Hylomorphism and Mereology (Proceedings of the Society for Medieval Logic and Metaphysic) [1 ed.] 1527511634, 9781527511637

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Hylomorphism and Mereology

Also available in the series: The Immateriality of the Human Mind, the Semantics of Analogy, and the Conceivability of God Volume 1: Proceedings of the Society for Medieval Logic and Metaphysics Categories, and What Is Beyond Volume 2: Proceedings of the Society for Medieval Logic and Metaphysics Knowledge, Mental Language, and Free Will Volume 3: Proceedings of the Society for Medieval Logic and Metaphysics Mental Representation Volume 4: Proceedings of the Society for Medieval Logic and Metaphysics Universal Representation, and the Ontology of Individuation Volume 5: Proceedings of the Society for Medieval Logic and Metaphysics Medieval Skepticism, and the Claim to Metaphysical Knowledge Volume 6: Proceedings of the Society for Medieval Logic and Metaphysics Medieval Metaphysics; or Is It “Just Semantics”? Volume 7: Proceedings of the Society for Medieval Logic and Metaphysics After God, with Reason Alone-Saikat Guha Commemorative Volume Volume 8: Proceedings of the Society for Medieval Logic and Metaphysics The Demonic Temptations of Medieval Nominalism Volume 9: Proceedings of the Society for Medieval Logic and Metaphysics Skepticism, Causality and Skepticism about Causality Volume 10: Proceedings of the Society for Medieval Logic and Metaphysics Metaphysical Themes, Medieval and Modern Volume 11: Proceedings of the Society for Medieval Logic and Metaphysics Maimonides on God and Duns Scotus on Logic and Metaphysics Volume 12: Proceedings of the Society for Medieval Logic and Metaphysics The Metaphysics of Personal Identity Volume 13: Proceedings of the Society for Medieval Logic and Metaphysics Consciousness and Self-Knowledge in Medieval Philosophy Volume 14: Proceedings of the Society for Medieval Logic and Metaphysics

Hylomorphism and Mereology: Proceedings of the Society for Medieval Logic and Metaphysics Volume 15 Edited by

Gyula Klima and Alex Hall

Hylomorphism and Mereology: Proceedings of the Society for Medieval Logic and Metaphysics Volume 15 Series: Proceedings of the Society for Medieval Logic and Metaphysics Edited by Gyula Klima and Alex Hall This book first published 2018 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2018 by Gyula Klima, Alex Hall and contributors All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-5275-1163-4 ISBN (13): 978-1-5275-1163-7

TABLE OF CONTENTS

Introduction ............................................................................................... vii Alex Hall Multiplex Composition and the Prospects for Substantial Unity ................. 1 Andrew Arlig There is More Than One Way to Slice a Cake: Comments on Multiplex Composition and The Prospects for Substantial Unity .............................. 21 Gyula Klima How Unicity Theorists Can Recover the Elements from Material Substances ................................................................................................. 29 Shane Wilkins Many Exits on the Road to Corpuscularianism: A Response to Wilkins ..... 45 Thomas Ward Boethius of Dacia on the Differentiae and the Unity of Definitions.......... 53 Rodrigo Guerizoli What Has Aquinas Got Against Platonic Forms? ...................................... 67 Turner C. Nevitt Mereological Hylomorphism and the Development of the Buridanian Account of Formal Consequence............................................................... 81 Jacob Archambault Appendix ................................................................................................. 105 Contributors ............................................................................................. 107

INTRODUCTION ALEX HALL

The Proceedings of the Society for Medieval Logic and Metaphysics (PSMLM) collects original materials presented at sessions sponsored by the Society for Medieval Logic and Metaphysics (SMLM). SMLM was founded in 2000 by Gyula Klima (Director), Joshua Hochschild, Jack Zupko and Jeffrey Brower, in order to recover the profound metaphysical insights of medieval thinkers for our own philosophical thought. The Society currently has over a hundred members on five continents. Alex Hall took up the position of Assistant Director and Secretary in 2011, with secretarial duties passing to Timothy Kearns in 2014. The Society’s maiden publication appeared online in 2001 and the decade that followed saw the release of eight more online volumes. In 2011, PSMLM transitioned to print and republished volumes 1-8 as separately titled editions. Sharp-eyed readers of these volumes will note the replacement of our (lamentably copyrighted for commercial use) lions, who guarded the integrity of the body of an intellectual tradition thought to be dead, with the phoenixes that mark this print rebirth. Volumes 9 and 10 appeared in a dual print/online format. With Volume 11, PSMLM switched to print only. Friends of the lions will be happy to note that they remain at their post, protecting the first ten volumes of the PSMLM at http://faculty.fordham. edu/klima/SMLM/, where interested readers can also keep up with SMLM activities and projects. This fifteenth Volume of PSMLM collects papers on the themes of hylomorphism and mereology, presented at SMLM sponsored sessions at the 2015 meeting of the American Catholic Philosophical Association hosted by Boston College and the 2016 International Congress on Medieval Studies at Western Michigan University. Mereology is the metaphysical theory of parts and wholes, including their conditions of identity and persistence through change. Hylomorphism is the Aristotelian metaphysical doctrine according to which all natural substances, including living organisms, consist of matter and form as their essential parts, where

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the substantial form of living organisms is identified as their soul. Volume 16 (forthcoming) will treat axiology and the virtues. Citing recent interest in hylomorphism in debates over the unity of material objects, Andrew Arlig weighs the merits of scholastic accounts in his “Multiplex Composition and The Prospects for Substantial Unity.” Arlig raises what he terms ‘easy’ and ‘hard’ problems for medieval theories and concludes that these theories’ prospects are “dim.” The easy problem emerges from the idea that multiplex substances (e.g. a statue) are subject to various exhaustive, non-overlapping divisions, e.g. the left and right side of a statue, on the one hand, and its prime matter and substantial form, on the other. It may appear that such multiplex objects are in fact multiple wholes. In response, Arlig contends that there is a path forward to addressing the easy difficulty inasmuch as the existence of a substance that is subject to hylomorphic partitioning is the precondition for exhaustive divisions of the substance into, e.g. left and right sides. The hard problem, however, develops out of this supposed ontological priority. On the medieval account, the human soul seems to be a hylomorphic composite inasmuch as it is receptive of accidents. As the human soul, therefore, also stands in need of a unifying principle itself, it is ill-suited in this role, namely, as the unifying principle of a substance. In “There is More Than One Way to Slice a Cake,” Gyula Klima identifies Arlig’s easy problem as problematic only inasmuch as the transitivity of identity seems to have broken down. Klima notes that medieval thinkers handle such cases by distinguishing substantial and accidental terms, akin to Saul Kripke’s rigid and non-rigid designators. Talk about something by means of accidental terms (as when we talk about halves of statues) picks out accidental forms, whereas talk about something by means of substantial terms, picks out substantial forms. The former designate nonrigidly, the latter rigidly. Using a mixture of both, Klima contends that it is easy to see that transitivity of identity does not have to break down. Rather, in such contexts, we are not identifying different totalities with one unit; we are simply identifying one and the same item differently, in terms of rigid and non-rigid designators. Again, Klima denies that its ability to receive accidental forms is a reason to conclude that the soul is subject to hylomorphic composition. Aquinas, for instance, would deny a literal reading to phrases such as ‘spiritual matter’ and draw on distinctions such as the soul’s having its act of being as a substantial form of the body and having it as that act whereby it is the subject of its accidents. Klima

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concludes that the prospects of reviving scholastic hylomorphism are bright, provided we do this in its proper conceptual context. Hylomorphism allows us to tell apart genuine substances, e.g. a human being, from mere conglomerates of spatially collocated bodies, e.g. Lego Batman. On this account, it might seem that every composite material object has just one substantial form that makes its integral parts parts of that unique thing, e.g. this heart is the heart of Socrates. At least Aquinas sees it this way. As a consequence, he adopts a unitarian theory. By way of contrast, pluralists such as Scotus point out that features of material objects persist after the corruption of their substantial forms. If the Rosemary shrub hadn’t been a conglomerate of substantial forms, why does the herb retain its scent? Shane Wilkins and Thomas Ward discuss the relative merits of these stances as regards the unity or multiplicity of substantial forms. Wilkins’ “How Unicity Theorists Can Recover the Elements from Material Substances” contends that unitarians can account for the persistence of certain of a substance’s characteristics after the corruption of its substantial form inasmuch as the elements that make up the substance remain specifically, if not numerically, the same when the form of the substance is corrupted. In “Many Exits,” Ward maintains that unitarians are not entitled to the claim that elements can jump substances. Moreover, Scotus’s pluriform substances are essentially ordered toward the whole; so, with his version of pluralism we needn’t fear corpuscularianism. Rodrigo Guerizoli draws attention to the fact that it is difficult to establish a coherent picture of Aristotle on the notion of differentiae, especially as accounts taken from his Metaphysics and Topics seem at odds with one another. Guerizoli’s “Boethius of Dacia on the Differentiae and the Unity of Definitions” presents a strong realist interpretation that reconciles the texts by means of the medieval distinction between how (modus) and what (res) we can signify or pick out. Boethius was an early modist (modistae) thinker. Modism proposes a strong correlation between thought, language and things. Conceptual differences are due directly to differences between existing things and their relations. So, for instance, the conceptual and linguistic difference between subject and predicate is a direct reflection of the ontological distinction between substance and accident, or in general between what is informed and what informs it. For this conception, the syntactical complexity of a definition (say, “rational animal”) that is truly predicable of the definiendum, the simple term it defines (say, “man”),

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generates the following problem: what corresponds to the multiplicity of the parts of the definition in the thing referred to by the definiendum? Guerizoli identifies three theses that Boethius draws from the Metaphysics and Topics. From the Metaphysics, Boethius takes (1) the thesis of the sufficiency of the final differentia – which proposes that definitions are complex only syntactically, the semantic content is sufficiently expressed by the differentia, which signifies the substance of the subject. (2) the thesis of the priority of the genus and (3) the thesis of the plurality of the differentiae are drawn from the Topics, and hold that the genus would reveal more of the nature of the definiendum than what is indicated by the differentia, and that multiple differentiae may be needed to specify the definiendum, respectively. Boethius wishes to hold on to (1) because he is a unitarian as regards substantial form. Allowing that the differentia suffices for definition pre-emptively steers pluralists away from, e.g. the claim that, for a human, ‘animal’ signifies the sensitive soul and ‘rational’ the intellectual. Yet (1) is at odds with (2) and (3), which respectively call for a complex formula and multiple differentiae. In response, Boethius allows that a complete definition is to be given in terms of the genus and the single perfect differentia (refusing to give priority to either) while rejecting (3) outright. Aquinas draws on Plato’s theory of forms in order to illustrate his own notions of God and angels. Moreover, he describes the relationship between God as subsistent being and creatures somehow participating in that being in very Platonic terms. And yet Aquinas himself roundly rejects Plato’s theory of forms, taking several opportunities to criticize it across the course of his career. Yet, if Plato’s theory is in fact incoherent, then doesn’t this implicate Aquinas’s metaphysics of participation inasmuch as it is grounded in Plato’s theory? “What Has Aquinas Got against Platonic Forms?” by Turner Nevitt argues that Aquinas does not believe that Plato’s theory of forms is incoherent. In fact, Aquinas admits that God could create things akin to such forms, e.g. a separate, subsisting whiteness as in the sacrament of the Eucharist. Again, Aquinas never states that Plato’s theory is self-contradictory. In light of these considerations, Nevitt looks to Aquinas’s commentary on the Metaphysics in support of his contention that, in fact, Aquinas did not think that Plato’s theory is incoherent. Rather, Aquinas rejects Plato’s theory in the interest of parsimony as Aquinas believes that Plato’s forms are unnecessary as they cannot explain any of the things that Plato posited them to explain,

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such as the changes things undergo, the nature and existence of things, and our knowledge of them. The late-thirteenth and the early-fourteenth centuries saw the gradual subsumption of Aristotelian syllogistic under a general theory of consequences, which focused on logical relations between propositions, rather than their terms. Jacob Archambault’s “Mereological Hylomoprhism” studies the development of the theory of consequences as it played out alongside the metaphysical debate over the number of substantial forms in a composite. In this connection, Archambault points to a distinction between physical hylomorphism, which posits that terrestrial objects are composites of matter and form and mereological hylomorphism, which looks on matter and form as distinct, proper, and integral parts of a hylomorphic compound. A study of Buridan’s theory of consequences, with its distinction between material and formal aspects of a proposition, reveals a mereological hylomorphism at work in Buridan’s logic that strictly mirrors Buridan’s physical hylomorphism. For, although Buridan is a unitarian as regards substantial form, Archambault notes that Buridan believes that matter and form are disjoint and (divinely) separable integral parts of a composite substance; hence, in this and other important ways, Buridan’s unitarian thesis differs from Aquinas’s. Archambault finds grounds for Buridan’s break with Aquinas in the dialectic of the debate over the number of substantial forms in a composite and notes that further study may likewise disclose a connection between the broader sense of ‘formal consequence’ recognized by Duns Scotus and William of Ockham and their shared commitment to hylomorphic pluralism.

MULTIPLEX COMPOSITION AND THE PROSPECTS FOR SUBSTANTIAL UNITY1 ANDREW ARLIG

It is one of the commonplaces of Aristotelian metaphysics that many of the things that we most care for – and especially mundane, corporeal substances – have hylomorphic structure. Of course, “hylomorphism” names a family of theories. Thus, given the recent interest in hylomorphism as a solution to certain problems pertaining to material constitution and the relation of mind to body,2 it is perhaps worth spending some time on an earlier Scholastic version of hylomorphism to test its prospects as an account of the unity of substances. In this paper, I will only make a short, tentative foray into what deserves a more thorough investigation. Primarily, I want to test the edges of a version of Scholastic hylomorphism with respect to a specific set of assumptions of medieval mereology, namely, that there are a variety of part–whole relations and that many of the parts of substances themselves seem to be divisible into parts. Divisibility and wholeness are closely aligned with Scholastic notions of unity. Indeed, divisibility often seems to be at odds with unity. Hence, if it turns out that the parts of a substance have parts, their role as principles of unity might be called into doubt.

1

Unless otherwise noted, all translations are mine. See for instance, the recent work of Kathrin Koslicki (2008) and Mark Johnston (2006). Jeffrey Brower’s new book on Aquinas (2014) aims in large part to demonstrate that Aquinas’s version of hylomorphism has much to offer to current metaphysical disputations about the structure, unity, and identity of material things.

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Multiplex Composition and the Prospects for Substantial Unity

Medieval mereology a la Boethius (a quick summary) Boethius’s On Division provides Scholastics with many of the mereological notions that they then employ in their thinking about the composition and structure of objects. We will, therefore, begin with a quick summary of some of the key ideas that Boethius puts forward about the division of things into their parts. Boethius observes that there are a number of items that count as true wholes. I say “true whole” because Boethius takes pains to distinguish wholes and their divisions from other items that also are divisible, such as genera (in so far as they are divisible into species) and words (voces) into their significations. Because these other items are divisible, there is a sense in which they have parts, and indeed, in Boethius and later writers, the products of these divisions are often said to be “parts”.3 This is not just a matter of laziness on their end. The relation of a species to a genus is a kind of partial ordering. So, in some extended sense, the species-to-genus relation has some features of what is now taken to be constitutive of mereological structure. Nonetheless, if pressed, Boethius will reaffirm that a genus is not really a whole and a species is not its part. Once we put aside these other composites and we turn to examine only the true wholes, we still encounter a bewildering landscape. Now let us speak of the division of the whole into parts, since this is the second division after the division of the genus. When we say “whole” we mean many things. For that which is continuous – such as a body or a line, or anything of that sort – is a whole. We also say that non–continuous things are wholes – for example, a whole flock, a whole population, or a whole army. Again, we call that which is universal – such as human or horse – a whole, since these things are wholes of their parts – i.e. of humans and horses. And for this reason, we say that each human is a particular. And again, that which consists out of certain powers is called a whole. For example, of soul one is the power of reasoning, another is of 3

See, e.g., Boethius On Division 887b: “This ought to be said: the genus is a whole in division, and a part in definition; and the definition is in such a way as if parts compose a whole of a sort, and division is in such a way as if a whole is resolved into parts; and the division of a genus is similar to the division of a whole, whereas the definition [is similar] to the composition of a whole. For in the division of a genus, animal is the whole of human [sc. corresponding to human], since under it human is embraced. But in a definition, [animal] is a part, given that the genus combined with the other differentiae composes the species.”

Andrew Arlig

3

sensing, and another of basic metabolic functioning (vegetandi); these are parts, not species [of soul].4

There are wholes that divide into continuous parts and those that divide into discrete ones. There are wholes that divide into homogenous parts and those into heterogeneous ones. There are also wholes divisible into matter and form. Interestingly, Boethius insists that the universal in so far as it is divisible into individuals is a true whole. We are also told that a single manifold, or multiplex, object admits of several distinct kinds of division. Therefore, it is in these many ways in which we speak of “the whole”. And first, if it should be continuous, the division of the whole should be made into those parts out of which the whole is perceived to consist. Otherwise, a division is not made. For you divide the body of a human this way into its parts: into a head, hands, chest, feet, [and so forth]. [And this is how to do it] even if by some other manner a correct division could be made with respect to the proper parts. However, for those things whose composition is manifold, the division is also manifold. For example, an animal is separated into those parts that have parts similar to themselves – e.g. into flesh and bone – and also into those that do not have parts that are similar to themselves – e.g. hands and feet. In the same manner both a ship and a house also [are divisible]. We resolve a book into verses, and these into words, and again, the [words] into syllables, and syllables into letters. And thus it happens that syllables and letters and names and verses are seen to be specific parts of the whole book. Yet, in another way, [some of these] are not taken to be parts of the whole, but rather parts of parts.5

For example, a gold statue of David is divisible into its shape, or form, and the gold. It is also divisible into its right and left halves. It is divisible into portions of gold. And it is divisible into head, torso, hands, feet, and so forth. Each of these divisions, we should note, exhausts the entirety of the object. Some of these divisions are clearly into overlapping parts. But strikingly, some of the divisions that this one multiplex object can accept result at their termini into sets of parts that both exhaust all that there is of the divisible starting point and are non-overlapping. Let’s move from the gold statue – which brings with it some complications that I wish to ignore – to 4

Boethius On Division 887d-888a. Boethius On Division 888a-b.

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the gold itself. This gold is a substance. It is divisible into a right and a left half, or a top and a bottom. It is also divisible into portions of the gold. Perhaps these two divisions can be aligned with one another, for we could say (I think quite reasonably) that a division into a right and a left (or top and bottom) is not a complete division – this division has not reached what I am calling a terminus. The division under examination is one of a whole into homogeneous parts, and such a division does not reach its terminus until we resolve the gold down to its smallest gold portion. But now go back to the starting point, to this gold. Now divide it into what are often called its “essential parts”, that is, into its substantial form and the prime matter.6 These two divisions, the first into homogeneous parts and the second into essential parts both exhaust the object. They also seem to not overlap. No portion of the gold is a proper part of either the prime matter or the form. It also appears that neither the form nor the prime matter is a proper part of any proper part of the gold.7

The easy problem So here is a question about the unity of this gold: Boethius seems to define a kind of whole in virtue of how it is divided. Given that we have two exhaustive, non-overlapping divisions of the same putative object, doesn’t it appear that we have two wholes that are the same as this one object? To sharpen the point, consider Walter Burley’s suggestion that the same object is divisible, exhaustively it seems, into a full set of material parts, and it is also divisible into a full set of formal parts. It should be understood that “whole” and “part” can be taken in several senses. “Part”, for instance, sometimes has the sense of essential part. (The Philosopher and the Commentator in many places call this the qualitative part, and they call the integral part the quantitative part.) And it is in this sense that “whole” is taken in the sense of either a whole with respect to 6

See Boethius On Division 888b: “There is also a division of the whole into matter and form. For in one manner the statue consists of its parts, and in another manner of matter and form – i.e. out of bronze and its figure (species).” 7 Here I admit that there are some complications. As many of you know, there is a robust debate in the Scholastic period about precisely how a substantial form imbues its matter. Is it extended through the matter in such a way that part of the form is here and another part there? Is it wholly in each bit of the matter (in so far as we can individuate the bits, of course)? It is for this reason that Bob Pasnau once proposed that Aquinas is in fact committed to the view that a stone, or my hunk of gold, is in fact not a substance (see his 1997, 130-2).

Andrew Arlig

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form or a whole with respect to matter, and placed opposite to these, there is the part with respect to form and the part with respect to matter. The parts with respect to form are those that always remain the same so long as the whole remains the same and complete. The parts with respect to matter are those that flow in and flow away. Examples of the former include the hand and the head as well as others of the sort that remain the same so long as the whole remains the same. Examples of the latter include flesh and marrow, since these flow in and flow away even as the whole remains the same. And just as “part” is spoken of in these two senses – one with respect to the matter, the other with respect to the form – “whole” is likewise spoken of in two ways, one with respect the form and one with respect to the matter. Accordingly, a man in youth and in old age has the same soul at every time [that he exists] and is the same whole with respect to the form. But he is not the same [whole] with respect to the matter, since at one age he has one matter and at a different age a different matter. This is because the matter of the food that has been incorporated into the augmented thing’s nature 8 the [thing’s] matter. When considered in terms of that which is augmented or diminished, new matter is continuously acquired and old matter is continuously lost, and hence, it is not the case that a man always remains the same with respect to the matter, even though he might remain the same with respect to the form.9

The material object is thus the same thing as two wholes. But the full set of material parts has different conditions for persistence from the full set of formal parts. If X and Y have different conditions for persistence, X and Y are distinct. Ergo, the material object is the same as two distinct wholes. But how can this hold unless this material object fails to have any interesting sort of intrinsic unity? If you have been sitting on the edge of your seat waiting to protest, don’t worry, I see the solution too. This Boethian methodology for determining what is a whole fails to account for the ontological subordination of some parts to others. Go back to my hunk of gold. No portion of gold can be a part of the prime matter, because it would not be a portion of gold unless there were a thing composed of prime matter and the right substantial form. If the form were not present, the portions of prime matter would not be gold. (They might not even be portions – since on some views, all accidental properties, including quantitative properties depend upon the substance and hence upon the substantial form.) In other words, even though the two divisions of the gold are exhaustive, one is ontologically or 8

Following the editors’ recommendation that we should add “auget”, or something similar (p. 301, note 6). 9 Walter Burley De toto et parte; ed. Shapiro and Scott, p. 300.

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“naturally” prior. It is a precondition for there being a division into homogeneous parts that there is essential, hylomorphic composition. This is also how we can address the puzzlement prompted by Burley’s treatment of composition.

The harder problem: the parts of souls in that they are forms I might be overlooking some interesting wrinkles that will need to be ironed out, but overall, I think there is a clear path forward toward solving this first puzzle about unity in the face of multiplex composition. Hence, I call it the easy puzzle about multiplex objects. The harder puzzle involves one of the essential parts, namely, the substantial form, and it comes into view when we look at one kind of substantial form, namely, the human soul. This harder problem arises from the fact that, on the one hand, there are compelling reasons to identify structure, complexity, and therefore parts in the soul. But since a soul is a form, it also has the job of unifying the human animal. But it seems that no substantial form, let alone a soul can unify the animal if it itself has parts. The argument against the divisibility of forms can be found in at least two versions in two places in the Aristotelian corpus. The first is at the end of Metaphysics Zeta;10 the second is De Anima 1.5. Since the argument in the De Anima is specifically geared toward the soul, I will point you to it. Some say that the soul has parts (meriste), and thinks with one part, and desires with another. In this case what is it that holds the soul together, if it naturally consists of parts? Certainly not the body; on the contrary the soul seems rather to hold the body together; at any rate when the soul is gone the body dissolves into air and decays. If then some other thing gives the soul unity, this would really be the soul. But we shall have to inquire again, whether this is a unity or has many parts (hen e polumeres). If it is a unity, why should not the soul be directly described as a unit? And if it has parts, the progress of the argument will again demand to know what is its combining principle (ti to sunechon ekeino), and thus we shall proceed ad infinitum.11

10

Metaphysics 7.17, 1041b18-28. Aristotle De Anima 1.5, 411b5-14; trans. Hett (Loeb).

11

Andrew Arlig

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Here is how the argument seems to go: Suppose X is constituted by a set of parts PX. PX will need something external to it to unify it. Call this Y. But now suppose that Y also has parts, PY. PY too will need something external to it to unify Y. Call this Z. Now Z will either be partless or it will have parts. If Z is partless, then we have found our principle of unity, and Z ought to be the form, not Y. But if not, the argument will run again. (And so it might go to infinity.) Therefore, if Y had parts, Y cannot be the form.12

12

Compare to Siger of Brabant’s interpretation of the argument from the De Anima and Metaphysics: “[…] it is contrary to the ratio of form that it be composed out of many parts. Aristotle makes such an argument in the seventh book of his Metaphysics: If some being and some unity must exist out of many, and if it must not be that these many exist in the way that a heap does, then it must be the case that there is something that unites these many things, the cause of the being and unity of these things, and this will be a form. But if again this [i.e. the unifying form] is a composite out of many, then the argument goes in the same manner, and it will proceed infinitely. Therefore, it is contrary to the ratio of form that it can be composed out of many parts. And this line of reasoning is confirmed by the fact that the aforementioned composition of a form would be out of many which are actually distinct from one another. In these sorts of cases [Aristotle’s] proposal – namely, that out of many there cannot come to be something one, unless there is some third thing that unites them, which will be a form – holds true. However, a being and unity can come to be without a third thing unifying them so long as the many out of which it comes to be are not distinct in act, but exist rather as potency and act (as matter and form exist). In this case, one of the [many components], namely the form, is the cause of the being and unity of the matter, and thus out of matter and form something one may come to be. And this is not because there would be a third thing, which is the cause of the being and unity of these, but because matter and form do not have existence through distinct causes of being. Rather, one is the cause of the being of the other, as matter in itself is not some being; it only potentially exists (tantum potest esse). So, it is through this matter that form per se is united to matter; it is not through a unifying intermediary that it is per se the cause of the being of that. […] And the above-mentioned argument about form, specifically, the form that is soul, is one that Aristotle gave at the end of the first book of De Anima. If the vegetative, by which something is a living body, and the sensitive, by which something is animal, were diverse parts of the soul, Aristotle argues that there would have to be a third thing that unifies them, and this third thing would be more the soul. And again if form were a composite out of many parts distinct in act, then as we have seen, because it has a form [the first form] would not be one in act in an absolute sense (simpliciter), although it might be granted that it would be one in virtue of a last act. But there would not be one in virtue of a last substantial act, since a form possessing a form, from which [the former] is actually distinct, is not related as a substantial act to a potency, as it

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If the argument is sound, then assuming that a substantial form is responsible for the unity of the substance, no substantial form can have parts. But perhaps this is not Aristotle’s intention. After all, he is on record in numerous places – in the De Anima no less13 – asserting that the soul has parts. Rather, the purpose of the argument in De Anima 1.5, and also in Metaphysics 7.17, might be to target a specific way of partitioning the soul or form.14 After all, we have already learned that “part” is said in many ways. Perhaps De Anima 1.5 is not ruling out the idea that the soul might have certain sorts of parts. If this right, the argument in De Anima 1.5 would have a different construal – such as something like the following: Suppose X is unified to degree D and that X is constituted by a set of parts PX. PX will need something external to it to unify it, namely, Y. But now suppose that Y has a degree of unity that is on the same par as or weaker than X. If that were true, Y would be unable to unify PX to degree D. For example, if X were a substance, then Y would be unable to make X one substance. At best, Y could make PX into an aggregate.

On this construal, the form could be divisible into parts, so long as this division is compatible with the form being more of a unity than the composite that it unifies. So far; so good. The trick, however, will be to show that the divisions of the soul never result in a set of parts that compromises the greater unity of the soul with respect to the unity of its composite.

Partitioning the soul, part 1 The soul, as it happens, is threatened by partitioning at numerous turns. For one thing, Boethius (following Aristotle’s practice) divides the soul by means of its powers.

has already been said” (Siger of Brabant Quaestiones Naturales (Paris), q. 1; Siger de Brabant 1974, pp. 114-19, selection from pages 114-16). 13 See, for example, De Anima 2.2, 413b5-9, 413b13-16, 413b27-414a1; 3.4, 429a10-18. Also On Memory 450a16-18; On Sleep and Waking 454a11-14. 14 This is, for instance, Johansen’s reading of De Anima 1.5 (see 2014, 42). See also Corcilius and Gregoric 2010, 82-5.

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Of the whole which consists of powers, its division ought to be made in this manner: Of soul, one part is in plants, another in animals; and again, of that which is in animals, one is rational and another is sensible; and after that, these are dissected by means of other subdivisions. But soul is the whole of these things, not their genus. They are parts of the soul, not as in quantity, but as in some power or virtue. For the substance of the soul is combined out of these powers. Thus, it happens that a division of this sort has something similar to both the division of the genus and of the whole. For it is because each part of which soul is predicable implies [soul] itself, that [this division] is compared to the division of the genus, [a genus] of which wherever there is a species, the genus itself immediately follows. However, this must be compared to the nature of a whole: not every soul embraces all the parts, but some [embrace only] some of them.15

Once a soul’s powers appear as principles for partitioning the soul, hosts of other possible divisions of the soul into parts seem to present themselves. For example, it appears that, given the powers manifest in different parts of the body, the soul itself might be divisible in quantity or place. And even if some powers come bundled together, when it comes to some low-level organisms, the soul itself seems to be divisible into two new souls if we cut the organism in two.16 Moreover, plants clearly live even when divided (diairoumena), and some of the insects also; which implies that the parts have a soul specifically if not numerically the same as that of the whole (hos ten auten echonta psuchen toi eidei, ei kai me arithmoi); at any rate each of the two parts has sensation and moves in space for some time. It is not at all surprising that they do not continue to do so; for they have not the organs necessary to maintain their natural state. But none the less all the parts of the soul are present in each of the [divided] parts [of the worm], and the [soul parts] are homogeneous both with respect to each other and with respect to the whole. [So] although they [viz. the parts of the soul] are not separable from one another, the whole soul is thus divisible.17

Some of these potential ways of partitioning the soul itself can be easily managed. For example, its seems that one can admit that powers of the soul manifest in different parts of the body (or, in the case of the intellect, in no part of the body) without cutting up the soul itself by drawing some 15

Boethius On Division 888c-d. See De Anima 1.5, 411b19-27; and 2.2, 413b16-24. See also mentions of the physical partition of plants and annelids in On Length of Life ch. 6, 467a18-23; and On Youth 468a23-b12. 17 Aristotle De Anima 1.5, 411b19-27; Hett trans. (modified). 16

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fairly plausible distinctions, such as between a thing (a substance) and its activities (accidents), or between a thing and the instruments that it needs to perform its operations and functions. One might even be able to hold that in the case of plants and annelids, the partition of the soul is only accidental.18 Or, in the case of plants (which seem to be the true threat, as their partitions can survive and flourish), one can merely concede that there is no such thing as a plant. A plant is perhaps better thought of as a community of organisms, as opposed to one complete substance.19 When pressed, these solutions might reveal some soft spots, but I want to move on to what I see to be the toughest challenge to the Scholastic hylomorphic theory. It pertains to the human soul, which on the one hand is a substantial form of the composite human being, but on the other something that is able to subsist in its own right (per se), at least for a spell, and which is itself the subject of several accidental changes. That the human soul must subsist in its own right is a requirement of the faith. The human soul must be able to survive separation from the body. The human soul also seems to be the subject of accidental changes, since a human intellect does not think about the same one thing throughout its long existence. Rather, it thinks about many things: right now a cat, later the Pythagorean Theorem. It also seems to be able to learn: there was a time when I did not know the Pythagorean Theorem. 18

This is Albert the Great’s solution: “We say that the soul is one and has power parts (partes virtuales), whereas the body is one and has organic parts, which all have a continuous connection (continuationem) to one, the heart. Thus, one ought to say that the soul is in the heart and from there its powers emanate into the whole body. And thus, it is not a whole in the whole such that it is a whole in each part [of the body]. Rather, it is in each part in virtue of some one of its powers. […] And yet even if we grant that [the soul’s] essence is present to each of its powers, it is not necessarily true that if a power is separated its essence is separated. For this power is attached to this organ, whereas the essence of the soul is not. Rather it is in the heart, which is the organ to which the essence of the soul has been assigned. And thus the essence is not separated from the heart unrestrictedly, it is only separated with respect to this operation, which it has in a part that has been separated. For as we said above [in Book 1, tract. 2, ch. 16], when a body is divided necessarily the soul is divided accidentally, although it was not divided in the way that a form which is spatially spread out in a body [can be]” (De Anima, Book 2, tract. 1, cap. 7; p. 75, ll. 34-54). 19 This seems to be Aristotle’s own way out. In a remarkable little passage from On Youth Aristotle claims that animals which can survive for a spell when divided are “like a concretion of several animals, whereas the best constituted animals do not show this defect, because their nature is one as much as it can be” (468b9-12).

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That a human soul is a thing that subsists in its own right and that it is itself the subject of accidents leaves the soul – which by hypothesis is a form – open to partitioning into hylomorphic parts. This would be a remarkable and, I think, unwelcome result. The thought that the human soul might itself have hylomorphic structure, of course, is not a thought that I came up with. It was a proposal that was front and center in the thirteenth century. Thus, I am entertaining once more an old view and I am going to propose the perhaps scandalous thought that it is still a legitimate challenge to the Scholastic hylomorphist who nevertheless insists that the human soul has the two characteristics mentioned just above.

Partitioning the soul, part 2: universal homomorphism redux? I will rehearse Bonaventure’s argument as it pertains to angels. But it should be clear how his line of reasoning also will apply to a human rational soul, assuming that it too is self-subsistent and capable of being the subject of accidents. Bonaventure first observes that there are numerous kinds of composition. Some of these kinds of composition are uncontroversially applicable to angels and a fortiori human souls. An angel, for example, is “composite” when considered in relation to its principle, or causal origin. An angel is also composed out of its substance, or actuality, and potency, for if there were no potency in an angel, it would be absolutely actual – i.e. a god. Parallel to this metaphysical structure, an angel has a logical composition, namely, a composition of genus and differentia. Finally, all created substances, including angels are composed of their being and their essence. Moreover, [an angel] can be considered as a being in its own right (ens in se). And in terms of this to the extent that it actually exists there is in it the composition of being (ens) and existence. To the extent that it exists as something essential [i.e. that it has an essence], in it there is composition of “that through which it is” (quo est) and “what it is” (quod est). And to the extent that it exists as an individual or person, in it there is composition of “what it is” (quod est) and “who it is” (quis est).20

Therefore, even though an angel is said to be simple, it is not absolutely simple, since it exhibits these aforementioned modes of composition. At 20

Bonaventure In II Sent., dist. 3, pars 1, art. 1, q. 1.

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the same time, Bonaventure acknowledges that angels do lack some forms of composition: It is not composed out of quantitative parts, and it is not composed out of “a corporeal and a spiritual nature”, by which he means a soul and a body. This much, Bonaventure takes to be agreed upon by all-comers. Where he breaks ranks with his opponents is on the question of whether angels and intellects in general have hylomorphic composition. That it seems so is demonstrated in the following fashion: [a] Based on the account of change (mutationis). Nothing changeable is simple. An angel in accord with its nature is changeable and indeed has changed. Therefore, it possesses composition. And it’s being different comes from matter. In anything where there is change, the principle of changeability is present. And the principle of changeability is matter. Therefore, etc. […] Again, [b] this position can be demonstrated through the account of action and passion: Nothing both acts and suffers as the same thing and with respect to the same thing. But an angel, the same one, both acts and suffers. Therefore, it has one principle with respect to which it acts and another principle with respect to which it suffers. The principle with respect to which it acts is form; the principle with respect to which it suffers can be nothing other than matter. Therefore, etc. The major premise is obvious. The minor is also clear, since it is the role of an angel to both give and receive illuminations. […] Moreover, [c] this seems so through the account of individuation. Among angels there is a distinction of hypostasis, and it is not in virtue of origin. Thus, the following argument can be constructed: Every numerical distinction comes from an intrinsic, substantial principle, since even if all accidental features were put to one side, there are still distinct items in the sense of numerical differences. This does not come from form. Therefore, it comes from a material principle. […] Moreover, [d] this position can be demonstrated by means of the nature of essential composition. An angel has a definition, and accordingly it participates in the nature of a genus and of a differentia. The former is a nature in virtue of which it agrees with others; the latter is a nature in virtue of which it differs. Therefore, given that necessarily the whole truth of the definition is really found in any angel, necessarily one must posit a diversity of natures in the angel. It is impossible that many natures come together to construct a third unless one has the ratio of possibility and the other the ratio of actuality. For nothing comes to be out of two things existing in potentiality, and likewise nothing comes to be out of two things existing in act. Therefore, necessarily, [one must be existing in potentiality, and the other in act.]21

21

Bonaventure In II Sent., dist. 3, pars 1, art. 1, q. 1.

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To summarize this long passage, Bonaventure identifies four phenomena that will force us to concede that intellects must have hylomorphic structure: (1) Rational substances are changeable, which means that there must be the proper internal structural features to accommodate change; specifically, there must be an active (“formal”) part and a passive (“material”) part. (2) Rational substances both act and suffer. Hence, there must be the proper internal structural features to accommodate, namely, an active (“formal”) part and a passive (“material”) part. (3) Rational substances are individuals. All individuals must have a principle of individuation. The only principle of individuation available is the combination of a formal element with a material element. (4) Rational substances have an essence and a definition, which requires that there be both a part that is responsible for the substance belonging to a general class (the genus) and a part that is responsible for the substance belonging to its most specific class. The former is a “material” element; the latter a “formal” element.

Bonaventure thinks it is an open and shut case that all created substances, including angels and other putatively “simple” intellects, exhibit these phenomena. I do not see a cause or account (ratio), by means of which one can defend [these claims] unless the substance of an angel – indeed, any essence of a created per se being – is composed out of different natures. But if there is composition out of different natures, these two natures will be disposed towards one another in the manner of an actual thing to a potential one – that is, of form and matter. And once this has all been laid out it seems to be closer to the truth (verior esse) that in an angel there is composition out of matter and form.22

In short, there is no intelligible option for explaining these phenomena other than to posit that the metaphysical parts that make these phenomena possible are a material nature and a formal nature.

22

Bonaventure In II Sent., dist. 3, pars 1, art. 1, q. 1.

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Bonaventure’s specific arguments vary in quality, and many readers will know how various thirteenth-century philosophers responded to them. But I want to suggest that (1) and (2) point to a common problem and deserve a second look. Averroes pronounced that a simple substance couldn’t be the subject of accidents.23 Boethius was covering the same terrain when he asserted that a form couldn’t be the subject for other forms. Therefore, nothing is said to be on account of matter, but rather on account of a proper form. Yet, the divine substance is form without matter, and hence, it is one and it is that which is. The remaining forms are not that which are. For each and every one has its being from those out of which it is (that is, from its parts) and so it is this and that (that is, its parts conjoined), not this alone or that alone. For example, since an earthly human consists of a soul and a body, it is the body and the soul, not (going part by part) either a body or a soul. Therefore, he is not that which is. But what is not from this and that, but is only this, this is that which is, and this is the most beautiful and the most powerful, since nothing outshines it. But for this reason this is a one in which there is no number; nothing is in it apart from that which is. Nor, in fact, can it be a subject, since it is a form, but forms cannot be subjects.24

Once I buy into the basic hylomorphic account for change, this simple thought seems on the face of it to be right. At the very least the burden of proof seems to be on the Aristotelian who wishes to violate this dictum. And it is here that the Aristotelians seem to be resorting to some ad hoc measures to work around this dictum. For instance, consider these two arguments: [Argument 1, and a reply] Next it will be asked whether the human intellect is a composite of matter and form. It appears that it is. The Commentator proves in his On the Substance of the Sphere [1, 4 B] that a simple substance cannot be the subject of accidents. His argument is this: As it was said in the first book of the Physics [cf. 1.7, 190b20], form along with matter is the cause of all accidents being in a subject. Now, the intellect is the subject of accidents. Therefore, etc. [ad 1] In opposition to the first, one should reply that some accidents are real. Examples of these are the white, the dark, and things of this sort, and for these kinds of accidents it cannot be the case that a simple substance is 23

See Averroes De substantia orbis 1, 4 B. Boethius On the Trinity 2, 28-43.

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their subject. But other accidents are intentional, and for these kinds a simple substance can very well be a subject.25

[Argument 2, and a reply] Again, every potency is receptive in virtue of its material nature (per naturam materiae). According to both Aristotle [cf. De Anima 3.4, 429a1516] and the Commentator [cf. Averroes In De anima 3.3], //10// intellect has a receptive potency. Accordingly, it has this in virtue of a material nature. Therefore, [intellect is composed of matter and form.] To [this objection] it should be said that there are two kinds of receptive potency: one which is a potency in relation to reception and dismissal and transmutation, and it is this kind that is in virtue of material nature; the other consists in pure reception, and this is not in virtue of material nature. It is this [second] sort that is in the intellect.26

Given that the intellect is the subject of accidents, it must be complex, and it is hard to see how this complexity can be anything other than either hylomorphic complexity or something like hylomorphic complexity. It thus is interesting to observe that many Scholastics who resist universal hylomorphism concede that rational souls and other intellects have something like hylomorphic composition: [Exhibit 1] However, there is in a human soul something that is “material” and something “formal”. The material element is the possible intellect, by which everything can come to be, since the soul in virtue of the possible intellect is in potency to all material forms. The formal element in the soul is agent intellect by means of which all things are made. Nevertheless, this “material” item should be distinguished from prime matter, for [prime matter] is the principle of corruption, whereas the “material” [element in the soul] is not. Furthermore, they differ in the manner in which they receive things. Prime matter receives forms as individuals, that is, as these [forms] (individuales et has). The intellect receives material forms

25

Anonymous “Semi-Averroist” Quaestiones in De Anima Book 3, q. 2; Giele et al. 1971, pp. 303-5. 26 Siger of Brabant Quaestiones in tertium De Anima, q. 6; Siger de Brabant 1972, pp. 17ff.

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[Exhibit 2] Consequently, we should inquire whether the intellect is a composite of matter and form. And it seems that it is. [obj. 1] It is certain that the intellect has some sort of composition. But it cannot be composed out of two actual entities; rather [it must be composed] out of one that is in potency and another in act. What is in potency is matter, and what exists in act is form. Therefore, it is composed out of matter and form. […] Therefore, there is some sort of composition in the intellect, but as we have seen, this is not a [composition] out of matter and form. We should say that the intellect is composed out of a material [constituent] and a formal [constituent], just as [a definition is composed] out of a generic form and a difference-making form (forma differentiae). Accordingly, it is composed out of a “material” form and an act. For it is not the case that all forms are simples, and since all the parts of a definition are forms, it must be the case that one is material in relation to the other and that anything [arising out] of them is a composite. Therefore, it is clear how it will go in the case of the other [sc. the intellect]. [ad 1] To the first argument [in favor of hylomorphic composition] it should be said that it is true that the intellect has some sort of composition and that this composition is not out of two pure acts. Accordingly, it is out of two acts, of which one is “material” in relation to the other and where the other is “formal”.28

Assuming that these quasi-formal and quasi-material parts are real – and for at least some Scholastics, they are – the unity problem comes back into view. Parts imply decomposability and dependence. Furthermore, every genus is naturally prior to its proper species, whereas a whole is posterior to its proper parts. In some cases, the parts that compose the whole precede the completion of its composition only in nature, in other cases, in reason as well as time. Hence, it happens that we resolve a genus into posterior things, but a whole into prior things.29 27 Anonymous “Semi-Averroist” Quaestiones Book 3, q. 2; Giele et al. 1971, p. 304. 28 Siger of Brabant Quaestiones in tertium De Anima, q. 6; Siger de Brabant 1972, pp. 17ff. 29 Boethius On Division 879b-c. See also On Division 880a: “There is still the matter of giving the differences between the distributions of the word and the whole. They differ in this way: the whole consists of parts, but the word does not

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Worse, and more to the point at issue, the existence of parts appears to necessitate the existence of an external principle of unity. Otherwise, one of the standard arguments for God’s absolute simplicity appears to lose its force.30 Of course, as we already noted, the existence of parts in a specific unifier need not compromise the ability of that unifier to unify something else. But the burden of proof seems to be on the advocate of this line of response to show that even though a soul – again, a form of a special sort – has quasi-hylomorphic composition, this kind of composition is more unified than the unity that the soul then goes on to impose on the (true) hylomorphic composite. It is here that I want to challenge the Scholastic to make the case that this is true; for I see no obvious way forward that does not amount to a case of positing a new sort of thing that can accomplish just this task. This, alas, has the stink of an ad hoc maneuver. The prospect for reviving a thirteenth-century version of hylomorphism seems rather dim.

So, should we be platonists? It is sometimes easy from our vantage to forget that there was nothing inevitable about the fact that mainstream Scholasticism adopted the Aristotelian dictum that a soul is a substantial form. Other authorities, such as Augustine and Boethius subscribed to the platonic view that a human soul is a separable substance that is like a form in many respects, but strictly speaking it is not a form. Thirteenth-century philosophers would have also encountered this platonic position in Avicenna’s De Anima. Avicenna concedes that a soul can be thought of as a form in that it consist of those things that it signifies. And the division of a whole is made into parts, whereas that of the word is not made into parts, but rather into those things that the word signifies. Hence, it happens that when one part is removed, the whole perishes, but if a word designates many things, when one thing that it signifies is removed, the word remains.” 30 Here I am thinking of the argument rehearsed by, among others, Aquinas: “The second reason [why God is altogether devoid of composition] is that every composite is posterior to its components and it is dependent upon them. God is the first being, as was demonstrated above. The third reason is that every composite has a cause. For things that are diverse in their own right (secundum se) do not converge into some sort of unity unless by means of some additional cause that unites them. God, however, does not have a cause […]” (Summa theologiae I, q. 3, art. 7).

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perfects, or completes, the body. Moreover, the soul is “quite distinct from the substance that has its being through the soul, and it is that on account of which the substance [i.e. the whole human being] is what it is.”31 Moreover, the soul is the “active” constitutive part of the human being, which is placed in relation to a “potential” constitutive part, namely, the body. However, when push comes to shove, Avicenna makes it abundantly clear that the soul is not a form in the strictest sense of the term; it is only a form in an extended, analogical sense. The argument that he offers was well known to early thirteenth-century Scholastics.32 Hence, Avicenna prefers to characterize the soul as the perfecting constitutive part of the whole human being. The soul at the time of its creation is created in a body, and it has a tendency toward its specific body.33 Nevertheless, once it has been created, the human soul does not require a body in order to exist. “The soul achieves its first entelechy through the body; its subsequent development, however, does not depend upon the body but on its own nature.”34 The human soul’s relation, then, to its body is accidental. Platonism in the sense that I am using it stresses the per se subsistence of the soul, and in particular, the notion that at least some souls – namely, intellects – are separable and can exist on their own at least for some time. Clearly, Platonism is friendlier than Aristotelianism on this score to orthodox theism. It is also easier to see how a platonic soul can do many of 31

Avicenna De Anima I, c. 1, p. 20. For one such example, see John Blund Tractatus de anima II.i, §§14-16 (pp. 56): “It is held by Aristotle that the soul is the perfection of an organic body that possesses life in potency. But one might object: Form gives being and matter is intrinsically (in se) imperfect. Hence, every perfection is a form. Thus, since a soul is a perfection of an organic body that possesses life in potency, a soul is a form. But no form is a thing existing in its own right (per se existens) once it is separated from the substance. Therefore, since a soul is a form, a soul cannot be said to be a thing existing in its own right once it is separated from the substance. Therefore, a soul cannot exist separately (separari) from a body, but it will perish along with the body. To this one should say that the name “soul” designates a thing as it is in a complex. For it signifies a substance under a certain accidental condition, namely, in relation to an organic body insofar as this [body] is animated and vivified by that [soul]. It is in virtue of this accident that it is said to be the perfection of the [body], specifically, because this [viz. the soul] animates that [viz. the body].” 33 Avicenna denies that souls pre-exist the body and that they can migrate from one body to another: De Anima V, cc. 3-4; Kitab al-Najat, book 2, section 6, cc. 12 and 14 (Rahman (trans.) Avicenna’s Psychology, pp. 56 f. and pp. 63-4). 34 Avicenna Najat, 2, 6, c. 12 (Avicenna’s Psychology, p. 58). 32

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the things that a soul allegedly does. It can be a subject for accidents, and hence it can think and think different things at different times. So, should we give up on hylomorphism and shift to Avicennianism? Not necessarily. If we take seriously the unity argument presented above, it seems that the Avicennian is in trouble too. Bonaventure’s arguments apply mutatis mutandis to the platonist’s picture. And it is far from clear how he can sidestep them. But if the platonic soul has hylomorphic parts, or parts that are sufficiently like hylomorphic parts, then the Avicennian, like our Aristotelian, needs to tell us why the composition of the soul is a tighter kind of unity – one which is tight enough to allow the soul to then glue the parts of the composite human together. Indeed, the Avicennian’s road may be even tougher: Recall that Avicenna must concede that the union of the soul to the body is accidental. How can an accidental union of the soul to body yield a union that is greater than that of a ship with its sailors? In short, if we won’t allow the Aristotelian to waffle his way out of the hard questions about unity, certainly we should hold our Avicennian platonist to the same standards.

Bibliography Albertus Magnus. 1968. De Anima, in Alberti Magni Opera Omnia, VII, part 1. Edited by C. Stroick, Aschendorff: Monasterii Westfalorum. Aristotle. 1957 [1936]. On the Soul. Parva Naturalia. On Breath. 2nd revised edition. Translated by W. S. Hett. Loeb Classical Library, vol. 288 (Aristotle, vol. 8). Cambridge, MA: Harvard University Press. Avicenna. 1968. Liber de Anima seu Sextus de Naturalibus, IV-V. Edited by S. van Riet. Louvain / Leiden: Éditions Orientalistes / E. J. Brill. —. 1972. Liber de Anima seu Sextus de Naturalibus, I-III. Edited by S. van Riet. Louvain / Leiden: E. Peeters / E. J. Brill. Boethius. 1998. De divisione liber. Critical edition, Translation, Prolegomena, and Commentary by John Magee. Leiden / Boston / Cologne: Brill. Bonaventure. 1938. Opera Theologica Selecta. Editio minor. 5 volumes. Edited by L. M. Bello et al. Quaracchi / Florence: Collegii S. Bonaventurae. Brower, Jeffrey. 2014. Aquinas’s Ontology of the Material World: Change, Hylomorphism, and Material Objects. Oxford / New York: Oxford University Press.

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Corcilius, Klaus and Pavel Gregoric. 2010. “Separability and Difference: Parts and Capacities of the Soul in Aristotle.” Oxford Studies in Ancient Philosophy 39: 81-120. Giele, Maurice, Fernand van Steenberghen, and Bernard Bazán. 1971. Trois Commentaires Anonymes sur le Traité de l’Ame D’Aristote. Philosophes Médiévaux 11. Louvain: Publications Universitaires. Johannes Blund. 1970. Tractatus de Anima. Edited by D. A. Callus and R. W. Hunt. London: For the British Academy by Oxford University Press. Johansen, Thomas K. 2012. The Powers of Aristotle’s Soul. Oxford: Oxford University Press. —. 2014. “Parts in Aristotle’s Definition of Soul: De Anima Books I and II.” in Klaus Corcilius and Dominik Perler (eds.), Partitioning the Soul: Debates from Plato to Leibniz. Topoi: Berlin Studies of the Ancient World, vol. 22. Berlin / Boston: Walter de Gruyter, pp. 39-61. Johnston, Mark. 2006. “Hylomorphism,” Journal of Philosophy 103, 65298. Koslicki, Kathrin. 2008. The Structure of Objects, Oxford: Oxford University Press. Pasnau, Robert. 1997. “Olivi on the Metaphysics of Soul”, Medieval Philosophy and Theology 6, 109-132. Rahman, Fazlur. 1952. Avicenna’s Psychology: An English Translation of Kitab al-Najat, Book II, Chapter VI with Historico-Philosophical Notes and Textual Improvements on the Cairo Edition, London: Oxford University Press. Siger de Brabant. 1972. Quaestiones in tertium De Anima. De Anima Intellectiva. De Aeternitate Mundi. Edited by Bernardo Bazán. Philosophes Médiévaux 13. Louvain: Publications Universitaires. —. 1974. Écrits de Logique, de Morale et de Physique. Edited by Bernardo Bazán. Philosophes Médiévaux 14. Louvain: Publications Universitaires. Walter Burley. 1966. De toto et parte, ed. H. Shapiro and F. Scott, Archives d’Histoire doctrinale et Litteraire du Moyen Age 33, 299303.

THERE IS MORE THAN ONE WAY TO SLICE A CAKE: COMMENTS ON ANDREW ARLIG’S MULTIPLEX COMPOSITION AND THE PROSPECTS FOR SUBSTANTIAL UNITY GYULA KLIMA

Whoever coined the adage in the title of this paper “There is More Than One Way to Slice a Cake” probably had in mind a very down-to-earth truth: you can slice a cake in two halves or into four quarters, etc. But as soon as we come to reflect on what is going on in the process of cutting up a cake, we should promptly realize that it involves a lot more than just a blunt instrument like a knife. For of course before even putting the knife to the cake, we may very well have a plan as to how to cut it. Indeed, we may say that the division of the cake has already been done in our mind before even putting the knife to work for halving or quartering the cake. Furthermore, a little more reflection should reveal another important difference between applying the knife in the process of physically cutting up the cake and applying the mind in marking out the cuts even before making any physical cuts into the cake. The process of physically cutting up the cake into its integral, quantitative parts by the knife yields two or more actually distinct slices, none of which is the same as the original cake. By contrast, the conceptual carving up of the same cake by the power of our intellect leaves it physically intact: we have the same physically intact, integer unit as before, even if we mentally managed to mark where we would need to cut it to turn it into a conglomerate of slices, rather than having the same unit we had before, while noting the as yet potential slices it could be divided into. Indeed, applying this sharper instrument, namely, the mind, we can come up with even more ways for cutting up the same unit, without actually destroying its unity and integrity, and thereby its very existence. Take a somewhat more complicated natural object, like the lump of gold that just

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There is More Than One Way to Slice a Cake

happens to be a statue, or the hapless Socrates, the usual subject of vivisection of scholastic thought experiments, in which our medieval colleagues would quite literally “go medieval on him”, conceptually halving or quartering his body, or dividing his soul from its powers, or separating his soul from his body. As you can see, these conceptual divisions can leave the same unit quite intact; still, they can divide him in a number of much weirder ways than a simple knife can. Indeed, using this method we can carve up Socrates in any old way we want in a process of exclusive and exhaustive division. We can take any quantitative part of his body and say that the whole of Socrates is nothing but his fingernail on his left pinkie and the rest; or any of his organic parts, such as his heart and the rest; or any of his functional parts, like his immune system, and the rest. Apparently, the possibilities are endless. But Professor Arlig tells us that not all these possible conceptual divisions are on the same footing; some of them are more fundamental, indeed, “prior” to others. This distinction is coming up in the paper as a reply to a putative sense of discomfort that was supposed to be growing on us as we were supposed to observe that as a result of these various ways of dividing up the same unit we would have to swallow the idea that obviously distinct totalities resulting from these different divisions are identical to the same unit. Although Professor Arlig’s paper doesn’t quite spell out the source of this growing discomfort, his paper assures us that the solution lies in distinguishing between the different priorities among different types of divisions. In order to try to evaluate the suggested solution, let me first try to spell out my feeling of discomfort concerning the different sorts of totalities resulting from the different sorts of divisions presented by the paper, and then see whether the suggestion for its solution does indeed solve the problem. One would think that the mere fact that you can conceptually carve up a single material substance in so many different ways should not generate any paradox. Just because you can have a third of Socrates and the rest, or his soul and the rest, these would be just different conceptual divisions of the same physically intact whole. However, the paper has a somewhat tricky way of presenting a difficulty: the whole resulting from one way of mentally cutting up Socrates is one totality, and the whole resulting from cutting him up another way is another totality. The two totalities are

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obviously distinct, yet they are both identical to the same item, namely Socrates. So, whatever happened to the transitivity of identity? To be sure, the paper doesn’t quite spell out the difficulty in this way. But in the end, that’s just the problem. As the paper puts it: “doesn’t it appear that we have two wholes that are the same as this one object”? [p. 2] This formulation should certainly give us pause: if there are two objects, then they are two because one is not the other and vice versa; they are distinct objects. But how on earth can two distinct objects be identical to one and the same object? Putting the same point in another way; of course, when I divide a cake into its thirds or into its quarters, in a sense I am identifying two totalities, namely, the totalities of thirds and quarters, but of course this is just a sort of idle way of speaking about the fact that I have two different ways of conceptually dividing up the same unit, and so there is nothing mysterious about the fact that the two divisions qua different divisions can yield the same unit, which is the unit I started out mentally carving up in the first place. So, if I say, Socrates = his three thirds = his four quarters, I am not really talking about two distinct items being identical with the same item; I am only talking about one and the same item identified in three different ways (this time identified in terms of two different ways of exclusive and exhaustive divisions along its dimensive quantity, and in terms of the same thing left undivided), which of course does in no way go against the transitivity of identity. Still, there is a certain deeper problem in identifying parts and wholes, where the transitivity of identity can indeed break down in temporal contexts involving contingent identities, as the passage quoted by Professor Arlig from Walter Burley points out. Consider the following scenario. John Buridan, the great nominalist philosopher of the 14th century, walks out to the river in Paris. He points to the water in front of him, and says: ‘Haec aqua est Secana’. Next week, when I will be in Paris, I will go to the same spot, point to the water in front of me (I promise), and will utter the same words. Both what Buridan said and what I will say will be true, since both of us will have said that the water we are pointing to is the Seine. But then, if the water Buridan pointed to was the Seine, and the water I will point to will be the Seine, shouldn’t the water Buridan pointed to and the water I will point to be the same? But how can it possibly be the same, given that the water Buridan pointed to was literally water under the bridge and is now somewhere out

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There is More Than One Way to Slice a Cake

in the ocean or even frozen in the North Pole’s ice, while the water I will point to is not even there yet? However, if the breakdown of transitivity is a matter of contingent identity due to temporally contingent reference, then it may not have to do with anything particularly mereological. Indeed, let’s take Socrates again, but this time without subjecting him to the usual vivisection in mereological contexts. We know that before marrying Xanthippe, he was a bachelor, and of course, when he was a bachelor, he was contingently identical with a bachelor. But the contingency of this identity immediately revealed itself when he married Xanthippe, and so he became identical with a married man. Still, despite the fact that a married man was identical with Socrates, who in turn was identical with a bachelor, at no time was it the case that a married man was identical with a bachelor, in the same way that the water Buridan was pointing to was identical with the Sein, which in turn will be identical with the water I will be pointing to next week, but still it will never be the case that the water Buridan was pointing to is the same water I will be pointing to next week.1 Accordingly, although I don’t quite see how Professor Arlig’s proposed solution to a problem he did not quite spell out would directly handle the transitivity problem I just spelled out, nevertheless, I can see how that problem can be handled if we embed it into the conceptual framework of medieval logic, in which, at least in what I usually refer to as the via antiqua conception, concrete common terms refer to substances because of signifying their forms. To put the point very simply, within that framework we can have contingent identities between items referred to by means of terms that are (what we might call after Kripke) ‘non-rigid designators’, namely, terms that signify accidental forms of their referents, whereas we can have necessarily transitive identities between items referred to by terms that signify the substantial forms of their referents. Thus, when we are referring to Socrates as a bachelor or as a husband, we are referring to the same substance by means of terms that signify an accidental, relational feature of him (namely, the feature of not having or having a wife). Again, when we are referring to Socrates as his two halves, 1

For more on this issue, see Klima, G. (2013), “Being, Unity, and Identity in the Fregean and Aristotelian Traditions”, in Edward Feser (ed.): Aristotle on Method and Metaphysics; Philosophers in Depth, Palgrave Macmillan, pp. 146-168. See also: http://faculty.fordham.edu/klima/FILES/Buridan%20on%20Substantial%20Unity %20and%20Substantial%20%20Concepts.pdf

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we are referring to him by means of a term that signifies an accidental feature of him, namely, his dimensive quantity being mentally divided by us in two halves, etc., etc. So, given that the transitivity of identity would necessarily hold in temporal contexts only in cases of identity statements with rigid designators, no wonder the transitivity of identity can break down in cases when we are identifying the same item in terms of its nonrigid designators. In fact, from this perspective, I wouldn’t find “the prospects for reviving a thirteenth-century version of hylomorphism” as “dim” as Professor Arlig does. For I would argue that, putting it in its proper theoretical context, thirteenth-century hylomorphism provides us with a principled metaphysical basis for the distinction between rigid and non-rigid designators, which in turn can help dispel a number of alleged difficulties both in medieval and contemporary mereology. The principled metaphysical basis in question is the distinction between substantial vs. accidental forms, providing substances with their substantial vs. accidental being, establishing them as per se vs. per accidens units (on the basis of the Aristotelian principle of the convertibility of being and unity), which in turn establishes their conditions of persistence, i.e., identity over time as long as they exist. Since per accidens units are only contingently unified, no wonder they dissolve without the dissolution of the substance. By contrast, per se units are non-contingently unified, so equally no wonder they are not dissolved without getting themselves and their components qua parts of the original destroyed. This is the unifying role of the substantial form, accounting for the difference between genuine, even if divisible and possibly structured units, and the mere conglomerate or aggregate of however tightly connected actual individuals. Accordingly, there isn’t any great mystery in the fact that the same substantial form-plus-prime-matter compound is not the same as the same subject-plus-accidental-form or acquired-or-lost-quantity compound. Thus, the same lump of clay that is once a resemblance of Aristotle and later isn’t does not have to be a distinct entity once mysteriously coinciding with another entity and next failing to coincide with the same. It’s just the same lump, once having this shape, next having another shape. But the reason why it’s the same lump is not its “lumpiness”, but its being the same entity, having the same substantial form, which makes it to be the same entity as long as its matter is informed by this very same substantial form, giving it the same, uninterrupted substantial act of being.

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Obviously, this interests us primarily because we are interested in one specific kind of substantial form, namely, the human soul, which has one further alleged peculiarity amongst all material substantial forms, namely, that in contrast to all other forms it is also a subject of forms inherent in it, namely, acts of thought and will, i.e., intellections and volitions (at least), with respect to which it can undergo change. This ability to undergo change, according to Prof. Arlig’s paper, is supposedly the basis for concluding that even our allegedly immaterial souls, let alone the purely spiritual substances of angels are also subject to some sort of hylomorphic composition. However, it should be clear that even the medieval upholders of “universal hylomorphism” would have used double quotes (if they had had that device) all around phrases like “matter and form” in their application to angels and human intellectual souls. Indeed, Aquinas, who squarely rejected the idea of universal hylomorphism, which would have assigned them a composition from form and some kind of “spiritual” as opposed to “corporeal” matter, had no problem with assigning the human intellective soul the status of being both a material form, because of its informing matter, and, because of being a spiritual substance, a subject of its purely spiritual accidents, an immaterial form. Of course, Aquinas had some more cards up his sleeve, such as the distinction between a form’s having its act of being as a form (because of which something else, namely a substance, has its existence) and its having its act of being as the subject of its own accidents (because of which it has its own accidental acts of being provided by its own accidents), but we need not go into those details here.2 In any case, I should say that Prof. Arlig’s paper did not provide me with the justification for wanting to go down an alternative route, as the last section of his paper suggests. If Augustinian-Neo-Platonism with substance-dualism is supposed to be the way out of the alleged quagmire of Scholastic Aristotelianism, as the paper (well, somewhat hesitantly) suggests, then we are doomed, because that is just the road we went down after Descartes, and look where it landed us: interaction problem, other minds, solipsism, the Matrix, and the need to know what it’s like to be a bat, let alone John Malkovich! Do we really want all that again?

2

See, however, Klima, G. (2009) “Aquinas on the Materiality of the Human Soul and the Immateriality of the Human Intellect”, Philosophical Investigations, 32(2009), pp. 163-182, and Klima, G. (2015) “Universality and Immateriality”, Acta Philosophica, 24(2015), pp. 31-42.

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From this perspective, I would say that the prospects of reviving the basic principles of scholastic hylomorphism are actually rather bright, provided we do this not in the context of our own, conflicting and rather unsystematic metaphysical intuitions, but rather in its proper conceptual context that tightly connects the notions of form, meaning and concept in logic to the notions of being and unity in metaphysics. For then mereology will find its proper place within metaphysics as the doctrine of various forms of unity and multiplicity having as its baseline the per se unity of substance despite its divisibility in various ways into all sorts of sub-units, that is, its parts, with the exception of the absolute indivisibility of the Divine Substance.3

3 Cf. Klima, G. (2000) “Aquinas on One and Many”, Documenti e Studi sulla Tradizione Filosofica Medievale, 11(2000), pp. 195-215.

HOW UNICITY THEORISTS CAN RECOVER THE ELEMENTS FROM MATERIAL SUBSTANCES SHANE MAXWELL WILKINS

Aquinas famously argues for the unicity of substantial forms; the thesis that every composite material object has exactly one substantial form. Scotus objected to this thesis on the grounds that it requires an implausible position on the status of the fundamental physical constituents of materials substances. If the unicity thesis is true, numerically the same element cannot at one time be among Socrates’s parts and later separate. This medieval debate merits further investigation since most contemporary hylomorphists have essentially adopted Scotus’s atomistic conception of matter. First, I shall argue, with Aquinas, that this account of matter sits uneasily together with other important hylomorphic commitments. Second, I will defend the unicity thesis against Scotus’s central objection and some related, contemporary worries.

Introduction Many material substances of familiar kinds decompose into heterogeneous parts. Take me, for instance. I am composed of a heart, lungs, liver, kidneys, and so on. Call these my integral parts.1 Each of these integral parts are themselves further decomposable into smaller, heterogeneous parts. But the process of decomposition cannot continue to infinity; there must be some fundamental level at which my parts cannot be understood as themselves having more ultimate parts of a different kind.2 Let us call material substances like myself, which are composed out of parts of different kinds mixed bodies and let us call those fundamental parts 1

To distinguish them from my metaphysical parts, namely my form and matter. Integral parthood was usually thought to be transitive, so if I have a heart as one of my parts, and that heart has a bit of the element of water as one of its parts, then I have that bit of water as one of my parts as well. Abelard, however, denied this. For details, see (Arlig 2015).

2

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How Unicity Theorists Can Recover the Elements from Material Substances

elements.3 The question I shall investigate in this paper is this: Do the elements that compose the mixed body of a material substance remain numerically the same before, during and after their careers are parts or not? More concretely: Is the leftmost atom of carbon in my pinky finger numerically the same carbon atom now that it was before when it constituted some other substance I ingested, or not? Aquinas would have thought not. Most educated people today who learned a little chemistry in school would say yes. Aquinas wasn’t a simpleton, so why would he go so badly wrong here? One initially attractive thought is that Aquinas’s intuitions just weren’t informed by the right empirical data; hardly his fault since he lived 700 years before Mendeleev. The faulty science interpretation is wrong though. In the first section of the paper below, I argue Aquinas’s view here arises not from false empirical beliefs about chemistry, but from important metaphysical commitments connected to his hylomorphism. In the last fifteen years hylomorphic theories have enjoyed a remarkable resurgence of attention from contemporary metaphysicians, meaning that Aquinas’s question – and his answer to it – deserve a fresh investigation. I will conclude this introductory section, by formulating a list of features a successful hylomorphic theory of the elements needs to have. In the second section of the paper, I will present Aquinas’s own arguments (primarily from the De mixtione) in favor of his position and argue Aquinas’s theory does in fact fulfill those desiderata. Then, in the final section, I will consider an important objection to Aquinas’s position from Duns Scotus, who attempts to elaborate an alternative account of hylomorphism. I will argue Aquinas need not be moved by these Scotistic considerations and indeed can nudge the Scotist down a slippery slope that leads away from hylomorphism altogether. If all that I’ve said up to this point has been correct, I will then conclude, Aquinas’s position might not be as crazy as it seems.

3

The elements are homomerous: every part of the element of water is itself water. This is just to say the elements are continua, infinitely divisible bodies each division of which retains the same nature as the whole.

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The Metaphysical Context of a Mereological Conundrum Let us begin the inquiry with a brief review of the context which makes our question about the status of the elements significant. I will begin the discussion of the context by identifying three points upon which Aquinas and Scotus agreed, and then turn to one crucial issue upon which they disagreed.

Commonplaces All parties to the dispute about the ontological status of elements subscribed to the following three principles: (1) Hylomorphism – Material substances such as Socrates as composed of matter and a substantial form. (2) Elemental Composition – Mixed bodies (including the material substances) are composed of elements. (3) Power Coordination – The substantial form of a substance conveys powers on the substance by ‘coordinating’ the powers of the elements out of which the substance is composed.

All the parties were committed to the hylomorphic picture of reality described in Aristotle’s Physics books I and II, which supplied the basic metaphysical background against which this question about the status of the elements makes sense. On this view, there is a genuine difference between generation as the real coming-into-being of a new substance and mere cases of accidental alteration, as when a congeries of parts is rearranged as happens for example when the grains of sand in a heap are blown by the wind. What distinguishes generation from mere alteration is the presence of a substantial form, which unifies the parts of the whole into a new, distinct entity of a different type.4 I take the elemental composition principle to have been something like a commonplace of basic science, something like we today regard the atoms in Mendeleev’s periodic table as the ultimate constituents of the objects we observe around us. The analogy here is not anachronistic. Aquinas was perfectly well aware that material objects might have such miniscule parts that what appears to us to be a uniform solid might actually be composed 4

Cf. Aristotle, Metaphysics, Z.

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How Unicity Theorists Can Recover the Elements from Material Substances

of heterogeneous parts that simply cannot be distinguished by the naked eye.5 More to the point, the medievals were perfectly aware of the fact that some substances were made out of other substances. Medieval metallurgists and miners knew how to smelt iron from ore, and they used a process known as cupellation to refine pure silver from the common lead-silver ores that were actually mined. Finally, the last commonplace of the time was a commitment to a powersbased understanding of causation moored in the hylomorphic account of substantial forms. Regarding the conception of powers in scholastic philosophy, Marilyn McCord Adams writes: According to Aristotelian metaphysics, natures are complexes of powers. When appropriately coordinated, the collective exercise of such powers converges on an end. In the sublunary world, elemental powers are simple and deterministic. Even where more complex living things are concerned, the ‘coordination’ of their powers is ‘built-in’ in such a fashion that – given relevant circumstances – they function to achieve their end (McCord Adams 1996, 499).

The idea here is that the substantial form of the substance is supposed to be the thing which performs this ‘coordinating’ function.6 Thus the substance can have new powers which are not powers of any of its parts, precisely because the substantial form can combine the powers of the parts in some way.7 Now there was broad agreement about the these three claims, but of course the claims are quite broad and of course as medieval philosophers got down to business trying to actually use these claims to explain the 5

Aquinas speaks in the De mixtione of certain mixed bodies which are mixtures (i.e. blended into a unity) only ‘according to sensation,’ which “happens when bodies come together that are insensible because of their smallness” (2). Cf. “… sequitur quod non sit vera mixtio, se ad sensum solum, quasi iuxta se positis partibus, insensibilius propter parvitatem” (109). Note that when I quote from the De mixtione I will use the English translation of Spade, but I am reproducing the Latin text found in (Aquinas 1998). 6 Cf. also (Pasnau 2011, 581). 7 Cf. [b][11-31]. “What a syllable is, then, is not only the elements, the vowel and the consonant, but also something else, and the flesh is not only fire and earth, or hot and cold, but also something else.”

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phenomena around them, differences of opinion arose about how the details were meant to be filled in. Let’s now turn to one of the most important of such disagreements.

The Parting of the Ways One disagreement about how to fill in the details of this picture was what to say about the substantial forms of the elements that compose the substance. Do the elements retain their substantial forms when they become part of the mixed body, or do they lose their substantial forms? Defenders of The Unicity of Substantial Form, such as Thomas Aquinas and John Buridan, maintained that each composite material object has exactly one substantial form, namely the substantial form of the whole and so each of the integral parts, down to the elements cannot have its own independent substantial form. So, for instance, my substantial form is the one sole substantial form by which I am a substance, a body, a living thing, a thing with sensory powers, and so on.8 And that same single substantial form is what makes my heart a heart, and a valve of the heart a valve, and so on down until that form is making each of the elements what it is. Proponents of the Plurality of Substantial Forms, on the other hand, deny this. According to plurality theorists, the elements can retain their substantial forms, because a plurality of distinct substantial forms can exist within a single substance. There were important arguments on both sides. Aquinas, for the unicity theorists, argued that the plurality view destroys the unity of the substance. If Socrates were an animal and were rational in virtue of different forms, then these two, in order to be united simpliciter, would need something to make them one. Therefore, since nothing is available to do this, the result will be that a human being is one thing only as an aggregate, like a heap, which is one thing secundum quid, and many things simpliciter.9 8

Of course, Aquinas also thinks that immaterial objects, like angels, only have a single substantial form too, but since the present paper is concerned with resolving a problem that afflicts Aquinas’s account of material objects, I have offered a slightly narrower definition of the thesis that Aquinas himself would have done. 9 Quaestiones disputatae de anima, q. 11. “Sic ergo, si secundum diversas formas Socrates esset animal et rationale, indigerent haec duo, ad hoc quod unirentur

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How Unicity Theorists Can Recover the Elements from Material Substances

In other words, Aquinas is saying that plurality theorists are giving up the central insight that lies behind the hylomorphism principle, namely that what substantial forms do is create new units, not merely alter spatial relations among pre-existing parts. However, despite Aquinas’s arguments, the unicity position faced strong objections, and the majority of medieval philosophers endorsed the plurality position. Scotus, for instance, anticipating a common line of thought in contemporary debates about material constitution, argues that the living organism and its body must be two distinct objects, with two distinct substantial forms, since the same body can go on existing after the death of the organism, and so by the indiscernibility of identicals, the living organism and its body must be two distinct, but collocated entities.10 Let us call this The Corpse Objection. The motivating idea behind the Corpse Objection is that it appears that unicity theorists cannot do justice to the Power Coordination principle. The corpse appears to have many of the same powers as the living body, including apparently having a heart and other integral parts that retain their shapes. Pasnau (2011, 582) cites Zabarella as giving the example of the smell of dried herbs; the living plant is gone, but the body that remains still smells like rosemary, and it simply seems to strain credulity to believe that this is now a numerically distinct, but qualitatively identical smell from the smell that the living plant had.11 If what substantial forms do is coordinate the powers of the elements into the powers of substances, and some of the same powers appear to remain in the body after the substantial form of the living organism has departed, then this shows that there must be a substantial form of the body present in the corpse that gave it these powers which survive the death of the person.

simpliciter, aliquo quod faceret ea unum. Unde, cum hoc non sit assignare, remanebit quod homo non erit unum nisi aggregatione; sicut acervus, qui est secundum quid unum et simpliciter multa.” 10 Cf. Ordinatio IV, q. 11, a. 3, “If this is, and that is not, then they are not the same entity in being.” The logic of Scotus’s position pushes him to a spatial collocation position, but he seems to find this position at least embarrassing, even if not outright absurd. See also Reportatio II-A, d. 15. For helpful discussion see (Ward 2014, 133-134). 11 This is the medieval equivalent of what David Lewis once called an ‘incredulous stare’.

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I do not mean to suggest that the only argument in the pluralist camp is an incredulous stare. There are other difficulties that the unicity position faces. At least Aquinas’s version of the unicity theory requires one to treat the matter which undergoes substantial generation and corruption as prime matter which is “pure potentiality.” Scotus already recognizes that this theory faces a number of difficulties. One of them is to explain how “the same matter” continues under generation and corruption, which is to say that Scotus thinks that Aquinas’s account of generation looks like creation ex nihilo, rather than generation out of a substrate.12 The idea of this second objection is to try to press the unicity theorist on the principle of Elemental Composition. If the elements lose their substantial forms when they become parts of a substance, as the unicity theorist claims, then strictly speaking those elements cease to exist, and so in what sense is the mixed body “composed” of the elements?

The Desiderata for Element Recovery Having now surveyed the dialectical context, let us return to our main question. Our question was whether the elements that compose the mixed body of a material substance remain the same individuals, i.e. retain their substantial forms, or not? We have already seen that unicity theorists like Aquinas have to say no, under pain, they say, of giving up the fundamental insight of hylomorphism in general. Further, we have seen that two important pressures on the position are to reconcile this view with both the Elemental Composition principle and the Power Coordination principle. Therefore, what the unicity theorists need to do is offer a theory of elements that respects these two principles. Aquinas was attempting to provide just such a theory in his treatise De mixtione. The essence of his position there is to insist that the elements are recoverable from the mixed body and that this is the only position that will respect all three of the commonplaces mentioned above. So, I will turn now to considering the position he develops there in more detail, and then I will consider whether Aquinas is correct that his position is superior to those the plurality theorists can hold.

12

For further discussion of Scotus’s argument here, see (Cross 1998, 17). For reasons of space, however, I will not consider this objection and Thomistic responses to it any further.

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How Unicity Theorists Can Recover the Elements from Material Substances

Aquinas on Recovering the Elements The De mixtione begins with Aquinas reciting arguments for and against two different positions on the status of the elements in a mixed body.

Avicenna’s Pluralist Position The first position Aquinas considers is Avicenna’s. Avicenna held that the substantial forms of the elements remain in the mixture.13 Aquinas thinks this position is impossible, because it would require one body (Socrates) to also be simultaneously many bodies (each of the individual elements that compose Socrates). But this is impossible, Aquinas says, “therefore, the four elements will not exist in each part of the mixed body” (2). I take Aquinas’s point here to be that endorsing something like spatially collocated objects, as we saw above Scotus himself will have to do, is ridiculous. I don’t think this is just Aquinas preemptively answering Scotus’s incredulous stare with an incredulous stare of his own. Rather, I think what Aquinas is angling at here is the same thing he was arguing in the passage from the De anima above: allowing spatially colocated bodies destroys the unity of the substance, and therefore undermines the purpose for adopting hylomorphism in the first place, namely to distinguish genuine cases of generation from mere alterations. Aquinas also offers a second, related argument against the Avicennian theory that turns on the incompatibility of the properties of the elements. Fire is hot and water cool, and since these properties are incompatible, one and the same thing cannot have incompatible properties in the same location. Hence if elemental fire and elemental water are both parts of one mixed body, they must be located in different places; and therefore again the mixed body will be a congeries of different parts, which merely appear to form a mixture to the naked eye because our power of vision is not strong enough to distinguish one from another. Aquinas’s defective chemistry obscures his point here, so let’s update the example. Suppose I have two isolated atoms, sodium and chlorine, which have incompatible properties, in this case the sodium is a metal and chlorine is not a metal. Nothing can both be and not be a metal at the same time, so if the sodium atom and the chlorine atom both retain their substantial forms when they 13

In The Physics of the Healing I.6 Avicenna gives an example suggestive of the Scotist’s incredulous stare. He mentions that sometimes a person has a certain scar which the corpse also retains in death.

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form an ionic bond to yield sodium chloride, then the NaCl molecule must be a metal in one part, and a non-metal in another part. But Aquinas’s point is that if the NaCl is a metal in one part (where the sodium is) and a non-metal in another part (where the chlorine is) then the NaCl is not a genuine substance after all, but a mere congeries of a metal object and a non-metal object which happened to located close together, rather than a genuine new unit that is neither Na, nor Cl, but NaCl throughout. This argument differs from the first since the issue at stake here isn’t so much the hylomorphist’s distinguishing generation from mere alteration. Rather, I think what Aquinas is doing is pushing against the claim that pluralist view can do better justice to the elemental composition principle than the unicity theory can.

Averroes’s Search for a Middle Ground Having criticized Avicenna’s pluralist position, Aquinas now turns to consider the view of Averroes. As Aquinas tells it, Averroes argued that “the forms of the elements do not remain in their fullness in the mixed [body], but are reduced to a certain intermediate” (2).14 Or in other words, that the sodium and chlorine do not retain their whole original substantial form when they form NaCl, but they retain as it were quasi-substantial forms, and so even though atomic sodium is a substance, molecular sodium is only a quasi-substance. Aquinas notes that Aristotle (correctly) observed that nothing could be the contrary of substance,15 so these quasisubstances would have to be some kind of entity intermediate between genuine substances and mere accidents. Aquinas give a number of quite persuasive arguments that there simply is no such middle ground to occupy. To give just one brief example, Aquinas points out that by definition a substance is that which does not exist in another, and by the excluded middle one either has this property or one does not.

Aquinas’s Own Position Aquinas now turns to give his own theory of the elements, which turns on the distinction between the substantial form and its powers.16 On 14

Cf. Averroes In de caelo, III.67. Categories, ch. 5. Every being is either a substance or the modification of a substance, but neither substances nor the modifications of substances are contrary to substances; therefore substances have no contraries. 16 For one locus classicus, see Aquinas’s view on the distinction between the soul and its powers in Summa theologiae, Ia, q. 77. a. 1. 15

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Aquinas’s position the substantial form essentially co-opts the role of the original substantial forms of the elements. So, on Aquinas’s telling, the original substantial form of the sodium atom and the chlorine atom are destroyed when the atoms become ionically bonded, but the new form of the salt takes over the role of conferring qualitatively similar powers on the elemental parts. Thus I can localize a bit of prime matter playing the role of the “sodium atom” in the compound even though that bit of matter is not strictly speaking a sodium atom. There are two things to note about this position. First, the powers of the elements in the mixture are qualitatively similar to the powers of the elements in isolation. Aquinas is thinking, plausibly, that there should be some change in the powers of the elements when they come to compose a mixed body, otherwise the mixed body would just be an aggregation, not a genuine new kind. And yet something of the qualities of the elements must be involved in making the mixture what it is. Aquinas illustrates this by noting the intermediate qualities of mixed bodies somehow partake of the extremes of the qualities of the elements that compose them, just as grey partakes of both black and white. Again, let’s update the example and say the NaCl molecule has to recruit some of the powers of the sodium and the chlorine atom in order to give the molecule its powers. Presumably, for instance, we could ask a crystallographer to tell us why NaCl forms a cubic crystal and that answer would be given in terms of the relative charges and sizes of the two ions. Or, as Aquinas says, “the qualities of simple bodies are found in the proper quality of a mixed body” (4). I think this is an appealing feature of Aquinas’s view, because it means that Aquinas’s account offers the right combination of continuity and change to satisfy the Power Coordination principle in a plausible way. Second, as noted above, the deep reason Aquinas’s position here is possible is his insistence on the difference between the substantial form and the powers it confers.17 And so, Aquinas can say, “the quality of a simple body is other than its substantial form. Nevertheless, it acts in virtue of the substantial form” (4). So, there still remains in the salt molecule a part having the qualities of the sodium atom, which is acting, not in virtue of the substantial form of a sodium atom (since for Aquinas there is no more sodium atom, strictly speaking), but in virtue of the substantial form of the salt molecule directly. Furthermore, on account of 17 Cf. also the discussion in q. 12 of the disputed question on the soul, where Aquinas firmly argues that the soul is distinct from its powers.

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these qualities inhering in that part of the NaCl molecule, it makes good sense why we can dissolve the molecule and recover an element from the mixed body. True, on Aquinas’s account it won’t be the numerically same item that existed in the molecule, which might provoke Scotus’s incredulous stare, but there is no magic involved. In conclusion then, Aquinas appears to offer a satisfactory theory that respects all three of our desiderata. For, there seems to be a perfectly good reason to say that: (i) the substantial form of the whole is creating a genuine, novel unity, satisfying the hylomorphism principle, and (ii) there are elements composing the mixed bodies of material substances in the sense that the sole substantial form of the whole entity is conferring on prime matter the different active and passive qualities of distinct elements of those types, satisfying the elemental composition principle and (iii) yet those active and passive powers are as it were recruited into a new functional unity by the substantial form of the whole, satisfying the power coordination principle. It is no mean feat to tell a plausible story like Aquinas’s that explains what needs explaining and yet hits the required desiderata. However, a plausible story isn’t yet a compelling argument, and at least one modern commentator, Thomas Ward, would object to the way in which I have “updated” Aquinas’s examples in the light of modern chemistry. So, let us now begin inquire if Aquinas’s position is actually correct, or plausible in the light of modern science.

Warding off an Objection Thomas Ward argues that it is not. On Ward’s view, Aquinas (and his fellow unicity theorist John Buridan) face an important difficulty, a difficulty which Scotus’s position, a variant of the pluralist position, could in principle avoid.

The Objection The problem, as Ward sees it, is this: Howsoever we update our theory of elements or our theory of elemental composition (e.g. from mixing to bonding), we will not get substances which have elements as actual parts. For Scotus, however, one could easily

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How Unicity Theorists Can Recover the Elements from Material Substances envision a chemical theory which would allow us to have substances with elements as parts.18

I take Ward to be offering an argument here that goes something like: 1. A hylomorphic theory of the elements in a material substance could be acceptable to a contemporary audience if and only if it is possible for the hylomorphic theory to be developed in such a way to treat the elements as actual parts. (Premise) 2. It is not possible for Aquinas’s hylomorphic theory to be developed in such a way to treat the elements as actual parts. (Premise) 3. But it is possible for Scotus’s hylomorphic theory to be developed in such a way to treat the elements as actual parts. (Premise) 4. Hence, Scotus’s hylomorphic theory could be acceptable to a contemporary audience, but Aquinas’s could not. (from 1-3)

The upshot of Ward’s argument is that contemporary hylomorphists would do well to look to Scotus for help filling in the mereological details of their metaphysical theories rather than to Aquinas. His argument is clearly valid, but is it sound? Premise (2) is clearly correct, given the interpretation of Aquinas I have given above. If, as the unicity theorists maintain, the unity of the substance requires that there be only one substantial form in a composite, then parts of substances simply cannot themselves be substances and so the elements that compose the mixed bodies cannot be actual distinct substances. What features of Scotus’s version of the plurality thesis make it possible for Scotus to avoid this conclusion? In brief, Scotus rejects the view that the parts of substances can’t be substances. Scotus accounts for the unity of the substance in a different way: he believes that the integral parts of the substance such as the heart and the lungs are themselves distinct substances, which nevertheless form a genuine substantial unity insofar as these distinct substances are “essentially ordered” towards one another: i.e.

18

(Ward, forthcoming).

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the heart depends on the lungs and vice versa, even though the two are distinct substances.19 Yet though Scotus believes the integral parts of a substance are themselves substances, he nevertheless agrees with Aquinas that the elements that compose these integral parts are present in the mixed body only potentially or virtually.20 Ward argues Aquinas and Scotus reach this same conclusion for importantly different reasons. For Scotus, as Ward explains, The reason why the elements cannot together compose one substance is because the theory of the elements tells us that each kind of element has its proper sublunary place and the natural activity of each elemental substance is to reach its proper place. Any compound in which the elements actually exist, then, is susceptible to internal corruption as the elements attempt to move apart from each other and toward their natural places.

In other words, Scotus believes the elements in a mixed body are present only virtually because he happens to hold false scientific beliefs based in medieval chemistry and not because he is required to do so by the deep commitments of his hylomorphic mereology, unlike Aquinas. Hence, Ward continues, if we are required to say that the elements remain as actual parts of the mixed bodies, then Scotus’s view has the advantage over Aquinas’s insofar as contemporary hylomorphists can simply ignore Scotus’s false chemical beliefs and still endorse his metaphysical views, just as premise (3) says. But are there compelling reasons to think contemporary hylomorphists really must endorse the actual existence of the elements within mixed bodies, as (1) says? Ward, as far as I can see, simply assumes this is the case. However, this is simply to beg the question against Aquinas, who could make at least two cogent objections to Ward’s (1).

Two Replies on Behalf of the Thomist The first reason thing Aquinas could say is (1) is false because the unicity of substantial forms is a metaphysical thesis, not an empirical one. To 19

Cf. Scotus, Questiones super libros metaphysicorum Aristotelis VII, q. 20. See Ward’s very careful reconstruction of Scotus’s reasoning here in (Ward 2014, 98106). 20 Ordinatio II, d. 15.

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make the case for (1) Ward or other contemporary hylomorphists would have to detail exactly how the empirical discoveries of contemporary science are supposed to shed light on the metaphysical question of whether the carbon atom I exhale is numerically, as opposed to merely specifically identical with the carbon atom which was previously numbered among my parts. I presume Ward thinks the reason to believe (1) is that we are required to do so by our best science. But all the empirical sciences discover are the qualities and properties of things, not the identities and differences of substances and Aquinas has a story to tell which appears to explain why the carbon atom that was once a part of me and the carbon atom now in isolation have the same qualities. In other words, I cannot see how Ward can defend his premise (1) without begging the question against Aquinas. The second reason to be suspicious of Ward’s friendly amendments to Scotus’s theory of the elements is that it is not clear that Scotus’s version of the plurality thesis is clearly superior to the unicity view on other metaphysical grounds. In the first place, Scotus’s metaphysical principles entail the existence of spatially collocated objects, which Aquinas would find ridiculous and which seemed to make even Scotus himself a bit queasy. Co-incident entity theories come with their own sets of problems that proponents of this updated version of Scotism will have to solve. To name just one: what grounds the difference between the distinct, collocated entities, given that they are composed of the parts at the same times? The Scotist might take a page from Mark Johnston (2006) and argue hylomorphism can ground the distinctness of collocated objects just in the distinctness of their forms. But notice that taking this tack requires one to regard the forms as extrinsic to the parts they unify. On Johnston’s view, forms appear to become something very much like mere spatial configurations of parts, and thus it becomes unclear how such merely extrinsic principles could also play the role of coordinating the powers of the composite substance in the way hylomorphists had traditionally held. The upshot of this second response is that if medieval mereology really needs updating in the way Ward thinks, it is not obvious that the theory which obtains is really hylomorphism any longer. Hence any good argument for hylomorphism would be a good argument against the claim that we need to countenance the elements as actual parts in the mixed body.

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A second problem for Ward’s repristinated Scotism is how exactly to make sense of the notion that the integral parts of a composite substance are each independent substances with their own forms and identity conditions, and yet that these are “essentially ordered” to one another in the right way to yield a unified substance. To be a substance presumably is to be precisely the kind of thing that is not essentially dependent on the existence of anything else, yet these integral parts are ex hypothesi essentially dependent on one another. One can of course respond by tweaking the notion of substance and dependence to try to avoid the implicit contradiction; but then the reworked conceptions begin to appear ad hoc.

Concluding Unhistorical Postscript Where do these considerations leave us? Have the Thomist and the Scotist simply exchanged incredulous stares? Scotus can save the numerical identity of the accidental features in the living body and the corpse, but only at the cost of endorsing something that looks equally suspicious, a doctrine of co-incident entities. One might be tempted to say Aquinas has simply done the reverse: safeguarding the principle of one object to a place by sacrificing the identity of the accidents. However, this isn’t quite right. The proper analysis of the dialectical situation is that the Thomist holds a position which is not ruled out by the empirical data and has at hand arguments with which to push the Scotist towards an increasingly revisionary version of hylomorphism. I think this is the right strategy for the Thomist: to attempt to show that pluralist versions of hylomorphism, including Scotus’s, are unstable compromises with non-hylomorphic, atomistic views. Attempting to flesh out that case in greater detail goes beyond the scope of the present paper. All I have attempted to show above is that Aquinas’s view is not obviously crazy.

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References Adams, Marilyn McCord. 1996. “Scotus and Ockham on the Connection of the Virtues”. In John Duns Scotus: Metaphysics and Ethics, edited by L. Honnefelder, R. Wood, and M. Dreyer, 499-522. Brill. Aquinas, Thomas. 1888. Summa Theologiae. Sancti Thomae de Aquino Opera Omnia iussu Leonis XIII P. M. —. 1997. “On the Mixture of the Elements: To Master Philip of Castrocaeli,” edited by Paul Vincent Spade. —. Quaestiones Disputate De Anima. Aristotle. 1984a. Categories. In The Complete Works of Aristotle, edited by Jonathan Barnes. Vol II. Princeton University Press. —. 1984b. Metaphysics. In The Complete Works of Aristotle, edited by Jonathan Barnes. Vol II. Princeton University Press. —. 1984c. Physics. In The Complete Works of Aristotle, edited by Jonathan Barnes. Vol I. Princeton University Press. Arlig, Andrew. 2015. “Medieval Mereology”. In Stanford Encyclopedia of Philosophy. Avicenna. 2009. The Physics of the Healing: Books I and II, edited by Jon McGinnis. Brigham Young University Press. Cross, Richard. 1998. The Physics of Duns Scotus: The Scientific Context of a Theological Vision. Oxford University Press. Johnston, Mark. 2006. Hylomorphism. The Journal of Philosophy. 103 (12): 652-98. Pasnau, Robert. 2011. Metaphysical Themes: 1274-1671. Clarendon Press. Ward, Thomas M. Forthcoming. “Parts, Wholes, and The Elements in Some Medieval Philosophers.” In On What There Was: Conceptions of Being 500-1650 East and West, vol. 8. Brepols. —. 2014. John Duns Scotus on Parts, Wholes, and Hylomorphism. Brill.

MANY EXITS ON THE ROAD TO CORPUSCULARIANISM: A RESPONSE TO WILKINS THOMAS WARD

0. Introduction Wilkins argues that Aquinas’s view about elemental mixture is cogent and can even be maintained today, with modern chemistry’s very different understanding of the number and natures of the elements. Critics of Aquinas on this issue tend to assume that modern chemistry requires us to maintain that elements or various compounds (such as molecules) actually exist in the substances they make up, such as organisms. This assumption is incompatible with Aquinas’s unitarianism about substantial form. Since Aquinas holds that each material substance is composed of prime matter and exactly one substantial form, it follows that no material substance can have any material substances as parts. No one can gainsay this entailment, so defenders of Aquinas need to attack the modern assumption that empirical science requires us to hold that substances such as organisms can have substances such as atoms and molecules as actual parts. This is what Wilkins does. Wilkins begins by stating three assumptions shared by many medieval hylomorphists. He calls these assumptions desiderata which must be satisfied by any good theory of elemental mixture. Wilkins then addresses the dispute between unitarians and pluralists about substantial forms. He moves on to provide an account of Aquinas’s theory of the ontological status of the elements in a mixture, and argues that this theory both satisfies the three desiderata and is consistent with the claims of empirical science. He then considers my recent argument that Scotus’s version of pluralism about substantial forms is easier to adapt to modern science than Aquinas’ theory. He criticizes my argument.

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In the following I want to discuss Wilkins’ three desiderata, focusing on the third. Then I will raise some concerns about Aquinas’s theory of elemental mixture. Next, I will concede Wilkin’s claim that empirical science does not require us to reject unitarianism about substantial form, but I will argue that Wilkins main criticism of Scotus’s version of pluralism about substantial form – that it commits us to collocated substances, misses the mark. It does commit us to this, but this isn’t a problem.

1. The desiderata Here are three views Wilkins identifies as common to medieval hylomorphists, and in particular to Aquinas and Scotus. (1) Hylomorphism: Material substances such as Socrates as composed of matter and a substantial form. (2) Elemental Composition: Mixed bodies (including the material substances) are composed of elements. (3) Power Coordination: The substantial form of a substance conveys powers on the substance by ‘coordinating’ the powers of the elements out of which the substance is composed.

I want to raise a concern about the third desideratum, power coordination. It seems correct to me, as far as it goes, to say that a substantial form “conveys powers on the substance.” We might qualify this a bit though. Powers are both active and passive, but the passive powers of a substance are due in large part, if not exclusively, to matter, not substantial form. But my concern with this third desideratum is really about the second part. Wilkins says substantial form conveys power by coordinating powers of the elements out of which it is composed. The thing to note is that this can’t be the only way the substantial form conveys powers. After all, none of these thinkers would hold that for every material substance, all of its powers could be explained solely in terms of elemental powers and their coordination. To take an obvious case, human intellective power can’t be explained at all by elemental powers and their coordination. So at best Wilkin’s third desideratum describes just one of the ways in which medieval hylomorphists thought a substantial form conveys powers to its substance.

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2. Aquinas’s view of mixture Leaving this quibble aside, I’ll now move on to Wilkins’ account of Aquinas’s theory of elemental mixture. The basic idea is that when a material substance is produced by mixture of the elements, the original qualities of the elemental substances are brought into an intermediary state which disposes the elements to receive the new substantial form of the mixed body. At the moment the new substantial form begins to inhere in the prime matter of the elements, the elements themselves are corrupted and a new substance begins to exist. But somehow that intermediary quality which disposed the elements for receiving the new substantial form lingers in the new substance. This entitles us to say that there is a sense in which the elements themselves continue to exist in the new mixture, since something of their powers remains via that lingering intermediary quality. I’ve tended to read Aquinas here as claiming that numerically the same intermediary quality persists through the corruption of the elements and the generation of the new substance. On this reading, the big problem for Aquinas is that accidents in general and powers in particular can’t jump substances, as Aquinas elsewhere says.1 So he doesn’t seem entitled to claim that elemental qualities can jump elements and begin to be the qualities of new mixed substances. But on Wilkins’ reading numerically the same qualities do not persist through the corruption of the elements and the generation of the mixture. Instead, Wilkins thinks Aquinas thinks that some quality qualitatively similar to the quality of the elements begins to inhere in the new mixture, and it’s the qualitative similarity of the new to the old which is supposed to explain how the elements have existence by their powers in the new substance. So on Wilkins’ reading, Aquinas’s theory satisfies his three desiderata in the following ways: (i) (Hylomorphism) the substantial form of the whole is creating a genuine, novel unity, satisfying the hylomorphism principle, and (ii) (Elemental composition) there are elements composing the mixed bodies of material substances in the sense that the sole substantial form is conferring on prime matter the active and passive qualities of elements of those types, satisfying the elemental composition principle and (iii) (Powers coordination) yet those active and passive powers are as it were recruited into a new functional unity by the substantial form of the whole, satisfying the power coordination principle. 1

De generatione et corruption I.10.6.

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On this reading, the big problem for Aquinas would seem to be the lack of explanation of how the new substance comes to have this qualitatively similar quality. Can Wilkins offer on Aquinas’s behalf an account of how a brand new substance with brand new accidents is somehow guaranteed to have powers which are qualitatively similar to the powers of the elements from which the new substance came to be?

3. The updated Scotus? 3.1 Empirical science inconclusive Having raised this concern about Wilkins’ account of Aquinas’s theory, I’ll now turn to his formulation and criticism of an argument I implicitly made about the update-ability of Scotus’s theory of elemental mixture. Wilkins offers support to his case for Aquinas by formulating an argument implicit in something I wrote, and then arguing against the first premise of that argument. The argument Wilkins formulates goes like this (1) A hylomorphic theory of the elements in a material substance could be acceptable to a contemporary audience if and only if it is possible for the hylomorphic theory to be developed in such a way to treat the elements as actual parts. (Premise) (2) It is not possible for Aquinas’s hylomorphic theory to be developed in such a way to treat the elements as actual parts. (Premise) (3) But it is possible for Scotus’s hylomorphic theory to be developed in such a way to treat the elements as actual parts. (Premise) (4) Hence, Scotus’s hylomorphic theory could be acceptable to a contemporary audience, but Aquinas’s could not. (from 1-3)

And I accept this as a fair rendering of my line of reasoning. Wilkins concedes premises (2) and (3) but criticizes premise (1), for two different reasons. First, empirical science doesn’t strictly require that the elements remain actual in a mixture, so (1) is false. I concede this. I suppose I’d want to say something weaker, that all else being equal, better to have a theory of elemental composition which allows for the possibility of their actual

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existence in a mixture. If nothing else, this view has the advantage of tracking common sense and the way scientists often talk about how organisms work at the biochemical and chemical levels.

3.2. The issue of collocation But is all else equal? The second objection Wilkins has to (1) is that he’s not sure that pluralism of the sort Scotus endorses is coherent. According to Wilkins, Scotus’s pluralism entails collocated bodies, and Wilkins finds this problematic. The sort of collocation Wilkins seems to have in mind is the sort entailed by Scotus’s view that some integral parts of some substances are themselves substances. So, for example, let’s say that the heart of Socrates is a substance and Socrates is a substance. Socrates’ substantial form exists all throughout Socrates, so every part of Socrates is human. But the heart’s substantial form exists all throughout the heart. So it looks like there will be two collocated things: a heart, and a heart-of-a-living-human. Other versions of pluralism hold that the whole body is a substance, but the integral parts of a body are not themselves substances. (I call this standard pluralism.) On this view, the body will have one substantial form in virtue of which it is a body. But it will have another substantial form, in virtue of which it is a body of a human being. So it looks like there will be two collocated things: a body and a human being. The way to deal with the standard pluralist case points the way forward for dealing with the Scotist case. The standard pluralist has to say that the body is related to the form of the body and the form of a human being in two different ways. It is related to the form of the body as whole to part, since its two metaphysical constituents, prime matter and the form of the body, jointly compose the body. But it is related to the form of a human being as co-part of one whole, the human being, since the whole body functions as proximate matter which, with a human soul, composes a human being. Now for the more complicated Scotist case. On my view, Scotus denies that the whole body is a substance; instead it’s an essentially ordered network of integral parts, each of which is its own substance. All these parts together, related in a special way, serve as the proximate matter of a human being. So consider the heart. Assume for simplicity’s sake that it’s

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composed of prime matter and just one substantial form, the substantial form of the heart. The heart is related to its substantial form as whole to part, since its two metaphysical constituents, prime matter and the form of the heart, jointly compose the heart. The heart itself is related to the body as part to whole, since it is part of this essentially ordered network of organic parts. And this body is related to the human being as part to whole, since it is the proximate matter which, with a human soul, composes a human being. Not all parthood relations are transitive, but these are: the heart is a part of a human being by transitivity, since it is part of a body which is itself part of a human being. The basic move in either case is to say that careful pluralism about substantial form requires us to say that no two or more substantial forms are related to the same substance or the same part of a substance in exactly the same way, and similarly that no two or more substances are related to one and the same substantial form in exactly the same way. Wilkins worries that this way of explaining collocation requires us to say that substantial forms are merely extrinsic unifying principles of the substances of which they’re forms. But we must be careful here. The form of a heart is intrinsic to the heart, on Scotus’s view. The form of the body is intrinsic to the body, on the standard pluralist view. The form of a human being is intrinsic to a human being, on either pluralist view. But, no, the form of a human being is not intrinsic to the body, on the standard pluralist view, since the body is the matter of a human being. But this is exactly how a hylomorphic account of composition should turn out. (Consider, by analogy: on Aquinas’s view the form of a human is extrinsic to prime matter in the sense that it doesn’t help make up what prime matter is; instead, prime matter and form together are intrinsic principles of a human being.) Here’s a second way of responding to the collocation view. Isn’t it the case that Aquinas is committed to the collocation of substances and accidental unities? And isn’t the way to explain this simply that an accident is related to an accidental unity and a substance in different ways? It’s related to an accidental unity as part to whole, and it’s related to a substance as co-part of the same whole. So in the end I don’t think of Wilkins’ collocation objection as particularly worrisome or embarrassing. Even if you don’t like my way of making sense out of collocation, namely by distinguishing different ways in which

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forms are related to substances and substances related to forms, you still don’t get a strong reason to prefer Aquinas over Scotus and the pluralists, since Aquinas seems to have an analogous issue to deal with when it comes to the relation between substances and accidental unities. Now when it comes to elemental composition, Scotus denies that the elements actually exist in a mixture for reasons Wilkins discusses. I note that these reasons do not have to do with the metaphysics of hylomorphic composition but rather the old chemical theory itself. For this reason it’s possible that, given his metaphysics of hylomorphic composition, a different chemistry could have led Scotus to a different view about elemental existence in mixtures. If current science tells Scotus that there are actual atoms making up his body, Scotus would have no reason to object. So I don’t take collocation to be a reason for rejecting pluralism, and therefore don’t take it to have force against the first premise of the argument Wilkins formulated on my behalf.

4. Conclusion: is pluralism really hylomorphism? Nevertheless, I concede his first objection to this premise – namely, that empirical science doesn’t strictly require the abandonment of Unitarianism – and so I join Wilkins in rejecting premise (1) as formulated. Since empirical science can’t settle the issue for us, strictly speaking, it comes down to a kind of contest about relative metaphysical “costs” associated with either the Thomistic unitarian view or the Scotistic pluralist view. The superficial way to weigh these costs, according to Wilkins, is to say that on the one hand Scotus commits us to collocated bodies whereas on the other hand Aquinas commits us to weird views about things that look continuous through time and change actually turning out to be two or more different things (recall his formulation of the Corpse objection). Wilkins seems to concede that it would be hard to decide which is the heavier cost. The deeper problem for Wilkins is that he thinks pluralism is an unstable compromise with corpuscularianism. The suggestion here, I take it, is that pluralism in its logical extreme is not a version of hylomorphism worthy of the name. The worry here seems to be rooted in the traditional unitarian

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concern that pluralists can’t adequately account for the unity of material substances, and perhaps also the very closely related concern that pluralists can’t account for the irreducibility of material substances to the parts they’re made of. The reason to consider corpuscularianism a byword is, I take it, that it seems to imply that all there is to a substance is a bunch of corpuscles in close proximity to each other, moving more or less together. Hylomorphism is supposed to save us from that kind of reductionism. In some sense Wilkins’s closing point here is incontrovertible. Pluralism is more like corpuscularianism than unitarianism, at the very least in the sense that by definition it entertains more actual parts making up a substance than does unitarianism. In a second sense I think there is a promising historical case to be made that pluralism together with rejections of the Thomistic understanding of prime matter as pure potentiality somehow paved part of what became the way to early modern theories of bodies. But in a strictly philosophical sense I think Wilkins’s concern is overblown. First, Scotus is as explicitly anti-reductionist as they come; moreover, he explicitly addresses the issue of the unity of a pluriformed substance, taking the preservation of unity as a feature his theory of hylomorphism must have if it is to be viable. Second, there’s a Whiggish danger in attributing to Scotus the seeds growing into, or pavers leading the way to, later philosophical views (pick your favorite metaphor). If I take a step toward the edge of a cliff it doesn’t follow that I’ll keep walking until I fall off. If I go on to walk off the cliff then it will be true that that first step was the first step in my walk of doom. But I don’t need to keep walking. I might have very good reasons for taking that step – and equally good reasons for taking no more steps. If Scotus takes us a step toward corpuscularianism, it’s our fault if we keep walking after he stopped.

BOETHIUS OF DACIA ON THE DIFFERENTIAE AND THE UNITY OF DEFINITIONS RODRIGO GUERIZOLI

It is notoriously difficult to draw a comprehensible picture of the Aristotelian notion of differentia. As a matter of fact, on that concept Aristotle seems to say “everything and the contrary of everything”.1 For instance, in Topics VI.1, Aristotle affirms that whoever defines “should first place the object in its genus, and then append its differences”.2 He thus appears to admit that expressions which follow the pattern GD1D2D3…Dn, where G stands for a genus and D1, D2 etc. stand for differentiae, may be considered, at least from a formal point of view, to be well-constructed definitions (or, rather, we would say, well-constructed definientia). Let us call this the thesis of the plurality of differentiae. Yet, there is another issue at stake in the passage. Aristotle also suggests that there is an order among the components of the definitions. The genus comes first, and then the differentiae appear. Why this order? According to the text, the arrangement is justified because “the genus seems to be the principal mark of the substance of what is defined”.3 This remark may be fleshed out with other passages from the Topics. In I.5, Aristotle holds that “a genus is what is predicated in what a thing is of a number of things exhibiting differences in kind”,4 and in IV.2 he maintains that “a thing’s differentia never signifies what it is, but rather some quality, as do walking and biped”.5 Thus, the priority of the genus, certainly a logical priority and

1

M. Mariani, “Aristotele e la differenza”, in A. Fabris, G. Fioravanti and E. Moriconi (eds.), Logica e teologia. Studi in onore di Vittorio Sainati, Pisa: ETS, 1997, 3-21 (here 3). 2 Aristotle, Topics, VI.1, 139a28-29. I use W. A. Pickard-Cambridge’s translation, published in The Complete Works of Aristotle. The Revised Oxford Translation, J. Barnes (ed.), Princeton, NJ: Princeton University Press, 1984. 3 Aristotle, Topics, VI.1, 139a29-31. 4 Aristotle, Topics, I.5, 102a31-32. 5 Aristotle, Topics, IV.2, 122b16-17.

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Boethius of Dacia on the Differentiae and the Unity of Definitions

perhaps also a chronological one,6 results from the fact that for every definition the genus alone indicates the “what-it-is” (ti esti) of the definiendum at stake. Let us call this the thesis of the priority of the genus. Although these theses seem like they straightforwardly arise from these texts, both face harsh criticism from Aristotle himself in the Posterior Analytics, in the Metaphysics, and also, to the interpreter’s great sorrow, in the Topics itself.7 The most drastic revision of the theses of the plurality of differentiae and the priority of the genus is to be found in Metaphysics VII.12, although, again, it might be objected that the lesson of this chapter does not correspond to Aristotle’s final word.8 Be that as it may, it is useful to refer to that text insofar as it combines his reflection on the complexity of definitions with an account of how definitions relate to the hylomorphicmereological structure of sensible substances. In Metaphysics VII.12 Aristotle aims to solve a puzzle regarding the capacity of definitions to indicate intrinsically unified things. For, on the one hand, definitions are expected to signify sensible substances, i.e., complex hylomorphic compounds possessing intrinsic unity; yet, on the other hand, insofar as they are expressions composed of significative parts, definitions seem to indicate nothing but the conjunction of what is signified by each of their parts. It is doubtful, however, that such a signification by conjunction could grasp the characteristic non-accidental unity of sensible substances. In order to guarantee that definitions have such a capability, Aristotle endorses an eliminativist approach in Metaphysics VII.12. Definitions, he argues, are complex expressions just syntactically, for their semantic content is sufficiently expressed by that one term that is called the “last differentia”, which sufficiently signifies the “substance and the definition of the object”.9 One could hardly be further from the lesson taught in the 6

See L. Gili, “Saggio di commento al libro Z”, in L. Gili, I Topici di Aristotele. Libri Z-H: la definizione, Roma: Aracne, 2010, 83-114 (here 86), and, from a biological perspective, Aristotle, Generation of Animals, II.3, 736b2ss. 7 For a detailed study of these tensions see L. Angioni, “Defining Topics in Aristotle’s Topics VI”, in Philósophos 19 (2014), 151-193. 8 See A. Code, “An Aristotelian puzzle about definition: Metaphysics Z.12”, in J. G. Lennox and R. Bolton (eds.), Being, Nature, and Life in Aristotle. Essays in Honor of Allan Gotthelf, Cambridge: Cambridge University Press, 2010, 78-96 (here 91). 9 Aristotle, Metaphysics, VII.12, 1038a25-6. I use D. Bostock’s translation, published in Aristotle, Metaphysics. Books Z and H, Oxford: Clarendon Press, 1994.

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Topics VI, for the thesis of Metaphysics VII.12 of the sufficiency of the final differentia is clearly incompatible with both the idea of the plurality of differentiae and the idea of the priority of the genus. Medieval commentators were conscious of the difficulties surrounding Aristotle’s theory of definition and the role it reserves for the notion of differentia. In particular, they were aware that, if taken at face value, some theses from Topics VI diverge from teachings expressed in Metaphysics VII. In what follows I present an analysis of how Boethius of Dacia, who was “among the most prominent of those arts masters whom Étienne Tempier (…) accused of overstepping the limits of their faculty”,10 understood, in his reception of Aristotle, the relation between the complexity of definitions, the notion of differentia, and the intrinsic unity of sensible substances. Regrettably, no commentary on the Metaphysics written by Boethius has come to us, although self-citations in the works we possess attest the composition of such a text. Additionally, the questions on the Metaphysics published in the Corpus Philosophorum Danicorum Medii Aevi, which made use of Boethius’s lost commentary, are of little help here, for the last problem they discuss – “whether the compound is a substance” – refers to a passage of VII.3. We are thus left with Boethius’s commentary on the Topics, a text written between 1270 and 1280 in a form that combines literal exposition with fairly autonomous question-form studies of several systematic aspects of Aristotle’s work.11 My hypothesis is that through the analysis of some questions Boethius discusses in his commentary on the Topics, we can reconstruct both the general lines of his thought on definitions and his precise view on the three aforementioned theses. At the base of Boethius’s account of definition lies his strongly realist description of the relations between world, thought, and language. Being one of the earliest modistae, Boethius argues for a causal connection between the ways things are and our thoughts about them, and, further, between the ways we think about things and the grammar we use to express these concepts. He also contends that the different kinds of concepts we have, which shape a grammatical system governing all 10

R. Wielockx, “Introduction”, in Boethii Daci Quaestiones super librum De anima I-II, R. Wielockx (ed.), Hauniae: Librarium Universitatis Austro-Danicae, 2009 (Corpus Philosophorum Danicorum Medii Aevi XIV), 11-113 (here 12). 11 See N. J. Green-Pedersen, “Introduction”, in Boethii Daci opera. Topica – Opuscula, N. J. Green-Pedersen et al. (eds.), Hauniae: G. E. C. Gad, 1976 (Corpus Philosophorum Danicorum Medii Aevi VI.1), VII-XL (here XXVIs.).

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languages, are due directly to differences between existing things and the relations that hold amongst them.12 Thus, different modes of being (modi essendi) determine different modes of understanding (modi intelligendi), which in turn determine different modes of signifying (modi significandi). In this context, the first difference within the modes of being occurs between substances and accidents. Substances are seen as beings that possess determination and actuality in such a way that they can underlie other beings but cannot inhere in anything.13 The first feature distinguishes substances from matter, for matter has no actuality per se; the second differentiates them from accidents, whose mode of being requires the ability to inhere in something else.14 It is from this extramental substanceaccident distinction that the mental and linguistic notions of subject and predicate derive. It is worth noting that this entails neither that subjectterms necessarily signify substances, nor that predicate-terms refer only to accidents. Rather, it merely means that regardless of what a predicate-term signifies, it is always implied by that signification that the item signified somehow belongs to what is referred to by the subject-term. And the same holds, mutatis mutandis, for the subject-term. Further, Boethius affirms that every mental or spoken proposition contains either a term predicated of the substance of the thing signified by the subject-term – and I call that thing the subiectum – or a term predicated of some accidental feature of it. Moreover, predicate-terms may signify accidental features of the subiectum that are caused by the subiectum itself and that are convertible with it. A term of this kind is a proprium. But predicate-terms may also signify accidental features of the subiectum, caused either by the subiectum itself or by something external to it, which 12

See J. Pinborg, Die Entwicklung der Sprachtheorie im Mittelalter, Münster, Aschendorff, 1967; G. L. Bursill-Hall, Speculative Grammars of the Middle Ages. The Doctrine of the partes orationis of the Modistae, The Hague: Mouton, 1971; and I. Rosier, La grammaire spéculative des Modistes, Paris: PUF, 1983. 13 Boethius of Dacia, Quaestiones super librum Topicorum (hereafter QT), in Boethii Daci opera. Topica – Opuscula, op. cit., prooem., 5, ll. 61-64: “Quia enim, quod demonstratur, eius inhaerentia respectu alicuius subiecti ostenditur per causam alteram ab utroque, substantia autem non est in subiecto, ut docetur libro Praedicamentorum, ideo substantia non est demonstrabilis (...).” 14 Boethius of Dacia, QT, III q. 2, 170, ll. 30-34: “(...) substantia, quae dicitur eo quod substat accidentibus, solum est substantia in actu, et hoc modo materia non est maxime substantia. Cui enim inest accidens, hoc est aliquid, ut dictum est, et materia secundum se non est aliquid in actu.”, and II q. 12, 135, ll. 13-14: “Iuxta quod intellegendum quod accidentia ex suo inesse habent esse, et si insunt simpliciter, tunc sunt simpliciter et denominant simpliciter.”

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are not convertible with it. A term of this kind is an accident. Additionally, predicate-terms may signify the substance of the subiectum in an implicit or indeterminate way. A term of this kind is said to be a genus. And, finally, predicate-terms may signify the substance of the subiectum in an explicit and determinate way. A term of this kind, which differs from the others by being complex, is a definition. According to Boethius, this list of predicates is exhaustive,15 for, on the one hand, nothing more is to be found in a subiectum than a certain composition of substance and accidental features, and, on the other hand, the distinctions available to the intellect mirror the different modes of being, namely, to be a substance in a determinate, specific manner, to be a substance in an indeterminate, generic manner, to be an accidental feature not convertible with its subiectum, and, finally, to be an accidental feature convertible with its subiectum.16 Definitions are, thus, certain basic elements from which propositions are built. They are complex predicate-terms that signify the substance of the things signified by subject-terms in an explicit and determinate manner, and they arise directly on the basis of certain components of the world, namely, the substances themselves and their ontological aspect of being something determinate, i.e., of being hoc aliquid. The most manifest feature that a definition possesses in comparison to the remaining predicates pertains to its complexity. Definitions are said to have parts that are significative by themselves. Even though it might be eventually demonstrated that from the semantic point of view such a complexity is merely apparent, as Metaphysics VII.12 seems to suggest, it is from the analysis of that feature that Boethius begins his account of definition. The complexity of definitions, he claims, results from the task 15

For the use in this context of “predicate” (praedicatum) instead of the nowadays more usual “predicable” (praedicabile) see N. J. Green-Pedersen, “On the interpretation of Aristotle’s Topics in the 13th century”, in Cahiers de l’Institut du Moyen Age Grec et Latin 9 (1973), 1-46 (esp. 9-11). 16 Boethius of Dacia, QT, I q. 23, 63, ll. 24-34: “(...) omne quod de subiecto praedicatur, aut praedicat substantiam subiecti explicite sicut definitio aut implicite sicut genus – genus enim totam substantiam speciei significat, licet indeterminate et ideo implicite – aut praedicat aliquam dispositionem accidentalem subiecti quae habet causam propriam et convertibilem in subiecto, et sic est proprium, aut dispositionem accidentalem, quae non habet causam convertibilem cum subiecto, et sic est praedicatum accidentis. Et quia plura non inveniuntur in aliquo subiecto, ideo intellectus plura praedicata distinguere non potest, cum intellectus in intelligendo sequitur modos rerum in essendo.”

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they are meant to fulfill; that is to say, such complexity stems from the belief that with a definition one reaches “the most perfect cognition of a thing one may possess regarding its substance”.17 Because they are thought to comprise the maxima cognitio rei, definitions must grasp their definienda not only according to the intellectual content peculiar to each one of them, but they must also capture the intellectual content every definiendum shares with other, similar things. In order to perform such a task, definitions must accommodate different modes of signification of the same thing, so that they need to assemble different kinds of terms. On the one hand, a generic term, the genus, shall be placed in order for the definition to signify what the definiendum has in common with certain other things. On the other hand, one specifying term, a differentia, shall be mentioned for the definition to be capable of signifying the distinctive feature of the definiendum.18 Thus, definitions combine unity of reference and complexity of signification in order to grasp the substance of the things defined. They show complexity insofar as they are mereological wholes, whose parts, genus and differentia, are significative according to distinct intellectual contents, and they exhibit at the same time unity insofar as their parts refer to one and the same thing, i.e., to the definiendum as a whole. The general idea that definitions transmit the “perfect cognition of a thing according to its substance”19 guides Boethius in his answer to the thesis of the sufficiency of the final differentia that, one might argue, Aristotle defends in Metaphysics VII.12. The problem is explicitly treated in the Topics commentary, and a negative answer to the question of “whether the differentia is the sufficient definition of a thing” is provided. Boethius justifies his position by pointing out that, as a matter of fact, the differentia indicates the whole substance of the species to which the definiendum belongs, and that it does this “according to a proper and determinate 17

Boethius of Dacia, QT, VI q. 1, 271, ll. 19-27: “Dicendum, quod definitio est maxima cognitio, quae potest haberi de re quantum ad eius substantiam, et ideo debet notificare rem ipsam et quantum ad propriam rationem speciei, et hoc fit per differentiam, et etiam quantum ad rationem generalem, quod fit per ipsum genus. Ista autem partes, etsi sint unum in substantia, plures tamen sunt in ratione. Non enim sufficit cognoscere speciem secundum suam propriam rationem, sed oportet ipsam cognoscere secundum rationem communem, qua etiam convenit cum aliis, et haec ratio nomine generis importatur.” 18 Ibid. 19 Boethius of Dacia, QT, VI q. 13, 293, ll. 17-18: “Definitio enim est rei quantum ad suam substantiam perfecta cognitio.”

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intellectual content, i.e., according to an intellectual content which derives from the proper act of the substance of the thing defined”.20 Nevertheless, he adds, the differentia does not transmit the most perfect cognition one may obtain of a thing, for to the cognition transmitted by the differentia one might always add the knowledge of the same thing in accordance with the intellectual content obtained from what it has in common with other things belonging to further species of the same genus. Thus, in order for us to obtain the perfect cognition a thing, we require both the indeterminate and the determinate cognition of it, that is, we shall grasp it through both its genus and its differentia.21 In Metaphysics VII.12 the thesis of the sufficiency of the final differentia appeared to be motivated by the need to justify how, despite having parts, definitions may indicate intrinsic, as opposed to accidental, unities. The proposed solution, at least on one reading, consisted in restricting the semantic weight of definitions to their final differentiae. In the background of this suggestion lay the belief that to allow a distinction in terms of signification between the elements of the definitions amounts to accepting that definitions signify, as a whole, nothing but the actual, yet nonintrinsic, conjunction of diverse things. Such an opinion might even be endorsed. Indeed, defenders of the idea that material beings keep their unity despite their having different substantial forms may accept that, for instance, in the definition of humans, the genus signifies their sensitive souls while the differentia signifies their intellectual souls. But Boethius is a unitarian when it comes to the constitution of material things.22 According to him, to each concrete thing there corresponds only one substantial form. Otherwise, he believes, we are left with an insurmountable

20 Boethius of Dacia, QT, VI q. 16, 297-298, ll. 1-24: “Deinde quaeritur, utrum differentia sit sufficiens definitio rei. (...) Dicendum quod licet differentia totam substantiam speciei dicat, tamen genus debet poni in definitione rei, licet eandem substantiam importet, alio tamen modo. Genus enim substantiam rei importat indeterminate, hoc est sub ratione accepta ab actu in quo convenit substantia speciei cum aliis speciebus eiusdem generis, differentia autem eandem substantiam importat sub ratione propria et determinata, hoc est sub ratione accepta ab actu proprio substantiae definiti. Et quia magis cognoscit substantiam speciei, qui cognoscit eam sub ratione propria et communi, quam qui sub altero istorum modorum tantum, ideo oportet genus et differentiarm in definitione poni, nec sufficit per se alterum istorum.” 21 Ibid. 22 See J. Pinborg, “Zur Philosophie des Boethius de Dacia. Ein Überblick”, in Studia Mediewistyczne 15 (1974), 165-185 (here 167).

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paradox in terms of unity.23 It may appear, thus, somewhat surprising that he does not agree with the thesis of the sufficiency of the final differentia, for it seems to represent the most straightforward option available to a unitarian. Indeed, it is easy to claim that definitions signify intrinsic unities when there is just one element in them that is semantically relevant. But this view clashes with Boethius’s assertion that the cognition provided by definitions is complex and must refer to their definienda according to both what is proper to them and what they have in common with other things. Thus, he needs to find a third option, a way in which the genus plays a meaningful semantic role without compromising the ability of definitions to refer to intrinsic unities. His suggestion relies on the distinction between what a concept refers to (res significata) and the intellectual aspect according to which that reference is made (modus significandi). On that basis, he allows for concepts that refer to the same thing from different intellectual points of view. Genus and differentia follow exactly this pattern. They refer differently to the same thing, so that both remain semantically relevant without introducing any plurality with regard to the reference of the definition as a whole. Once the importance of the genus as an ineliminable element of definitions is assured, we may consider Boethius’s reaction to the thesis of the priority of the genus. He, again, explicitly discusses the question, and the way his commentary is constructed suggests that he accepts such a view. Indeed, the formulation of the question as to “whether among the elements placed in a definition the genus signifies more the substance of the definiendum” is immediately followed by three arguments quod non, and a reference to what Aristotle says in Topics VI defending that position. In the context of a typical scholastic text, this suggests that the author’s answer to the question at stake is affirmative. Nonetheless, I want to argue that Boethius does not commit to that thesis in any relevant sense. Admittedly, he accepts that the manner in which a genus is predicated differs from the modus praedicandi of a differentia. The genus is predicated according to a mode of signification that derives from the mode of being of substances; the differentia, in turn, is said according to a mode of being proper to what inheres in substances. In other words, while the genus signifies a quid per modum quid, the differentia signifies a quid per modum quale. On that basis, he adds, the genus is said to signify more the substance of the definiendum than the differentia. But, as a matter of fact, Boethius does not infer from this any full-fledged superiority of the genus 23

See Boethius of Dacia, QT, II q. 19, 145-146, ll. 18-22.

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over the differentia. Instead, he insists that the genus does not signify the substance of the definiendum in any more complete or more explicit manner than the differentia.24 On the contrary, he claims that the differentia signifies the definiendum in a more determinate way than the genus. As such, Boethius’s position reveals a strong commitment to the existence of a fine balance of the tasks performed by the elements of the definitions. If it is true that the modus praedicandi of the differentia is not as primitive as the mode of signification of the genus, this is somehow compensated for by the fact that the former signifies the definiendum in a more precise way than the latter. This justifies my claim that, despite the disposition of his text, Boethius’s account of definitions does not endorse the thesis of the priority of the genus in any relevant sense, i.e., in a sense in which the information transmitted by the genus would reveal more of the nature of the definiendum than what is indicated by the differentia. Finally, we may reconstruct Boethius’s position with respect to the thesis of the plurality of differentiae from further questions raised in his Topics commentary. In two of them, an interpretation of Porphyry’s definition of man as a “mortal rational animal” is provided. This definition seems to validate the idea of a plurality of differentiae, for it appears to be the consequence of the opinion that the genus “animal” might be specified through the convergence of two differentiae, neither of them able to sufficiently distinguish a certain definiendum from other things. Indeed, many things that belong to different species are mortal, and, likewise, both the men and the gods are, according to Porphyry, rational. Nonetheless, men alone are both mortal and rational, so that only by the conjunction of these differentiae can they be signified in what is exclusive to them.25 24

Boethius of Dacia, QT, VI q. 3, 273-275, ll. 1-39: “(...) utrum inter illa, quae ponuntur in definitione, genus significet maxime substantiam definiti. Et videtur quod non: (...) Contrarium: (...) Dicendum quod genus non magis complete nec magis expresse definiti substantiam significat quam differentia, sed quia significat ipsam per modum significandi, quo dicit quid definiti, secundum quem sibi competit modus praedicandi in quid de definito, talis autem modus praedicandi est substantiae in comparatione ad illud, cuius est substantia. (...) Differentia autem licet eandem significat substantiam, illum tamen modum significandi non habet nec illum modum praedicandi per consequens; ideo licet substantia, significet, non tamen per modum substantiae, et significat quid per modum qualis. Et haec est causa, quare genus dicitur significare substantiam definiti magis quam differentia.” 25 See Porphyry, Introduction 3.12, transl. J Barnes, Oxford: Clarendon Press, 2003, 11: “(...) a difference is that by which each type of thing differs. For man and horse do not differ in virtue of their genus – both we and the non-rational items are

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Boethius does not share this point of view. Admittedly, he acknowledges that in everyday life we propose and accept expressions composed of a plurality of differentiae as definitions. There are some simple factors that explain why this is so. It may occur, he argues, that we need to employ two words to refer to just one thing. In this case, the plurality of differentiae is nothing but a syntactic incident, without any semantic consequence. Or, perhaps, we do not know exactly what the specific differentia of a thing is; so that the conjunction of non-specific differentiae remains the only way that we have to refer to it. We would agree, however, that in such situations we possess no definition, strictly speaking.26 Finally, we may superfluously add a non-specific differentia to a specific differentia. The result would be an expression which indicates the substance of the definiendum, but which, due to its superfluous element, could not be considered a good definition. Coming back to Porphyry’s definition of man, it must be considered, according to Boethius, a case of an ill-constructed definition. On the one hand, “mortal”, he claims, is not a specific difference of man, but is, rather, a common affection caused by the fact that men are corporeal things.27 On the other hand, contrary to Porphyry’s claim, “rational” does indeed refer to a specific differentia of man, and the fact that we apply the term to other things, whether gods or angels, is sufficiently explained as a case of mere equivocity.28 Boethius’s criticism of Porphyry’s definition of man, and of other kinds of expressions composed of a plurality of differentiae, stems from his repeatedly stated conviction that a definition must communicate both what is proper to the definiendum and what it has in common with other things. From the fact that definitions are bound to perform the former task, he derives, ultimately, that, for every definition, some differentia must be mortal animals. But when rational is added it sets us apart from them. And both we and gods are rational. But when mortal is added it sets us apart from them.” 26 Boethius of Dacia, QT, VI q. 17, 299, ll. 22-26: “(...) quotienscumque in definitione alicuius speciei ponuntur plures differentiae formales, nulla illarum est differentia illius speciei, sed omnes ponuntur loco differentiae illius speciei, quae differentia est incognita vel forte non uno nomine significata.” 27 Boethius of Dacia, QT, VI q. 6, 280, ll. 16-20: “(...) si dicatur: ‘homo est animal rationale mortale’, loco unius ponuntur istae duae differentiae. Mortale enim per se non est differentia hominis, substantia enim hominis non complet, sed est passio causata ex contrariis, ex quibus corpus componitur.” 28 Boethius of Dacia, QT, VI q. 17, 299, ll. 31-32: “(...) si dicatur, quod rationale, quod est differentia hominis, convenit angelis, hoc est aequivoce.”

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convertible with its definiendum,29 so that the addition of any further differentia will result in a bad, superfluous definition. This claim is problematic, however. First, why cannot we consider the specific differentia as a second-order concept, i.e., as the conjunction of several non-specific differentiae? This seems to be the rationale behind Porphyry’s definition of man. But when that claim is rejected with the assertion that, as a matter of fact, “rational” is a specific, i.e., convertible differentia of “man”, the point is simply missed. Furthermore, let it be assumed that there are differentiae that are truly convertible with the species they are said of. Why would this mean that just one of such differentiae corresponds to each species? If there is more than one, however, an expression combining two specific differentiae could be coined, and the result would not be a bad definition, at least not according to the same criteria used to criticize Porphyry’s definition of man. Be that as it may, or, rather, problematic though it may be, it seems clear that Boethius does not assume the thesis of the plurality of differentiae as a constitutive part of his theory of definition. Let us recapitulate the general path of this investigation. I began by presenting three theses on definitions that one might formulate on the basis of different passages from Aristotle. The theses were the plurality of differentiae, the priority of the genus, and the sufficiency of the final differentia. The last thesis, which seems to provide a clear solution to a puzzle that definitions need to resolve with regard to their capacity to indicate intrinsically unified things, is clearly incompatible with the others, which are, in turn, compatible with one another. I then analyzed how Boethius of Dacia reacts to these theses from the point of view of some questions in his commentary on the Topics. Interestingly, he rejects all of them, and he outlines what we could call a strongly egalitarian view of the roles played by the elements of definitions. In well-constructed definitions, he claims, to one genus always corresponds one differentia; hence his dissatisfaction with the first and the third theses. Furthermore, the task that both elements perform is equally important for the definition as a whole to communicate that “most perfect cognition of a thing one may possess regarding its substance” that Boethius requires it to present. Thus, the second thesis is to be rejected. However, the problem of how an authentically complex expression can indicate intrinsic unities might still 29

Boethius of Dacia, QT, VI q. 17, 299, ll. 16-20: “Differentia enim debet speciem ab omnibus aliis distinguere. Quod autem speciem ab omnibus aliis distinguit, hoc proprium est speciei, quia quod commune est, hoc ab aliis non distinguit, et ideo oportet differentiam propriam esse speciei.”

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remain. The distinction between what is referred to by a concept and the intellectual aspect under which such a reference is made affords Boethius the opportunity to address that difficulty, for, as a matter of fact, he claims, it is exactly the same item that is referred to, under different intellectual aspects, by both elements of the definitions. There is, thus, no reason to think that the unity of the objects referred to by definitions is in danger. I conclude with two remarks, one historical, and one systematic. The historical remark refers to the relation between Boethius of Dacia and Thomas Aquinas. Much has been written about it, especially in connection with the condemnation of 1277, the problem of the eternity of the world, the relation between theology and philosophy, and the value of the philosophical life. Frequently the differences between Boethius and Thomas have been highlighted, and for ostensibly good reasons.30 When it comes to a theory of definition, however, the authors seem to largely agree. Indeed, any reader of the De ente et essentia will find herself fairly at home when confronted with Boethius’s commentary on the Topics.31 As a matter of fact, it is hard to find an issue on which they manifestly diverge. The systematic remark I would like to make concerns, in turn, Boethius’s rejection of the thesis of the plurality of differentiae. This seems to be the weakest aspect of his account of definitions, for his arguments fail to undermine quite reasonable views on the issue. And, actually, the bedrock of his opinion – namely, that to every definiendum there must correspond only one specific differentia – consists, I suggest, in a bold metaphysical conviction that is presented, however, in a slightly different context. The question in which it appears asks whether there can be different definitions of the same thing, and it is enough to say that Boethius defends the view that for each thing there is just one true and perfect definition. Peculiarly, this particular claim is justified by means of a general principle, namely, that “in every genus, there is only one that is

30

See H. Roos, “Der Unterschied zwischen Metaphysik und Einzelwissenschaft nach Boethius von Dazien” in P. Wilpert (ed.), Universalismus und Partikularismus im Mittelalter, Berlin: De Gruyter, 1968, 105-120 (here 115); J. H. J. Schneider, “The Eternity of the World. Thomas Aquinas and Boethius of Dacia” in Archives d’histoire doctrinale et littéraire du Moyen Âge 66 (1999), 121-141; Thomas d’Aquin et la controverse sur L’Éternité du monde, C. Michon (ed.), Paris: Flammarion, 2004; Thomas d’Aquin/Boèce de Dacie, Sur le bonheur, R. Imbach/I. Fouche (eds.), Paris: Vrin, 2005. 31 See J. Bobik, Aquinas on Being and Essence. A Translation and Interpretation, Notre Dame, IN: Notre Dame University Press, 1965.

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perfect”.32 If this principle is true, as Boethius believes it is, and if we allow a less technical reading of the term genus in this instance, then it could also be applied to the context of the supposed multiplicity of differentiae belonging to the same species. The result would be that for each species there would be just one most perfect differentia, i.e., just one truly specific differentia. I think that herein lies the deeper foundation of Boethius’s rejection of the thesis of the plurality of differentiae, although it is worth repeating that he does not make this derivation explicit. The problem, however, is that a principle like that may be anything but indisputable.33

32

Boethius of Dacia, QT, VI q. 13, 292, ll. 18-20: “In unoquoque autem genere quod perfectum est tantum unum est.” 33 This work was supported by the Alexander von Humboldt Stiftung, the Brazilian Coordination for the Improvement of Higher Education Personnel, the Brazilian National Council for Scientific and Technological Development, and the Rio de Janeiro Research Foundation. I am grateful to these institutions and to the staff of the Thomas-Institut at the University of Cologne, where the research was conducted.

WHAT HAS AQUINAS GOT AGAINST PLATONIC FORMS? TURNER C. NEVITT

The Platonic elements of Aquinas’s metaphysical thought are now widely recognized.1 These elements are perhaps on clearest display in Aquinas’s account of the existence and nature of God and creatures, which he explains in fundamentally Platonic terms of participation and divine ideas.2 God is being itself subsisting, and creatures exist to the extent that they participate in being. God’s mind contains the ideas of each creature, 1

The seminal work on this topic was of course that of Fabro and Geiger. See Cornelio Fabro, La Nozione Metafisica di Partecipazione Secondo S. Tommaso d’Aquino, 2nd ed. (Turin: Società editrice internazionale, 1950), Cornelio Fabro, Participation et Causalité Selon S. Thomas D’Aquin (Leuven: Publications Universitaíres de Louvain, 1961), and L.-B. Geiger, La Participation dans la Philosophie de S. Thomas d’Aquin (Paris: Vrin, 1942). Other early work includes Arthur Little, The Platonic Heritage of Thomism (Dublin: Golden Eagle Books, 1950) and Robert J. Henle, Saint Thomas and Platonism (The Hague: Martinus Nijhoff, 1956). Norris Clarke’s critical reviews of both books are worth mentioning here (along with his own work on the topic). See W. Norris Clarke, “Review of Arthur Little, The Platonic Heritage of Thomism,” Review of Metaphysics 8 (1954): 105-124 and “Review of Robert J. Henle, Saint Thomas and Platonism,” Thought 32 (1957): 437-443. For more recent work on the topic see, for example, Fran O’Rourke, Pseudo-Dionysius and the Metaphysics of Aquinas (Leiden: Brill, 1992) and Rudi te Velde, Participation and Substantiality in Thomas Aquinas (Leiden: Brill, 1995). For shorter introductions to the topic see Wayne J. Hankey, “Aquinas and the Platonists,” in The Platonic Tradition in the Middle Ages: A Doxographic Approach, edited by Stephen Gersh and Maarten Hoenen (Berlin: Walter de Gruyter, 2002), pp. 279-324 and Fran O’Rourke, “Aquinas and Platonism,” in Contemplating Aquinas: On the Varieties of Interpretation, edited by Fergus Kerr (Notre Dame: University of Notre Dame Press, 2003), pp. 247-279. 2 In addition to the work already mentioned, see especially Wayne J. Hankey, God in Himself: Aquinas’s Doctrine of God as Expounded in the Summa Theologiae (Oxford: Oxford University Press, 1987) and Vivian Boland, Ideas in God According to Saint Thomas Aquinas: Sources and Synthesis (Leiden: Brill, 1996).

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and creatures are what they are insofar as they reflect God’s ideas of them. Even such cursory statements of Aquinas’s metaphysical views are recognizably Platonic. But of course everyone also recognizes that Aquinas roundly rejects Plato’s theory of separate forms or ideas. Throughout his career Aquinas consistently follows Aristotle in criticizing Plato and his followers for their commitment to the existence of separately subsisting forms.3 There is no whiteness existing in itself apart from any particular white things or any particular person’s thoughts about them. And the same goes for every other natural form, from humanity to heat. To suppose that such forms subsist separately in themselves is contrary to reason, to the truth, and even to the faith, Aquinas says.4 And yet Aquinas is happy to appeal to Platonic forms as examples to illustrate his own metaphysical views. In the De ente et essentia, for instance, Aquinas argues that there could only be at most one thing whose essence is existence itself subsisting, which he goes on to identify as God. To illustrate his point Aquinas compares subsistent existence to a separate heat, which he claims would also have to be unique if it existed.5 In the Summa theologiae Aquinas makes a similar point about angels, arguing that there could only be one angel in each angelic species given that angels are subsisting forms. To illustrate his point Aquinas compares an angel to a separate whiteness or humanity, which he claims would also have to be unique if it existed.6 Earlier in the Summa Aquinas argues that God must have the full perfection of being since God is being itself subsisting. To illustrate his point Aquinas again compares God to a separate heat, which he claims would also have to have the full perfection of heat if it existed.7 These are just a few examples, but they are hardly isolated ones. Indeed, Aquinas appeals to Platonic forms for such purposes quite a lot.8 3

For all the texts in which Aquinas mentions Plato and his followers, see Part One of Henle, Saint Thomas and Platonism. For an analysis of the texts, especially their criticism of Plato and his followers, see Part Two. But note Clarke’s critical review of the book mentioned above. 4 Summa theologiae (ST) I, q. 6, a. 4; ST I, q. 84, a. 5; In De divinis nominibus, proem. References to Aquinas’s works are to the Busa-Alarcon edition available online at . Translations are my own. 5 De ente et essentia (DEE) c. 3. 6 ST I, q. 50, a. 4. 7 ST I, q. 4, a. 2. 8 For some other examples, see DEE c. 4; Quodlibet (QQ) VII, q. 1, a. 1, ad 1; QQ III, q. 1, a. 1; Summa contra gentiles (SCG) I, c. 28, n. 2; SCG I, c. 43, n. 5; ST I, q. 4, a. 2; ST I, q. 7, a. 1, ad 3; ST I, q. 44, a. 1; ST I, q. 75, a. 7; De veritate q. 23, a. 7, ad 10; De potentia (QDP) q. 3, a. 5; De spiritualibus creaturis a. 1 & a. 8; De

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It is puzzling for Aquinas to use Platonic forms to illustrate his own views about God and angels, given that he himself criticizes and rejects such forms. As Sir Anthony Kenny says, “It is surely a strange procedure, in order to show a difficult concept to be intelligible, to compare it with another notion which on one’s own account is absurd.”9 In fact, Kenny thinks Aquinas’s use of such examples is not merely strange; it borders on self-contradiction. As Kenny explains: Using a Platonic Idea as an illustration of the intelligibility of a thesis is a dangerous procedure. If we believe there are no Platonic Ideas, it is not because an exhaustive search has failed to discover any, but because the notion of such an Idea contains self-contradictory or incoherent elements. Such incoherence will surely infect the notion we are using the Idea to illustrate.10

The risk of such incoherent self-contradiction is especially worrying for Aquinas’s understanding of God as subsistent existence, which forms the foundation of his entire metaphysics of being and participation. His comparison of the idea of God as subsistent existence to the idea of a separate whiteness or heat suggests that Aquinas thinks of God like the Platonic form of being itself, as Kenny notes.11 If Kenny is right that Aquinas considers the notion of a Platonic form to be absurdly incoherent, then he is surely right that it is odd and risky for Aquinas to appeal to such a notion to illustrate his own views about God. Such a procedure would cast doubt upon Aquinas’s entire metaphysics. But does Aquinas consider the notion of a Platonic form to be incoherent? I at least am not convinced that he does. The very fact that he uses Platonic forms as the stock examples to illustrate his own views about God and angels suggests that Aquinas does not consider them to be selfcontradictory. Even Kenny recognizes that Aquinas sometimes talks in a way that “makes it look as if he is not opposed to Platonic Ideas on general or logical grounds.”12 More than that, however, Aquinas actually says at malo q. 5, a. 1, ad 4; De malo q. 16, a. 3 & a. 9, ad 5; De substantiis separatis c. 14; In De divinis nominibus c. 5, l. 1; Super De causis l. 3, l. 4, & l. 9; Compendium theologiae I, c. 15; In libros Physicorum VIII, l. 21, n. 13; Expositio Peryermeneias I, l. 10, n. 6. 9 Anthony Kenny, Aquinas on Being (Oxford: Oxford University Press, 2002), p. 113. 10 Ibid., p. 38, n. 20. 11 Ibid., pp. 113, 121, 141, & 193. 12 Ibid., p. 102.

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one point that he thinks God could create a Platonic form such as a separately subsisting whiteness. To that extent, then, Aquinas must think that Platonic forms are in fact possible. Now the text in which he grants this possibility is fairly early, and as far as I know unique. But it is also absolutely clear. And yet Aquinas’s rejection of Platonic forms is also quite clear. What remains unclear, however, is just why Aquinas rejects such forms. What exactly has he got against them? That is the question I want to begin to answer in this paper. First I want to consider the text in which Aquinas grants that Platonic forms are indeed possible, since it helps to motivate a reassessment of his reasons for still rejecting Platonic forms. Then I want to consider some of Aquinas’s main critical discussions of Platonic forms. Given this paper’s length, the best I can do is offer a brief summary of Aquinas’s reasons for rejecting Platonic forms. But I think even such a summary treatment can show that the general form of all his reasons (abstracting from their particular details) fits the pattern of a single line of argument: an argument from simplicity or parsimony. In other words, Aquinas rejects Platonic forms not because he thinks they are impossible, but because he thinks they are unnecessary. If I am right about this, then Aquinas’s use of Platonic forms as examples to illustrate his own views about God and angels is not as odd or risky as Kenny suggests. Of course his use of such examples may still be absurdly incoherent. But that is something Kenny or others would need to show. Let me turn, then, to the text in which Aquinas grants the possibility of Platonic forms. The text is Quodlibetal Questions VII, q. 4, a. 3. The question under discussion is whether God could make whiteness and other qualities exist without any quantity, as he makes quantity exist without a subject in the sacrament of the altar. The question arises out of the medieval theory of Eucharistic transubstantiation. According to that theory, the consecration turns the substance of bread into the body of Christ, while the accidents of bread – its shape and color and so on – still remain. But the remaining accidents do not come to inhere in the body of Christ: Christ’s body does not become that shape and color and so on. Instead, such accidents inhere in the accident of quantity – the remaining surface of the bread – which does not itself inhere in anything. Rather, God keeps the bread’s surface in existence without its being the surface of anything. So, given that God can perform such a miracle with the quantity of a surface, could God also do so with a quality such as whiteness? Could

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God make whiteness exist without its being the whiteness of anything? That is the question. Aquinas begins his reply by pointing out that God can do anything that does not involve a contradiction for God to do – a point Aquinas often makes about the proper extent of divine omnipotence.13 He then distinguishes between the nature of whiteness and other bodily qualities and their individuation. Their nature is what divides such qualities into their various species, he says, while their individuation is what distinguishes this sensible whiteness from that sensible whiteness. Aquinas then draws his first conclusion (the first half of his answer to the question): Miraculously, therefore, the nature of whiteness could be made to subsist without any quantity. And yet such whiteness would not be like this sensible whiteness; it would be a certain intelligible form along the lines of the separate forms that Plato posited.14

Aquinas goes on to explain why he thinks there could only be one separate whiteness. Whiteness is individuated and thus multiplied by being received in a subject, he says, at least in the subject of quantity (i.e. a surface). Hence, for there to be more than one whiteness, whiteness has to exist in a particular thing or things, and thus no longer be separate. So there could only be at most one separate whiteness. Now whatever you make of Aquinas’s reply here, this much is clear about it: the separately subsisting whiteness in question would not be any particular sensible whiteness. It would not be the whiteness of any particular thing. It would be a purely intelligible whiteness. In other words, it would be the Platonic form or idea of whiteness, as Aquinas himself says.15 Aquinas goes on to argue that not even God could make an individual sensible whiteness exist without any quantity, even though he can make individual quantity exist without a subject, as he is supposed to do in the Eucharist. Aquinas’s reasons for drawing this second conclusion (the second half of his answer to the question) need not concern us here. The 13

In Sententiis (In Sent.) I, d. 42, q. 2, a. 2; In Sent. III, d. 1, q. 2, a. 3; QDP q. 1, a. 7; QDP q. 5, a. 3; QQ III, q. 1, a. 1; QQ IV, q. 3, a. 2; QQ V, q. 2, a. 1; QQ XII, q. 2, a. 2; SCG II, c. 22, n. 3; SCG II, c. 25, nn. 10ff; ST I, q. 25, a. 3. 14 QQ VII, q. 4, a. 3. 15 Anthony Kenny at least would certainly agree. See Kenny, Aquinas on Being, pp. 102 & 162-163.

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important point to note is that Aquinas says explicitly that Platonic forms such as a separately subsisting whiteness can be made to exist by God. And if he thinks that such forms can be made to exist by God, then he must not think that the notion of such forms is absurd in the sense of being self-contradictory or impossible. Otherwise he would not grant that God can make such forms, since he thinks God’s power only extends to doing what does not involve a contradiction. Clearly, then, Aquinas does not think that the very notion of a Platonic form is absurdly incoherent. Or at least he did not think so at the time of writing Quodlibet VII, q. 4, a. 3. The text of Quodlibet VII comes from the very first quodlibetal disputations that Aquinas held in 1256 during his first regency at the University of Paris.16 So this is an admittedly early text. And I am not aware of any other texts in which Aquinas so plainly grants the possibility of Platonic forms (the parallel passages to this question given in the Leonine edition are only about the accidents that remain in the Eucharist). But I am not aware of any other texts in which he so plainly denies the possibility of Platonic forms either. In this connection I should point out that standard translations of Aquinas can be misleading in their rendering of his criticisms of Platonic forms. For they often translate his Latin term “inconveniens” as “absurd” or “impossible,” which makes it look like Aquinas rejects Platonic forms for reasons like those Anthony Kenny suggests above. Of course sometimes the Latin term “inconveniens” can have the strong sense of “absurd” or “contradictory,” but Aquinas’s use of the term often has the weaker sense of “unfitting” or “unsuitable.” Aquinas has other ways of saying that something is absurd in the sense of self-contradictory or impossible. Criticizing Avicebron’s position on matter in the soul, for example, Aquinas says: “Yet this reason is silly (frivola), and the position is impossible (impossibilis).”17 But Aquinas never says such a thing about Plato’s position on separately subsisting forms, at least not in his main critical discussions of them. So let me turn to some of those main discussions. I want to focus especially on Aquinas’s treatment of Platonic forms in his commentary on Aristotle’s Metaphysics, which he composed late in his career between 1270 and 1272.18 Aquinas’s other works do not contain any arguments against 16

On the dating of Aquinas’s works, see Jean-Pierre Torrell, St. Thomas Aquinas: The Person and His Work, trans. Robert Royal, rev. ed. (Washington: Catholic University of America Press, 2005). 17 Quaestiones de anima q. 6. 18 Cf. supra n. 16.

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Platonic forms that do not appear at least in some form in this commentary, and the arguments in his other works are rarely if ever more fully elaborated. His commentary on the Metaphysics is also particularly helpful for understanding the nature of Aquinas’s arguments against Platonic forms, since he comments on the form and force of those same arguments as they appear in Aristotle’s work. Overall, then, Aquinas’s commentary on the Metaphysics is a fairly comprehensive and representative guide to his case against Platonic forms. It is certainly his most extended discussion of them. Aquinas’s commentary on Aristotle’s Metaphysics contains two major critical treatments of Platonic forms, the first in book I, lectios 14 to 17, and the second in book VII, lectios 13 to 16. Aquinas begins the first discussion of Platonic forms with an important distinction between Plato’s position on the existence of separately subsisting forms and his reasons for holding that position.19 Some of his arguments aim at Plato’s position, Aquinas says, while others aim at Plato’s reasons for holding that position. The distinction between these two kinds of arguments characterizes all of Aquinas’s critical discussions of Platonic forms.20 And it is crucial for my purposes here. My chief concern is with arguments aimed at Plato’s position on the existence of separate forms. Those are the only kinds of arguments that could even attempt to show that the very notion of a Platonic form is itself absurdly incoherent. Arguments aimed at Plato’s reasons for holding that position are irrelevant to the question of whether separate forms are possible in themselves. The same is true of arguments aimed at any of Plato’s other positions. After marking the above distinction, Aquinas immediately turns to an argument against Plato’s position on separately subsisting forms or ideas, which is an argument from parsimony: The Platonists were wrong to posit ideas as separate substances for this reason. They were looking for the causes of these sensible beings, and yet they bypassed sensible things, inventing other new beings equal in number to sensible things. And that seems unfitting. When you are looking for the causes of certain things, you should clarify them, and not add other things, which extends the investigation required… Just as it is easier to verify the number of fewer things, so it is easier to verify the nature of fewer things. Hence when Plato multiplied the kinds of things there are in order to 19

Sententia libri Metaphysicae (In Met.) I, l. 14, n. 1. Cf. Henle, Saint Thomas and Platonism, pp. 294-308.

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What Has Aquinas Got Against Platonic Forms? explain sensible things, he just added difficulties, taking on something harder in order to explain something easier, which is unfitting.21

So one problem Aquinas has with Plato’s position on separate forms is that it unnecessarily multiplies the kinds of things there are. Indeed I think this is the only problem Aquinas has with Platonic forms as such. All of his other arguments against the existence of such forms (except some of the dialectical arguments addressed to Plato himself) aim to show that they are in fact unnecessary. A brief examination of these other arguments should help to make this clear. After this argument from parsimony against Plato’s position on separate forms, Aquinas offers a series of dialectical arguments against Plato’s reasons for holding that position. First he points out that Plato’s reasons for positing the forms do not in fact necessitate their existence. Then he offers a host of arguments to show that one of Plato’s reasons for positing forms would equally necessitate the existence of separate forms other than those that Plato himself posited. Scientific knowledge is about necessary things, Aquinas explains. Thus Plato thought that such knowledge could not be about sensible things, which are corruptible, and must instead be about separate things, which are incorruptible. Hence Plato posited separate forms for everything that we can know scientifically. But, Aquinas argues, this reason for positing separate forms would necessitate the existence of many more kinds of forms than Plato himself posited. These include forms for negations, forms for corruptible things qua corruptible (i.e. qua singular sensible things), forms for relations, forms for accidents, a third class of forms halfway between sensible things and the separate forms that Plato himself posited, and a third class of forms common to sensible things and to the separate forms that Plato himself posited. The first of these last two objections about the need to posit a third class of forms makes reference to the famous “third man,” which is worth discussing in a bit more detail. People often think of the third man argument as a proof of the absurdity or incoherence of Platonic forms, but that is not how Aquinas understands it. He only ever mentions the third man argument in his commentary on the Metaphysics, and then only a few times.22 When it first appears here in book I Aquinas explains that the “third man” can be taken in three ways. First, the “third man” could mean 21

In Met. I, l. 14, n. 1. In Met. I, l. 14, nn. 7-9; In Met. VII, l. 13, nn. 21-22; In Met. XI, l. 1, n. 15.

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a third man in addition to two sensible men. But this cannot be what Aristotle means here, Aquinas thinks, since the existence of such a third man is the very position Aristotle is arguing against. Second, the “third man” could mean a third man in addition to the sensible man and the ideal man. But that cannot be what Aristotle means here either, since his second objection about the need for a third class of forms is about the need for just such a third man, and it would be pointless for Aristotle to give the same argument twice. Hence Aquinas thinks the “third man” here must mean a third man halfway between the sensible man and the ideal man. As he explains, in the case of things like numbers and lines Plato posited three kinds of things: (1) sensible objects, (2) separate ideas, and (3) separate objects halfway between the two. But Aquinas thinks there is no good reason to restrict the need for such separate objects to things like numbers and lines. If we need to posit a third kind of thing in their case, then we should need to do so in the case of things like men too: thus the third man, which Plato did not himself posit. Hence Plato’s reasons for positing separate forms require the existence of more kinds of forms than he himself posited, which is unfitting. That is the third man argument. Aquinas ends by noting that Aristotle makes this same argument in the later books of the Metaphysics. The later reference to a “third man” in book XI of the Metaphysics is certainly the same kind of argument. But the later reference to a “third man” in book VII of the Metaphysics seems more like the second way of taking the “third man” above, which applies to Aristotle’s second objection about the need for a third class of forms in book I. As Aquinas explains in book VII, “third man” can be taken in two senses, either as a third man common to two sensible men such as Socrates and Plato, or as a third man common to the sensible man and the common man, both of which are unfitting. A third man in the latter sense is required because both the sensible man and the common man share a name and a definition, just as two sensible men do. This was one of Plato’s reasons for positing separate forms, as Aquinas explains. Thus the third man argument in book VII is not about a third man halfway between the sensible man and the common man, but about a third man common to the sensible man and the common man. And this was Aristotle’s second objection about the need for a third class of forms in book I. But Aquinas’s discussion of both objections in lectio 14 of book I makes it clear that he sees them as dialectical arguments aimed at Plato’s reasons for positing separate forms, as I noted above. Plato’s reasons require the existence of more kinds of forms than Plato himself posited; there is no good reason to posit only the

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separate forms that Plato himself did, which is unfitting. Yet there is no suggestion in either objection that Aquinas thinks the third man renders Platonic forms absurd or incoherent. Lectio 15 continues book I’s dialectical arguments against Plato’s reasons for positing separate forms. These arguments all claim that Platonic forms are unnecessary for sensible things. As Aquinas explains: “Plato intended to conclude that the ideas exist because they are somehow necessary for sensible things. Hence by showing that the ideas cannot be useful to sensible things, Aristotle destroys Plato’s reasons for positing the ideas.”23 He then quotes Aristotle’s claim that of all the difficulties against Plato, this is the greatest, namely that Platonic forms do not confer anything upon sensible things. Aquinas goes on to offer five arguments to show that Platonic forms cannot serve as the causes of change for sensible things, or as the sources of our knowledge of sensible things, or as the exemplars of sensible things, or as the substances or formal causes of sensible things, or as the efficient causes of sensible things. Lectio 16 offers six dialectical arguments against Plato’s position that separate forms are numbers. This is a different position from Plato’s position on the existence of separate forms as such. Whether such forms can exist at all is a different question from whether they should be conceived of as numbers. And a negative answer to the latter question does not necessitate a negative answer to the former. So I shall pass over the arguments of lectio 16. Lectio 17 offers six dialectical arguments against Plato’s position that separate forms are sources of the existence of sensible things, followed by four dialectical arguments against Plato’s position that separate forms are sources of our knowledge of sensible things. Again these are different positions from Plato’s position on the existence of separate forms as such. But it is worth pointing out that even though Aquinas says that lectio 17 argues against Plato’s positions on separate forms as sources of being and knowledge, these positions are indistinguishable from Plato’s reasons for positing the existence of separate forms. As Aquinas himself explains later in book VII, lectio 5: The Platonists only posited the forms so that we could have knowledge of these sensible things by means of them, and so that these things could exist by means of participating in them… From this, then, the Philosopher shows us the destruction of the forms. For if the forms are only posited for the sake of our knowledge of things and for the sake of the existence of things, 23

In Met. I, l. 15, n. 1.

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and if another position suffices for this when it is posited instead, it follows that it is pointless to posit the forms.24

Thus disputing Plato’s positions on separate forms as sources of being and knowledge amounts to disputing Plato’s reasons for positing separate forms in the first place. Hence I think lectio 17 is best read as merely picking up and extending the dialectical arguments against Plato’s reasons for positing separate forms that Aquinas began in lectio 14. I have passed over the details of most of these arguments from book I of the Metaphysics because my primary concern here is with the overall nature of the arguments. With the exception of the opening argument from parsimony against Plato’s position on the existence of separate forms (and the arguments against his position on separate forms as numbers), all of Aquinas’s arguments in book I aim at Plato’s reasons for positing separate forms. So none of his arguments have any direct bearing on the possibility or impossibility of separate forms as such. Instead they all concern the explanatory roles that Aquinas thinks such forms were meant to play, but cannot. And Aquinas’s argument from parsimony against Plato’s position on the existence of separate forms does not claim that such forms are absurdly incoherent or impossible; it claims that they are unable to explain sensible things and our knowledge of them. So, taken altogether, Aquinas’s many arguments against Platonic forms in book I of the Metaphysics seem to me to constitute one extended objection to separate forms: they are unnecessary because they cannot explain any of the things that Plato posited them to explain, and thus positing them is inappropriate. Aquinas’s second major discussion of Platonic forms is in lectios 13 to 16 of book VII of his commentary on the Metaphysics. These lectios all argue against the position of the Platonists that universals are substances. This is an importantly different position from Plato’s position on the existence of separate forms as such. The difference comes out when Aquinas first clarifies the terms of the discussion at the beginning of lectio 13. The term “universal” can be taken in two senses, he explains: In one sense it can be taken for the nature itself, to which the intellect attributes the intention of universality. And universals in this sense, such as genera and species, signify the substances of things insofar as they are predicated as what things are… In another sense universal can be taken precisely as universal, insofar as the aforementioned nature is under the 24

In Met. VII, l. 5, nn. 14-15.

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What Has Aquinas Got Against Platonic Forms? intention of universality, that is, insofar as animal or man is considered as a one-in-many. And this is the sense in which the Platonists held that animal and man in their universality are substances, which is what Aristotle aims to disprove in this chapter.25

So the arguments of lectio 13 are all aimed at Plato’s position that the nature of sensible things, taken in the second sense as a universal or a onein-many, is a substance. But such arguments have no direct bearing on whether the nature of sensible things, taken in the first sense just in itself, can exist separately. And it is arguably the nature in this first sense that Aquinas has in mind when he says in Quodlibet VII that God could make whiteness exist separately like a Platonic form. For he says that it would be the separate existence of an intelligible nature, which divides things into their species, rather than the existence of an individuated one, which makes things this or that. In any case, whether separate forms can exist at all is obviously a different question from whether they should be thought of as universals in the second sense above. Since the arguments in lectio 13 all aim at Plato’s position on the latter question, they all miss his position on the former. The same is true of the arguments in lectio 14, which all aim at Plato’s position that universals qua universals are substances existing separately from sensible things. Since these arguments all concern the separate existence of the nature of sensible things taken in the second sense as a universal or a one-in-many, they have no direct bearing on the separate existence of the nature of sensible things taken in the first sense as the nature just in itself. So I shall pass over the details of the arguments of lectios 13 and 14. Lectio 15 then offers three dialectical arguments claiming that Platonic forms cannot be defined. Aristotle makes these arguments, Aquinas explains, “because the Platonists posited the forms especially so that they could use them in definitions and demonstrations, which are about necessary things.”26 Now definitions and demonstrations are the ways Aquinas thinks we acquire scientific knowledge of things. So I think lectio 15 is best read as a further extension of the main argument from parsimony that Aquinas began in book I. Platonic forms are unnecessary because they cannot explain our knowledge of things. Lectio 16 then offers two arguments against the Platonic position that unity and being are universal substances, which again is a different position from Plato’s

25

In Met. VII, l. 13, nn. 5-6. In Met. VII, l. 15, n. 1.

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position on the existence of any separate forms as such. So I shall pass over the details of these arguments as well. This brief summary of Aquinas’s major discussions of Platonic forms shows that he only ever offers one argument against Plato’s position on the existence of separate forms as such: the argument from simplicity or parsimony. All of his other arguments either aim at Plato’s other positions or at Plato’s reasons for holding his positions. And none of Aquinas’s arguments claim that Plato’s separate forms are absurdly incoherent or impossible in themselves; they claim that such forms are unnecessary, since they cannot explain any of the things that Plato posited them to explain, such as the changes things undergo, the nature and existence of things, and our knowledge of them. So, Aquinas thinks separate forms should be rejected. As I said above, I think this is Aquinas’s only reason for rejecting separate forms. If I am right about this, it not only helps to explain why Aquinas is happy to appeal to such forms as examples to illustrate his own metaphysical views about God and angels; it also helps to explain why he can sometimes appear to reject Plato’s position on separate forms by criticizing Plato’s reasons for positing them. Such a procedure only seems legitimate within the context of an argument from parsimony.27 You cannot normally reject a conclusion just because the arguments for it are bad. After all, it might still be true, and other arguments for it might be good. In order to reject a conclusion, you normally need independent reasons to think it is false – unless you are making an argument from parsimony. In the context of such an argument, the failure of Plato’s separate forms to explain what he posited them to explain is reason enough to reject them, especially if a better explanation is available. And of course Aquinas thinks a better explanation is available. Where Plato’s separate forms fail, he thinks Aristotle’s inherent forms succeed, explaining the changes that things undergo, the nature and existence of things, and (given our ability to abstract such forms) our knowledge of things. In other words, Aquinas rejects Plato’s separate forms for the same reasons that he accepts Aristotle’s inherent forms. As Aquinas himself says, “if another position suffices… it is pointless to posit the forms.”28

27

For an alternative explanation of this procedure, see Henle, Saint Thomas and Platonism, pp. 294-308. 28 In Met. VII, l. 5, n. 15.

MEREOLOGICAL HYLOMORPHISM AND THE DEVELOPMENT OF THE MEDIEVAL SUBSTITUTIONAL ACCOUNT OF FORMAL CONSEQUENCE JACOB ARCHAMBAULT

1 Introduction This paper contributes to an explanation of how a sea change in logic from the later 13th to the early 14th century relates to the dialectic of certain metaphysical debates during the same period. The changes we refer to are: (1) The development of the concept of consequence, first as a replacement for the framework of Aristotle’s Topics, then as a broader category under which syllogistic, too, was subsumed. (2) The division of consequences into natural and accidental, and the later replacement of this division by that into formal and material varieties. (3) The accompanying growth of hylomorphism, and particularly mereological hylomorphism, in thinking about consequence. Both the development of systematic treatises on consequence and the application of hylomorphic language to consequences first take place in the later middle ages, culminating in the work of the Parisian arts master John Buridan. Buridan is not the first Latin author to implicitly appeal to or systematically explicate a distinction between formal and material consequence;1 but it is Buridan’s version of the distinction that becomes 1

The former honor appears to belong to Simon of Faversham; the latter, to William of Ockham. See Simon of Faversham, Quaestiones Super Libro Elenchorum, ed. Sten Ebbesen et al. (Toronto: Pontifical Institute of Medieval Studies, 1984) q. 36; William of Ockham, “Summa Logicae,” in Opera Philosophica, ed. Philotheus Boehner, Gedeon Gàl, and Stephen Brown, vol. 1 (St. Bonaventure, NY: Franciscan Institute, 1974) III-3. 1, p. 589.

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widely adopted throughout continental Europe in the later middle ages, ultimately laying the groundwork for today’s model-theoretic accounts of formal consequence. After setting forth the requisite definitions, I introduce Buridan’s distinction between formal and material consequence as presented in his Treatise on Consequences: first giving the generic structure of the distinction, then placing the distinction in its historical development. I then introduce Buridan’s metaphysical views: focusing on the question of whether several substantial forms may be present in the same subject; drawing from Buridan’s questions on Aristotle’s Physics and De Anima; and contrasting the views found there with the unicity theory of Aquinas. I then place Buridan’s logic specifically, and its development more broadly, against the backdrop of these developments in metaphysics over the same period. We find that Buridan’s logical hylomorphism reduplicates the peculiarities of his physical hylomorphism. In particular, both Buridan’s logical and physical hylomorphism are mereological in character, i.e. they both identify the form of a being (or consequence) with a proper part of the being itself – an identification explicitly rejected by Aristotle. Buridan himself subsumes the distinction between the formal and material under that between the natural and accidental in his commentaries on Aristotle’s physical treatises. This subsumption may help explain how the distinction between formal and material consequence ultimately supplants that, found in earlier treatises on consequences, between natural and accidental consequences. We conclude that while Buridan’s mereological hylomorphism in physics did not necessitate his logical hylomorphism, it did help facilitate it.

2 Definitions Hylomorphism is a thesis in metaphysics originating with Aristotle, according to which terrestrial objects are composites of matter and form. Matter is what an object is made out of; form, what it is made into. A human being is made almost wholly out of the elements of carbon, oxygen, hydrogen, nitrogen, calcium, and phosphorus. But a human is not these things alone – a corpse is all these things, but no longer a human – but these things conformed into the mould of humanity. Mereological hylomorphism is a kind of hylomorphism according to which matter and form are distinct, proper, and integral parts of a hylomorphic compound. Parts are distinct when they contain no part

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common to each; proper, when they are not identical with the whole itself; integral, when they are parts in the way the hand or heart is part of the human body. Aristotle himself explicitly rejects this form of hylomorphism.2 In its most restricted sense, ‘logical hylomorphism’ refers to the identification of logic per se with formal logic, where the latter concerns the behavior of certain parts of sentences and arguments deemed ’formal’. In a broader sense, ‘logical hylomorphism’ refers to the application of the concepts of matter and form to logical argument.3 Logical hylomorphism is mereological when this application is grounded in a partition of elements in a language into formal and non-formal types. Later medieval logic tends to be hylomorphic only in the second sense. To a greater or lesser degree, the philosophical logic of Tarski and his successors tends to be hylomorphic in both senses.4 A consequence is a relation of following between objects of an appropriate type. Though in common parlance, consequences may relate actions, 2

Aristotle, Metaphysics, trans. W. D. Ross (Oxford: Clarendon Press, 1924) Bk. VII. 10, pp. 1034b 33-36a 25. 3 The former understanding appears in John MacFarlane, “What Does It Mean to Say That Logic Is Formal?” (University of Pittsburgh, 2000), J. C. Beall and Greg Restall, Logical Pluralism (Oxford: Clarendon Press, 2006), and Owen Griffiths, “Problems for Logical Pluralism,” History and Philosophy of Logic 34, no. 2 (2013): 170-82; the latter, in Julie Brumberg-Chaumont, “Universal Logic and Aristotelian Logic: Formality and Essence of Logic,” Logica Universalis 9, no. 2 (2015): 253-78. Both are present in Catarina Dutilh Novaes, “The Different Ways in Which Logic Is (Said to Be) Formal,” History and Philosophy of Logic 32, no. 4 (2011): 303-32; Catarina Dutilh Novaes, “Reassessing Logical Hylomorphism and the Demarcation of Logical Constants,” Synthese 185, no. 3 (2012): 387-410; Catarina Dutilh Novaes, “Form and Matter in Later Latin Medieval Logic: The Cases of Suppositio and Consequentia,” Journal of the History of Philosophy 50, no. 3 (2012): 339-54, albeit with greater focus on the former understanding. 4 Cf. Alfred Tarski, “On the Concept of Following Logically,” trans. Magda StroiĔska and David Hitchcock, History and Philosophy of Logic 23, no. 3 (2002): 155-96; Alfred Tarski, “What Are Logical Notions?” History and Philosophy of Logic 7, no. 2 (1986): 143-54; Gila Sher, The Bounds of Logic (Cambridge, MA: MIT Press, 1991); Greg Ray, “Logical Consequence: A Defence of Tarski,” Journal of Philosophical Logic 25, no. 6 (1996): 617-77; Mario Gómez-Torrente, “A Note on Formality and Logical Consequence,” Journal of Philosophical Logic 29, no. 5 (2000): 529-39; Luca Bellotti, “Tarski on Logical Notions,” Synthese 135 (2003): 401-13; Beall and Restall, Logical Pluralism; John MacFarlane, “Logical Constants,” in The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, 2009, https://plato.stanford.edu/archives/fall2015/entries/logical-constants.

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objects, or events, in academic discourse the relata of consequences are usually restricted to statements or sets (or multisets, or lists ...) of statements. What follows is called the consequent; what it follows, the antecedent. A formal consequence is one valid in virtue of its formal parts; more specifically, a formal consequence is one for which every substitution of like terms by like in its non-formal parts remains a valid consequence. A material consequence is one valid in some other way. The formal parts of a consequence are identified with the logical vocabulary occurring in its sentential parts. In natural language, these include words like ‘every’ and ‘some’, ‘possible’ and ‘necessary’, ‘is’ and ‘isn’t’, ‘if’, ‘and’, and ‘or’; in artificial languages, their symbolic analogues ‫ ׊‬and ‫׌‬, ‫ ב‬and Ɠ, ൌ and ൓, ՜, ‫ר‬, and ‫ש‬. In modern logic, the (non-)formal parts of a consequence are also called its (non-)logical parts; in medieval logic, the non-formal parts are called categorematic terms; the formal parts, syncategoremata. Writing in the latter half of the thirteenth century, Nicholas of Paris explains the distinction thus: As the Philosopher states [Physics II, 2; 194a 21-27], those which are in art and reasoning are taken up in proportion with and imitation of those which are in nature. Now among natural [beings] we thus see that there are some which by nature are disposed in themselves to do something without any outside support, while there are others which are not disposed to move except [when] moved: just as a man moved by himself and not by another writes letters, so a pen is moved not by itself but by a man. It is similar among beings of reason, especially among words: some perform their purpose without the aid of another, i.e. they signify (for every word is for the sake of something to be signified, since, as Aristotle states [De interpretatione I; 16a 3-4], words are indicators of those impressions which are in the soul: that is, they signify ideas which are signs of things; and in this way utterances signify things), and such utterances are called categoremata, that is, signifying; there are others which do not signify per se but in connection with others, and these are called syncategoremata.5 5

H. A. B. Braakhuis, De 13de Eeuwse Tractaten over Syncategorematische Termen (Meppel, 1979) I. 2-15. Ut dicit Philosophus [Physics II, 2; 194a 21-27], ea que sunt in arte et ratione sumuntur ad proportionem et imitationem eorum que sunt in natura. In naturalibus vero ita videmus quod sunt quedam que per naturam nata sunt in se aliquid agere sine alieno suffragio, alia vero sunt que non sunt nata movere nisi mota, sicut homo a se motus et non ab alio protrahit litteras, calamus non a se sed ab homine motus. Similiter se habet in rebus rationis, maxime in vocibus, quod quedam faciunt id ad quod sunt sine auxilio alterius, scilicet significant, quia omnis vox est

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3 Logic 3.1 John Buridan’s account of formal consequence The earliest account of consequence to explicitly distinguish formal from material consequences by appeal to the distinction between categorematic and syncategorematic terms belongs to the fourteenth century Parisian logician John Buridan. Buridan distinguishes formal from material consequences thus: A consequence is called ‘formal’ if it is valid in all terms retaining a similar form. Or, if you want to put it explicitly, a formal consequence is one where every proposition similar in form that might be formed would be a good consequence. ...A material consequence, however, is one where not every proposition similar in form would be a good consequence, or, as it is commonly put, which does not hold in all terms retaining the same form.6

Since Buridan’s logic countenances non-formal consequences, it is not hylomorphic in the strict sense. Since it appeals to the distinction between form and matter, it is hylomorphic in the broader sense. Furthermore, since it relies on a distinction between formal and material parts to determine the logical form of a sentence, it satisfies the conditions for a specifically mereological account. Buridan describes the form and matter of consequences thus: I say that when we speak of matter and form, by the matter of a proposition or consequence we mean the purely categorematic terms, namely the subject and predicate, setting aside the syncategoremes attached to them by ad significandum, quoniam, ut dicit Aristotiles [De interpretatione I; 16a 3-4], voces sunt notae earum que sunt in anima passionum, idest significant intellectus, qui sunt signa rerum; et ita voces significant res; et tales voces dicuntur categoreumata, idest: significantes; alie sunt que per se non significant sed in coniunctione ad alias; et tales dicuntur sincategoreumata. 6 John Buridan, Treatise on Consequences, trans. Stephen Read (Bronx, NY: Fordham University Press, 2015) I. 4, p. 68: Consequentia ‘formalis’ vocatur quae in omnibus terminis valet retenta forma consimili. Vel si vis expresse loqui de vi sermonis, consequentia formalis est cui omnis propositio similis in forma quae formaretur esset bona consequentia [...] Sed consequentia materialis est cui non omnis propositio consimilis in forma esset bona consequentia, vel, sicut communiter dicitur, quae non tenet in omnibus terminis forma consimili retenta.

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Thus on Buridan’s account, a consequence is formal if and only if it is good for all uniform substitutions on its categorematic terms. For this reason, it is rightly regarded as a medieval predecessor to the modeltheoretic approach to formal consequence found in the work of Alfred Tarski,8 which transforms Buridan’s uniform substitution criterion on terms into one over models, i.e. over orderings of objects satisfying sentential functions obtained from initial sentences by substituting like non-logical constants with like variables.9

3.2 The development of the Buridanian account The earliest extant treatises on consequences arise at the turn of the fourteenth century. Of these, two are anonymous, while a third is by Walter Burley, the English ‘extreme realist’ and prominent foe of William of Ockham who later wrote his treatises On the Essence of the Art of Logic at Paris in the mid-to-late 1320s.10 Prior to Buridan’s account, one finds two different divisions of consequences. The earlier, that between natural and accidental consequences, is already

7

Ibid. I. 7, p. 74. Catarina Dutilh Novaes, “Medieval Theories of Consequence,” in The Stanford Encyclopedia of Philosophy, 2016, https://plato.stanford.edu/archives/fall2016/entries/consequence-medieval. 9 Note that Tarski’s understanding of ‘model’ is not the same as that found in model-theory today. For examination of the concept as it appears in Tarski, see Timothy Bays, “On Tarski on Models,” Journal of Symbolic Logic 66, no. 4 (2001): 1701-26; Mario Gómez-Torrente, “Rereading Tarski on Logical Consequence,” Review of Symbolic Logic 2, no. 2 (2009): 249-97. 10 The anonymous treatises are edited in Niels Jørgen Green-Pedersen, “Two Early Anonymous Tracts on Consequences,” Cahiers de L’Institut Du Moyen-Âge Grec et Latin 35 (1980): 1-28; Burley’s, in Niels Jørgen Green-Pedersen, “Walter Burley’s de Consequentiis: An Edition,” Franciscan Studies 40 (1980): 102-66. English translations of these are found in Jacob Archambault, “The Development of the Medieval Parisian Account of Formal Consequence” (Fordham University, 2017). Burley’s De Puritate is edited in Walter Burleigh, De Puritate Artis Logicae, ed. Philotheus Boehner (St Bonaventure, NY: Franciscan Institute, 1955), and translated in Walter Burley, On the Purity of the Art of Logic, trans. Paul Vincent Spade (New Haven: Yale University Press, 2000). 8

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implicit in Boethius,11and later found in Garlandus Compotista, William of Sherwood, Duns Scotus, and Walter Burley.12 The other, that between formal and material consequences, is found in Simon of Faversham’s Questions on Aristotle’s On Sophistical Refutations, implicitly appealed to in the earliest extant treatise on consequences, and first explicated by William of Ockham.13 The relations between these divisions can be garnered to a small degree from Ockham’s mention of natural consequence in his discussion of positio impossibilis, a debating exercise (obligatio) discussed in the Summa Logicae section on consequences involving the positing of an impossible proposition;14 and to a greater degree from an exchange in Burley’s De Puritate where both divisions are used.15 Though the earlier and later distinctions existed side by side for a short time, the formal/material distinction eventually came to replace the natural/accidental one. According to the earlier distinction, a natural consequence is one where the antecedent is contained in the consequent, and holds by appeal to an intrinsic topic; an accidental consequence is one which fails to satisfy this containment criterion, but holds in some other way. ‘Topic’ is said in two ways. In the former sense, it refers to some general feature of a thing, appealed to, often as the middle term of a syllogism, to arrive at new knowledge concerning its bearer or something else; in the second sense, it refers to the rule appealed to in an inference pertinent to such a feature. Inferences appealing to intrinsic topics include those from a genus to a species and conversely, from something about a part to something about the whole it is a part of, from ascribing something to a thing under a certain description to ascribing it to the thing directly, from the positing of the cause to the positing of its effect, and others. Consequences invoking extrinsic topics are liable to appeal to more ‘synthetic’ relations, and include inferences involving analogy, geometrical similarity, contrariety and other 11 Boethius, De Hypotheticis Syllogismis, ed. L. Obertello (Brescia: Paideia, 1969), 835B. 12 William of Sherwood, “Syncategoremata,” ed. James R. O’Donnell, Mediaeval Studies 3 (1941): 80, Garlandus Compotista, Dialectica, ed. Lambertus M. de Rijk (Assen: van Gorcum, 1959), 141, John Duns Scotus, “Lectura,” in Opera Omnia, by John Duns Scotus, vol. 17 (Vatican: Typis Polyglottis Vaticanis, 1966) I, d. 11, q. 2, pp. 136-137, Green-Pedersen, “Walter Burley’s de Consequentiis,” 128-29. 13 Simon of Faversham, Quaestiones Super Libro Elenchorum qq. 36-37, GreenPedersen, “Two Early Anonymous Tracts on Consequences,” 7, par. 18, William of Ockham, “Summa Logicae” III-3. 1, p. 589. 14 Ibid. III-3. 42. 15 Walter Burleigh, De Puritate Artis Logicae, 80.13-29, 84.8-86.21.

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kinds of opposition, and appeals to authority.16 Natural consequences are always relevant consequences; accidental consequences need not be. Burley explains the division thus: A natural consequence is when the consequent is in the understanding of the antecedent, nor can the antecedent be true unless the consequent is true; as ‘if a man is, an animal is’. An accidental consequence is twofold: some hold on account of the terms or on account of the matter, as ‘God exists is true, therefore God exists is necessary’; and this holds on account of the terms or the matter, since truth in God and necessity are the same. Other accidental consequences are so: from the impossible anything follows; and the necessary follows from anything. An example of the first: ‘You are an ass, therefore you are a goat, and a stone...’, etc. An example of the second, as ‘you are running, therefore God exists’. Again, an accidental consequence is when the consequent is not in the understanding of the antecedent.17

In Burley and the early anonymous tracts, the distinction between natural and accidental predication is intended as extending a distinction between per se and accidental predication, as in ‘a man is an animal’ and ‘a man is a musician’, respectively. There were difficulties in the implementation of the expansion, particularly i) the conflation of accidental predication and essential predication between accidents (e.g. ‘to run is to move’), and ii) irregularities in the treatment of existential import.18 In Ockham’s account, the formal/material division of consequences is determined by whether or not a consequence holds by a middle: formal consequences hold by middles, material consequences do not. Further, a formal consequence may hold only by an extrinsic middle, Ockham’s example being ‘From a necessary major premise and an assertoric minor follows a necessary conclusion’; or by both an intrinsic and extrinsic middle, as in ‘Socrates does not run, therefore a man does not run’. Here, an extrinsic middle is a rule licensing an inference; an intrinsic middle, a premise on which the antecedent implicitly depends, ‘Socrates is a man’ in this case. Ockham’s examples of material consequences are those from an impossibility or to a necessity: ‘If a man runs, God exists’ and ‘A man is 16

Boethius, “De Differentiis Topicis,” in Patrologia Cursus Completus. Series Latina, ed. J. P. Migne, vol. 64 (Paris: Chadwyck-Healy, 1841-1855), 1173-1216 Bk. II. 17 Green-Pedersen, “Walter Burley’s de Consequentiis,” 128-29, par. 70. 18 Archambault, “The Development of the Medieval Parisian Account of Formal Consequence,” 76-79.

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an ass, therefore God does not exist.’19 Ockham’s later Elementarium Logicae gives the consequence ‘an animal is debating, therefore a man is debating’ as another example of a good material consequence.20 Simon of Faversham’s early example of a material consequence is similar to that in the Elementarium.21 Not all formally valid consequences in Ockham’s sense are formally valid in Buridan’s sense. Rather, Buridan regards as formally valid only those formal consequences Ockham says hold solely by an extrinsic middle. Furthermore, Scotus and Burley’s containment criterion for natural consequence is orthogonal to Buridan’s uniform substitution criterion for formal consequence. Thus, we have two transformations: first, that from the natural/accidental distinction to the formal/material distinction; then later, from a topical to a substitutional grounding of the latter distinction, with a corresponding restriction of the class of formal consequences.

19

William of Ockham, “Summa Logicae” III- 3. 1, p. 589. William of Ockham, “Elementarium Logicae,” in Opera Philosophica, ed. Eligius M. Buytaert, vol. 7 (St. Bonaventure, NY: Franciscan Institute, 1988), 59304 VI. 4, p. 163. For the case for the authenticity of the Elementarium, see Philotheus Boehner, “Three Sums of Logic Attributed to William Ockham,” in Collected Articles on Ockham (St. Bonaventure, NY: Franciscan Institute, 1958), 70-96. 21 Simon of Faversham, Quaestiones Super Libro Elenchorum q. 36, p. 200: When it is said that ‘an animal is a substance; therefore a man is a substance’ is a good consequence, I reply that this consequence does not hold in virtue of form, but rather in virtue of matter. Because according to the Commentator on the first book of the Physics, an argument which is valid in virtue of form must hold in all matter. This consequence, however, holds only for features which are essential ... and so this consequence is not formal. Et cum dicitur ‘Hic est bona consequentia: ‘animal est substantia, ergo homo est substantia’’, dico quod ista consequentia non tenet ratione formae, sed ratione materiae. Non tenet ratione formae quia secundum Commentatorem I Physicorum sermo concludens virtute formae debet tenere in omni materia; ista autem consequentia tantum tenet in essentialibus, et hoc propter identitatem naturae importatam in talibus per antecedens et consequens; et propter hoc consequentia ista non est formalis. Translation from Christopher J. Martin, “Formal Consequence in Scotus and Ockham: Towards an Account of Scotus’ Logic,” in Duns Scotus in Paris, 13022002: Proceedings of the Conference of Paris, 2-4 September 2002, ed. O. Boulnois, E. Karger, and G. Sondag (Turnhout: Brepols, 2004), 135. 20

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To better understand the ‘logic’ of these logical developments, let us now embark on a short metaphysical detour.

4 Hylomorphism 4.1 Parvus error in principio... After briefly discussing the meaning of ens,22 Thomas Aquinas’ de ente et essentia then transitions to a discussion of essence: treating first the names of essence23 and their origin,24 then distinguishing the way essence is in substances and accidents.25 He then divides substances into simple and composite,26 and proceeds to treat the way essences exist in composite material substances.27 Aquinas’ discussion of material substance begins with a refutation of three successive positions: that essence is identical with matter,28 that it is identical with form,29 and that it is something added to or other than matter and/or form.30 In other words, Aquinas first proves that matter and form are necessary for a definition of the essence of a material thing, then that they are sufficient for it. This position is confirmed by the authority of Boethius,31 Avicenna,32 and Averroes,33 and then by a direct proof from reason.34 Aquinas then writes the following:

22

Thomas Aquinas, De Ente et Essentia, ed. L. Baur et al., n.d., http://www.corpusthomisticum.org/oee.html. 23 Namely, form, quiddity, and nature. 24 Beginning at ‘et quia illud per quod res constuitur...’ 25 At ‘Sed quia ens absolute et per prius dicitur de substantiis...’ 26 ‘Substantiarum vero quaedam sunt simplices et quaedam compositae’ 27 ‘In substantiis igitur compositis...’ 28 ‘quod enim materia sola non sit essentia rei planum est...’ 29 ‘Neque etiam forma tantum essentia substantiae compositae dici potest, quamvis hoc quidam asserere conentur’ 30 ‘Non autem potest dici quod essentia significet relationem quae est inter materiam et formam vel aliquid superadditum ipsis’ 31 ‘Et huic consonat verbum Boethii...’ 32 ‘Avicenna etiam dicit...’ 33 ‘Commentator etiam dicit super VII metaphysicae...’ 34 ‘Huic etiam ratio concordat...’

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But since matter is the principle of individuation, from this it may seem to follow that essence, which contains within itself both matter and form, is of particulars, and not universals; from which it would follow that universals would not have definitions, if essence is that which is signified by a definition.35

This is the first place in the text where Aquinas puts forth an objection to his own position, and it is the only place where an argument contradicting Aquinas is phrased as an objection.36 The remainder of the first chapter engages in a refutation of the underlying position, and defense of the position that Aquinas contrasts with it.37 The argument above can be summarized as the following reductio. If matter is the principle of individuation, then whatever contains matter is individuated. But whatever is individuated is particular, and not universal. Therefore, whatever contains matter is particular, and not universal. But by hypothesis, the essence of a composite contains both matter and form. Therefore, essences of composites would be particular, not universal. But an essence is what is signified by a definition. Therefore the definition of composites would signify particulars. But the definition of a composite cannot signify a particular, since particulars are indefinable. Thus, universals corresponding to composite entities, which are only intelligible insofar as they are separated from matter,38 would lack definition. But this is false.

35 Ibid. ch. 1: Sed quia individuationis principium materia est, ex hoc forte videtur sequi quod essentia quae materiam in se complectitur simul et formam, sit tantum particularis et non universalis. Ex quo sequeretur quod universalia diffinitionem non haberent, si essentia est id quod per diffinitionem significatur. 36 Later in chapter 1, Aquinas will allude to another argument presumably from the same point of view (beginning at the words, ‘Quamvis autem genus’), and in chapter three he will address the thesis of Ibn Gabirol concerning spiritual matter at length. But in both of these cases the rejection of the thesis is simultaneous with its introduction. 37 Aquinas’ defense of the position he sets out lasts at least until the sentence beginning ‘Sed diffinitio vel species comprehendit utrumque’ ibid. ch. 1. 38 Aquinas makes this claim in the beginning of chapter 3 of the De ente. The argument goes through without it, but the presumption that Aquinas’ opponent would also hold this belief is supported both by the strength it lends to the argument itself and by the relatively high level of acceptability Aquinas assumes for this premise when he himself uses it.

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Aquinas’ response to the objection begins by further specifying how matter individuates,39 thus implying that his opponent misconstrues this claim rather than rejects it outright. Given this, Aquinas likely intends the reductio to be directed against the thesis that essence embraces both matter and form. Given that the problem in the argument arises from the inclusion of matter in essence, Aquinas’ imagined interlocutor cannot hold that essence is identical to matter, nor that it is some relation between or superaddition to matter and form. Therefore, Aquinas likely has in mind an opponent who identifies essence and form. Call the position stated the form-essence identity thesis.40 Aquinas’ response is concerned to show how it is possible for matter to be included in essence. Aquinas’ suggests that not prime, but signate matter is the principle of individuation.41 This is then followed by an exposition of the meaning of ‘body’, and then an analogous shorter exposition of the meaning of ‘animal’. In each case, Aquinas is at pains to show that predicates such as those in ‘a tree is a body’, ‘a tiger is an animal’, ‘Plato is rational’, ‘Socrates is human’ are not predicating a part of a thing to the integral being to which it belongs – as would be the case in the statement ‘Socrates is human’ if ‘human’ signified only Socrates’ form, and not his

39

‘Et ideo sciendum est quod materia non quolibet modo accepta est individuationis principium, sed solum materia signata’ (ibid). 40 The likelihood of this is bolstered by the presence of ‘form’ on Aquinas’ list of names of essence (‘Dicitur etiam forma ...’); by the explicit recognition, unique among the positions mentioned, of the thesis as a live option advanced by others (‘... quamvis hoc quidem asserere conentur’); by the presence, again unique among the three suggested alternatives, of a counterargument to Aquinas’ initial rejection: after Aquinas argues that the exclusion of matter from essence would entail that mathematical and natural definitions did not differ from each other, he revises his opponent’s position by suggesting that matter is included in the definition of substance as something added to its essence, which revision he then also refutes. This is then followed by a concession to the form-essence identity theorist - ‘even though the form alone is by its mode the cause of the esse of this kind [of being (i.e. a composite)]’ - supported by an analogy to the composite character of tastes: like tastes, an essence i) contains multiple parts, ii) takes its name from only one of those parts, and iii) has only one of those parts, properly speaking, as a cause. 41 Pace Henrik Lagerlund, “John Buridan and the Problems of Dualism in the Fourteenth Century,” Journal of the History of Philosophy 42, no. 4 (2004): 371. Thus, the premise ‘whatever contains matter is individuated’ is ambiguous, blocking the straightforward conclusion ‘whatever contains matter is particular,’ as well as any incongruous conclusions drawn from it.

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matter – but instead signify the whole of the subject they are predicated of, albeit in different ways.42 From here, let us consider an objection alluded to later in chapter 1: Although a genus signifies the whole essence of a species, it does not follow from this that diverse species of which the genus is the same are one essence. For the unity of a genus arises from its very indeterminacy or indifference: not such that that which is signified by a genus be one nature numerically in diverse species, upon which supervenes another thing which is the difference determining it, just as form determines matter which is one numerically; but such that a genus signifies some form, neither determinately the same as nor other than what [its] difference determinately expresses, which [difference] is [itself] nothing other than that which was indeterminately signified by the genus.43

Aquinas’ denial of the validity of the inference from i) ‘a genus signifies the whole essence of a species’; to ii) ‘diverse species of which the genus is the same are one essence’, suggests the affirmation of that connection by an opponent. Similarly, Aquinas’ mention of the thesis ‘that which is signified by a genus is one nature numerically in diverse species’ suggests an affirmation of that thesis by his target. Lastly, the stress that Aquinas places on the indeterminate signification of genus contrasts with the determinacy of all signification insisted on by the position with which he is contrasting his own. This, then, suggests the following line of reasoning. The whole essence of a species is signified by its genus. That which is signified by a genus is one nature numerically in diverse species. But to say that the whole essence of a species is signified by a genus is to say that that species is wholly its genus, which is absurd. For to signify is to 42

‘Sic ergo: genus significat inderminate totum id quod est in specie, non enim significat tantum materiam; similiter etiam differentia significat totum et non significat tantum formam; et etiam diffinitio significat totum, et etiam species’ (ibid). 43 Thomas Aquinas, De Ente et Essentia ch. 1: Quamvis autem genus significet totam essentiam speciei, non tamen oportet ut diversarum specierum, quarum est idem genus, sit una essentia, quia unitas generis ex ipsa indeterminatione vel indifferentia procedit: non autem ita, quod illud quod significatur per genus sit una natura numero in diversis speciebus, cui superveniat res alia, quae sit differentia determinans ipsum, sicut forma determinat materiam, quae est una numero; sed quia genus significat aliquam formam, non tamen determinate hanc vel illam quam determinate differentia exprimit, quae non est alia quam illa quae indeterminate significabatur per genus.

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designate determinately. Now if every essence in a genus is divided into different species by a difference, and this is only possible if that entity is not wholly determined by its genus, then if a genus signified the whole of an essence, it would follow that that essence was incapable of numerical division into further species, and therefore these diverse species would be themselves one essentially: for instance, to be human would be identical to being a cow, since both are species of the same genus ‘animal’. Therefore, to avoid this sort of ‘crowding out’ of the differences between species, it is necessary to posit that the genus only signifies part of the essence of a species. The essence of a species, then, would likely be nothing other than the metaphysical summing of its difference, genus, and any other higher genus to which it belonged; while the entity would be these in addition to individuating matter. Put otherwise, we can state the thesis as the following error: the essence of a species is the combination of the plurality of substantial forms of the entities belonging to that species, abstracted from individuating matter.44 The thesis that multiple substantial forms may inhere in a single substance was widespread in the later thirteenth and early fourteenth century. Popularly associated with Solomon Ibn Gabirol,45 though already present in Alexander of Aphrodisias,46 its later advocates include John Pecham, Richard of Mediavilla,47 Bonaventure,48 Duns Scotus,49 and William of

44

An alternative position might identify the essence of an entity not with the combination of its substantial forms, but exclusively with the highest of those forms, leading to a view reminiscent of (but not identical to) the Cartesian identification of the self with thought. Cf. Lagerlund, “John Buridan and the Problems of Dualism in the Fourteenth Century.” 45 Avicebron, Fons Vitae, ed. C. Baeumker, trans. John of Spain and Dominic Gundisalvi (Munster: Aschendorff, 1895) Bk. 2, ch. 8, 37-39; Bk. 3, ch. 3, par. 22, 81. 46 Alexander of Aphrodisias, On the Soul, ed. and trans. A. P. Fotinis (Washington, DC: University Press of America, 1979) Bk. 1, ch. 13, 9. 47 James A. Weisheipl, “Albertus Magnus and Universal Hylomorphism: Avicebron (a Note on Thirteenth-Century Augustinianism),” in Albert the Great: Commemorative Essays, ed. F. J. Kovach and R. W. Shahan (Norman, 1980), 255, Roberto Zavalloni, Richard de Mediavilla et La Controverse Sur La Pluralité Des Forms, vol. 2, Philosophes Médiévaux (Louvain: Éditions de l’institut supérieur de philosophie, 1951).

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Ockham.50 The acceptance of a plurality of substantial forms in a single substance was often coupled with a number of other theses.51 For our purposes, the most important of these shall be the identity posited, typically in discussions on the soul, between a substantial form and its powers. The case for the plurality of substantial forms depends on the form-essence identity thesis as follows. One starts with the assumption that matter individuates, without the qualification that signate matter individuates. This then requires that essences not contain matter. Given the association of matter with individuation – that is, with the division of a species into separate individuals52 – form becomes straightforwardly associated with unity: Socrates and Plato are both human because they both partake of the 48

John Francis Quinn, The Historical Constitution of St. Bonaventure’s Philosophy, vol. 23, Studies and Texts (Toronto: Pontifical Institute of Medieval Studies, 1973) index. 49 Étienne Gilson, Jean Duns Scot: Introduction à Ses Positions Fondamentales (Paris: J. Vrin, 1952), 490-97, Prospero Stella, L’ilemorfismo Di G. Duns Scoto (1955: Società Editrice Internazionale, 1955), 187-229. Richard Cross, The Physics of Duns Scotus: The Scientific Context of a Theological Vision (Oxford: Clarendon Press, 1998), 47-76. The traditional reading of Scotus’s hylomorphism has been contested in Thomas M. Ward, “Animals, Animal Parts, and Hylomorphism: John Duns Scotus’s Pluralism About Substantial Form,” Journal of the History of Philosophy 50, no. 4 (2012): 531-58; Thomas M. Ward, John Duns Scotus on Parts, Wholes, and Hylomorphism, 2014. On Ward’s reading, mediating forms such as those of corporeity or sensitivity are not admitted on Scotus’ hylomorphic pluralism: rather, only the forms of organs are admitted as substantial forms, in addition to the unifying substantial form of the whole. Wards reading, however, is pieced together from a small number of non-central texts; explains away Scotus’ use of key phrases associated with the traditional position as figures of speech; and arguably is based on a misreading of one of its central supporting texts. See Ward, “Animals, Animal Parts, and Hylomorphism,” 542-545; 548, fn. 58; Giorgio Pini, “Duns Scotus on Material Substances and Cognition: A Discussion of Two Recent Books,” British Journal for the History of Philosophy 24, no. 4 (2016): 772-73. In this article, I assume the traditional reading of Scotus’ hylomorphism. 50 Marilyn McCord Adams, William Ockham, vol. 2 (Notre Dame: University of Notre Dame Press, 1987), 633-70. 51 Weisheipl, “Albertus Magnus and Universal Hylomorphism,” 242-43, Maurice De Wulf, History of Mediaeval Philosophy, trans. Ernest C. Messenger (London: Green; Co., 1926), vol. 1, p. 335. 52 For this understanding of the problem of individuation, see the essays in Gyula Klima and Alexander W. Hall, eds., Proceedings of the Society for Medieval Logic and Metaphysics, vol. 5 (Cambridge Scholars, 2005), 38-78.

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numerically identical form of human. That different substantial forms would, in addition, be separate from each other, and not merely from the supposita which partake of them, would follow from their determinacy and numerical self-identity. In metaphysics, this implies that the positing of a multiplicity of substantial forms is a specification of the form-essence identity thesis; and that according to this thesis, a form is conceived of as having the same sort of unity found in entities, i.e. determinate unity, instead of being conceived of, as Aquinas thinks it should, as having the indeterminate unity appropriate to essences. In logic, this suggests an analysis on which for any entity ‫ ݔ‬to be ‫ ܨ‬is for it to contain the form ‫ ܨ‬as one of its metaphysical parts. Furthermore, since the forms are of their own nature determinately separate from one another, ‘is’ statements predicated of different forms, such as ‘man is an animal’, if taken as statements about forms, must be false. For if one insists i) that every form is identically itself and not any other, and ii) that every form is completely determined, then to posit that ‘man is an animal’ as a statement about forms would be to equate humanity and animality. Therefore, statements like ‘man is an animal’ would need to be analyzed as concerning not containment relations between the significates of essential predicates, but rather the coincidence or non-coincidence of those essences in their supposita.53 Aquinas’ opponents are thus not merely denying that essences contain matter, but are entrenched in their commitment to that claim by a host of other claims: that matter, without qualification, individuates; that every form must be determinately one and numerically identical to itself; that propositions seemingly about the relationship, intersection, and hierarchy of forms are in fact statements about the relationships of those essentially disparate forms to different chunks of matter.

53

Indeed, Aquinas makes precisely this point in the responsio of Question 11 of his Quaestiones de anima, that statements like ‘man is an animal’ would only be true per accidens on the analysis given by adherents to the plurality of substantial forms. Thomas Aquinas, Quaestio Disputata de Anima, ed. Robert Busa and Enrique Alarüon (Turin, 1953), http://www.corpusthomisticum.org/qda01.html q. 1, a. 11, co.

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4.2 ...magnus est in fine Buridan’s Quaestiones de anima first turns to the plurality of substantial forms in book II, question 4, where Buridan asks ‘whether in the same animal, the vegetative and sensitive souls are the same.’54 In spite of agreeing with Aquinas’ answer to the question, Buridan differs from Aquinas in his estimation of the character of his proof. While Aquinas regards his answer as proven according to the standards of Aristotelian scientia,55 Buridan sees the matter as difficult to decide demonstratively;56 and apart from an appeal to the authority of Aristotle’s Metaphysics VII, Buridan decides the question not scientifically, but dialectically.57 Buridan describes the position of those who hold there to be a plurality of substantial forms in one suppositum in the following: Those who posit several souls and substantial forms in the same suppositum ground their opinion [by saying] that according to the grade and order of quidditative predicates of genera and the species subordinated successively to them, there are in the same [individual] several subordinate substantial forms: as in Socrates there is a first form by which he is a substance; another by which he is a body; another by which he is living; another by which he is an animal; and another specific [form] by which he is a man. And just as prime matter is naturally in potency toward the first – that is, the most general – of those [forms]; and as this is the first act of this matter, wherefore from these comes something one per se: so also the second form has itself toward the composite of the first matter and form,(ex materia et forma prima) such that that composite is per se in potency with respect to the second form. And that [second form] is the formal act of the composite itself. Therefore, from these comes something one per se, just as occurred from the first matter and form.58 54

John Buridan, Questiones de Anima, 2017 II.4.1. ‘Et hoc consequens est ei quod in praecedentibus ostendimus de ordine formarum substantialium, scilicet quod nulla forma substantialis unitur materiae mediante alia forma substantiali, sed forma perfectior dat materiae quicquid dabat inferior et adhuc amplius’ Thomas Aquinas, Quaestio Disputata de Anima q. 1, art. 11, co. 56 ‘Ista questio bene est difficilis quia difficile est demonstrare aliquam partem’ John Buridan, Questiones de Anima II.4.10. 57 ‘Pono igitur rationes probabiles ad probandum quod non sunt sic in equo anime diverse sensitiva et vegetativa’ ibid. II.4.15. 58 ‘Tenentes enim plures animas et formas substantiales in eodem supposito fundant suam opinionem quod, secundum gradum et ordinem predicatorum quidditativorum generum et specierum subordinatarum sibi invicem sunt in eodem 55

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This same pattern is then repeated with a third form, and so on until the final, most specific substantial form is added. Buridan’s description agrees with Aquinas’ picture of the multiple-form defender as thinking of determinate forms as determinate additions to each other, and hence with the absence of a notion of the indeterminate containment of a species in its genus. Though Buridan uses the phrase ‘this matter,’ he does not use it as a technical term designating signate matter, but to refer back to the matter he mentions in the preceding clause, i.e. prime matter. Thus, the sentence ‘this is the first act of this matter, wherefore from these comes something one per se’ should be read as asserting that from the union of prime matter and first form – in Buridan’s list, substance – comes something one per se. Hence, Buridan, too, takes the defender of multiple substantial forms to hold that prime, not signate matter, individuates. And with the plurality theorist, Buridan likewise assumes a composite is a union of form and prime matter.59 Both the main body and replies to objections in Buridan’s response to question 4 consist, in great part, in playing the principles of his opponents against them. For instance, he suggests that multiple-substantial-form positers must be committed to the thesis that an individual horse is composed of an animal and a plant, since it has non-identical vegetative and sensitive forms which could be separated from each other by the divine will.60 As a result of this strategy, the exact shape of Buridan’s own commitments on this question remains largely unpronounced. But his answer to the third objection gives us some clues about his own position. Objection three argues as follows: Again, to inhere in something on account of itself is to inhere in it by its nature or essence: therefore, to inhere in an animal insofar as it is an animal is to inhere in it on account of the nature by which it is an animal. And so again to inhere in a living thing insofar as it is a living thing is to inhere in plures forme substantiales subordinate, ut in Sorte est prima forma qua est substantia, alia qua est corpus, alia qua est vivens, alia qua est animal, et alia specifica qua est homo. Et sicut materia prima est naturaliter in potentia ad primam istarum, scilicet generalissimam, et quod ista est primus actus istius materie propter quod ex eis fit unum per se, ita secunda forma se habet ad compositum ex materia et prima forma, scilicet quod compositum illud est per se potentia respectu secunde forme. Et ista est actus formalis ipsius compositi. Ideo fit ex eis unum per se, sicut fiebat ex materia et forma prima’ ibid. II.4.10. 59 See ibid. II.7.25; III.6, 1st argument contra. 60 Ibid. II.4.16.

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it on account of the nature by which it is a living thing. But sensitive being inheres in Brunellus insofar as [he is an] animal and not insofar as [he is] living; and vegetative being inheres in him insofar as [he is] living, and not insofar as [he is an] animal. So sensitive being inheres in him by the nature by which he is an animal, and not by the nature by which he is living; and conversely with vegetative being. Therefore in Brunellus there is one nature according to which he is an animal, and another according to which he is living, and these are the vegetative and sensitive souls. Therefore, etc.61

Buridan replies: Brunellus, by his very essence and nature, is Brunellus and a horse and an animal and a living being and a body. And when it is said that sensitive being inheres in Brunellus insofar as [he is] an animal and not insofar as [he is] a living being, we understand by this that this is true per se and primary: ‘an animal is sensitive’; and not this: ‘a living thing is sensitive’; so that by ‘being on account of itself’ a convertible predication of terms is understood (whether primary or immediate or something of this sort) in accordance with how a reduplication is multiply put forth. So the locution was not speaking of a real inherence.62

The objection is a topical argument, taking ‘to inhere in something on account of itself is to inhere in it by its nature or essence’ as a propositio maxima, and then applying it to the specific cases of sensitive and

61

‘Item inesse alicui secundum se est inesse sibi per suam naturam vel essentiam. Ideo inesse animali secundum quod animal est inesse sibi per naturam per quam est animal. Et sic etiam inesse viventi secundum quod vivens est inesse sibi per naturam per quam est vivens. Sed Brunello inest esse sensitivum secundum quod animal et non secundum quod vivens, et esse vegetativum inest sibi secundum quod vivens et non secundum quod animal. Igitur esse sensitivum inest sibi per naturam per quam est animal et non per naturam per quam est vivens, et esse vegetativum econverso. Ergo in Brunello est alia natura secundum quam est animal et alia secundum quam est vivens, et iste sunt anima vegetativa et sensitiva, igitur et cetera’ ibid. II.4.3. 62 ‘Brunellus, per eandem eius essentiam et naturam, est Brunellus et equus et animal et vivens et corpus. Et cum dicitur quod Brunello inest esse sensitivum secundum quod animal et non secundum quod vivens, nos per hoc intelligimus quod hec est vera per se et primo, ’animal est sensitivum’ et non hec, ’vivens est sensitivum,’ ita quod per ’esse secundum quod ipsum’ intelligitur predicatio convertibilis terminorum, vel prima aut immediata aut huiusmodi, prout ’reduplicatio’ multipliciter exponitur. Ita quod ista locutio non erat de reali inherentia’ ibid. II.4.22.

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vegetative being, to infer that sensitive and vegetative natures are distinct in the same supposit. Buridan’s response denies the consequence, providing an alternative exposition of the propositio maxima. While the multiple form theorist runs the risk of positing as many forms as there are quidditative predicates (such that Brunellus is a horse by equinity, an animal by animality, etc.), Buridan’s response suggests that there is only one truth-maker for all of these predicates. If the positers of several substantial forms have made essences determinate and terrestrial, Buridan will retain the element of determinacy in his opponent’s account while preventing several such substantial forms from inhering in one suppositum. Thus, the truthmakers for the statements ‘a pig is an animal’ and a ‘horse is an animal,’ are left essentially disparate, leaving two equivocal uses of the term ‘animal’, albeit permissible from the standpoint of common speech. Elsewhere, it is confirmed that Buridan, like the plurality theorists, retains the image of forms as distinct, integral parts of the composite. In his Questions on the Metaphysics, he writes Aristotle rebuked Plato for wanting to remove matter from the quiddities and dispositions of sensible substances; and Physics I posits that sensible substance is essentially a composite of matter and form. And so form is an integral part of it.63

Hence, though Buridan remains an opponent of the multiplicity of substantial forms in the same suppositum, he agrees with its advocate, against both Aquinas and Aristotle, in regarding forms as integral parts of their composites. Buridan’s hylomorphism, like that of the plurality view both he and Aquinas argue against, thus satisfies the conditions for being a mereological hylomorphism. Let us finally examine a passage from the succeeding question from Buridan’s De Anima questions. Again, if a power were an accident of the soul, the soul would be in potency towards it, since a subject is in potency toward all its accidents. Therefore, either it itself would be in potency to this power – and then, by the same reasoning we would be able to say the same thing again from the 63

John Buridan, In Metaphysicen Aristotelis Questiones Argutissimae (Paris, 1518) VII.12, cor.

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start – or it is in potency to the other power through another power, and so we would proceed to infinity, which is unfitting.64 Here, Buridan follows the question of whether sensitive and vegetative souls are the same in the same animal with that of whether the powers of the soul are distinct from the soul itself. Buridan will answer in the negative. In the above objection, the objector argues by reductio that the soul is not distinct from its powers. The objector argues, from the hypothesis that the powers are accidents, to the dilemma that positing them as separate either leads to nugatoriness or to an infinite regress. In arguing that the soul is distinct from its powers, the objection thus assumes that the only way for a power to be distinct is for it to be an accident.65 Nowhere, neither in his reply to the question and the objection nor elsewhere in the QDA, does Buridan deny this assumption that the distinctness of what inheres entails accidentality.

5 Logical hylomorphism With the above laid out, we return to our discussion of the development of formal consequence. The above remarks provide us with the following two modest conclusions, as well as a direction for further research. First: the metaphysical thesis of the plurality of substantial forms appears to have provided a dialectical medium for the shift from Aquinas’ account of the inherence of a single substantial form in a suppositum, to Buridan’s account. In spite of his agreement with Aquinas in rejecting a plurality of substantial forms in a single substance, Buridan agrees with the plurality theorist against Aquinas: 1) in the acceptance of the form-essence identity thesis 2) in the assumption that identity or distinctness of species and genus must be determinate identity; 3) in regarding the union of the composite as one between form and prime matter; 4) in the accompanying metaphysical assimilation of the relation between form and matter to one between essence and accident; and 5) in the corresponding logical analysis,

64

John Buridan, Questiones de Anima II.5, obj. 14. This is required from the straightforward reading of the proof as a modus tollens: if it is to work, it must be assumed that ‘powers are distinct from the soul’ is antecedent to ‘a power is accidental to the soul’. This is again assumed in the ‘since’ clause of the first sentence: it assumes enthymematically that every power, if distinct from its subject, is an accident (hence that the soul, being a subject, would be in potency towards all its powers). 65

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rejected by Aquinas, of essential predications in terms of reference to forms inhering in a common suppositum. Second: Buridan’s logical hylomorphism, according to which the matter and form of a proposition are disjoint integral parts of a proposition – namely, categorematic and syncategorematic terms66 – strictly mirrors his physical hylomorphism, according to which matter and form are disjoint integral parts of a composite substance. Thus, while Buridan’s physical hylomorphism does not necessitate his logical hylomorphism, the specific shape of the former does seem to have facilitated that of the latter. It is further likely that both the identification of form with essence or nature – excluding matter – and the assumption that distinctness of what inheres entails its accidentality – an assumption equally applicable to the relation of substantial form and prime matter – played some role in the gradual assimilation of the natural/accidental division of consequences to that into formal and material varieties. Now, what remains for further research is to fill in the middle piece of this puzzle – namely, to further investigate what connections there may be between the pluricity theory and those more ‘pluralist’ accounts of formal consequence in existence prior to Buridan. It is clear enough that those authors, such as Scotus and Ockham, who use a broader sense of ’formal consequence’ tend also to be hylomorphic pluralists.67 It remains to be 66

Strictly speaking, the phrase ‘categorematic terms’ is redundant, and ’syncategorematic terms’ a contradiction in terms. On Buridan’s vocabulary, termini are the ‘ends’ of a proposition, in which it ‘bottoms out’. These are categorematic by construction. Likewise, syncategoremata are never the base units of a proposition, but always functions on smaller units. However, Nomina sunt ad placitum, and so the phrase ‘(syn)categorematic term’ is used here in accordance with more recent usage. 67 Further points of connection include: that Scotus held substantial union to be one of prime matter and substantial form, Richard Cross, “Duns Scotus’s AntiReductionistic Account of Material Substance,” Vivarium 33 (1995): 138; and that Scotus sees the extension of a substantial form beyond those corporeal parts manifesting its powers as accidental John Duns Scotus, Quaestiones Super Libros Metaphysicorum Aristotelis, ed. G. Etzkorn et al., vols. 3-4, Opera Philosophica (St. Bonaventure, NY: Franciscan Institute, 1997) VII.20, par. 19, pp. 383-384. That the soul is identical with its powers has also been regarded as closely linked to the plurality thesis. See Weisheipl, “Albertus Magnus and Universal Hylomorphism,” 242-43, De Wulf, History of Mediaeval Philosophy I, p. 335. For Scotus’ influence on Walter Burley, see Ottman Jennifer and Rega Wood, “Walter Burley: His Life and Works,” Vivarium 37, no. 1 (1999): 1-23; for an examination

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determined whether this connection may be more than accidental. That it would, however, appears at present to provide the path of least resistance from the predominantly syllogistic framework of Aquinas to Buridan’s substitutional, mereological account of formal consequence.

of the interconnection between metaphysical and logical disputes in Scotus and Ockham, see Martin, “Formal Consequence in Scotus and Ockham.”

APPEN NDIX

Volumes 155, 2017 The Proceeedings of thee Society for Medieval Loogic and Meetaphysics (P.S.M.L.M M.) is the pubblication of th he Society forr Medieval Logic L and Metaphysicss, collecting original o materrials presentedd at sessions sponsored s by the Socieety. Publicatioon in the Proceedings consstitutes prepu ublication, leaving the authors’ rightt to publish (aa possibly moodified version n of) their materials elssewhere unafffected. The Society for Medievall Logic and Metaphysics M (S S.M.L.M.) is a network of scholars founded withh the aim of fostering f collaaboration and d research based on thee recognition that t ™ recovvering the proofound metaph hysical insight hts of medievaal thinkers for oour own philosophical thou ught is highly desirable, and, despite the vvast conceptuual changes in the intervvening period d, is still possiible; but ™ this rrecovery is onnly possible if we carefullyy reflect on th he logical frameework in whhich those in nsights were articulated, given g the paraddigmatic diffe ferences betw ween medievaal and moderrn logical theorries. The Societty’s web sitte (http://facu ulty.fordham.eedu/klima/SM MLM/) is designed to serve the puurpose of keeeping each otther up-to-datte on our current projeects, sharing recent r results,, discussing sccholarly questtions, and organizing m meetings. If you are innterested in joining, pleasee contact Gyuula Klima (Ph hilosophy, Fordham Unniversity) by e-mail e at: klim [email protected] © Society foor Medieval Logic L and Mettaphysics, 20117

CONTRIBUTORS

Andrew Arlig, Brooklyn College of the City University of New York Gyula Klima, Fordham University Shane Wilkins, Fordham University Thomas Ward, Baylor University Rodrigo Guerizoli, Universidade Federal do Rio de Janeiro Turner C. Nevitt, University of San Diego Jacob Archambault, Highlands Latin School