensibly conditioned positing. The first is problematic affirmation under conditions of schematization in intuition (e. g. the constructions of concepts in pure mathematics); the second is assertoric affirmation under conditions of empirical (i. e. sensation-involving) intuition in perception. The first is requisite for knowledge of an object (e. g. a line in space: KrV B137-138), the second for knowledge of an independently existing object (e. g. a house: B162). Similarly, the subject of material knowledge can be determined in two ways: either a priori, with reliance solely on the form of sensible representation, or a posteriori, with reliance also on the matter; in the latter case, Kant speaks also of the determination of the existence of the subject, and I shall do the same in what follows.

250

Stephen Engstrom

quantity, making possible quantitatively diverse positing uses of the concept: singular, plural, universal. Second (re [ii]), the use of a predicate for a possible determination of the subject rests on consciousness of the predicate as external to the subject and hence contains no thought of the predicate as excluding the possibility of other, opposing determinations of the subject in different sensible conditions, a possibility that in turn grounds the possibility of negative and infinite judgments, in addition to affirmative. Finally (re [iii]), the analysis makes apparent that in the real use of the form of categorical judgment the copula has an existential as well as a predicative function. 32 It is also apparent that the order of (i) and (ii) is retained in their joint actualization in (iii), and that the previously noted hylomorphic character of general logic’s analysis of categorical judgment is preserved, in that (i) and (ii) constitute the matter for (iii), and in their joint actualization in (iii) they constitute its informed matter. From this analysis it can be seen that in the real use of the categorical form, the act of subordinating the predicate to the subject constitutes a representation in which what is thought through the subject and what is thought through the predicate are conceived as so ordered that while the former does not depend for its possibility on the latter, the latter depends for its possibility both on the former, as its internal condition (or as the real of whose existence it is a determination), and also on a further condition, lying outside it. In conformity with the order in the acts figuring in the judgment there is an order in what the judgment represents, a relation involving a real subject and a determination of its existence. Thus, (a) just as the positing of the subject is prior to the predication that determines it, so the existence of a real subject is prior to a determination of its existence; (b) just as the predication depends on the positing of the subject it determines, so a real determination depends on the existence of a real subject; and (c) just as the predication depends also on some condition in sensibility outside the positing of the subject, so a determination of a thing’s existence depends also on some condition in reality outside the existence of the real subject, namely on something indeterminately represented through the sensible condition on which the predication is conscious of itself as also depending. It is not difficult to see that the above-described relation between a real subject and a determination of its existence that is represented in the real use of the categorical form is the very relation represented through Kant’s category of substance and its correlative concept of accident. There are however two points that call for comment. The first concerns an apparent discrepancy. In the table of categories, the concepts of substance and

32

It should be remembered that our concern here, as was stated, is with the primary, affirmative case. But the point holds even where the judgment is universal. Preserving the insight expounded in the traditional logic of Aristotle, Kant locates existential import not in the singular and particular as opposed to the universal function of judgment, but in the affirmative as opposed to the negative. It also bears noting that the positing mentioned in (i) is not a free-standing pure existential judgment. Pure existential judgments (S is, S exists) are always derived from affirmative categorical judgments, in which posited subjects are determined. In our initial consideration of categorical judgment, the existential function of the copula was ignored because general logic, expounding the understanding not “in respect of its material use” but “solely according to form” (L 9:14), “abstracts [. . .] from all relation of knowledge to the object, and considers only the logical form in the relation of cognitions to one another” (KrV A55 /B79).

The Category of Substance

251

accident are expressed by the terms ‘subsistence’ and ‘inherence’. Although ‘inherence’ correctly serves to indicate that the dependence of an accident on its subject differs from that of an effect on its cause, the term was commonly employed, as Kant later observes, to ascribe a special existence to accidents; yet such an ascription is precluded by what is represented in a synthetic categorical judgment, in that the predication is just a determination of the positing of the subject, representing how the posited subject’s existence is determined. Kant immediately goes on to add, however, that certain misconceptions arise from ascribing existence to an accident and advises that it is more precise and correct to characterize the accident, not as an existent in its own right, but as “the way in which the existence of a substance is positively determined”. 33 Second, the foregoing characterization of what is represented in the real use of the categorical form may seem to leave open whether the use of a concept as subject includes the thought of a first subject, a subject not itself predicable of any other. But closer consideration of the first moment in the real use of the categorical form will reveal the involvement of that thought. That moment, as I said, lies in the use of a concept S as subject for a possible synthetic judgment, a use beginning in an understanding of what (an) S is. Now insofar as this concept is to serve as subject of a judgment of the categorical form in its real use, it must include the original concept of an object – the first understanding of an object, as knowable – in its first theoretical application as the concept of the real, or what exists independently of the knowledge of it. The diverse concepts actually used as subjects in the synthetic judgments that constitute the real use of the categorical form will also, of course, contain further determinations making up their specific content. But all differences among the subject concepts will consist in this, that certain determinations present in one will be absent in another. Hence no such determinations are requisites that must be contained in a concept if it is to serve as subject of such a categorical judgment. On the contrary, the containment of each such determination in any such concept is constituted by a synthetic judgment, in which that determination is predicated in respect of some prior concept serving as subject. Every such synthetic categorical judgment therefore contains, as its absolute inner condition, a concept free of all determinations, without which the first moment in the real use of the categorical form would not be possible at all. This common concept is thus the first inner ground of the possibility of the real use of the categorical form, and it therefore belongs to that form in its potential for such use. And since this first concept of a subject involves an at least implicit consciousness of itself as such, it is also, through that self-consciousness, the concept of a first subject.

33

KrV A80 /B106, A186-187/B229-230; cf. Ak 29:769–770. The root misconception that Kant appears to have in mind is the thought that accidents, notwithstanding their dependence on substance, are existents in their own right and as such things whose dependence might be transferred from one substance to another. One notable instance of this error is the doctrine that motion is communicated by transfer; as Kant elsewhere observes, this doctrine, if taken literally, infringes the principle “accidentia non migrant e substantiis in substantias” (MAN 4:550). Another instance, which infringes the same principle, is the Scholastic notion of sensible (and intentional) species (cf. P § 9), which was generally rejected by the modern philosophers (see e. g. Descartes’s Optics Discourse One [VI 85 (I 153)], his Principles I.64 [VIIIA 31 (I 215)], Leibniz’s Monadology § 7 [PPL 643], and § 84 of his fifth letter to Clarke [PPL 710]). If the analysis set out above is correct, this principle – an old Scholastic maxim (cf. Ak 29:769) – is grounded in the form of categorical judgment in its real use.

252

Stephen Engstrom

This common concept is the category of substance, the concept of a first subject, a subject of predicates that is not itself a predicate. Though like every other concept it is a general representation, it is not in the first instance a representation of a general object, such as a genus. As the concept of a theoretically knowable object, it is the representation of an individual, in that the object of theoretical knowledge is understood from the start to be representable in concreto, in empirical intuition, and moreover to be just as it would be represented to be in the complete knowledge of it and as such determinate in all respects, a subject of all the predicates that would be represented as determining its existence in that complete knowledge. 34 Yet this concept, being basic to the knowledge of all that exists, is nevertheless a representation that is not only general but universal and so not a concept that can be used as a predicate in any synthetic, determining judgment. In sum, then, since the concept is the original representation of an individual, the subject it represents has no generality and so is not predicable in any sense at all, not even analytically (and hence is Aristotelian primary substance, or individual substance), and the concept itself, on account of its universality, can be predicated only analytically, never as a determination (and hence, when used in abstracto, constitutes the original concept of an Aristotelian secondary substance).

2.2

From the pure category to its schema

Although the categorical form of judgment in its potential for material use constitutes, under the name of the category of substance, theoretical cognition’s original concept of an object, it is a merely formal, logical representation, universal in application and empty of determinate content. It is thus not surprising that, although metaphysicians inquiring into the first principles of knowledge may, in their analysis, focus their attention on the object represented through this concept and seek to “consider it naked”, as Descartes said, Locke and many other philosophers regard pure substance considered in isolation from all accidents as an “unknown support”, of which we are “perfectly ignorant”. Kant too, referring to substance so considered as “the substantial”, or “the substratum”, observes that what is thus represented is not as such any knowable thing; for it is conceived as what would remain after removal of all determinations, yet determinations are precisely what would be predicated of it in the synthetic judgments in which any knowledge of it would consist. 35 In this observation, Kant echoes the point we saw Leibniz make in explaining the inevitability of the “apparent thinness” of Locke’s notion of pure substance in general.

34

Cf. KrV A571-572 /B599-600. To say that this concept is the representation of an individual is not to say that it is a singular representation. Like any other concept, it is general. Only when used in conjunction with singular representation (sensible intuition) can it be used to pick out one individual. (I here use ‘individual’ in a merely logical sense, a sense that distinguishes an individual from any genus or species, but neither entails nor precludes either divisibility or multiplicity.) 35 P 4:333, KrV A414 /B441; cf. NE II.xxiii.2, 218. The thought of the substantial as what would remain after actual removal of all determinations confusedly reifies what is represented in using a concept in abstracto, violating the principle that every object of theoretical knowledge is determinate in all respects. No substance depends on any of its accidents, but it hardly follows that a substance could have no accidents at all. The “removal” of an accident is always its replacement by another. The confusion is aggravated by the misconception noted earlier, that accidents exist in their own right.

The Category of Substance

253

Yet while neither Leibniz nor Kant accepts Locke’s denial that we have any distinct idea of substance in general, they recognize that his skepticism reflects a genuine insight. Whether substance is regarded as the last subject of inherence or as the first subject of predication, there is no disputing that it is not to be found in the immediate objects of perception, or in what Kant terms “appearances”, objects of empirical intuition consciously represented prior to determination by categories. 36 Because the category of substance originates in a self-conscious act of spontaneity, a mere form of combination of concepts in categorical judgment, which is not derived from any affection of receptivity, 37 it is exercised in every material use of that form and hence – insofar as this form is basic – in every material use of all other forms as well. In all theoretical knowledge, then, substance is at least implicitly understood to be an object necessarily thought and hence thought as necessary in all such knowledge in every cognizing subject. Every perception, on the other hand, is contingent, depending for its actuality on present sensation. And since sensation is the effect of an object on the consciousness of an individual subject, neither sensation nor the perception depending on it is ever common to diverse subjects or diverse occasions. Appearances, therefore, as immediate objects of perception, are likewise contingent and likewise tied to subject and situation. Not being objects of representations that can be shared by diverse and differently situated cognizing subjects, they are not themselves objects of theoretical knowledge at all. If, therefore, as all parties agree, what the concept of substance represents cannot be found in the immediate object of perception, it is incumbent on metaphysicians such as Leibniz and Kant, who recognize that this concept originates in the understanding, to provide an account of how this first logical subject can represent anything real. And if the metaphysics is to be immanent, the account must be informed by the further recognition that the objects of theoretical knowledge must be knowable in experience, in that, sensation being the necessary material condition of knowledge of independently existing things, it is only through perception and experience that knowledge of reality is possible. To certify this category as eligible for use in theoretical knowledge, then, it is necessary to show that what it represents is possible, knowable in experience, notwithstanding the impossibility of finding it in the objects of perception. To do this would be to arrive at a real definition, or to establish what Kant refers to as the concept’s real possibility, the possibility of the object it represents. 38 In metaphysics, however, the question of real possibility must be handled differently from the ways in which it is addressed in the special sciences, whether technical or empirical. To establish a concept’s real possibility in a technical science, it suffices to show constructibility. In Euclidean geometry, for instance, as both Leibniz and Kant point out, possibility is established by making evident – either by a genetic definition or by 36

“The undetermined object of an empirical intuition is called appearance” (KrV A20 /B34); perception lies in the empirical – i. e. sensation-involving – consciousness of such an object (B207). Appearance in the sense here intended is what I referred to earlier as appearance in the empirical sense (i. e. mere appearance in contrast to phenomenon, or in other words the appearing of an object of experience in contrast to the object itself). I call it an immediate object to indicate that it has no being outside the perception. 37 As concepts belonging to metaphysics rather than to mathematics, the categories are, in respect of their content, given, but they are given a priori, not empirically; their content accordingly originates in a pure self-conscious act of synthesis, not from any affection of receptivity (cf. L §§ 4–5). 38 Or in other words its “objective reality”, or relation to an object. Cf. KrV A240-242 /B300.

254

Stephen Engstrom

a demonstration that relies exclusively on such definitions along with the recognized axioms and postulates – that the concept in question can be constructed, that is, that a figure satisfying the conditions it specifies can be generated a priori. 39 In the case of empirical concepts, real possibility is established a posteriori, by identifying an instance in experience. The concepts of metaphysics, in contrast, are necessary, being fundamental to all theoretical knowledge. So the possibility of their objects cannot be established by showing them to be objects of a possible or an actual experience; it can be established only by showing their necessity in any experience at all. This requirement may seem only to make all the more hopeless the prospect of securing a real definition of the category of substance. If substance cannot lie in the objects of perception, it surely cannot lie in those objects necessarily. The sensible representation of an appearance and the intellectual representation of substance are, as Kant puts it, heterogeneous (KrV A137-138 /B176-177). A more auspicious prospect emerges, however, if, bearing in mind the unity-securing function of the intellect, we notice in the very heterogeneity of these representations an indication that they are complementary, figuring as matter and form of a third thing, namely experience, or empirical knowledge. If matter and form are understood along traditional lines, as they are by Kant, namely as the determinable and its determination (KrV A266 /B322), then according to this hylomorphic analysis, on which perceptions are the matter and the category is the form, experience lies in determinate perception, or perception so far as it is categorially informed. Experience can accordingly be characterized as “the product of the understanding out of materials of sensibility” and as “knowledge through connected perceptions”, 40 for what the understanding’s form-giving function, carried out through the category, produces is the determinate combination – the connection – of perceptions that constitutes the unity of knowledge. Spelling out this idea involves two steps. First, an account is needed of how the category’s determination of sensible material can furnish a representation that enables an advance from a nominal to a real definition of substance. Such a representation cannot of course be of anything in the appearances, the objects of bare perception, for such objects are undetermined by any category. But this does not rule out the possibility of a representation of something in the phenomena, the objects of experience. If, as Kant argues, there is a condition to which the material of experience is recognized to be universally subject, namely time, then thinking an object through the category and in accordance with the 39

In one of his many illustrations of the need for real definitions, Leibniz notes that we regard it as evident that a figure described by the motion of a straight line in a plane about a fixed end is possible, but we might doubt whether it is possible for there to be a curve such that, given any segment of it, the lines connecting any point on the segment with the segment’s endpoints will always form the same angle. The two concepts represent the same figure, a circle, but whereas the first is simply a genetic version of Euclid’s definition and his corresponding postulate, Euclid demanded a demonstration in the case of the second. (See On Universal Synthesis and Analysis, or the Art of Discovery and Judgment [PPL 230].) 40 P 4:316, KrV B161. It can also be characterized, in accordance with the Copernican way of thinking, as “knowledge that determines an object through perceptions” (B218). Obviously the common contemporary tendency to understand ‘perception’ and ‘experience’ (or ‘perceptual experience’) as near synonyms needs to be suspended here, if we are to appreciate Kant’s distinction between Wahrnehmung (perceptio) and Erfahrung (cf. e. g. P § 20), which is kindred to the traditional contrast between aisth¯esis and empeiria. According to this distinction, experience is not bare perception, though as knowledge – namely empirical knowledge (empirisches Erkenntnis) (B218) – it does count as objective perception (cf. A320 /B376).

The Category of Substance

255

concept of that condition – and so thinking the object as phenomenon – can furnish such a representation, a representation that can be incorporated into the category. In his doctrine of the schematism of the categories, Kant identifies this representation as that of the permanence of the real in time. Second, the distinctive modality of metaphysical concepts – their necessity – means that showing the possibility of the object of this representation – or, what comes to the same, showing that the representation, when incorporated into the category, yields a real definition – must be a matter of showing the representation to figure constitutively in experience, as a formal condition of its possibility, even in respect of its specific character as sensible (temporal). Kant addresses this second task in his proof of the first law of nature, that in all change among appearances, substance, as permanent, persists. The proof will be considered below (2.3), after a brief discussion of the first step. Perception is presupposed in experience as its material, in that the object of theoretical knowledge, existing independently of the knowledge of it, must, if it is to be known, be given and thereby appear to the subject: it must, through being present to the senses, affect consciousness, and the affections must be apprehended in the perception, or empirical consciousness, of an appearance – the appearing of the object – in intuition. Now as this characterization of perception already makes apparent, perception too can be analyzed hylomorphically. As empirical consciousness, perception depends outwardly on a material condition, namely sensation, or the effect of an object on consciousness, and inwardly on a formal condition, namely consciousness in its capacity to determine sensibility – a passive power of representation – to represent an object in intuition. These two conditions underlie respectively the diversity and the unity of that representation in perception. Through the senses, diverse sensations are available to figure as material of a single perception. But since sensibility is a passive power to represent, it is not itself the source of the unity of its intuition. That unity can be secured only through sensibility’s being affected by perception’s inward, formal condition of consciousness, which, as pure activity, contains its unity originally within itself. The unity of empirical intuition is accordingly the work of a power of consciousness – under the name of the imagination (the power to represent an object in intuition even without its presence) – to determine sensibility inwardly in an act of combination, a “synthesis of apprehension”, which depends in turn for its unity on the unity of consciousness that it expresses. Kant argues, as we noted, that space and time are synthesis-enabling forms respectively of outer and of inner sense, and we need now to incorporate this doctrine into the foregoing analysis of perception. As forms of sensible representation, space and time are not themselves objects perceived, but conditions according to which perceptible objects are represented in the perception of them. Insofar as perception depends, materially, on affections of consciousness from without, it represents objects in outer intuition, under the form of space. But the representations of these appearances depend for their unity on the imagination’s synthesis, an act through which sensibility is inwardly determined, and such determination is represented in inner intuition, in accordance with the form of time. Thus, the self-affecting synthesis of the imagination generates, on the occasion of affections of consciousness from without, perceptions of appearances in outer intuition, that is, in space, and that self-affection yields inwardly-directed consciousness of those same perceptions – or, what comes to the same, their immediate objects, the appearances – in inner intuition, as successively ordered in time.

256

Stephen Engstrom

Yet consciousness of succession among one’s perceptions no more constitutes experience – empirical knowledge of independently existing objects – than do the perceptions themselves. Successively ordered perceptions furnish the material of experience, but judgment and hence concepts are required in addition, in order to represent, through perception, independently existing objects as ordered in time. For such representation, inner intuition and its form are not enough; a concept of time – a representation of time in general – is required, together with the concept of an object in general, articulated in the categories. And the latter concept must incorporate the former into itself in an act of self-determination, yielding the concept of an object of experience in general. Such an object will be known under a determinate, discursively represented temporal form that expresses, and so bears analogy with, intellectual form. With these considerations in place, it is readily apparent that the category of substance and its correlative concept of accident must determine themselves as concepts of objects of experience respectively through the representation of the real so far as it is permanent and through the representation of the real so far as it is changeable. For as we saw in the foregoing explication of this category, the original concept of substance is the first use of the concept of the real, prior to the representation of any determination – including limitation – of its existence. The concept of an accident, in contrast, is just the representation of such a determination, and as such it includes consciousness of the possibility of other, opposing determinations where conditions differ. Thus the former concept cannot be expressed through a representation of temporal limitation, whereas the latter must be (as will be further explained below). As can be seen, the schema of substance represents in sensible terms the necessity thought through the category: as the representation of the existence of the real through all time, it bears, in a sensibly conditioned way, the mark of the a priori in its other guise, as universality (cf. KrV B3-4). Kant remarks that the schemata “realize” the categories while also restricting their application to objects of experience, or to phenomena; he thereby intimates what he later says explicitly, namely that it is only insofar as the categories as nominally, logically conceived – the pure categories, as he will go on to call them – incorporate their schemata that they constitute full-fledged, really definable concepts. 41 The logical concepts constitute their form, the schemata their content. 41

KrV A146 /B185-186, A240-243 /B300-301. Insofar as it is only through their being restricted to phenomena by the incorporation of their schemata that the categories are “realized” and so rendered suitable for a real use in theoretical knowledge, the unrestricted use that is made of them in traditional metaphysics, where they are employed in conjunction with ideas of reason rather than with schemata, is illicit. In practical knowledge, however, the categories allow of a legitimate unrestricted application in conjunction with reason’s ideas, one in which they are not so much “realized” as “idealized,” or used as the original representations of the good (though in such application they also work to realize themselves through making their object actual). Thus, while the unrestricted use of the category of substance in traditional rational psychology is criticized as transcendent in the Paralogisms of Pure Reason (in that the rational psychologist mistakes self-consciousness for a purely intellectual theoretical knowledge of the cognizing subject as thing in itself), the unrestricted use of this category in practical knowledge – a use that constitutes the concept of a person – is immanent and legitimate (cf. KpV 5:16, 48, 66). Moreover, since the schema restricts this category’s use to knowledge of “phenomenal substance” (KrV A146 /B186), which as the permanence of the real “is wholly a sum of mere relations” (A265 /B321), it enables theoretical knowledge only of what, absolutely speaking, is but an analogue of substance as originally conceived (A180-181 /B223-224). Thus while we find in the theoretical use of this concept one traditional conception of substance, as matter, or permanent subject of change (whose movements are effects of other substances acting on it), it is only through the category’s practical use, in which the concept of

The Category of Substance

257

Further light can be thrown on this point by noting that in Aristotle too we find some indication of it. Aristotle begins his treatment of the category of substance by setting out the core logical idea of a subject of predicates that is not itself a predicate, the idea that Leibniz and Kant articulate in their nominal definitions; but as his discussion proceeds he draws attention to a further feature – an element that Kant holds to be needed for the real definition – when he remarks that what is “most distinctive” of substance is that it is capable of retaining its identity while receiving contraries, such as hot and cold. 42 This feature goes beyond the core logical notion, which includes no thought of the real possibility of a contrariety of predicates in a subject. Aristotle’s characterization of this feature does differ from Kant’s schema in that it makes no reference to time. But it is clear that Kant too has this feature in view, for as he points out elsewhere, only with the representation of time can we make comprehensible the possibility of a combination of contradictorily opposed predicates in one and the same object. 43 It is the schema of permanence, then, that enables comprehension of what Aristotle identifies as the distinctive mark of substance, the capacity to receive contraries without loss of identity. But to confirm that the incorporation of the representation of permanence into the category of substance constitutes the latter’s realization, its real definition, it is necessary to show the possibility of this concept’s object through showing its necessity in experience. To identify a schema that expresses in sensible terms the pure category’s thought of necessity is not yet to show that the category, completed by its schema, is a necessary condition of experience – and thereby of all theoretical knowledge – even in respect of its sensible (temporal) character. As we shall next see, this necessity can be shown by exhibiting the role the schematized concept plays in making possible experience of change, a role that establishes its place in the first law of nature.

2.3

From the category of substance to the first law of nature

We have noted that perception is the material of experience, and that the unity of perception’s empirical intuition is secured through sensibility’s being inwardly affected in the synthesis of the imagination. In accordance with the sensible form under which such inner affection is represented, the subject is immediately conscious of its perceptions and their immediate objects, the appearances, as successively ordered in time. But this an end is introduced through the idea of the good, that it can be employed to represent individual substances as understood in the traditionally favored conception, namely as self-moving entelechies. Two stages in this employment can be distinguished: a primary, practical application, in the representation of individual human persons, and an extended, natural-teleological application, in the representation of organisms. But these further uses lie outside the immediate concerns of immanent theoretical metaphysics. 42 Aristotle expresses the logical concept when he says, “it is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all” (Categories 5, 2b15-17, tr. Ackrill; cf. Metaphysics VII.3, 1028b36-29a2). He points out the other feature when he later remarks, “It seems most distinctive of substance that what is numerically one and the same is capable of receiving contraries” (Categories 5, 4a10-11, tr. Ackrill, modified). 43 Cf. KrV B48. This comprehensibility condition reflects the hylomorphic character of theoretical knowledge as discursive. Such knowledge begins in experience, in which intellectual and sensible powers cooperate as form and matter, and however abstract the intellectual representations may be that arise through reflective analysis, their cognitive standing depends on the possibility of their use in that same original experience, without which their relation to independently existing objects is lost.

258

Stephen Engstrom

inward consciousness is of a subjective order of apprehension, the order of the states of that consciousness itself. Experience, in contrast, as theoretical knowledge, is of independently existing objects and is shareable by diverse subjects. The representation of objective order that constitutes experience therefore depends on more than the immediate consciousness of order among perceptions secured through the imagination’s synthesis. It must take place through an act of the faculty of knowledge, the understanding, whereby through the use of a category the order among the perceived appearances – or, more precisely, the order among the phenomena thought through the appearances – is represented as determined. 44 Kant points out that while the order of perceptions and their appearances is successive, it does not follow that in experience the cognized order of the phenomena represented through those appearances is likewise successive. I may in experience recognize as simultaneous what I represent through the predicate hot and what I represent through the predicate fluid, even though the appearance on which I rely in the use of fluid precedes the appearance on which I rely in the use of hot. That the subjective order of perceptions’ appearances is successive does not by itself entail that the objective order of the phenomena known in experience is successive. But while many predicates differing in content are merely diverse, like hot and fluid, others, as we noted, are not only diverse but opposed, for instance hot and cold, fluid and solid. Such concepts cannot be predicated absolutely of one and the same thing. The intellect requires that in the use of them as predicates the copula – the act of relating the concepts serving as subject and predicate in the categorical judgment – be modified so as to preserve the agreement requisite for the unity of knowledge. This can be done in either of two ways, as the copula can be modified either in its first moment, the positing of the subject, or in its second, the predication wherein that positing is determined. The first way is through quantification, introducing diversity in the positing of the real; the second is through qualification, limiting the predication. These modifications depend for their comprehensibility on sensible conditions, namely the forms of sensible intuition: diversity in the positing of the subject depends on space (this S here is hot; that one there is cold), and limitation of predication depends on time (this S was fluid; now it is solid). In experience, then, what is represented through a use of opposed predicates that relies on successively perceived appearances must be ordered by reference either to different places in space or to different positions in time. The first way of ordering constitutes the experience of diversity of existing things; the second the experience of change. In the former case, the represented order can be one of simultaneity, in the latter, only of succession. This representation of order, however, cannot be merely arbitrary. For an arbitrary representation lacks the determinacy requisite for knowledge. In experience, therefore, the representation must be determinate. Now representations are determinate only so far as they exclude the representations to which they are opposed. Since the two modes of order in time – simultaneity and succession – are opposed, the determinate representation constituting experience of objective succession must exclude represen-

44

We have already noted that a category is a form of judgment in its potential for material use, and since that material use consists in the determination of materials provided by sensible intuition, the categories can be characterized as “concepts of an object in general, through which its intuition is regarded as determined in respect of one of the logical functions of judgment” (KrV B128).

The Category of Substance

259

tation of simultaneity. But this requires that what is represented through the opposing concepts not be predicated of diverse subjects, thought through diverse positings of the real, occupying different places in space. The opposition must rather be regarded as to be accommodated solely through qualification of predication, in which the concepts are used with reference to different positions in time. For such accommodation to be possible, however, the two concepts must be predicated of an identical subject, for opposing predicates in diverse subjects do not preclude simultaneity. And insofar as the two predicates are referred to different positions in time, that identical subject must exist continuously through time, in that without continuity there can be no identity. This continuous existence is just the permanence of substance. Substance, as permanent, is therefore presupposed in all experience of change. And since the representation of simultaneity, the other mode of temporal order, implies no thought of coming to be or passing away, the presupposition holds for all experience of the real in time. The preceding argument may seem vulnerable to an objection that has often been raised against Kant’s proof, namely that it fails to establish permanence in the strict sense of the term: To show that experience of objective change presupposes something that endures through the change is not to show that it presupposes something absolutely permanent, which neither comes to be nor passes away. 45 In this objection, however, some crucial points are overlooked. As was noted, the original thought of the posited subject precedes all determination of its existence, including any supposed limitation of the latter in time. So if knowledge of the subject as thus limited in existence is possible, it must derive from experience. But that no experience could be the source of such knowledge becomes apparent once we take into account the essential difference between change on the one hand and an absolute beginning or ceasing to exist on the other. Change involves real opposition, an opposition between real predicates, whereas absolute beginning or ceasing includes only a logical opposition, between existence and non-existence. Now experience, as we noted, depends materially on perception, and perception in turn on sensation, as the effect on consciousness through which alone the real can be known. So it is possible to have experience of change, but never possible to have experience of absolute non-existence and so never possible to have experience of an absolute coming to be or passing away. Absence of perception does not constitute perception of absence. Inferring the absence of a thing from the absence of perception can be warranted if we are concerned only with a relative coming to be or passing away, as in the case of things of a specific kind, such as droplets of dew, where, having an empirically determinate concept that specifies perceptible marks, we are equipped with a schema that enables us to determine absence as well as presence in experience. But the concept of the real has no schema beyond that of something in time that corresponds to sensation in general, and this correspondence does not imply that existence entails actual sensation in all conditions. Phenomena are appearances, but not mere appearances (mere appearings). Only the possibility of sensation is entailed; absence of actual sensation in a particular instance does not exclude that possibility. 46 45

See for example Strawson 1966, 128–131. The response to this objection that I offer here is similar in some respects to that of Guyer 1987, 230–232. 46 The considerations advanced in this paragraph go beyond what is explicitly set out in Kant’s discussion in the First Analogy, but they look no further than to his preceding proof of the principle of the Anticipations of

260

Stephen Engstrom

When we think of nature along traditional lines as the complete object of physical science, we think of the totality of objects knowable through experience and conceive of them as things whose existence is determined according to law. The foregoing argument has outlined the chief considerations that enter into the proof 47 of the first law of nature so understood, a law that, as Kant notes, has always been implicitly presupposed by ordinary human understanding as well as by the students of nature. 48 The proof shows that all change (all coming to be and passing away) in objects of experience is nothing but alteration, or succession of opposing determinations of what is permanent in those things. And it is this permanent substratum, represented though the schematized category of substance, that constitutes nature’s fundamental law, indeed the ground of the possibility of all of nature’s laws and thereby of nature itself, in that these laws, being nothing but the fixed ways in which objects knowable through experience are determined in their existence, depend for their fixity – their permanence – on a permanent substratum in those things. It is thus through the presupposition of substance in experience that law secures its footing in the world, constituting it as an order of nature. 49

Bibliography Aristotle. Categories and De Interpretatione. Ackrill, J. L. (tr.). 1963. Oxford: Clarendon Press. Engstrom, S. 2017. Knowledge and Its Object. In: O’Shea, J. (ed.). Kant’s Critique of Pure Reason: A Critical Guide. Cambridge: Cambridge University Press. Frege, G. 1891. Funktion und Begriff. Jena: Herman Pöhle. Geach, P. T. 1965. Assertion. Philosophical Review 74, 449–465. Guyer, P. 1987. Kant and the Claims of Knowledge. Cambridge: Cambridge University Press. Jolley, N. 1984. Leibniz and Locke. Oxford: Oxford University Press. Longuenesse, B. 1998. Kant and the Capacity to Judge. Princeton: Princeton University Press. Strawson, P. F. 1959. Individuals. London: Methuen. Strawson, P. F. 1966. The Bounds of Sense. London: Methuen. Wilson, M. D. 1999. Ideas and Mechanism. Princeton: Princeton University Press.

Perception, on the strength of which he argues that “a proof of an empty space or an empty time can never be derived from experience” (see KrV A172-173 /B214). 47 Although Kant calls his argument a proof, he emphasizes that since it is of a principle, not a theorem, it does not and could not have the character of a demonstration. It does not attempt to derive the principle from any higher knowledge, but shows that it is presupposed in experience and so makes possible the very thing – that same experience – that serves as its own ground of proof (KrV A184-185 /B227-228; cf. A148-149 /B188, A736-737 / B764-765). 48 KrV B227; cf. Aristotle, Metaphysics I.3, 983b6-18. 49 This paper was initially presented in 2016 at a workshop on Kant and Leibniz on substance at the University of Illinois at Chicago, and short versions were read in 2018 at conferences at UCLA and Columbia. I am grateful to the participants for helpful discussion, and I particularly thank Katherine Dunlop, Daniel Sutherland, and an anonymous referee for their useful comments.

Book Reviews

Clark, A. 2016. Surfing Uncertainty. Prediction, Action and the Embodied Mind. Oxford / New York: Oxford University Press. 424 pp. ISBN 978-0-19-021701-3 It was the formal model of the Turing Machine that inspired 20th century cognitive science and philosophy to a large extent. The vision of the brain that depicts it as large network machine, related to recent successes of deep learning neural networks and other elaborated forms of machine learning, could take a similar role in the 21th century. At least, this is the strong impression which a reader of Andy Clark’s latest book may get. Clark, who is also known for his defence of the extended mind hypothesis (Clark & Chalmers, 1998), presents us a broad picture of a unifying theory of how the brain (and the mind) works. Central to Clark’s book is the thesis of predictive processing (PP) that the brain can be described as a multi-layer-hierarchical generative neural network that constantly predicts the incoming streams of sensory signals and learns from the resulting prediction errors. Building his arguments on critically and carefully assessed evidence from a large stock of empirical studies, Clark suggests that this single model can, in an integrative way, explain perception, learning, awareness and action and a many other sorts of related mental phenomena, like, for example, imagining, emotions, social cognition, illusions and mental disorders as autism and schizophrenia. Importantly, he also claims that the proposed model of brain functioning combines quite well with the core ideas of embodiment and enactivism. The book is divided in three parts, each having a main topic, which is supplemented by previews and prearrangements of topics covered more extensively in a later part of the book. This allows Clark to slowly unfold the complex, interwoven topics of his book, making their golden threads easily accessible, even to outsiders or newcomers to the field of cognitive science. Part I of the book is largely devoted to introducing the reader to the basic prediction processing model of perception and attention, which in part II is extended to include action (motor command and control) and then, shown to facilitate explanations of diverse mental phenomena. In the final part III, Clark goes on to reflect about the predictive processing approach to the brain from a more general perspective discussing ‘productive laziness’, the relation between embodiment /enactivism and predictive processing, doubts about the adequacy of the model (raised by the Dark Room Puzzle and novelty-seeking), and the role of representations. The book is well written, as the author uses clear, precise and easy accessible language, mostly devoid of technical terms. Many notions, not part of the regular philosophical vocabulary, are explained when they are introduced. The style is entertaining and creative, for section headings the author has often selected clever, catchy phrases, innuendos, sometimes even a clever pun. At some points, Clark may seem to repeat his main ideas, somewhat like an ongoing mantra. But perhaps it helps the reader to not lose sight of the big picture that is hidden in the mosaic of fascinating details Clark writes about. The general picture Clark suggests may appear far-fetched at first: Isn’t mental life way too complex to be explained by such a simple model that identifies sub-personal

262

Book Reviews

prediction-minimization as the primary function of the brain? How likely is it that the evolution of the brain, which is shaped by historical contingencies, culminates in a coherent system exhibiting a single primary function, instead of a patchwork of various functions? But during the course of the book, the reader may be surprised about how much light a predictive brain might shed on the mind. In chapter 1 the author introduces the reader to the predictive processing model of perception, contrasting it with traditional approaches of cognitive science that “depict perception as a cumulative process of ‘bottom-up’ feature detection” (13). Referring to Hohwy et al. (2008), a first illustration of PP’s explanatory power is presented in the case of binocular rivalry (33–37). According to PP, a top-down and lateral flow of neural signals aims at predicting the current sensory signals, while attempting to minimize the resulting prediction error. Those predictions errors that still occur are propagated both upwards and laterally through the network (25), which Clark summarizes by the slogan: signalling the news. In reaction to the feed forward processing of the prediction error the network is updated. This “functional asymmetry” (31) in information processing, which is central to PP, initiates, in Clark’s words, “an energetic dance between multiple top-down and bottomup signals” (14). When the system succeeds to predict the incoming sensory stream, by generating the signal for itself, a perceptual experience is formed (14). These ideas of prediction-driven learning in a hierarchical multi-layer network are first briefly outlined and accompanied by a short overview on historical advances in machine learning, beginning with the ‘Helmholtz machine’, and finally explained in most detail on page 31, where Clark describes the implementation of a predictive processing network by Rao and Ballard (1999). The mathematical details of the PP model are largely left out. This has the clear advantage that the book remains accessible for readers without sufficient background in mathematics. However, at some points in the book, the lack of specifity leaves the reader with some questions (e. g. in chapter 7). What should be addressed by models of perception in general, of course, is the problem of how an organism can perceive its environment, the world, although it has only direct access to the stimulation patterns of its sensory receptors. Clark mentions this problem in passing, in section 1.2., where he reacts to a chicken-egg worry about how prediction is possible without knowledge: How does all that knowledge – the knowledge that powers the predictions that underlie perception [. . .] – arise in the first place? Surely we have to perceptually experience the world before we can acquire the knowledge to make predictions about it? (Clark, 2016, p. 14)

As many other optimists about neural networks who are impressed by their recent empirical successes, he claims that predictive-driven learning provides a “powerful way to make progress under such initially unpromising conditions” (17) since when you are “able to detect only the ongoing changes in your own sensory registers [. . .] [o]ne thing you can do [. . .] is busily to try to predict the next state of those very registers”. Yet, what about the doubts about connectionist models as have been expressed by proponents of the classical approach (knowledge bases) to learning and cognition (e. g. Fodor & Pylyshyn 1988, Chomsky 1980)? As Clark seems to believe, the main problems about connectionist models had been the dependency on pre-categorized data and the distribution of error in the network which have been solved (according to Clark). Awareness of the need of

Book Reviews

263

connectionist explanations of the compositional structure of thought are largely missing in Clark’s picture, as well as critical reflections on the sheer amount of data neural networks need to be trained on in order to learn (and how this relates to Chomsky’s poverty of stimulus argument). An immediate consequence of the PP account of perception is that the same neural network is taken to explain both perception and (abstract) learning. In chapter 2 the mechanism of precision estimation and prediction error weighing is introduced: Additionally to predicting the incoming sensory signals, the PP network estimates the precision (inverse variance) of its predictions and balances the bottom-up influences of prediction errors on the network according to the estimated precision of its respective predictions. This allows the network “flexibly to extract signal from noise” (56). Clark, relating to work by Karl Friston, then describes attention “simply as means by which certain error unit responses are given increased weight, hence becoming more apt to drive response, learning and (as we shall later see) action” (57). Results on gaze allocation are interpreted as evidence in favour of the model. Once, we accept the error weighting process and the attention model, it is small a step towards action, because, as Clark suggests, generative models include best sampling expectations and action can be partially seen as a tool for precision-expectation-based sensory sampling (65). Although precision weighting is by far the most important aspect and explanatory ploy of the PP model, a clear and detailed depiction how it actually works is missing. In chapter 3 the constructive nature of perception is addressed. Since predictions are assumed to form our perceptions, it is suggested that visual illusions are a consequence of exceptional circumstances which do not fit into the well-adapted perceptual expectations of the neural network (85). In a similar fashion perception of omissions (e. g. of notes in a music piece) is explained (89). Again, the worry how predictions allow an agent to perceive the world at all, here stated in form of a lucky imagining or hallucinating argument, is countered by maintaining that perception is different from imagination and hallucination in that it is counterfactually robust and allows attention-based modulation of sensory prediction errors (92/93). One might object perhaps, that his defence is somewhat too quick, because we would, for example, also like to know what exactly constitutes the robustness and veridity of perception (in contrast to hallucination), if both processes depend on the same neural apparatus. The general picture of imagination, here described, is that it is co-emergent with perception: If a generative network (a network that generates signals that are predictions of sensory signals) is the foundation for perception then the same network perhaps can generate signals independently of sensory stimulation (93). This account of imagination as being co-emergent with perception is underlined by citing evidence for an overlap between activation patterns that “encode the scenes when merely imagined and when they are perceived” (97). Although Clark in this chapter has also to say something about memory and a relatively new proposal to describe memory in terms of a hierarchical predictive network (“PIMMS and the Past”), it is definitely the most speculative and incomplete part of the book. Memory, especially biographical memory, also raises some questions about the correctness of the predictive processing account of the brain. For biographical memory, seems not to be involved in sub-personal prediction-making. So why is there episodic biographical memory? Chapter 4 shows how an account of action can be build from the basic PP model. Following Friston and others, it is suggested that in contrast to perception motor control

264

Book Reviews

is subjunctive. Instead of predicting actual proprioceptive trajectories, what happens in motor control, is the prediction of non-actual trajectories that would result in performing the desired action (121). Central is the claim that instead of adjusting predictions to reduce prediction errors, in action the reduction is achieved by making the prediction real (121). As Clark presents the case, by referring to works by Friston and others, this picture is supported by empirical evidence. What distinguishes the model from traditional approaches to motor control is (i) that no inverse model of motor control and (ii) no cost functions are postulated (125). However, it has in Clark’s opinion also the implication that desires, rewards and pleasure are not the causes of action but only a consequence. Rather, our behaviour is caused by “sub-personal webs of probabilistic expectation” (129). If Clark is right about that point, the PP account of action is deeply at odds with our regular conception of agency for we normally distinguish between what we expect (in a descriptive sense) and what we desire or want to be the case (in a normative sense). But perhaps, the PP proposal that predictions of non-actual future proprioceptive signals can be the cause of bodily action, can be best understood by identifying these predictions, at least in some cases, with desires and intentions. In chapter 5 Clark deals with the question how an agent comes to understand his own actions and, importantly, the actions of others. The relevant kind of understanding considered here, is ‘experiential understanding’ as it was for example described by Maurice Merleau-Ponty. In Clark’s words: “Some kind of deep, primary, or ‘embodied’ understanding that enables us to appreciate the meaning of an observed action” (152). One problem that is related to experiential understanding is that the meaning of an action is contextdependent, as Clark illustrates by a “Dr Jekyll or Mr Hyde” example of a man holding a knife to a human chest. Clark’s claim is then that the process that generates experiential understanding cannot solely rely “on the feedforward (‘bottom-up’) flow of sensory information” (153). Instead he considers the top-down predictions and the flexible precisionweighting, which are part of the PP model, to handle this problem. Going from there, he argues for a deflationary view on mirror neurons that assumes that mirror neurons are produced by associative sequence learning. Of course, there remains a problem of action attribution, but this is accounted by precision-weighting on proprioceptive prediction errors (158). In chapter 6 Clark discusses the mind-world relation in the light of the PP model of perception. The main question posed in the chapter is whether the PP model of perception implies that perception is indirect. He cites views expressed by Frith (2007) and Hohwy (2007) who hold that we actually perceive the brain’s model of the world or the brain’s best hypothesis. Clark agrees with them in so far that perception is “in some sense an inferential process” but he thinks that their views are mistaken in two ways. He first rejects the idea that the inference-based routes that produce perception introduce a “representational veil between agent and world” (170). Instead he claims that only by probabilistic apparatus of prediction-driven learning the agents is able “to see through the veil of surface statistics” (170). The details are missing here though. Their second mistake, Clark holds, is “a failure to take sufficient account of the role of action” (170), stressing that prediction-driven learning presents us no action-neutral image of the world but one full of possibilities for action (171). Aside from that topic we find some discussions on the question of innateness of knowledge, the close relationship between perception and action, decision-making, and externalism.

Book Reviews

265

Chapter 7 explores conscious experience through the lens of PP. Clark is largely concerned with showing how the PP model was used to give explanations of mental health conditions like schizophrenia. Schizophrenia is associated with two characteristic positive symptoms, hallucinations and delusions. Clark reports the suggestion made by Fletcher and Frith (2009) that both symptoms can be explained by “falsely generated and highly weighted waves of prediction error” (206). As Clark tells us, in the PP model, high weighted waves of prediction error are equivalent to low weighted precision of predictions. All what counts is the balance between top and bottom levels (212). This is assumed to initiate a self-entrenching process (80/81) in which hallucinations cause delusions which reinforce the original hallucinations. The highly weighted proprioceptive error signals are taken to form the impression that one’s own actions are performed by someone else (219). The more detailed explanation given on page 219 though seems to imply that precision weighting is not merely jointly determined by top-down predictions and the incoming sensory signals, but actually in some cases also performed independently of these factors, to compensate a bad tuning of the prediction machine, as Clark puts it, “under such conditions, the only way to restore movement is to artificially inflate the precision of the higher level states”. But this, so it seems, is not permitted by the general constraints of the model. At least, this passage is unclear in important ways, and some mathematical hints could have helped to clarify the exact mechanism. Besides schizophrenia, Clark discusses PP accounts of the feeling of conscious presence, the lack of which is linked to depersonalization disorder (227), and emotions like fear in the dark (235). In Chapter 8 Clark examines the relationship between PP and embodiment by relating the PP account of the brain to the idea of predictive laziness (Simon, 1956) and the principle of ecological balance (Pfeifer & Bongard, 2006). The idea is that many cognitive and agency tasks are solved by heuristics that actively use the body and the environment as a resource. We find a treatment of the Darkened Room Puzzle (Friston, Thornton & Clark, 2012), which asks why a creature that is driven towards a reduction of prediction error is not inclined to increase deprivation and why the minimization of prediction errors is not inconsistent with a striving for novelty. The answer Clark suggests is twofold. What he first observes is that there are creature-defining expectations (basic needs) that cannot be adjusted in a way that leads the organism to seclude itself to a dark room and wait for death (264). The “positive attractions of novelty” are, Clark admits, more difficult to explain, but he thinks that part of the answer is found in “culturally-mediated lifetime learning” (266), an innate tendency “to seek out ‘just-novelty-enough’ situations” (266) and the creation of designer environments (ch. 9) that “actively favour [. . .] noveltyseeking and exploration” (266). Chapter 9 mainly tries to answer what is so special about humans from the perspective of PP. Clark suggests two ideas. One is that the human neural network adapted in ways that allow an “even more complex and context-flexible hierarchical learning than is found in other animals” (276). Complementary to this is the second idea that humans create socially and culturally formed environments which constantly “provide new and evermore-challenging patterns that will drive learning” (277). We find this latter idea already in Dewey’s description of the school as a social institution (Dewey, 1916), but the novelty or relevance of Clark’s description perhaps consists in applying it to learning as a mental process per se.

266

Book Reviews

Clark in his aim to cover the grand vision of the predictive processing brain in all its aspects is sometimes too busy to concentrate on describing and discussing the important details that should be elaborated when the ambition is to present a workable theory. Details, that bear philosophical challenges as well. For example, one substantial philosophical claim Clark states in his introduction is that “to match the given picture [. . .] [by predicting] just is to understand a lot about [. . .] [a domain] and [. . .] [domain-relevant] causes” (5) that seems to be foundational for the whole PP approach to perceptual experience (as it conveys some form of immediate understanding). This perspective on prediction is quite optimistic, and its justification is not discussed. There are other researchers on machine learning who are more critical on the relation between prediction and understanding (e. g. Wheeler, in a conference talk in 2017). And the yet unresolved interpretation problem in quantum mechanics also indicates that there are important differences between making successful predictions and understanding. For the project of the book, these are perhaps minor issues though. Overall, Surfing Uncertainty is an impressive book that can be read by researchers and graduate students likewise. The author achieves his goal to present a broad picture of “a well-supported vision of the brain” (28) as a predictive machine and combines it with the specific proposal of predictive processing. He can show that predictive processing is conceptually elegant, computationally well-grounded and has a good chance of being neutrally implemented (as his citing of several research studies in computer- and neuroscience indicates). While the book cannot answer all the questions it poses, it may inspire future discussions and help to deepen our understanding of the mind in unexpected ways.

Literature Bernecker, S. 2014. How to understand the extended mind. Philosophical Issues, 24, 1–23. Chomsky, N. .1980. On Cognitive Structures and their Development. A reply to Piaget. In: PiattelliPalmarini, M. (ed.). Language and Learning. The debate between Jean Piaget and Noam Chomsky. Harvard University Press. Clark, A. /Chalmers, D. 1998. The extended mind. Analysis, 1, 7–19. Clark. A. 2013. Expecting the World. Perception, Prediction, and the Origins of Human Knowledge. Journal of Philosophy, 9, 469–496. Clark, A. 2015. What “Extended Me” knows. Synthese, 11, 3757–3775. Clark, A. 2016. Surfing Uncertainty. Prediction, Action and the Embodied Mind. Oxford: Oxford UP. Clark, A. 2017. A Nice Surprise? Predictive Processing and the Active Pursuit of Novelty. Phenomenology and the Cognitive Sciences, 1–14. Clark, A. 2017. How to Knit Your Own Markov Blanket. Resisting the Second Law with Metamorphic Minds. In: Metzinger, T. /Wiese, W. (eds.). Philosophy and Predictive Processing, 3. Frankfurt am Main: MIND Group. Dewey, John. 1916. Democracy and education. New York: The Free Press. Fletcher, P. /Frith, C. 2009. Perceiving is believing. A Bayesian approach to explaining the positive symptoms of schizophrenia. Nature Reviews Neuroscience, 10, 48–58. Fodor, J. /Pylyshyn, Z. 1988. Connectionism and cognitive architecture. A critical analysis. Cognition, 28(1–2), 3–71. Friston, K. 2010. The free-energy-principle: a unified brain theory? Nature Reviews Neuroscience, 11, 127–128.

Book Reviews

267

Friston, K. /Thornton, C. / Clark, A. 2012. Free-energy minimization and the dark-room problem. Frontiers in Psychology, 3, 1–7. Frith, C. 2007. Making up the mind. How the brain creates our mental world. Oxford: Blackwell. Hohwy, J. 2007. Functional integration and the mind. Synthese, 159(3), 315–328. Hohwy, J. /Roepstorff, A. /Friston, K. 2008. Predictive coding explains binocular rivalry. An epistemological review. Cognition, 108(3), 687–701. Lupyan, G. /Clark, A. 2015. Words and the World. Predictive Coding and the Language-PerceptionCognition Interface. Current Directions in Psychological Science, 4, 279–284. Pfeifer, R. /Bongard, J. 2006, How the body shapes the way we think. A new way of intelligence. Cambridge, MA: MIT Press. Rao, R. /Ballard, D. 1999. Predictive coding in the visual cortex. A functional interpretation of some extra-classical receptive field effects. Nature Neuroscience, 2(1), 79. Simon, H. A. 1956. Rational choice and the structure of the environment. Psychological Review, 63(2), 129–138. Searle, John. 1980. Minds, Brains and Programs, Behavioural and Brain Sciences, 3, 417–457. Wheeler, G. 2017. Remarks on Machine Learning and Instrumental Predictions. Reasoning and Argumentation in Science. Conference at the Munich Center for Advanced Studies, 31.5.-2. 6. 2017.

Martin Nitsch, Heinrich-Heine-Universität Düsseldorf Esposito, R. 2005. Persons and Things. Cambridge /Malden: Polity. 147 pp. ISBN: 978-07456-9065-0 In this brief book, Roberto Esposito, Professor of Theoretical Philosophy at the Scuola Normale Superiore, Italy, questions the distinction between persons and things. As a biopolitical theorist, Esposito’s work, along with that of other contemporary Italian political theorists such as Negri and Vattimo, builds on, departs from and develops the work of continental philosophers such as Foucault, Derrida and Merleau-Ponty. Esposito, in his latest contribution to bio-political theory, argues that we should re-conceptualise politics from the perspective of bodies; which are neither persons nor things. In Persons and Things Esposito shows that persons and things have traditionally been characterised as not only different, but opposite; i. e. they are defined in mutually exclusive terms. The distinction has, according to Esposito, been a common element in our thought; to the point that it has become, in effect, a ‘presupposition that serves as the implicit ground for all other types of thought’ (2). This distinction, however, is increasingly inadequate as a means of meeting the challenges posed by our changing world. The increasing use of technological objects, the rise of the bio-hacking movement, and the changing role of bio-medicine in our lives leads Esposito to doubt the validity of the strict binary distinction between persons and things. The problems and paradoxes created by attempting to apply the traditional framework leads Esposito to argue for the development of a body-centric point of view. Focusing on the body is a means of reconceptualising our lives and politics: bodies are neither persons nor things. As bodies cannot be adequately conceptualised from either side of the distinction, we are in need of a new perspective, one that acknowledges the body as having a peculiar ontological consistency. Persons and Things, whilst lacking analytic rigour at times, constitutes an interesting philosophical reflection on an increasingly relevant theme: how we relate to our bodies. This review will take the following structure. Firstly, I will offer a brief

268

Book Reviews

synopsis of the main arguments in the book following Esposito’s three-part structure. I will then proceed to offer a few critical remarks in order to finally conclude by returning to the question of how Persons and Things can help us reflect on the biotechnological revolution. Persons and Things is divided into three parts which focus on the person, the thing and the body respectively. In the first section, devoted to the person, Esposito traces a selective (non-comprehensive) history of the concept of the person from Roman law, through Christian theology to the works of Locke and Kant. In Roman Law, the concept of person was used as a means of differentiating between those humans who were, in addition to being human, persons and those who did not have this additional status. Hence, in Roman law, the notion of person denotes a normative status, one which it not coextensive with the notion of human. The notion of the person in Roman law, then, separates humans into two classes: persons and non-persons. In the Christian canon, this distinction is reinterpreted as ‘an ontological division within the human-person composite’ which separates the two substances that make the human distinct: flesh and spirit. This development laid the foundations for the third progression of the notion of the person from theology to philosophy. Philosophical conceptions, which Esposito analyses through the work of Locke and Kant, explicitly link personhood to moral agency. The concept of the person, hence, is often used as a way to “exclude some types of humans from the benefits granted to others” (32) and implies a hierarchy between things and persons in which persons take precedence over things. The notion of personhood can, in virtue of the hierarchy implied by the concept, be used to justify the subjugation of some humans to others as those who are deemed non-persons are reduced to the status of things. This historical usage of the term still informs current bioethical thinking. In contemporary liberal bioethics, personhood is conceived of as a matter of thresholds “that only fully include adults in good health who are endowed with consciousness and therefore capable of self-determination” (53). Having a notion of the person which leads to a hierarchy of value amongst humans is, for Esposito, a worrying phenomenon. Once personhood (and the normative status that is implied in its application) is denied, the door to slavery, oppression and injustice is opened. The notion of the person as independent from the thing leaves the body in an ambiguous position, often making the body “the channel through which the person was transformed into a thing” (29). The second section of Persons and Things focuses on to the notion of things. In this chapter, Esposito draws on an eclectic group of sources; including Heidegger, Roman Law, Walter Benjamin, Marx, Plato and Lacan, in order to trace the genealogy of the notion of the thing across time and through cultures. Esposito then uses this genealogy as a basis for a discussion of the ways in which the value of the thing can be diminished. Firstly, Esposito draws on the etymology of thing (‘res’, ‘eiro’) to argue that things attained significance, originally, due to their importance to humans. Esposito argues that, once we moved away from this etymological usage and into the language of ‘being’, we introduced negation into the notion of thing. In defining what one thing is, we inevitably suggest “everything it is not, or in other words, its difference from every other thing” (60). This tendency is present in the work of both Plato and Aristotle, who rarify the thing through the notion of ‘essence’. The thing becomes, hence, a composite; it contains a true part (the ‘form’ or eidos) and a part that is non-essential, and by extension, less real. Furthermore, in accounting for the ultimate existence of things, Aristotle and Plato both suggest that

Book Reviews

269

things are the products of craftsmen, either human or divine (whether the ‘demiurg’ or the ‘unmoved mover’). Having discussed Plato and Aristotle, Roberto Esposito turns to the relationship between words and things. Language, Esposito claims, does not correspond strictly to the world; it is, in part, representation. Language, like the rarification inherent in the discussion of the essences of things, takes away from the reality of the thing. In order to represent something a distance from that which is represented is necessary. The third way in which things can be robbed of their value is by being treated in accordance with their exchange value and not their use value. Exchange values, in so far as they reflect the time necessary to produce the objects, become not a thing “but the reversed outcome of relationships between people” (83). This leads Esposito to conclude (rather hastily) that focusing on exchange values, as well as robbing objects of their value, requires that a certain group of persons become things, i. e. the proletariat. Finally, things can be robbed of their value by their reproducibility. Esposito reinterprets Walter Benjamin’s remarks about the technical reproducibility of artistic objects reducing the object’s aura to claim that, in a world of proliferation, things can become eternal in time but will ultimately lose ontological depth. The thing, in proliferating, becomes less real. The third, and final, section of Persons and Things is devoted to the notion of the body. Here Esposito develops his positive account of the body as a response to the challenges which the binary distinction between persons and things cannot explain. The first of these challenges is tied to the development of technology. In a world of biotechnological advances, persons can no longer be identified with their bodies: our bodies increasingly survive us as persons, and our persons now survive the loss of body parts and the mixture of our bodies with things. Hence, the distinction between person and thing is no longer as easily applicable as was thought. The second challenge to the hegemony of the person-thing distinction is its inability to explain the contribution the body makes to knowledge. The body, in having a unique function as a medium through which things and people interact, influences the outcome of knowledge. Drawing on Spinoza and Nietzsche, as well as the work of phenomenologists such as Husserl and Merleau-Ponty, Esposito claims that the body is irreducible and ever present in our lives, essentially being a “precondition of every action I perform” (120). In attempting to conceptualise the body and the ownership thereof, Esposito follows the tradition of Roman Law in not ascribing literal ‘self-ownership’ to people, considering the human body, at least in part, as belonging to the whole of humanity. Viewing the body through a self-ownership optic invariably reduces the body to the status of a thing. If we are to reject the traditional implications of the person-thing distinction, the body must not be a mere thing to be held by persons; we must move beyond the framework of people possessing and exercising dominion over things. The body, hence, must be seen as belonging to the category of that which is not held in private, but that which is held in common (res communes). Finally, Esposito discusses the notion of the political body and the role of bodies in society. Esposito sees in the recent tendency toward mass demonstrations (such as the Occupy movement, or the Arab spring) evidence of an incipient revaluing of the body in political action. Esposito reads these movements as implying that, in order for politics to

270

Book Reviews

exist, we need a public sphere which is not empty but “filled with living bodies united by the same protests or by the same demands” (147). Esposito’s Persons and Things is an attempt to conceptualise the role of the body in opposition to the notions of things and persons, a project of gargantuan proportions. In this, extremely brief, monograph Esposito is destined to give us a partial explanation of his theory and the implications thereof. The implications of conceptualising the body as res communes, for the ethics of transplantation for example, deserves a more detailed explanation. It is unclear from Esposito’s discussion whether considering the human body as res communes would imply, for example: (i) that organs can be taken without the consent of the person after they have died or (ii) that an opt-out system of organ donation is morally acceptable, or (iii) that the patenting of gene sequences is immoral; to name a few of the possibilities. In undertaking such a radical and speculative project in such a small book Esposito was also condemned to be partial in his interpretations of the history and development of the notions of person and thing across time and between cultures. For this reason, some of the justifications for the claims Esposito makes are not completely clear, at least not from the text as a self-contained piece. He quickly moves from topic to topic in language which is highly literary, making searching for the premises and conclusions to his arguments a daunting prospect. There are numerous occasions throughout the book in which the arguments move too quickly over highly contested terrain, inevitably overlooking important distinctions and leaving questions unanswered. Esposito, for example, doesn’t explain why conceiving of the body as res communes implies the body is not a thing; nor does he adequately justify the claim that valuing objects according exchange values inevitably leads to reducing some persons to the status of things. The complexity of the language, as well as the speed with which Esposito moves from idea to idea sketching a picture which draws on a vast amount of philosophers, makes this book inappropriate for (most) undergraduates. However, merely to judge this book as too short to achieve its aims, requiring more justification, and including only a partial interpretation of the history of the terms Esposito discusses would be a mistake. If read as an eloquent, literary, and thought provoking piece of philosophy, one can appreciate the virtues of this short book. It is not an attempt to justify every assertion, to hold every idea up to criticism, to judge the validity of an insight in logico-formal terms; it is an impassioned plea for a re-conceptualization of politics in the body’s terms. Whilst Persons and Things is not a ground-breaking (in as far as Merleau-Ponty preceded Esposito in placing the body at the centre of his philosophy) it does do something novel; it weaves insights taken from other authors and a historical overview (and critique) of the person-thing distinction with Esposito’s own insights into a concise, yet thought provoking, piece of philosophy. Having said this, there are problems with Esposito’s book which cannot be put down to space constraints. In his argument Esposito claims that once personhood (and the normative status that is implied by the term) is denied, the door to slavery, oppression and injustice is opened. Contra Esposito it could be claimed that, whilst this may be true, the rationale for not attributing full personhood to those who would not be ‘competent to consent’ is not the same as the rationale of slavery: not attributing personhood is a requirement of justice and can be seen as a way of satisfying the vulnerable person’s entitlement to protection. Esposito seems to claim that it is almost inevitable that, once

Book Reviews

271

we establish ‘grades’ of personhood, we will tend towards the destruction of ‘non-valuable lives’; not giving due consideration to the interests of those we have denied full personhood to. Esposito reinforces his claim by stating that this is, in fact, how we currently treat the human foetus. Whilst it may be true that it is possible that denying full personhood will lead to abuse, this is not necessarily true. It is equally true that wrongly ascribing full personhood to people can lead to abuse, as it would involve holding these people to standards they cannot plausibly reach, which would also constitute a grave wrong. Furthermore, in taking the destruction of the foetus as an example of how we treat nonpersons, Esposito fails to take into account the distinction between beings that are nolonger-persons and beings who have never-been-persons. In standard bioethical accounts the limits of what a medical practitioner can do to a being who was (but no longer is) a person are different to the limits of what one can do to a being that has never been a person. An example of how this ontological difference is morally relevant can be seen in cases involving the (non-consensual) treating of adults born with severely impaired cognitive functions. It is commonly considered acceptable to treat these individuals (who are unable to consent) only if the treatment accords with the best interests of the patients. Contrast this to the treatment of non-persons who were persons: Non-consensually treating a similarly impaired adult who was a person (e. g. dementia patients) must be justified in terms of advance directives or judgement by an appointed surrogate decisionmaker who takes into account the patient’s values and previously expressed wishes. Notwithstanding these problems, Esposito’s critique of the person-thing distinction is not to be ignored. During the first two decades of the 21st century we have seen an increasing merging of the thing and the person in the form of implants, transplants, and recently developed sophisticated technological options. Bodies now include artefacts, may be maintained by artefacts and, on occasion, bodies (including parts thereof) get reduced to the status of things. The tensions between this contemporary paradigm and the traditional thing-person dichotomy which Esposito identifies are important and merit critical attention. Refocusing on the body, and how it interacts with power structures, may prove to be a valuable tool for conceptualising the normative issues surrounding our increasing use of biotechnology and the increasing weight of bio-power in our lives. Whether these goals are best achieved by refocusing on the body through Esposito’s terminology and conceptual framework is an open question. To conclude I offer one suggestion why alternative frameworks may prove to be more fruitful: Esposito’s framework seems to lack a clear action guiding principle which, in a world which changes so rapidly (especially in the areas of biomedicine), is undoubtedly necessary. Joseph Tarquin Foulkes Roberts, University of Manchester

List of Contributors

Julia Borcherding New York University, [email protected] Katherine Dunlop University of Texas, [email protected] Stephen Engstrom University of Pittsburgh, [email protected] Patrick R. Leland Loyola University New Orleans, [email protected] Paul Lodge Mansfield College, University of Oxford, [email protected] Huaping Lu-Adler Georgetown University, [email protected] Jeffrey McDonough Harvard University, [email protected] Martin Nitsch Heinrich-Heine-Universität, Düsseldorf, [email protected] Gastón Robert King’s College London, [email protected] Joseph Tarquin Foulkes Roberts University of Manchester, [email protected] Gonzalo Rodriguez-Pereyra Oriel College, University of Oxford, [email protected] Timothy Rosenkoetter Dartmouth College, [email protected] Zeynep Soysal University of Rochester, [email protected]