Contradictions: Logic, History, Actuality 9783110340822, 9783110335743

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Elena Ficara Contradictions

Berlin Studies in Knowledge Research

| Edited by Günter Abel and James Conant

Volume 6

Elena Ficara

Contradictions

| Logic, History, Actuality

Series Editors Prof. Dr. Günter Abel Technische Universität Berlin Institut für Philosophie Straße des 17. Juni 135 10623 Berlin Germany e-mail: [email protected] Prof. Dr. James Conant The University of Chicago Dept. of Philosophy 1115 E. 58th Street Chicago IL 60637 USA e-mail: [email protected]

ISBN 978-3-11-033574-3 e-ISBN 978-3-11-034082-2 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.dnb.de. © 2014 Walter de Gruyter GmbH, Berlin/Boston Typesetting: le-tex publishing services GmbH, Leipzig Printing and binding: Hubert & Co. GmbH & Co. KG, Göttingen ♾ Printed on acid-free paper Printed in Germany www.degruyter.com

Acknowledgements This book goes back to a conference with the same title that took place at Technical University Berlin in the summer of 2011 and was generously supported by the Deutsche Forschungsgemeinschaft and the IZW. For help before, during and after the conference, I am particularly thankful to Günter Abel, Franca D’Agostini, Dagfinn Føllesdal, Hans Poser, Claudio Roller, Doris Schöps and Elisabeth Simon. For making the publication of this volume possible, I am especially grateful to the IZW, in particular to Günter Abel, for his friendliness and the unconditioned support of the project in every phase of its development. I am also grateful to Hadi Faizi, who helped me revising the English texts, and to Peter Remmers for his editorial advice. Finally, my thanks go to the publishing house De Gruyter, particularly to Gertrud Grünkorn and Konrad Vorderobermeier for help during the production of this volume.

Contents Elena Ficara Introduction | 1 Part I: Logic Graham Priest Contradictory Concepts | 13 JC Beall Rapunzel Shaves Pinocchio’s Beard | 27 Franca D’Agostini Paradoxes and the Reality of Contradictions | 31 Achille C. Varzi Logic, Ontological Neutrality, and the Law of Non-Contradiction | 53 Francesco Berto Representing the Contradictory | 81 Part II: History Enrico Berti Objections to Aristotle’s Defence of the Principle of Non-Contradiction | 97 Angelica Nuzzo The Justice of Contradiction. Logical Advancement and Historical Transformations | 109 Luca Illetterati Limit and Contradiction in Hegel | 127 Klaus Vieweg Zur Logik moralischer Urteile | 153

viii | Contents Part III: Actuality Gianni Vattimo Insuperable Contradictions | 173 Federico Vercellone A Disenchanted Reenchantment. Hermeneutics and Morphology | 181 Wolfgang Welsch Wie wir auf Konsistenz aus sind – und warum | 193 List of Contributors | 209 Index of Names | 215 Subject Index | 219

Elena Ficara

Introduction The notion of contradiction is of the greatest importance in several fields. It is a central topic in the history of ancient philosophy: the very beginning of philosophy in history seems to be closely connected to the discovery of contradictions in Greek language. It is of crucial importance in metaphysics: Aristotle’s inquiry into the nature of being is also, if not mainly, inspired by the need of avoiding (and diagnosing) the occurrence of contradictions. It is evidently, in many senses, one of the basic concerns of logic. The problem of contradiction is also the problem of disagreement: is it possible that contradictory theses are both true? Under normal circumstances, one of the two theses is false, and this means that one of the disagreeing parties is wrong. And yet, at least sometimes people disagree without any fault (or so it seems), and incompatible positions seem both right. In this sense, the theme of contradiction is also the core of any political reflection about democratic confrontation, relativism and the role of the concept of truth in political practice. Not only that, a complete theory about the problematic and heuristic relevance of contradictions in any field was typically given by the authors of German Idealism, and specifically by the tradition of Hegelianism, so the issue is also crucial for the history of philosophy after Kant, and for any inquiry into classical German philosophy. Finally, the problem of the existence, uses, and nature of contradictions is at the core of many contemporary discussions in philosophy: discussions about paradoxes, and the plausibility of paraconsistent logics,¹ but also about the status of human subjects, as located in social and political contexts, and about the destiny of Marxism.² All this stated, a typical problem affects contemporary theories on this topic. The main concern is that the authors working on it come from radically different philosophical traditions and contexts, and they can only very rarely communicate with each other, and share their results. The first aim of the book is thus to stimulate a genuine dialogue between different approaches, so that the understanding of the problem of contradictions becomes as complete as possible. Not only that, the same topic of contradictions, as suggested above, seems to be located at the intersection of different fields, tradi-

1 See the contemporary discussions about Graham Priest’s dialetheism, which are documented in many leading philosophical journals, as well as in Priest/Beall/Armour-Garb (2004). 2 See Judith Butler’s and Slavoy Žižek’s reconsideration of Hegelianism in Butler (1987) and Žižek (2012).

2 | Elena Ficara tions and schools, so it is particularly apt to overcome the divides between philosophical approaches, constituting a common ground of philosophical research. The papers collected in this volume present some of the most recent results of the work about contradictions in philosophical logic, examine the history of contradiction in crucial phases of philosophical thought (in ancient philosophy and in German philosophy after Kant), consider the relevance of contradictions for political and philosophical current times. Despite the differences between approaches and stiles, a basic question emerges, and it is more or less openly addressed in all the papers. It is the question of the irreducibility, reality, and productive force of (some) contradictions.³ The book has three parts. In the first part, Logic and Metaphysics, leading experts of philosophical logic and metaphysics focus on the problem – now at the centre of living debates about non-classical logic,⁴ and in particular about dialetheism⁵ – of the reality of contradictions, and on the link between logic and metaphysics. The second part, History, entails papers by specialists of ancient philosophy and post-Kantian philosophy, the two periods in history where the reflection on contradictions reached probably its greatest development. The papers analyse both Aristotle’s defence of the law of non-contradiction, dealing with some problems connected with it, and Hegel’s arguments for the reality and effectiveness of contradictions, and their relevance for practical and political philosophy. The last part, Actuality, is devoted to the role and uses of contradictions for cultural and political occurrences. It collects papers by eminent contemporary philosophers working in the mainly European tradition, on the political, aesthetic and biological implications of contradictions.

Graham Priest (Contradictory Concepts) examines a question at the very core of contemporary discussions within dialetheism. If dialetheism is the view that there are (some) true contradictions, then the problem is to assess if “the contradictions

3 Evidently, the meaning of the term “contradiction”, as well as that of the expression “true contradiction” is here at stake. For a first overview see Grim (2004), 49–72, as well as the papers collected in this volume (Part One: Logic). 4 See Priest/Beall/Armour-Garb (2004). 5 The terms ‘dialetheia/dialetheism’ were coined by Graham Priest and Richard Routley in 1981 (see Priest/Routley/Norman (1989), xx) and result from the union of the two Greek words ‘di-’ (two/double) and ‘aletheia’ (truth). A dialetheia is a true contradiction (a double truth), i.e. a true proposition whose negation is also true, and dialetheism is the view according to which there are some dialetheias (true-and-false propositions) and this does not imply any trivialisation of logic. For a clear overview, see Priest/Berto (2013).

Introduction |

3

are only in our concepts or also in reality”. Strictly speaking, dialetheism not only implies that our concepts might entail contradictions, it also implies the metaphysical insight that there are things that satisfy these concepts. But if we hold that contradictions are in reality, the view that there are facts of the form A and ¬A, and thus that there are not only positive, but also negative facts, seems inevitable. This view might prove to be – so Priest – “too rich to many stomach”. In the paper he focuses on the opposite perspective, the so-called semantic dialetheism,⁶ according to which contradictions are only in our languages, and do not concern reality. Assuming that contradictions are a merely conceptual and linguistic phaenomenon, Priest examines different strategies in order to get rid of them simply by changing our concepts, and shows that they all fail. As a matter of fact, semantic dialetheism, so understood, presents many difficulties, first of all expressive loss, i.e. the impossibility to think and express concepts – such as the concept of totality – which classically involve irreducible contradictions.

Jc Beall’s Rapunzel Shaves Pinocchio’s Beard goes back to a discussion, which appeared in Analysis, between himself and Peter Eldridge-Smith concerning the so called Pinocchio paradox,⁷ a version of the Liar paradox that involves the empirical world. In this paper, Beall presents a paradoxical tale, very similar to Pinocchio paradox. In the tale, grass is growing if and only if what Rapunzel says is false, and it happens that Rapunzel says that grass is growing. Evidently, this is a liar-like situation, since if what Rapunzel says is true, then grass is not growing and what she says must be false; and if it is false, then grass is growing and what she says must be true. Pinocchio’s paradox, similarly, says that Pinocchio’s nose is growing if and only if Pinocchio lies, and Pinocchio says that his nose is growing. At first sight, these versions of the Liar paradox seem to involve empirical-world gluts, i.e. sentences about the empirical world (noses and grass) that are both true and false. This would ultimately imply a metaphysical dialetheism of some sort,

6 Ed Mares has coined the expressions “metaphysical dialetheism”, distinguishing it from “semantic dialetheism”. In Mares (2004), 269, he defines the two notions as follows: “Both semantical and metaphysical dialetheism hold that there are true contradictions, or at least that it is possible for there to be true contradictions. That is what ‘dialetheism’ means. The difference between the two views concerns the status of these contradictions (. . . ) The metaphysical dialetheist holds that there are aspects of the world (or of some possible world) for which any accurate description will contain a true contradiction. Semantic dialetheism, on the other hand, maintains that it is always possible to redescribe this aspect of the world, using a different vocabulary”. 7 The Pinocchio paradox was invented by Peter Eldridge-Smith’s daughter, Veronique EldridgeSmith, and occasioned a discussion on empirical-world gluts documented in Analysis. See Eldridge-Smith/Eldridge-Smith (2010); Eldridge-Smith (2011); Beall (2011); Eldridge-Smith (2012).

4 | Elena Ficara for instance the view that there must be something in the empirical world that both is and is not, both has and has not a particular physical property. Jc Beall is one of the most eminent contemporary proponents of the view called semantic dialetheism, according to which contradictions arise because of our language, and because of the semantic behaviour of the concept of truth.⁸ Accordingly, Beall suggests here that Pinocchio’s and Rapunzel’s stories are mere tales, and not genuine paradoxes (that is: apparent valid arguments with true premises and an apparently false conclusion). In fact, the premises of both arguments are not true, they are only “true according to the story”. Truth in a story – so Beall – is insufficient for truth at some world. Evidently, in both Priest’s and Beall’s papers what is at stake is the question: what are the metaphysical and ontological implications of the thesis that there are true contradictions? Does the view that there are true contradictions have ontological implications? And what is the link between the semantic claim that there are true contradictions and the ontological one, according to which there effectively are contradictory states of affairs, or objects that make contradictions true? These questions are at the core of D’Agostini’s and Varzi’s papers.

Franca D’Agostini (Paradoxes and the Reality of Contradictions) explicitly addresses the first, examining the problem of the reality of contradictions, and of the kind of realism implied by the dialetheist’s thesis according to which some contradictions are true. D’Agostini considers the expression “true contradiction”, inquiring into its possible meaning as made true by real (non-constructed, nonfictional) facts. She first considers the kind of evidence involved in epistemic and semantic paradoxes, then argues for an interpretation of the realism involved by dialetheism as alethic realism, the view according to which a sentence or proposition 𝑝 is true if and only if things stand like 𝑝 says. In the perspective of alethic realism, a “fact” is simply what can make a proposition true, so there might be indeterminate kinds of facts: universal, as well as conditional, mathematical or physical, infra-subjective or intra-subjective, physical or intentional facts etc. All this stated, D’Agostini suggests that alethic realism is perfectly adaptable to three theses that classically constitute metaphysical realism, namely: the thesis that there are facts, that there is a unique true description of these facts, and that we can formulate true descriptions of facts. From this point of view, alethic realism turns out to be a particular version of metaphysical realism, which only requires that the field of what we count as really existing facts must be left open. All this

8 See Beall (2009).

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stated, D’Agostini claims that contradictions are alethically true, which means there are many different kinds of contradictions, in accordance with different kinds of facts. The interpretation of dialetheism in terms of alethic realism, so D’Agostini, may settle some controversies affecting the debate on dialetheism and state the metaphysical (not only semantic) reality of contradictions, without any commitment to metaphysical trivialism.

Achille Varzi (Logic, Ontological Neutrality, and the Law of Non-Contradiction) examines the connection between the universality of logic and its supposed ontological neutrality. If logic and its forms have to be universally valid, logic has to abstract away from content, and to be ontologically neutral. In Varzi’s reconstruction, Aristotelian logic, precisely because of its ontological presuppositions, was deemed insufficient as a canon of pure logic and overcome by modern FregeRussell logic. Also modern quantification theory, with its existentially loaded theorems and patterns, has been claimed to suffer from a defect of logical purity. In particular, Varzi focuses on the law of non-contradiction’s ontological implications, and on its critique. According to him, the critiques of the law of noncontradiction (beginning with Łukasievicz through paraconsistent logics and dialetheism) are moved by the attempt of overcoming its tacit ontological implications, and directed towards the achievement of a greater universality for logic. In this perspective, the main problem is the link between the metaphysical and the semantic point of view, and more specifically the relation between the (ontological) law of non-contradiction (it is not possible that both p and not p) and what Varzi calls the semantic principle of contravalence (it is not possible that a statement p both is and is not true). In particular, the failure of contravalence need not entail genuine ontological overdeterminacy or genuine counterexamples to non-contradiction. The problem is thus to discriminate between a merely de dicto dialetheia and a de re dialetheia. Varzi discusses two options, which can constitute an indication in order to argue that the law of non-contradiction is not an instance of the prejudices from which logic has tried to free itself throughout its history in the spirit of even greater ontological neutrality. In fact, every evidence we might have against the law requires that we deploy other principles, and it is those principles that might be deemed inadequate as canon of pure logical reasoning.

Francesco Berto (Representing the Contradictory) asks about the possibility of representing contradictory states. He therefore develops a semantic and syntactic extension of Priest’s basic relevant logic 𝑁4 . He introduces, on the syntactic

6 | Elena Ficara side, the representation operator ®, which allows both to capture our capacity of seeing or conceiving contradictions and logical impossibilities and to admit particularly anarchic non-normal worlds, including self-contradictory worlds. As a matter of fact, according to Berto contradictions are human phaenomena, linked to our finite and fallible condition. Thus if we can represent and conceive contradictions and other absolute impossibilities, non-normal worlds are natural candidates to model this human condition. In contrast, a logic that does not admit the possibility of representing contradictions is only able to grasp highly idealized epistemic notions, and cannot mirror the actual situation of human beings as finite, fallible, and occasionally self-contradicting cognitive agents.

Enrico Berti (Objections to Aristotle’s Defence of the Principle of Non-Contradiction) considers both Aristotle’s defence of the law of non-contradiction and some main objections to it (in particular Łukasiewicz’s and Dancy’s critiques,⁹ and Priest’s dialetheic arguments against Metaphysics Gamma¹⁰). In his view, according to Aristotle the law of non-contradiction does not stand in the way of saying and thinking contradictions; however, according to the Greek philosopher the emerging of a contradiction is always – so Berti – a sign of falsity. Not only that, the elimination of a contradiction is a necessary component of the logical and discussive process of refutation. Thus every dismissal of the law implies a challenge to the very procedure of refutation, and the risk of trivialism (the view according to which everything is contradictory, and therefore everything is true and can be proved). Dialetheism, arguing for the suspension of the law only in special cases, could represent a genuine alternative to trivialism. However – so Berti – dialetheism does not give a clear criterion to distinguish true contradictions from false ones.

Angelica Nuzzo (The Justice of Contradiction: Logical Advancement and Historical Transformations) focuses on the practical and juridical implications of Hegel’s logical idea of contradiction, giving a new account of one of the most contentious Hegelian views, the idea of a Weltgeschichte (history of the world) placed as conclusion of the sphere of objective spirit, and the thesis that Weltgeschichte ist Weltgericht (the history of the world is the tribunal of the world). According to this view, history does not only have the descriptive task of registering events, but

9 See Łukasiewicz (1910) and Dancy (1975). 10 Priest (2006).

Introduction

| 7

it also has a normative import. Nuzzo argues that Hegel’s view, which has often been disputed and variously challenged, is the direct and coherent consequence of the claim that historical processes are structured according to the dialectical logic of contradiction. According to Nuzzo, conflict and contradiction, rather than being a sign of imbalance and disharmony, are the motor of historical change, and thus the very conditions of a just political and practical order. In this perspective, the normative function of contradiction also emerges: conflict is justice and Weltgeschichte is Weltgericht because historical change is produced by strife. This also means that contradictions have a discriminative and ordering power; they do lead neither to chaos nor to nothingness but to epochal transformation.

Luca Illetterati (Limit and Contradiction in Hegel) considers the Hegelian thesis: “things are inherently contradictory”, arguing for the necessity of interpreting it in a literal, and not metaphorical or conciliatory way. In his reading, there is a strong connection between Hegel’s talk of contradiction and the problem of determination. In turn, the problem of determination is, according to Illetterati, linked to the question of limit: everything is contradictory insofar as everything is determinate, i.e. limited. As Kant himself implicitly already acknowledged in some subparagraphs of the Prolegomena to Any Future Metaphysics,¹¹ thinking the limit means to think a structure that constitutively entails a contradiction. In this sense, if the limit is both an inherently contradictory structure and the locus where everything is what it is, then the view “all things are inherently contradictory” is unavoidable.

Klaus Vieweg (Zur Logik moralischer Urteile) examines the central role of contradictions and antinomies within Hegel’s practical philosophy, in particular for morality. The concept of morality implies the opposition between particularity and universality (the particularity of the acting and wanting human being and the universality of the law), an opposition that Hegel interprets as contradiction. According to Hegel, and differently from Kant, the knowledge of the idea of the good is what allows an adequate understanding of the contradiction involved in morality. As to Kant, a non-cognitive faith in God is what makes possible to reconcile the opposition between the universality of the moral law and the particularity of the human will. From the Kantian point of view, the contradiction is not conceived but only presupposed as what has to be overcome. Hegel, differently, shows

11 Kant (1900ff.), AA IV.

8 | Elena Ficara the contradictory structure of the idea of the good as the identity of the opposites (particularity and universality).

Gianni Vattimo (Insuperable Contradictions) argues that philosophy has always tried to reconcile contradictions, and that the same title “Contradictions. Logic, History, Actuality” could be intended as the attempt of controlling, and in the end overcoming, contradictions. In explicit polemic with such an attempt, Vattimo defends the view that there are irreducible contradictions, and it is necessary to let contradictions speak, without controlling them. What he calls “ontology of revolution” constitutes, in his view, the only possible frame able to address irreducible contradictions. In this frame, contradictions emerge as the very place where, Heideggerianly, being “happens” (sich ereignet). In Vattimo’s view, to propose a reflection on contradictions that does not assume their reduction as its main task, is essential in order to meet the needs of contemporary culture, a culture that is characterised by a lack of emergency, rather then by a lack of conciliation.

Federico Vercellone (A Disenchanted Reenchantment. Hermeneutics and Morphology) sees in morphology (as the theory or logic of figures) the perspective that can best inherit the role of the koiné Gadamer wanted for hermeneutics. Not only that, the logic of figures is also able to deepen Adorno’s and Horkheimer’s idea of a dialectic of enlightenment, thus dealing with the peculiar contradictions of contemporary culture and science. In particular, Vercellone shows how the focus on the concept of image (or figure) allows overcoming Heidegger’s, Gadamer’s, but also Adorno’s one-sided critique of technology. According to Vercellone, technology, rather than being – as Heidegger wanted – an instrument of hiding what truly is, is fundamental in order to stimulate a “re-enchantment of the world”, that is a creative way of dealing with images, promoting a new human self-awareness. In this perspective, figures or images are, above all, contradictory forms, that is: forms of conceptualisation that at the same time show the limits of every conceptualisation.

Wolfgang Welsch (Wie wir auf Konsistenz aus sind – und warum) analyses the role of contradictions in different dimensions of human culture and life (everyday thought, philosophical and scientific reasoning, biological life), underlining that they all show an effort of overcoming contradictions. Welsch thus points out the centrality of consistency (intended as lack of contradictions) in different contexts, showing that the demand for logical consistency is rooted in more original

Introduction

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kinds of demands. He considers some typical cases where we call for consistency, first of all our everyday need for both other people’s consistency and consistency within ourselves, and secondly the philosophical claim (Heraclitus, Dögen, Cusanus, Hegel) that oppositions on a linguistic or argumentative level should be overcome on a higher argumentative level. In these cases, and despite the emergence of apparently irreducible contradictions, the need for consistency seems to prevail, a need that – according to Welsch – goes beyond the argumentative and logical dimension. In particular, the pressure for consistency is – so Welsch – a biological and ontological command: the physical, chemical, biotic forms of selforganisation are all ways of producing consistency.

References JC Beall, Spandrels of Truth, Oxford, 2009. JC Beall, “Dialetheists against Pinocchio”, in: Analysis 71, 689–691, 2011. J. Butler, Subjects of Desire. Hegelian Reflections in 20th-Century France, New York, 1987. R. M. Dancy, Sense and Contradiction. A Study in Aristotle, Dordrecht and Boston, 1975. P. Eldridge-Smith, “Pinocchio against the dialetheists”, in: Analysis 71, 306–308, 2011. P. Eldridge-Smith, “Pinocchio beards the Barber”, in: Analysis 72, 749–752, 2012. V. Eldridge-Smith, P. Eldridge-Smith, “The Pinocchio paradox”, in: Analysis 70, 212–215, 2010. P. Grim, “What is a Contradiction?”, in: Graham Priest, JC Beall, and Bradley Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 49–72, 2004. I. Kant, Kant’s gesammelte Schriften, edited by the Royal Prussian, later German, Academy of Sciences, Berlin (quoted as AA, followed by the indication of the volume), 1900ff. J. Łukasiewicz, “Über den Satz des Widerspruchs bei Aristoteles”, in: Bulletin international de l’Académie des sciences de Cracovie, Classe d’histoire et de philosophie, 1/2, 15–38, 1910. E. D. Mares, “Semantic Dialetheism”, in: Graham Priest, JC Beall, and Bradley Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 264–275, 2004. G. Priest, Doubt Truth to Be a Liar, Oxford, 2006. G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 2004. G. Priest, F. Berto, “Dialetheism”, in: The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), E. N. Zalta (ed.). http://plato.stanford.edu/archives/sum2013/entries/ dialetheism/, 2013. G. Priest, R. Routley, J. Norman (eds.), Paraconsistent Logic. Essays on the Inconsistent, Munich, 1989. S. Žižek, Less Than Nothing. Hegel and the Shadow of Dialectical Materialism, London and New York, 2012.

| Part I: Logic

Graham Priest

Contradictory Concepts 1 Introduction That we have concepts which are contradictory is not news. That there may be things which satisfy them, dialetheism, is, by contrast, a contentious view. My aim here is not to defend it, however;¹ and in what follows, I shall simply assume its possibility. Those who disagree are invited to assume the same for the sake of argument. The point of this essay is to think through some issues that the view raises. In particular, we will be concerned with two inter-related questions: 1. 2.

Are the dialetheias simply in our concepts/language, or are they in reality? And what exactly does this distinction amount to anyway? Assuming that they are only in our concepts/language, can we get rid of dialetheias simply by changing these?

I will take up these issues, in the two parts of the paper.²

2 Dialetheism, Concepts, and the World 2.1 Contradiction by Fiat A dialetheia is a pair of statements of the form 𝐴 and ¬𝐴 which are both true.³ We may think of statements as (interpreted) sentences expressed in some language – a public language, a language of thought, or whatever. In this way they contrast, crucially, with whatever it is that the statements are about. Let us call this, for want of a better name, the world. One thing that partly determines the truth value of a statement is its constituents: the meanings of the words in the sentence, or the concepts the words express. (Conceivably, one might draw a distinction here, but not one that seems

1 This is done in Priest (1995), (2006a), (2006b). The topic is discussed by numerous people in the essays in Priest/Beall/Armour-Garb (2004) and the references cited therein. 2 A longer version of this paper will appear as “Dialetheism, Concepts and the World”, in Joke Meheus, Erik Weber, and Dietlinde Wouters (eds.), Logic, Reasoning and Rationality, Springer. 3 Priest (2006a), 4.

14 | Graham Priest relevant for present purposes.) Let us call these things, again for want of a better word, semantic. In certain limit cases, such as ‘Red is a colour’, semantic factors may completely determine the truth value of a statement. In general, however, the world is also involved in determining the truth value. Thus, the statement that Melbourne is in Australia is made true, in part, by a certain city, a certain country – literally part of this world.⁴ Given that dialetheias are linguistic, one natural way for them to arise is simply in virtue of linguistic/conceptual fiat. Thus, suppose we coin a new word/concept, ‘Adult’, and stipulate that it is to be used thus:⁵ – –

if a person is 16 years or over, they are an Adult if a person is 18 years or under, they are not an Adult

Now suppose there is a person, Pat, who is 17. Then we have: (*) Pat is both an Adult and not an Adult. Of course, one can contest the claim that the stipulation succeeds in giving the new predicate a sense. Deep issues lurk here, but I will not go into them, since my concern is with other matters. I comment only that the stipulation would seem to be just as successful as the dual kind, endorsed by a number of people,⁶ which under-determine truth values – such as the following, for ‘Child’: – –

if a person is 16 years or under, they are a Child if a person is 18 years or over, they are not a Child

Assuming the stipulation of the kind involved in ‘Adult’ to work, we have a certain sort of dialetheia here. We might call it, following Mares (2004), a semantic dialetheia. Note that, in terms of the distinction just drawn between semantic and worldly factors, the epithet is not entirely appropriate. The truth of (*) is determined only in part by semantics; some worldly factors are also required, such as Pat and Pat’s age. Still, let us adopt this nomenclature.

4 Quineans would, of course, reject the distinction being made here between semantic and worldly factors. This is not the place to defend the notion of analyticity. I do so in Priest (1979) and Priest (forthcoming). 5 See Priest (2001). 6 E.g., Soames (1999).

Contradictory Concepts |

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2.2 Semantic Dialetheism The dialetheism engendered by the definition of ‘Adult’ is transparent. There are other examples which are, plausibly, of the same kind, though they are less transparent. One of these concerns dialetheias apparently generated by bodies of laws, rules, or constitutions, which can also be made to hold by fiat. Thus, suppose that an appropriately legitimated constitution or statute rules that:⁷ – –

every property-holder shall have the right to vote no woman shall have the right to vote

As long as no woman holds property, all is consistent. But suppose that, for whatever reason, a woman, Pat, comes to own property, then: –

Pat both has and has not got the right to vote.

Examples that are arguably of the same kind are given by multi-criterial terms.⁸ Thus, suppose that a criterion for being a male is having male genitalia; and that another criterion is the possession of a certain chromosomic structure. These criteria may come apart, perhaps as the result of surgery of some kind. Thus, suppose that Pat has female genitalia, but a male chromosomic structure. Then: –

Pat is a male and not a male.

In this case, there is no fiat about the matter. One cannot, therefore, argue that the contradiction can be avoided by supposing that the act of fiat misfires. What one has to do, instead, is to argue that the conditions in question are not criterial. Again, I shall not pursue the matter here. A final example that is, arguably, in the same camp, is generated by the Abstraction Principle of naive set theory:⁹ Abs Something is a member of the collection {𝑥 : 𝐴(𝑥)} iff it satisfies the condition 𝐴(𝑥).

7 The example comes from Priest (2006a), Section 13.2. 8 See Priest (2006a), Section 4.8, and Priest/Routley (1989), Section 2.2.1. 9 Priest (2006a), ch. 0.

16 | Graham Priest This leads to contradiction in the form of Russell’s paradox.¹⁰ Again, there is no fiat here.¹¹ If one wishes to avoid the contradiction, what one must contest is the claim that satisfying condition 𝐴(𝑥) is criterial for being a member of the set {𝑥 : 𝐴(𝑥)} – or, what arguably amounts to the same thing in this case, that Abs is true solely in the virtue of the meanings of the words involved, such as ‘is a member of’. Again, let us not go into this here. The point of the preceding discussion is not to establish that the contradictions involved are true, but to show that dialetheias may arise for reasons that are, generally speaking, linguistic/conceptual.

2.3 Contradictions in the World Some have felt that there may be a more profound sort of dialetheia, a contradiction in the world itself, independent of any linguistic/conceptual considerations. Let us call such dialetheias, following Mares again, metaphysical dialetheias.¹² A major problem here is to see exactly what a metaphysical dialetheia might be. Even someone who supposes that all dialetheias are semantic will accede to the thought that there are contradictions in the world, in one sense. None of the contradictions we considered in the previous sections, with perhaps the exception of Russell’s paradox, is generated purely by semantic considerations. In each case, the world has to cooperate by producing an object of the appropriate kind, such as the much over-worked Pat. The world, then, is such that it renders certain contradictions true. In that sense, the world is contradictory. But this is not the sense of contradiction that is of interest to metaphysical dialetheism. The contradictions in question are still semantically dependent in some way. Metaphysical dialetheias are not dependent on language at all; only the world. But how to make sense of the idea? If the world comprises objects, events, processes, or similar things, then to say that the world is contradictory is simply a category mistake, as, then, is metaphysical dialetheism.¹³ For the notion to get a grip, the world must be constituted by things of which one can say that they are true or false – or at least something ontologically equivalent.

10 Take 𝐴(𝑥) to be 𝑥 ∉ 𝑥, and 𝑟 to be {𝑥 : 𝑥 ∉ 𝑥}. Then we have 𝑦 ∈ 𝑟 iff 𝑦 ∉ 𝑦. Hence, 𝑟 ∈ 𝑟 iff 𝑟 ∉ 𝑟, and so 𝑟 ∈ 𝑟 ∧ 𝑟 ∉ 𝑟. 11 An example of a similar kind, which does have an explicit element of fiat, is that of the Secretaries’ Liberation League, given by Chihara (1979). 12 Mares (2004). A number of people have taken me (mistakenly) to be committed to this kind of dialetheism. See Priest (2006a), Section 20.6. 13 The point is made in Priest (2006a), Section 11.1.

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Are there accounts of the nature of the world of this kind? There are. The most obvious is a Tractarian view of the world, according to which it is composed of facts. One cannot say that these are true or false, but one can say that they obtain or do not, which is the ontological equivalent. Given an ontology of facts to make sense, metaphysical dialetheism may be interpreted as the claim that there are facts of the form 𝐴 and ¬𝐴, say the facts that Socrates is sitting and that Socrates is not sitting. But as this makes clear, there must be facts of the form ¬𝐴, and since we are supposing that this is language-independent, the negation involved must be intrinsic to the fact. That is, there must be facts that are in some sense negational, negative facts.¹⁴ Now, negative facts have had a somewhat rocky road in metaphysics, but there are at least certain well-known ways of making sense of the notion, so I will not discuss the matter here.¹⁵ If one accepts an ontology of facts or fact-like structures, then metaphysical dialetheism makes sense. Note, moreover, that if one accepts such an ontology, metaphysical dialetheism is a simple corollary of dialetheism. Since there are true statements of the form 𝐴 and ¬𝐴 then there are facts, or fact-like structures, corresponding to both of these.¹⁶ All the hard work here is being done by the metaphysics; dialetheism itself is playing only an auxiliary role.

3 Conceptual Revision 3.1 Desiderata for Revision Still, a metaphysics of facts (including negative facts) is too rich for many stomachs. Suppose that we set this view aside. If we do, all dialetheias are essentially language/concept dependent. In this way, they are, of course, no different from any other truths. But some have felt that, if this be so, dialetheias are relatively superficial. They can be avoided simply by changing our concepts/language. Compare the corresponding view concerning vagueness, held, for example, by Rus-

14 This isn’t quite right. Facts may not themselves be intrinsically negative: the relation between the facts that 𝐴 and that ¬𝐴 must be intrinsic. But this does not change matters much. 15 In situation semantics, states of affairs come with an internal “polarity bit”, 1 or 0. Facts with a 0 bit are negative. Alternatively, a positive fact may be a whole comprising objects and a positive property/relation; whilst a negative fact may be a whole comprising objects and a negative property/relation. For a fuller discussion of a dialetheic theory of facts, see Priest (2006b), ch. 2. 16 This assumes that all truths correspond to facts. In principle, anyway, one could endorse a view to the effect that some kinds of sentence are true in virtue of the existence of corresponding facts, whilst others may have different kinds of truth-makers.

18 | Graham Priest sell (1923). All vagueness is in language. Reality itself is perfectly precise. Vague language and its problems may, therefore, be avoided by changing to a language which mirrors this precision. Contradictions may certainly be resolved sometimes. Thus, consider the legal example concerning Pat and her rights. If and when a situation of this kind arises, the law would, presumably, be changed to straighten out the conflicting conditions for being able to vote. Note, however, that this is not to deny dialetheism. The situation before the change was dialetheic. The point of the change is to render it not so. Note, also, there is no a priori guarantee that making changes that resolve this particular contradiction will guarantee freedom from contradiction in toto. There may well be others. Indeed, making changes to resolve this contradiction may well introduce others. Laws comprise a complex of conceptual interconnections, and the concepts apply to an unpredictable world. There is certainly no decision procedure for consistency in this sort of case; nor, therefore, any guarantee of success in avoiding dialetheism in practice.¹⁷ But maybe we could always succeed in principle. Consider the following conjecture: –

Whenever we have a language or set of concepts that are dialetheic, we can change to another set, at least as good, that is consistent.

The suggestion is, of course, vague, since it depends on the phrase ‘at least as good’. Language has many purposes: conveying information, getting people to do things, expressing emotions. Given the motley of language use, I see no reason to suppose that an inconsistent language/set of concepts can be replaced by a consistent set which is just as good for all the things that language does. I don’t even know how one could go about arguing for this. Maybe we stand more chance if we are a little more modest. It might be suggested that language has a primary function, namely representation; and, at least for this function, given an inconsistent language/set of concepts, one can always replace it with a consistent one that is just as good. The claim that representation is the primary function of language may, of course, be contested; but let us grant it here. We still have to face the question of what ‘just as good’ means now, but a natural understanding suggests itself: the replacement is just as good if it can

17 Actually, I think that the change here is not so much a change of concepts as a change of the world. Arguably, the change of the law does not affect the meanings of ‘vote’, ‘right’, etc. The statement ‘Pat has the right to vote’ may simply change its truth value, in virtue of a change in the legal “facts”.

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represent every situation that the old language represents. Let us then consider the following conjecture:¹⁸ –

Any language (set of concepts), 𝐿, that represents things in a dialetheic way, can be replaced by a consistent language (set of concepts), 𝐿󸀠 , that can represent every situation that 𝐿 represents, but in a consistent way.

The conjecture is still ambiguous, depending on how one understands the possibility of replacement here. Are we to suppose this to be a practical possibility, or a merely theoretical one? If the distinction is not clear, just consider the case of vagueness again. If there is no such thing as vagueness in re, we could, in principle, replace our language with vague predicates by one whose only predicates are crisp. But the result would not be humanly usable. We can perceive that something is red. We cannot perceive that it has a wavelength of between exactly 𝑥 and 𝑦 Ångstroms, where 𝑥 and 𝑦 are real numbers. A language with precise colour predicates would not, therefore, be humanly usable. Any language that can be used only by someone with superhuman powers of computation, perception, etc., would be useless. To return to the case of inconsistency, we have, then, two questions: – –

Can the language be replaced in theory? Would the replacement be possible in practice?

A few things I say will bear on the practical question,¹⁹ but by and large I shall restrict my remarks to the theoretical one. This is because to address the practical question properly one has to understand what the theoretical replacement is like. In other words, not only must the answer to the theoretical question be ‘yes’, the answer must provide a sufficiently clear picture of the nature of the replacement. Nothing I go on to say will succeed in doing this. I have stressed the distinction mainly to point out that even if the answer to the theoretical question is ‘yes’, the replaceability conjecture has another hurdle to jump if the victory for those who urge replacement is to be more than Phyrric.

18 Batens (1999), 267, suggests that a denial of this conjecture is the best way to understand a claim to the effect that the world is inconsistent. “[I]f one claims that the world is consistent, one can only intend to claim that, whatever the world looks like, there is a language 𝐿 and a [correspondence] relation 𝑅 such that the true description of the world as determined by 𝐿 and 𝑅 is consistent”. He maintains an agnostic view on the matter. See also Batens (2002), 131. 19 I note that Batens (2002), 131, fn. 7, suggests that a consistent replacement for an inconsistent language might well be required to have a non-denumerable number of constants, which would make it humanly unusable.

20 | Graham Priest So let us address the theoretical question. Is it true? Yes, but for entirely trivial reasons. 𝐿󸀠 can be the language with just one sentence, ¥. ¥ is true of any situation. Thus, every situation is describable, and consistently so. (The language does not even contain negation.) But this is not an interesting answer to the question, and the reason is obvious. We have purchased consistency at the cost of the loss of expressive power. To make the question interesting, we should require 𝐿󸀠 to have the same expressive power as 𝐿 – or more. That is, everything that 𝐿 is able to express, 𝐿󸀠 is able to express. The idea is vague. What, exactly is it for different languages to be able to express the same thing? But it is at least precise enough for us to be able to engage with the question in a meaningful way.

3.2 The Possibility of Revision Return to the case of multiple criteria. A natural thought here is that we may effect an appropriate revision by replacing the predicate/concept male with two others, male1 , corresponding to the first criterion, and male2 , corresponding to the second. Pat is a male2 , but not a male1 , so the contradiction is resolved, and what used to be expressed by ‘𝑥 is male’, can now be expressed by ‘𝑥 is male1 ∨ 𝑥 is male2 ’. So far so good; but note that there is no guarantee that in this complex and unpredictable world the result will be consistent. The predicates ‘male1 ’ and ‘male2 ’ may themselves turn out to behave in the same inconsistent way, due to the fact that we have different criteria for ‘genitalia’ or ‘chromosome’. More importantly, the resolution of this dialetheia depends on the fact that the old predicate falls neatly apart into two, individuated by different criteria. This will not be the case in general. (Just consider the case of ‘Adult’, for example, which is not multicriterial in the same way.) We might attempt a more general way of resolving dialetheias as follows. Suppose we have some predicate, 𝑃, whose extension (the set of things of which it is true) and co-extension (the set of things of which it is false) overlap. Given that we are taking it that our predicates do not have to answer to anything in the world, we may simply replace 𝑃 with the three new predicates, 𝑃𝑡 , 𝑃𝑓 , and 𝑃𝑏 , such that the things in the extension of 𝑃𝑡 are the things that are in the extension of 𝑃 but not its co-extension; the things in the extension of 𝑃𝑓 are the things that are in the co-extension of 𝑃 but not its extension; the things in the extension of 𝑃𝑏 are the things that are in both the extension and co-extension of 𝑃. The co-extension, in each case, is simply the complement. The situation may be depicted by the following diagram. For future reference, I call this the Quadrant Diagram. The numbers refer to the quadrants.

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The left-hand side is the extension of 𝑃. The bottom half is the co-extension of 𝑃. Quadrant 4 comprises those things of which 𝑃 is neither true nor false, and for present purposes we may take this to be empty.²⁰ The three new predicates have as extensions the other three quadrants. Each of the new predicates behaves consistently. Any dialetheia of the form 𝑃𝑎 ∧ ¬𝑃𝑎 is expressed by the quite consistent 𝑃𝑏 𝑎, and the predicate 𝑃𝑥 is now expressed, again, as a disjunction, 𝑃𝑡 𝑥 ∨ 𝑃𝑏 𝑥.²¹ So far so good. But recall that the new language must be able to express everything that the old language expressed. A necessary condition for this is that any situation described by the old language can be described by the new. To keep matters simple for the moment, let us suppose that the old language contains only the predicate 𝑃 and the propositional operators of conjunction, disjunction, and negation. We have seen how any atomic sentence, 𝐴, of the old language can be expressed equivalently by one, 𝐴+ , in the new. If this translation can be extended to all sentences, then any situation describable in the old language is describable in the new. The natural translation is a recursive one. For the positive connectives:

(𝐴 ∨ 𝐵)+ is 𝐴+ ∨ 𝐵+ (𝐴 ∧ 𝐵)+ is 𝐴+ ∧ 𝐵+ But what of ¬𝐴? We certainly cannot take (¬𝐴)+ to be ¬(𝐴+ ). ¬𝑃𝑥 is true in the bottom half of the Quadrant Diagram, whilst ¬(𝑃𝑡𝑥∨𝑃𝑏 𝑥) is not true in quadrant 2.

20 Note that, if it is not, the same procedure can be used to get rid of truth value gaps. 21 Batens (1999), 271 and (2002), 132 notes this idea. He also notes that in such a transition the theory expressed in the new language may lose its coherence and conceptual clarity, making it worse.

22 | Graham Priest In this case there is an easy fix. ¬𝑃𝑥 is equivalent to 𝑃𝑏 𝑥 ∨ 𝑃𝑓 𝑥. So we can deal with the atomic case. What of the others? There is a simple recipe that works:

(¬(𝐴 ∨ 𝐵))+ is ¬(𝐴+ ) ∧ ¬(𝐵+ ) (¬(𝐴 ∧ 𝐵))+ is ¬(𝐴+ ) ∨ ¬(𝐵+ ) (¬¬𝐴)+ is 𝐴+ In other words, we can drive the negations inwards using De Morgan laws and double negation until they arrive at the atoms, where they are absorbed into the predicate. In this way, every sentence of the old language is equivalent to a consistent one in the new language. The end can therefore be achieved for this simple language. But, for the strategy to work, it must be implementable with much more complex and realistic languages. In particular, it must work for conditionals, quantifiers of all kinds, modal and other intentional operators; and it is not at all clear that it can be made to do so. At the very least, then, the onus is on the proponent of the strategy to show that it can. Moreover, there are general reasons for supposing that it cannot. Intentional operators would seem to provide insuperable difficulties. Take an operator such as ‘John believes that’, B. How are we to handle B𝐴? The only obvious suggestion is that (B𝐴)+ is B (𝐴+ ), and this will clearly not work. Even logical equivalence does not guarantee equivalence of belief: one can believe 𝐴 without believing ¬¬𝐴, for example. Hence, even if 𝐴 and 𝐴+ express the same situation in some sense, one could have B𝐴 without having B𝐴+ . The trouble is that belief and similar mental states are intentional, directed towards propositions/sentences. These seem to be integral to the intentional state in question, and so cannot be eliminated if we are to describe the intensional state. (Indeed, the same is true of all conceptual revisions. If people’s thoughts are individuated in terms of old concepts, one cannot describe those thoughts if the concepts are junked.) One possible suggestion at this point is simply to take (B𝐴)+ to be B𝐴 itself. Of course, if we leave it at that, we have not rid ourselves of the dialetheic concepts, since these are still occurring in the language. But we might just treat B𝐴 as a new atomic sentence – a single conceptual unit. The problem with this is clear. There would be an infinite number of independent atomic sentences, and the language would not be humanly learnable. The construction would fail the practicality test. And even then, given that the language contains other standard machinery, there would still be expressive loss. For example, we would no longer have a way of expressing things such as ∃𝑥(𝑃𝑥 ∧ B𝑃𝑥) or ∀𝑝(B𝑝 → 𝑝). Nor is this just a problem about mental states. It applies to intensional notions generally. Thus, consider the statement ‘That 𝐴 confirms that 𝐵’. This is not invari-

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ant under extensional equivalence. Let us make the familiar assumption that all creatures with hearts are creatures with kidneys. Consider the information that 𝑎1 , . . . , 𝑎𝑛 are creatures of kind 𝑘 with a heart. This confirms the claim that all creatures of kind 𝑘 have a blood circulation system. The information is extensionally equivalent to the information that 𝑎1 , . . ., 𝑎𝑛 are creatures of kind 𝑘 with kidneys. But this information does not confirm the claim that all creatures of kind 𝑘 have a blood circulation system.²²

3.3 Expressive Loss But worse is yet to come for the conjecture that we can, in theory, always replace an inconsistent language with a consistent one. Suppose that the project of showing that every situation describable in the old language can be described in the new can be carried out, in the way just illustrated or some similar way. This is not sufficient to guarantee that there is no expressive loss. Consider the naive notion of set again. This is characterised by the schema: Abs 𝑥 ∈ {𝑦 : 𝐴(𝑦)} ↔ 𝐴(𝑥) which gives rise to inconsistency, as we have noted. Let us suppose that it were replaced with different notions in the way that we have just considered. Thus, we have three predicates ∈𝑡 , ∈𝑏 , and ∈𝑓 , where 𝑥 ∈ 𝑦 is expressed by 𝑥 ∈𝑡 𝑦 ∨ 𝑥 ∈𝑏 𝑦.

Let us write this as 𝑥 ∈󸀠 𝑦. Given the above schema, we have: Abs󸀠 𝑥 ∈󸀠 {𝑦 : 𝐴(𝑦)} ↔ 𝐴(𝑥) and in particular:

𝑥 ∈󸀠 {𝑦 : ¬𝑦 ∈󸀠 𝑦} ↔ ¬𝑥 ∈󸀠 𝑥 Substituting {𝑦 : 𝑦 ∉󸀠 𝑦} for 𝑥 gives us Russell’s paradox, as usual. We have not, therefore, avoided dialetheism.²³ Why is this not in conflict with the discussion of the last section? The reason is essentially that the procedure of driving negations inwards, and finally absorbing them in the predicate, produces a language in which there is no negation. The instance of Abs󸀠 that delivers Russell’s paradox cannot, therefore, even be formed in this language, since it contains negation. The

22 More generally, relations relevant to confirmation are well known not to be invariant under linguistic transformations. See, e.g., Miller (1974). 23 This is observed by Batens (2002), 132. See also his (1999), 272.

24 | Graham Priest procedure guarantees, at best, only those instances of Abs󸀠 where 𝐴(𝑥) is positive (negation-free). We face a choice, then. Either dialetheism is still with us, or we lose the general schema that we had before. But the Schema effectively characterizes the naive concept of set membership. So if we go the latter way, even if every sentence of the old language has an equivalent in the new, there is still an expressive loss. We have lost a concept which we had before. We have lost the ability to express arbitrary set formation. Not everything that could be expressed before can still be expressed. This provides us with an argument as to why we may not always be able to replace an inconsistent language/conceptual scheme with one that is consistent. There are cases where this can be done only with conceptual impoverishment. That one may achieve consistency by throwing away a concept is not surprising. The notion of truth gives rise to contradictions. No problem: just throw it away! But such a conceptual impoverishment will leave us the poorer. If we were throwing away useless things, this might be no loss; but we are not. All the dialetheic concepts in 2.2 had a use, and so were useful. Indeed, the concepts may be highly useful – contradictions notwithstanding. Thus, for example, the ability to think of the totality of all objects of a certain kind – closely related to our ability to quantify over all such objects, and to form them into a set – would seem to be inherent in our conceptual repertoires. It plays an essential role in certain kinds of mathematics (such as category theory), and in our ruminations about the way that language and other conceptual processes work. But abilities of this kind drive us into contradictions of the sort involved in discussions of the limits of thought.²⁴ We could throw away the ability to totalise in this way. Maybe this would restore consistency, but the cost would be to cripple the kind of mathematical and philosophical investigations that depend on it. To do so simply in the name of consistency would be like doing so in the name of an arbitrary and repressive government diktat. The situation is not to be confused with that in which the concept of phlogiston was “replaced” by that of oxygen. We did not, in fact, dispense with the concept of phlogiston. We can still use it now. What we rejected was the claim that something satisfies this notion. We now think that nothing does; in consequence, the concept is of no scientific use. (Essentially the same must be said about the naive notion of set, by defenders of consistent set theories such as 𝑍𝐹.) Actually, it is not even the case that one can give up a concept in the way required. If we have the conceptual ability to totalise, in what sense can this be given up? One can refuse to exercise the ability, but this would seem to get us

24 A detailed discussion of all this can be found in Priest (1995).

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nowhere. (It would be like solving the Liar paradox as follows. 𝐴: ‘Suppose I say that I am lying’. 𝐵: ‘Don’t.’) If you have the ability to think certain thoughts, you cannot, it would seem, lose this without some kind of trauma to the brain, caused by accident or senility. And if this is the case, the recommendation to change our language/concepts fails the practicality test in this most fundamental way.

4 Conclusion This has been an essay about contradictory concepts, concepts which generate dialetheias. Assuming there to be such things, two further claims are tempting. 1: Dialetheias are merely in our concepts; there are no such things as contradictions in re. 2: Dialetheias may always be removed by revising our concepts. We have seen that there are grounds for resisting both of these suggestions. I think that Hegel would have been delighted; but that is another matter.²⁵

References D. Batens, “Paraconsistency and its Relation to Worldviews”, in: Foundations of Science 3, 259–83, 1999. D. Batens, “In Defence of a Programme for Handling Inconsistencies”, in: J. Meheus (ed.), Inconsistency in Science, Dordrecht, 129–150, 2002. C. Chihara, “The Semantic Paradoxes: A Diagnostic Investigation”, in: Philosophical Review 13, 117–124, 1979. E. D. Mares, “Semantic Dialetheism”, in: Graham Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 264–275, 2004. “Dialetheism, Concepts and the World”, in: J. Meheus, E. Weber, D. Wouters (eds.), Logic, Reasoning and Rationality, Springer, forthcoming. D. Miller, “Popper’s Qualitative Theory of Verisimilitude”, in: British Journal for the Philosophy of Science 25, 160–177, 1974. G. Priest, “Two Dogmas of Quineanism”, in: Philosophical Quarterly 29, 289–30l, 1979. G. Priest, Beyond the Limits of Thought, Cambridge (2nd edition: Oxford 2002), 1995.

25 Versions of this paper, or parts of it, have been given under various titles at a number of philosophy departments and conferences over a few years: the University of Melbourne, the University of Queensland, the Australasian Association of Philosophy (Australian National University), the University of Chapel Hill (North Carolina), the University of Connecticut, the Massachusetts Institute for Technology, Logic and Reality (Universities of Namur and Louvain la Neuve), the University of Gent, the City University of New York (Graduate Center), the Fourth Cambridge Graduate Conference on the Philosophy of Logic and Mathematics, and Contradictions: Logic, History, Actuality, Technische Universität, Berlin. I thank the participants for many lively discussions and helpful comments.

26 | Graham Priest G. Priest, “Review of Soames (1999)”, in: British Journal for the Philosophy of Science 52, 211– 215, 2001. G. Priest, In Contradiction: A Study of the Transconsistent, 2nd edition, Oxford (1st edition: Dordrecht 1987), 2006a. G. Priest, Doubt Truth to be a Liar, Oxford, 2006b. G. Priest, “Logic Disputes and the a Priori”, forthcoming. G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 2004. G. Priest, R. Routley, “The Philosophical Significance of Paraconsistent Logic”, in: G. Priest, R. Routley, J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Munich, ch. 18, 1989. B. Russell, “Vagueness”, in: Australasian Journal Philosophy 1: 84–92; reprinted in: R. Keefe and P. Smith (eds.), Vagueness: A Reader, Cambridge 1999, 61-8, 1923. S. Soames, Understanding Truth, Oxford, 1999.

JC Beall

Rapunzel Shaves Pinocchio’s Beard 1 A Rapunzel Story Stories of Rapunzel are many and varied. A newly discovered one, not publicly available before now, has emerged. The new story involves more ‘gluttiness’ than most known stories – indeed, a far-reaching spread of empirical-world gluts (i.e., sentences that, according to the story, are both true and false of the empirical world of the story). The chapters of the new story are many but much the same; each revolves around Rapunzel’s remarkable nature as a (what else to call it) falsity device. Example: according to the chapter on grass growing, we have a minor variation of the main theme, namely, the given chapter’s Rapunzel fact: –

Grass is growing iff what Rapunzel says is false.

And the chapter ends in grassy gluttiness: –

Rapunzel says that grass is growing.

Since, by the falsity principle, what Rapunzel says is false iff its negation is true, the world of the story is one in which, lo and behold, grass both is and is not growing – a glut involving grass growing!¹ What the story holds in glutty intrigue, it lacks in variation. The chapter on birds flying, like all the chapters, continues the theme: –

Birds are flying iff what Rapunzel says is false.

And the chapter ends with Rapunzel’s saying that birds are flying – and so more gluttiness results, involving birds flying and not. And so on: a glut in the story’s world for any claim at all – including, traditionally, both climbing and not climbing long braids of beautiful but bewitched hair, etc.

1 For literary theorists quick to renounce the law of excluded, let me note that the given Rapunzel story is post-post-modern: it enjoys the truth of 𝐴 ∨ ¬𝐴 for all 𝐴 in the story.

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2 Paradox? The question at hand is beyond literary merits of the new Rapunzel tale. The question, in light of recent debate (Beall (2011), Eldridge-Smith (2012)), concerns philosophical weight. Specifically, the question is: are these new paradoxes? The new Rapunzel tale is not paradoxical at all. To use Eklund’s phrase (2002), there’s no ‘pull’ towards thinking that we have apparently true premises and apparently valid reasoning backing an apparently false conclusion. Instead, we have a story in which craziness happens. The only apparently true premises are only apparently true according to the story; and that doesn’t make for paradox. But doesn’t the story make for at least possible paradox? Doesn’t it carve out some space of possibility of which such broad, empirical-world gluts are true? In short: if we can make even some sense of the story (even if we can’t imagine it in the sense of imaging), ought we not conclude that there’s a possible world – let me just say world – of which the story is true? No. Consider a story in which Goldbach’s conjecture is true, and another one in which it is false. Both are stories we can make some sense of (broadly speaking), even though one of them is true of no world whatsoever. The point, while perhaps largely uncontroversial, bears repeating: truth in a story is insufficient for truth at some world – insufficient, that is, for possibility. Stories are free, subject only to our whims; possibilities are beyond us.

3 Against Pinocchio’s Beard Plato’s beard, according to Quine (1948), purports to take us from (actual) nonexistence to (actual) existence. Eldridge-Smith (2012) gives us a variant, what we might call Pinocchio’s beard, which purports to take us from (impossible) fictions to (possible) worlds. In particular, the story of Pinocchio’s ‘paradox’ is one that is supposed to carry metaphysical import (Eldridge-Smith (2011)). But I don’t see it; it is no different, in the end, from the canvassed story of Rapunzel, which shows the absurdity of Pinocchio’s beard. To be fair, Eldridge-Smith isn’t relying on a general fiction-to-possibility principle; his sights are focused on a particular group of theorists, whom he thinks are subject to such a principle. In particular, Eldridge-Smith’s concern are conservative glut theorists (Beall (2009)) who think that there are no ‘empirical-world gluts’ – only ‘semantic ones’, only ‘spandrels of truth’. And his charge, at bottom, is straightforward: since target glut theorists take the Liar paradox to motivate gluts, they ought to take every version of the Liar paradox to motivate gluts.

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Eldridge-Smith’s argument (2012) is from a uniform-solution principle: same paradox, same solution. But what to make of the argument? While I’m happy to grant, at least for present argument, the uniform-solution principle, I reject the claim – essential to Eldridge-Smith’s argument – that the Pinocchio ‘paradox’ is the same basic paradox as the Liar. The reason is as above: I reject that Pinocchio’s ‘paradox’ is even paradoxical. What is required is apparently acceptable reasoning taking us from apparently acceptable premises to an apparently unacceptable conclusion. But even the conclusion of Pinocchio’s ‘paradox’ is apparently acceptable: it’s true that, according to the story, a nose both grows and doesn’t. (Of course, I can’t imagine such a story, in the sense of imaging it; but the surface structure and its implications are clear enough.) Not only do we have an apparently acceptable conclusion (about what, according to the story, goes on in the world); the premises themselves are apparently acceptable only if embedded in an according to the story operator (which, if removed, undermines the apparently acceptable reasoning). In sum, to have something count as a version of the Liar paradox, it needs to be paradoxical; it needs to at least appear to imply something about truth or possible truth. If there were a clear bridge between fiction and possible truth, then Pinocchio’s beard, employed by Eldridge-Smith (2011), would carry whatever weight is supported by the bridge. The trouble, dialectically, is that Eldridge-Smith (2012) relies on the alleged paradoxicality of his Pinocchio story to build such a bridge. But the alleged paradoxicality is only that: namely, alleged paradoxicality. One might persist in the thought that, at the very least, the Pinocchio ‘paradox’ is liar-like enough to put pressure on glut theorists to acknowledge ‘empirical gluts’, gluts beyond the ‘merely semantic’ liar gluts (the spandrels of truth). One might persist, in short, in trying to grow Pinocchio’s beard. What Rapunzel shows, I submit, is that there’s something deeply flawed in the reasoning behind Pinocchio’s beard: it leads to all-out absurdity. The problem with Pinocchio’s beard is that it demolishes the fiction–possibility divide. Stories are free: make them as you please. Possibility is different; possibility is independent of our creativity. There is no reason for glut theorists (of any stripe, ‘conservative’ or not) to think otherwise.²

2 I’m grateful to Aaron Cotnoir, Michael Hughes, Andrew Parisi, and Ross Vandegrift for feedback. I’m particularly grateful to Elena Ficara for lively conversation at the conference which occasioned this (or a variant of this) work, and also grateful for her patience with my delayed submission.

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References JC Beall, Spandrels of Truth, Oxford, 2009. JC Beall, “Dialetheists against Pinocchio”, in: Analysis 71, 689–691, 2011. M. Eklund, “Deep inconsistency”, in: Australasian Journal of Philosophy 80, 321–331, 2002. P. Eldridge-Smith, “Pinocchio against the dialetheists”, in: Analysis 71, 306–308, 2011. P. Eldridge-Smith, “Pinocchio beards the Barber”, in: Analysis 72, 749–752, 2012. W. V. O. Quine, “On what there is”, in: Review of Metaphysics 2, 21–38, 1948.

Franca D’Agostini

Paradoxes and the Reality of Contradictions 1 Introduction In a plausible reconstruction, dialetheism, that is the perspective according to which for some 𝛼, 𝛼 is true and ¬𝛼 is also true, is based on some simple theses: 1.

the inviolability of the Law of Non-Contradiction (LNC) is not justified by pseudo-Scoto’s argument, as the argument does not work in paraconsistent cases (so the justification is circular) 2. it is not justified either by Aristotle’s elenctic (discussive) argument, because this does not work for moderate paraconsistency, which admits of only some contradictions 3. there are no reasons to accept LNC as inviolable rule, except for the two mentioned in 1 and 2, so LNC is adopted by classical logic as such, without justification, as a fundamental rule of rationality 4. there is another, primary, rule of reason, and it is the “rule of evidence”, in virtue of which, if there is some evidence of contradiction, it is rational to accept it. They are all acceptable, I suppose. More controversial is the fifth: 5.

as there is some evidence of contradiction, in virtue of 1–4 we should accept that for some 𝛼, 𝛼 is both true and false: LNC sometimes fails.

In this reconstruction, the crucial point is the evidence of contradictions; or also: the effective occurring of true contradictions, somewhere, in some cases.¹ Usually, dialetheists mention as paradigmatic cases semantic and set-theoretic paradoxes; sorites (more generally: borderline properties); contradictions related to change, motion and infinity; dilemmas and other epistemic inconsistencies. And yet, in all these cases it is not so clear if the C (contradiction) involved is real as such. Even in case of micro-physical inconsistencies, one could always say the evidence of C is due to the language of modern physics. It is often contended that the modern theory of matter, instantiated by the Standard Model of

1 As I will explain later, I adopt here the empiricist notion of evidence as what is grasped as such. So if 𝛼 is evident to A, then A believes that 𝛼, and ‘𝛼’ is made true by the fact 𝛼.

32 | Franca D’Agostini Elementary Particles, Quantum Mechanics, and the Special Theory of Relativity, is successful, but not properly true. All this would mean that semantic dialetheism has a certain primacy, like it was somehow admitted by Hegel himself.² But if it is so, to what extent should we say that semantic contradictions are real, existent, or objectively evident? In Hegel’s use of the term ‘reality’ (as far as I can say) surely yes, they are, but is this actually the notion of ‘reality’ involved in the evidence of Cs, dialetheistically speaking?³ Evidently, on this point dialetheism bumps into wide philosophical (namely: epistemological and metaphysical) problems: what really counts for evident? What counts for real? I suggest a good approach to the theme is given by alethic realism, the realism “based on truth”.⁴ In a word, Cs are alethically real, and the question about the reality of Cs turns into the question: is alethic realism only semantic, or also metaphysical realism? What is interesting in alethic realism (which I interpret as a metaphysical version of semantic realism), is that it may convey a realistic perspective,⁵ without restricting the realm of facts to a specific sort of reality. Facts, intended in alethic perspective, are ‘what makes true’, which means that there might be semantic as well as strictly metaphysical facts, and the latter may be de se facts (such as the fact that I feel tired now) as well as de re (the fact that here and now there is a computer). To accept this, there is no need to renounce metaphysics (the theory of what real facts are like); and there is no need to accept that the world is trivial, and that the answer to the question ‘what does exist?’ is ‘everything’.⁶ What is only needed, is to enlarge the realm of what can make true. In this sense, the perspective is well adaptable to noneism, which not by chance is dialetheists’ traditional metaphysics.⁷

2 This is a controversial point, yet, there are positive suggestions concerning some sort of semantic dialetheism in Hegel’s work. See on this Ficara (2013). 3 “Hegel’s idealism meant that the distinction between objects that are experienced and mere ‘objects of thought’ has no particular ontological significance”. Priest (1987), 3. 4 The most eminent exponent of alethic realism, also called Cornell realism, was William Alston. See Alston (1993), Alston (1996), and Alston (2002). 5 One including the existence of independent, real, facts; the existence of a unique true description of these facts; and our possibility of giving sometimes a true description of them, and evaluating the truth or falsity of a certain description (see later). 6 I tried to show this in D’Agostini (2009b) and D’Agostini (2012). 7 See Priest (2005).

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2 Paradoxes and the Evidence of Contradictions 2.1 What Is a True Contradiction? A contradiction occurs when ‘𝛼’ is true, and ‘¬𝛼’ is true as well (where ‘𝛼’ is a proper truthbearer). In realistic perspective, ‘is true’ means: is made true by some facts or states of affairs. So ideally, there is a real contradiction when two contradictory states of affairs simultaneously occur in the same world, at the same time and under the same respect. Russell, in The Philosophy of Logical Atomism suggested that a same fact 𝛼 makes true the proposition ‘𝛼’, and makes false ‘¬𝛼’. So there would be only one fact, ultimately. The notion of falsemaking is discussed, but the point remains. Logically, it involves the semantics of negation.⁸ But metaphysically, and epistemically, we have to reflect on what could be a situation, or a case, which makes 𝛼 ∧ ¬𝛼 true: are there two cases, or only one? Is truly evidence the evidence involved? In empiricist perspective, Humean as well as Kantian,⁹ ‘evidence’ stands for the action of reality on an epistemic agent’s system of beliefs. I have the evidence that 𝛼 iff a certain real fact 𝛼 causally acts on my cognitive means, making me (truly) believe that 𝛼. In this account, ‘evident’ implies ‘true’, and ‘true’ implies ‘real’:¹⁰ if 𝛼 is evident, then ‘𝛼’ is true, and if ‘𝛼’ is true, then 𝛼 is real. So the notion of empirically evident C implies true and real C: the fact involved is not apparent, and it is not the result of some mistake either. Empirical evidence may fail, as in the process from 𝛼 (state of affairs) to ‘𝛼’ (belief, or proposition) something may go wrong, so I grasp 𝛼, but my formed belief (for some reasons) becomes ¬𝛼, or 𝛽. Surely, in that case, we cannot say 𝛼 was strictly evident to me. My evidence was only believed and not true evidence. And evidently, this also regards Cs. Cases of only apparent Cs are frequent, in the usual practice of believing and knowing. Sometimes, what seems to be 𝛼 ∧ ¬𝛼 is in fact something else: because say the two are not mutually exclusive, or are not jointly exhaustive, or do not jointly occur (so the same translation in terms of 𝛼 ∧ ¬𝛼 was wrong, actually). In this case, we would say the C is to be dissolved.¹¹ Some other times, we come 8 See Priest (2006), ch. 2. 9 Substantially confirmed by Burge (2010). 10 The idea that Kant’s conception of truth was not realist is a wrong idea: I leave this out, but for a wider discussion see D’Agostini (2012). 11 Dissolutions of Cs, as I will explain later, are also to be adopted in those cases in which the C is apparent, as it conceals under-determination, so the truth value glut is in fact a truth value gap.

34 | Franca D’Agostini to know that in fact only one of the two terms was in fact true. Then we simply solve the contradiction. Finally, sometimes the apparent C is in fact due to some glitch or mistake, concealed somewhere, or to some false assumption. We get rid of the false assumption, and the C disappears. And this is the reduction to absurd, or more generally: the epistemic reduction of Cs. A true C is epistemically given as such when all the three procedures fail. And usually, as ideally the three are ordered (if solution fails, try dissolution, if dissolution fails try reduction), we would say evident Cs are irreducible: the main logical method fails.¹²

2.2 What Is a True Paradox? According to the classical definition (Sainsbury (1995)), a paradox is the apparently unacceptable conclusion of an apparently acceptable argument. Acceptable arguments are sound, which means they have true premises, and valid inference. So there are five possibilities: 1. the premises are only apparently (not really) true; 2. the inference is only apparently (not really) valid; 3. in fact, premises are untrue and the inference is not valid (both 1 and 2 occur); 4. the conclusion is only apparently (not really) unacceptable; 5. premises are truly true, inference is truly valid, and yet the conclusion is unacceptable (false). Only in the last case we have a true paradox. In the other cases, the evidence (in the sense specified above) fails, because there is not really a paradox, rather: a fallacy (cases 1, 2, 3), or what Quine (1962) called veridical paradox: we thought the conclusion was false, but it was true, actually (case 4), and when we come to know it is true, the paradox disappears.¹³ Now if we ask: what is unacceptable? The reasonable answer is: 𝛼 (if 𝛼 is a truthbearer) is unacceptable iff we know (or believe) it is false, or contradictory.¹⁴ But epistemically, 𝛼 is visibly false when it contradicts something we know (believe) for sure: that ¬𝛼. So, ultimately: 𝛼 is unacceptable when it is contradictory; what is unacceptable is the C. 12 This may happen in two ways, as I specified in D’Agostini (2009b), corresponding to the two main kinds of paradoxes: sorites and antinomies. The first is 𝛼 → (𝛽 ∧ ¬𝛽) and ¬𝛼 → (𝛽 ∧ ¬𝛽), both from a proposition and from its negation we get a C. The second is 𝛼 → ¬𝛼, and ¬𝛼 → 𝛼, from a proposition we get its negation, and vice versa. 13 Lycan (2010) has recently proposed the idea that paradoxes come “in degree”, and it is fairly similar to my point: on this, and for the definition of paradox as resistant contradiction see D’Agostini (2009b), first part. 14 A third possibility is that 𝛼 is unacceptable insofar as meaningless. But in this case, one couldn’t say 𝛼 is properly a truthbearer.

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Now we have here a more restrictive definition: a true paradox, properly speaking, is a contradiction. And the evidence involved, is somehow unquiet evidence, of the kind ‘ “But this isn’t how it is” – we say. “Yet this is how it has to be!” “But this is how it is” —’, as Wittgenstein wrote in the Philosophical Investigations.¹⁵ When do we actually have this sort of unquiet evidence? Graham Priest, in In Contradiction and elsewhere, mentions the following paradigmatic cases of true Cs: 1. logical (semantic, set-theoretic) paradoxes, conveying the schema 𝜇 ↔ ¬𝜇; 2. transition states, or borderline cases (change, motion, borders and cut offs); 3. contradictory results due to the notion of infinity; 4. epistemic undecidable situations, such as the case in which I believe that 𝛼 and I believe that 𝛽, but I come to believe that ¬(𝛼 ∧ 𝛽); 5. normative conflicts, to say conflicts occurring in normative systems, when we have apparently consistent laws, which in some applications reveal not being simultaneously observable.¹⁶ This somehow confirms that effective-real contradictions are (conveyed by) what we usually call ‘paradoxes’: antinomies, sorites, infinity paradoxes, epistemic paradoxes, and those practical paradoxes that are dilemmas.¹⁷ Now the question is: are all these Cs effective, which is to say: evident, and evident insofar as real and truly irreducible? As to borderline situations (borders, cut offs, transition states, etc.) there is no doubt, or so it seems. Evidence is against LNC. The example Priest most frequently mentions is: when I am on the threshold of a room, I am in and out at the same time. Whether we truly have double phenomenic evidence or not, in these cases, is a controversial issue,¹⁸ because usually these are micro-phenomena, not captured by our perception. But this only holds for what Tyler Burge has called, in his monumental work on the Origins of Objectivity, “individual representationalism”: the idea that cognition is a strictly individual phenomenon. Burge notes: “there is a structural difference between perception and propositional attitudes”, but “the representational content of perception is a veridical condition, that when met by an appropriately sensed subject matter is veridical” (Burge (2010), 539). So we would say: border-contradictions seem to be evident insofar as real, and

15 Wittgenstein (1985), 112–113. 16 Priest (1987). 17 Otherwise, the idea that paradoxes ultimately are epistemic or logical structures conveying Cs, is implicit in most of the literature about non classical logic, and it is fairly reasonable to admit that we call “paradoxical” situations that are undecidable by over-determination. 18 See Priest (2006), 57–64. On the possibility or impossibility of perceptive Cs, see Sorensen (2003) and Sorensen (2008).

36 | Franca D’Agostini so because the conception of them is veridical, even if we cannot grasp them by conscious perceptive means. In other cases, and namely as to epistemic-doxastic Cs (I believe that 𝛼 and I believe that ¬𝛼), or as to liar-like Cs (𝛼 iff ¬𝛼), there might be some doubts. There are Cs, but one may say they are only apparent, or are the result of some glitch or mistaken assumptions, or occur in a special system or a field (say: a semantic field, intended as fictional or conventional), which we would not properly call real, as such.

3 Paradoxes in Epistemic Perspective The objective occurring of epistemic Cs is controversial, basically for two reasons: because natural epistemic systems are “fragmented”, or intrinsically heterogeneous, or irreducibly dynamic (so the two contradictory terms do not properly occur at the same time, and in the same context or field); or because very often what seems to be (or what passes off as) over-determination is in fact underdetermination. The first account somehow legitimates non-adjunctive approaches, that is those, which admit that 𝛼 and ¬𝛼 may occur, but not jointly (the basic rule of Adjunction fails: you get 𝛼, ¬𝛼 but not 𝛼 ∧ ¬𝛼).¹⁹ Knowingly, some interpretations of Hegel’s logic resolutely deny that it is a paraconsistent logic, stressing the dynamic nature of Hegel’s dialectics. In Sorensen’s perspective epistemic infra-subjective systems may be inconsistent,²⁰ as beliefs are so to say produced by “different bureaus in a firma”: the results obtained by one bureau may be ignored by another. However, I think the main point with epistemic Cs is the second explanation: that often, what epistemically seems to be a glut is in fact a gap, and over-determinacy is the superficial effect of underlying under-determinacy. Let’s see now some examples.

19 See Varzi (2004). 20 Sorensen (2001) has produced an elenctic argument to the effect that epistemic contradictions are somewhat unavoidable. The argument can be discussed, but I do not treat the problem here.

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3.1 There Is No Preface Paradox Here is a version of the preface paradox:

𝛼 = ‘In this list (in this book) there is some false sentence.’ 𝛽 𝛾 𝛿 In Priest’s account (1987), the author of the preface presumably believes each sentence in the book is true (insofar as she has written it), then she believes that 𝑇𝛽 ∧ 𝑇𝛾 ∧ 𝑇𝛿. But she says that in the book there are some false sentences, so she does not believe that 𝑇(𝛽 ∧ 𝛾 ∧ 𝛿). Contradiction. Beall and Restall (2006) suggest what we would call a dissolution by underdetermination. Suppose the author believes each sentence of the book is very likely true, so, say: 𝛽 is 0.8 true, 𝛾 is 0.9 true, and 𝛿 is 1 true. Now it happens she is also entitled to believe that there might be some false sentence in the book, as the conjunction 𝛽 ∧ 𝛾 ∧ 𝛿 will totalize 0.8 × 0.9 × 1 = 0.72. More precisely, let’s suppose the author’s epistemic standard is: (ES) I accept 𝜑 iff 𝑃(𝜑|𝑒) ≥ 0.8 I accept 𝜑 if and only if the probability of 𝜑 given the evidence 𝑒 is 0.8 or more. Given the evaluations above, the author must rationally accept each proposition 𝛽, 𝛾, 𝛿, as each singularly satisfies (ES), but she cannot accept 𝛽 ∧ 𝛾 ∧ 𝛿, which is 0.72, and therefore she also must accept 𝛼 as true (0.8 or more). So there is no C in the author’s beliefs. Surely, the probabilistic account of truth is a positive resource for epistemology. Rather, it is the best way to connect logic and epistemology. What Christensen (2004) has called “gradualistic model of beliefs”, as opposed to “binary model” is reasonable, and well captured by probabilistic calculus. In this case, Beall’s and Restall’s approach also gives good arguments in favour of non-adjunctive accounts, because what fails, in the author’s beliefs, is namely the adjunction rule. So we see that epistemic gradualism is able to dissolve epistemic Cs, at least in case of intra-subjective Cs, such as those conveyed by the preface paradox, or also: the lottery paradox.

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3.2 Reliability Conflicts In the preface paradox, there is no doxastic C: the author does not exactly know what is the false sentence in the book (or to what extent the proposed sentences are true), so he or she gives asymmetric evaluations. But are there cases in which A positively 0.8 believes that 𝛼 and also 0.8 believes that ¬𝛼? In principle, this may happen in two ways: because there is a conflict between the sources of belief, or because there is a real conflict between the pieces of evidence we get. An example of the first case is the reliabilist paradox. Suppose I am perfectly confident in both the Catholic Church and scientists. But it happens the Catholic Pope says that 𝛼, for instance: ‘a 14 day human proto-embryo is a human being’; and scientists say that not 𝛼: ‘a 14 day human proto-embryo is not a human being’. What should I believe? Also in this case the main point is under-determinacy: the conflict arises simply because I do not know what is true, as we simply lack a shared definition of what is a human being, and I have not enough information to judge which the preferable definition is. If the epistemic constraint conveyed by the two sources is strong enough, I may be possibly led to give 𝛼 a value 0.8 or so and ¬𝛼 a value 0.8 as well. And it should be noted that beliefs are contrastive: if I 0.8 believe that 𝜑, then I 0.2 believe that ¬𝜑. So as a matter of fact, my evaluations are: both 0.8 and 0.2 for 𝛼 and both 0.8 and 0.2 for ¬𝛼. However, this hardly captures the effective dynamic of beliefs of an epistemic agent who is cultivating some ideas regarding 14-day human proto-embryos. First, possibly the two sources will act one against the other, producing some global diminishing of the reliability of both. Second, if the agent has to take some decisions, she will produce some rational re-arrangement of the comparative reliability of one or the other source. In other terms, if I (Catholic, but fond of science) have to vote for a law concerning scientific research about stem cells, stated the opposite judgements of my sources of belief, I will diminish my confidence in the absolute reliability of the Pope (or science); or else, I will ignore the metaphysical question concerning the effective being ‘human’ of the embryo, and I won’t vote on the basis of metaphysical considerations. So the contrastive belief concerning one term will increase, or both 𝛼 and ¬𝛼 will result “not designed”. In any case, there won’t be any true doxastic C.

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3.3 Conflicting Pieces of Evidence In case of epistemic Cs conveyed by contradictory evidence, the 𝑒 in ES is double. In virtue of my evidence, P(𝛼) = 0.8 (or more), and P(¬𝛼) = 0.8 (or more) as well. Fermi-Hart paradox is a good example. The proposition E: ‘Extraterrestrial intelligent people do exist’ is typically over-evaluated, in virtue of the two arguments: (1) If advanced extraterrestrial civilizations existed, they would have contacted us There is no clear evidence that such a contact has taken place Therefore: it is highly improbable that civilizations of this kind do exist. (2) The universe is huge, or even infinite Therefore: it is highly probable that advanced extraterrestrial civilizations do exist. The two arguments seem to be compelling. We have the evaluation ¬𝐸 = 0.9 or so, in virtue of (1) and 𝐸 = 0.9 or so, in virtue of (2). Defenders of E will fiercely oppose the upholders of ¬𝐸, and vice versa. But what about the third person, the epistemic observer A, who takes into account both (1) and (2)? Surely, a rational A won’t admit 𝑃(𝐸 ∧ ¬𝐸) = 0.81, to say: that it is highly probable that ETs do exist and do not exist at the same time. Rather, she will think the issue is fundamentally under-determined. Possibly, the contrastive method would work, because the two arguments will act one against the other, yielding a global diminishing of the belief involved in the entire issue. And yet, in this case the situation is slightly different. Because here the effective contradiction won’t regard 𝐸 ∧ ¬𝐸, or the external conflict between reliability sources, but the two facts expressed in the two arguments. We have a fact, actually, which is the high estimate of probability, stressed by (2), and another fact, the lack of evidence, stressed by (1). These two are facts, in some sense (and especially, if one adopts a frequentistic vision of probability), so the relative propositions are true. Are these epistemic facts? Is their occurring to be interpreted in terms of some positive ‘𝛼 ∧ ¬𝛼’? This is arguable, given the general under-determinacy of the entire subject. But evidently, the problem is metaphysical: it concerns the nature of facts here involved. And in this sense, we have to move to the underlying question, which is the metaphysical question: the metaphysics of Cs, and paradoxes.

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4 Paradoxes in Metaphysical Perspective I am not sure that there are no epistemic contradictions. Maybe the probabilistic principle of complementation, interpreted in terms of contrastivity, does not really capture what truly happens in an epistemic agent’s “stock of beliefs”, when the believer is facing contradictory pieces of evidence. Not only that, as long as the meaning of ‘there are’ is not specified, the idea that there are or there are not Cs, of any sort, can hardly be defended. And yet, it is fairly reasonable to admit that epistemic contradictions do not involve absolute (realistic) truth, but only epistemic truth. Epistemic truth is typically incomplete, hence “gradualistic”, hence it can (should?) be treated by probabilistic means. And as we have seen, probabilistic approaches to Cs are often if not always dissolutive. Can liar-like Cs be treated in the same way? In fact, given the sentence 𝜇, which says: ‘𝜇 is false’, or other structures conveying some 𝜇 ↔ ¬𝜇, one would say there is true evidence of contradiction, which is not comparable to the only epistemic evidence above mentioned. And if evident implies true, as stated before (see here, section 2.1), it should be noted that this truth is categorical, it is the true (classical) truth, whose values are 1 and 0. This can be shown first by checking if the truth value gap strategy actually works when considering the kind of evidence conveyed by liar-like paradoxes.

4.1 Truth Value Gaps? Should we say that, when facing a liar-like C, we have lack of evidence, more than double (unquiet) evidence, and that a gappy strategy would be in order? In fact, this seems not satisfying, because, as it seems, no (known) case of gappy evidence is applicable to the Liar’s sentence. Allegedly, gappy sentences are: 1.

2.

“failed” or “ungrounded” assertions, such as pure (empty) self-references: Paul says ‘what Peter says is true’ and Peter says ‘what Paul says is true’; these are syntactically acceptable sentences, but they cannot be said to be true or false, because there is no ground to be checked, in order to see their truth (they are ungrounded), or because they “fail their assertive aim”, like Goldstein (2000) has suggested; category mistakes, like ‘this is a sad table’: if we admit it is false, then ‘this table is not sad’ is true, which means the table is happy, or something like that;

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3.

4.

5.

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failed presuppositions: ‘Smith’s children are all blond’, but Smith has no child; if you say it is false, this would mean some of Smith’s children are not blond, which is false as well; normative or future sentences, such as ‘the death penalty is unjust’, and ‘there will be a sea battle tomorrow’: they cannot be said to be true or false, because there is no state of affairs which may make them true or false; epistemic gaps, to say under-determined truths, such as: ‘there are extraterrestrial intelligent beings’, or ‘there are infinite twin primes’.

In fact, cases from 1 to 4 can be discussed, and possibly, the only true case of truth value gap is the last one.²¹ But there have been proposals of treating 𝜇 or similar sentences in terms of failed or ungrounded assertions (Kripke, Goldstein), or failed presuppositions (van Fraassen), or category mistakes (Martin). These proposals have explicative merits, but they cannot be applied in the ‘evidence’ perspective we are adopting here. As to 1: we cannot say 𝜇 is a failed assertion, properly: the fact involved is not of the kind of ‘snow is white’, but there are lots of non-empirical truths we correctly believe. Besides, the Liar tells us something definite: that it is true if false, and false if true, and this is surely a relevant information, as from this we infer lots of things concerning logic. As to 2: ultimately, 𝜇 is a sentence, so something that is syntactically apt to be called true or false; if 𝜇 said the fact 𝜇 is false, this would be a positive mistake, but 𝜇 does not say so. And evidently, 𝜇 is neither a normative nor a future sentence (case 4). Not only that (and more importantly), there is no lack of evidence (case 5), because we know everything about the sentence, we have all we need to state its truth or falsity. So the Liar perfectly succeeds in communicating what she wants to communicate: that what she’s saying is false. The problem is ours, insofar as we see that what she’s saying is false if true and true if false. Interpreting this in the sense that we are not able to say that 𝜇 is true, is fundamentally wrong, because we positively know it is true, though not only true.

21 For instance 1 and 2 are discussed by admitting that failed sentences or category mistakes are not properly ‘propositions’, so they are not truth value gaps but rather non-sentential expressions (like ‘yellow’ or ‘what’s the time?’). Example 3 may be discussed admitting that failed presuppositions are false, which is pragmatically proved by the fact that if you tell me ‘Smith’s children are all blond’, whereas Smith has no child, you are simply cheating me. As to 4, the question is highly controversial, my opinion is that normative and future sentences are true or false, as they convey, respectively: modal truth and probable truth.

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4.2 What Sort of Facts Are Liar-Like Facts? The dialetheist account of Liar paradoxes, reformulated in the perspective of the evidence involved in Liar-cases, will lead us to say that we correctly believe that 𝜇 and ¬𝜇, because the contradiction does not regard our personal lack of knowledge, but something more objective: a special sort of evidence, possibly concerning a special sort of reality. Is this semantic, that is to say: fictional, or conventional, reality? I do not think it is properly so, but to see this, we need a closer view on the sort of facts involved in liar-like Cs. We can easily see that 𝜇 and ¬𝜇 are made true, respectively, by two ‘facts’: the fact that ¬𝜇 → 𝜇, and the fact that 𝜇 → ¬𝜇, and classically, the passage from equivalence to contradiction can be stated in two ways. The first is by considering that we have self-refutation and self-foundation of 𝜇. By applying the ancient rule of consequentia mirabilis, like Sainsbury (1995) suggests, it follows that 𝜇 is surely true, because it is confirmed by its own negation, and ¬𝜇 is surely true as well, because it is denied by its own assertion. The structure 𝜇 ↔ ¬𝜇 can thus be reduced to 𝜇∧¬𝜇 by CM, in negative and affirmative form. The other way of ‘seeing’ the passage from 𝜇 ↔ ¬𝜇 to 𝜇 ∧ ¬𝜇 is what Field calls “the central argument from equivalence to contradiction” (2008, 7). Here the excluded middle has a decisive role: given 𝜇 ↔ ¬𝜇, and given 𝜇 ∨ ¬𝜇, by assuming 𝜇(𝐸∨) you get that ¬𝜇, so 𝜇 ∧ ¬𝜇, and by assuming ¬𝜇, you get that 𝜇, and then 𝜇 ∧ ¬𝜇 again. These are logical facts, which means they are occurring in a language (a fictional or conventional world), and under consideration of some very specific and well determined principles, such as the definition of falsity (FA) 𝐹𝜇 ↔ 𝑉¬𝜇, and the 𝑇 schema 𝑉𝜇 ↔ 𝜇. These two facts in turn confirm bivalence, i.e. that true and false are jointly exhaustive: ¬𝑉𝜇 → 𝐹𝜇, and ¬𝐹𝜇 → 𝑉𝜇. And so they confirm the passage from equivalence to contradiction. So in order to have 𝜇 ∧ ¬𝜇 we need a lot of special ‘facts’. From an epistemic point of view, the evidence of C is preserved, because one may note that the facts above are known, and consequently believed as such. So when facing a liar-like paradox I can say that I know that 𝜇 and ¬𝜇, – even if the real facts at stake are not exactly of the same kind of white snow, or similar facts.²²

22 Notably, the epistemic C will survive in conjunctive, but not distributive form: face to the Liar, we have 𝐵(𝜇∧¬𝜇), but not 𝐵𝜇∧𝐵¬𝜇. Because properly, I do not believe that only 𝜇, as I positively know that 𝜇 → ¬𝜇, and I do not believe that only ¬𝜇, because I know that ¬𝜇 → 𝜇. But exactly for the same reasons, I must believe that 𝜇 ∧ ¬𝜇. It is the opposite of the preface paradox: here the simplification rule fails.

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4.3 Is Pinocchio a Metaphysical Liar? Are semantic facts truly facts? I think there is an interesting suggestion, on this point, in Austin’s 1950 essay on Truth, where he, in passing, says that facts of the sort ‘p is true’ may be called soft facts. And this is the difference between the two parts, T‘p’, and p, of the T schema: the first is true with reference to a soft fact. Which means, for us: is made true by a soft fact. However, it is difficult to say that soft facts, i.e. semantic facts, are real, and that their evidence is exactly of the same sort of hard facts. A possible answer to this question would require a reconsideration of what counts for semantics, and what counts for facts. I will briefly discuss these points later. Now it is useful to focus on the discussion about the effective possibility of real liar-like Cs (against semantic dialetheism) arisen between Peter Eldridge-Smith and JC Beall with reference to Pinocchio paradox. Pinocchio paradox, devised by Veronique Eldridge-Smith (Peter EldridgeSmith’s daughter), is, I would say, a physicalistic version of the Liar paradox. Pinocchio says 𝑃 = ‘my nose is growing’; as Pinocchio’s nose grows if and only if he is lying, in the case given his nose is growing iff it is not growing. In Peter Eldridge Smith’s view, this is a liar-like paradox, as P logically behaves like the sentence 𝜇, which says ‘𝜇 is false’. But the special (physical) property it involves is by no means comparable to the property of ‘being true’. So we would have here a good counter-example to the etiology of paradoxes suggested by Tarski: “paradoxes arise from the use of semantic predicates”, because “having one’s nose grow is a facial not a semantic feature” (Eldridge-Smith/EldridgeSmith (2010), 213). We would have then here the case of a facial liar-like paradox. Eldridge-Smith also notes that “‘having one’s nose grow’ is not a synonym for ‘is not-true”’ (Eldridge-Smith/Eldridge-Smith (2010), 213): the nose grows because Pinocchio says something false, but this is a metaphysical and not a semantic relation. In a further article (see Eldridge-Smith (2011)) he also specifies that Pinocchio’s utterance conveys a metaphysical dialetheia, so it is also a counterexample to semantic dialetheism. JC Beall (2011) has observed that Pinocchio’s case is under the scope of the operator “according to the story. . . ”, which means the dialetheia involved is not metaphysical. And this is somehow unquestionable, stated that (as far as we know) Pinocchio’s case only exists in Collodi’s novel, which is a fictional world. One might say that also the standard Liar dialetheias are fictional, and so is any other dialetheia. Ultimately, if Cs are logical facts, they are fictional at least insofar as logic in itself is a fact of human language, and human language is human creation. In this sense, even the regime of truth and falsity, generally intended, is fictional. This is what Nietzsche thought (in the early paper about Truth and Lie

44 | Franca D’Agostini in Extra-Moral Sense), and this is what Kroon (2004) indirectly hypothesizes, by noting that, as far as we know, our world might be trivial.

4.4 There Is No Pinocchio Paradox (Metaphysically Speaking) The first point that is to be examined, in my view, is the effective (evident) occurring of the contradiction 𝐺 ∧ ¬𝐺 (Pinocchio’s nose grows and it does not grow) from 𝐺 ↔ ¬𝐺 (Pinocchio’s nose grows iff it does not grow), which is required (see 3.2) for considering liar-like contradictions as true contradictions. Let’s assume first that 𝑊𝑃 is the closest to our world among those in which Pinocchio’s internal device works in the way expected. So let’s suppose 𝑊𝑃 works exactly like our world W, but for the fact that Pinocchio (and only Pinocchio) has the special property of revealing his lies, in the way specified. Let’s also assume that in W𝑃 the Excluded Middle works, and then we are entitled to infer 𝐺 ∧ ¬𝐺 from 𝐺 ↔ ¬𝐺. Would there really be two states of affairs, related to G and ¬𝐺? Possibly not. As a consequence of the utterance, and if Pinocchio does not say anything else, the nose will grow, but it immediately will come back, and then it will grow, and come back again, etc., which is the simple recursive-revisional movement of truth, when involved in liar-like situations. So there is only one metaphysical fact ultimately: the one produced by the causal mechanism which relates 𝑃 to Pinocchio’s nose, but this fact is not contradictory, though we would describe it in terms of 𝐺 ↔ ¬𝐺. And there is another fact, possibly logical, or semantic (or epistemic): our inference that 𝑃 ∧ ¬𝑃. And this will surely be another, distinct fact: of the same kind of the arguments 1 and 2 in the Fermi-Hart paradox, but not of the sort of evidence strictly involved in them. In other terms, our logical inference that 𝑃∧¬𝑃 in 𝑊𝑃 is not supported by any non-logical evidence that 𝐺 ∧ ¬𝐺 (in the above specified sense of evidence). And, more importantly: we can accept this sort of inferential evidence only if we move from a metaphysical to a semantic consideration of possible worlds. The former is based on assuming that worlds are collections of facts (or states of affairs) the second is based on postulating that worlds are collections of propositions, to say: truthbearers. The former is based on considering what makes true, the latter is based on considering what is made true. It is not a negligible difference. Globally, the realm of truth consists of worlds containing what makes true and worlds containing what is made true, and it is in this global domain, that true (se-

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mantic or metaphysical) Cs do occur. But there are facts also in the worlds of truthmade things: namely semantic, or epistemic facts. So in Pinocchio’s metaphysical world there will be 𝐺 ↔ ¬𝐺, but not the fact 𝐺 ∧ ¬𝐺. Whereas in Pinocchio’s semantic world there will be both 𝐺 ↔ ¬𝐺 and 𝐺 ∧ ¬𝐺. If we accept the idea that a true paradox ultimately is a true contradiction, then Pinocchio paradox is not a paradox, in the metaphysical version of the story, while it is a paradox, but only in its semantic version. This possibly holds for all liar-like Cs. However, I am not sure that the same result should be extended to any case of contradictions, like semantic dialetheism contends. I am not sure that, for instance, borderline contradictions, which immediately present themselves in the form 𝛼 ∧ ¬𝛼, are only semantic, as such. But surely, contradictions occurring as a result of inferential truth, such as those conveyed by the schema 𝛼 ↔ ¬𝛼, are semantic, for at least a reasonable meaning of semantic. In fact, Eldridge-Smith’s case is extremely useful, I think, exactly in the sense suggested by Eldridge-Smith and Eldridge-Smith (2010): to reflect over the kind of paranormal properties that we possibly need to get the form 𝜇 ↔ ¬𝜇. As a matter of fact, the properties involved can be of the widest kind, say: heterological, not being a member of oneself, . . . , and maybe also ‘having one’s nose growing’. But without truth (namely: Df. 𝑇 and Df. 𝐹), you cannot have any passage from 𝜇 ↔ ¬𝜇 to 𝜇 ∧ ¬𝜇.

5 Dialetheism and Alethic Realism Supposing that liar-like contradictions are made true by semantic facts, what is a fact, and what is semantic? There are problems concerning both definitions. Burgess (2009) has suggested that maybe we should do away with the term ‘semantic’, because it is typically ambiguous. In fact, it means: ‘concerning meaning’, and also ‘concerning truth’. To think that the two aspects are one and the same means to assume (more or less implicitly): that reference is always reference to entities able to make sentences true; or, in contrast, that the truth of logic has nothing to do with entities actually subsisting in some way. These opinions could be not wrong, but evidently, the use of the term might be confounding, at least insofar as it may legitimate opposite implications. As to facts, the anti-referentialistic (second-Wittgensteinian, pragmatic and post-neopositivist) trend has suggested to cultivate a certain suspicion toward the notion of fact. Especially, insofar as by “fact” is meant the obscure independent entity that makes true all sorts of sentences. Are there conditional facts? Or negative facts? Or universal facts? Recent theories of truth have somehow overcome

46 | Franca D’Agostini these difficulties.²³ Yet a perplexity is still alive. See for instance Putnam’s recent ‘realistic’ turn: Putnam (2012) declares being a realist, but not a realist about truth.

5.1 Alethic Realism I suggest to consider the two problems in the perspective of alethic realism. According to alethic realists (see Alston (1996) and (2002)) a proposition or a sentence 𝜑 is true iff things stand like 𝜑 says. This is not properly (or not necessarily) a version of correspondence theory, but surely it is a version (slightly more robust) of truthmakers theory, that states: if 𝜑 is true, then there is something (some fact or state of affairs) which makes it true (see especially Armstrong (2004) and (2010)). In this account, alethic realism is 𝑎 realistic interpretation of the T schema: if 𝜑 is T, then things stand like 𝜑 says; and if things stand like 𝜑 says, then 𝜑 is T. It is also a plain version of the Platonic and Aristotelian notion of aletheia (as Künne (2003) has shown, the idea of correspondence was not contemplated in Plato’s and Aristotle’s definitions). In the perspective of alethic realism a ‘fact’ is simply what can make true a proposition, so there might be indeterminate kinds of facts: universal, as well as conditional, mathematical or physical, infrasubjective or intrasubjective, physical or intentional, etc. In fact, skepticism about the existence of a wide range of truth-facts is due to some implicit metaphysical position, which restricts facts to empirical or inter-subjectively observational facts. Let’s suppose I truthfully say: ‘I am tired today’: this simply means that there are certain conditions of my brain or muscular mass, which make true my assertion, and act on my self-perception so making me say-think ‘I’m tired today’. If I truthfully say ‘2 is a prime number’ there are positive conditions of mathematical language (or of mathematical reality: this is not relevant here), that make true my assertion, and make me believe and say that 2 is a prime. Significantly, if I truthfully say ‘I believe that God exists’, there are doxastic facts that make true what I’m saying: these are possibly hybrid facts, of a very complex nature, and more truthfully, I would have said something like: ‘yes, I 0.8 believe that God exists’, but again: this is not relevant here. These are de se facts that a restrictive metaphysics wouldn’t accept, because they are not inter-subjectively evident. But they are perfectly truth-apt, and this is revealed by the fact that I may lie on them. For instance, as a politician, I say ‘I believe in God’ (while I don’t), with the intention of gaining your approval. Or I

23 See D’Agostini (2011), ch. 5.

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am the Pope of the Catholic church, and evidently I say that I 0.8 believe a 14 day human proto-embryo is a human being, but I do not truly believe this: there are de se facts that make the negation of my sentence true. Truthmaker theories usually are physicalist, but this does not change the picture: simply one would say that doxastic facts supervene on physical facts, but supervening (soft) facts are able to make true. All this, I suggest, implies a meaning of the predicate ‘x is real’ which is beautifully adaptable to dialetheic reality, that is: to the notion of real C. Because in principle, there is no preliminary restriction on the natures a C may assume. There are paradoxical Cs of the form 𝜇 ↔ ¬𝜇, and they are called real insofar as both 𝜇 and ¬𝜇 are made true by logical (semantic) facts. There are soritical Cs, made true by the borders of properties we encounter in empirical (though possibly not phenomenical) experience. There are dilemmatic Cs, arising from latent inconsistencies of normative systems, so made true by normative facts.²⁴ There are modal Cs, made true by modal facts (be they intended as metaphysically or only semantically real, or in other way) etc. In principle, in the perspective of alethic realism there is no need to restrict facts to space-time occurrence, or to the actual world, or any other specific field. For a fact being a fact, it is enough for it to be able to make something true or false. This is somehow adaptable to the ‘open’ and ‘liberal’ metaphysics of noneism. Which is for me a non-restrictive metaphysics. And in this sense Kant, admitting the alethic existence also of transcendental objects (pure intuitions, schemas, categories, ideas), was not anti-realist, but rather somehow noneist.²⁵

5.2 Is Alethic Realism Truly Realism? In Alston’s view (see his (1996)), alethic realism is not committed to any sort of metaphysical realism. You can be alethic realist, so Alston claims, even refusing the independence thesis, that is the thesis, according to which real things or facts are independent from my mind, or from “conceptual schemas”. The sentence ‘there is a computer on this desk’ is said (or believed) true, even by those people who believe that the computer and the desk involved are produced by mental devices, or by linguistic stipulations. The idea that alethic realism does not necessary involve the independence of reality is arguable. Actually, the acceptance of the independence thesis seems to

24 I have developed the problem of the realistic truth of norms or moral judgment elsewhere: see D’Agostini (2013). 25 See D’Agostini (2012).

48 | Franca D’Agostini be the minimal condition for a theory being considered ‘realist’. As van Woudenberg (2002) has shown, there are at least some implicit assumptions, in alethic perspective, that can be said ‘metaphysical’, in a certain way. For instance: the existence of facts related to sentences, or the idea of truth as an objective property, related to positively existent properties. An epistemic agent A who believes that properties are all “secondary”, won’t admit that the object 𝜆 truly has the property F, so for A, no sentence F𝜆 will be true. On this point, I think a relevant circumstance should be taken into account. To keep to a reasonable sense of making, for making-𝛷 whatever object 𝜆, where 𝛷 is whatever property, the resulting 𝛷𝜆 must be distinct both from the act of making, and from what makes. So alethic realism, being committed to making-true, is minimally committed to a certain kind of independence, and namely: the independence of the made true proposition from the fact that makes it true. Even if in the perspective of my metaphysics the fact 𝛼 only occurs in my mind, in conceding that I am truthfully asserting ‘𝛼’ (or truthfully believing it), I must admit an independent (mental) fact 𝛼, which makes ‘𝛼’ true. This independence, ultimately, is what rules the distinction between metaphysics and semantics, in the sense above specified. Because I would say my 𝐺 ∧ ¬𝐺 is made true by the fact that 𝐺 ↔ 𝐺: while the former, in the case given, is only semantically true, and the latter is also metaphysically true.

5.3 Semantic or Metaphysical? At first sight, alethic realism is only committed to the idea that ultimately, there are (not specified) facts that may make true our sentences. In this sense, dialetheias are alethically real, and in this sense one would ask: what is the difference between this idea and the basic idea of semantic dialetheism, that is: that dialetheias are semantical, which means they do not stay out there, but only in the fictionalconventional realm of concepts and linguistic structures? Semantic dialetheists would say for instance that true Cs are due to concepts, say ‘overdefined’ concepts, like Mares (2004, 269–270) suggests, and therefore there are Cs, but they are conceptual and not real phenomena (constructed phenomena, in Beall’s terminology).²⁶ In this sense, semantic dialetheism is committed to the ontological thesis according to which ‘real’ facts are, say, natural facts, while Cs are not natural, not real but linguistic, so artifacts, or conventional facts. This is somehow confirmed by the idea that dialetheism ultimately is a fictional 26 See Beall (2004), 207. The underlying conception of truth of Beall’s semantic dialetheism is specified in Beall (2009).

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perspective (see Kroon (2004), 253), admitting that there are useful concepts, such as the concept of truth, though these concepts are “deeply flawed” because they convey Cs; while as to the world (to say as to true effective reality), it is not to be excluded that it might be “deeply inconsistent”, or rather trivial. In the perspective of semantic dialetheism, trivialism can thus be admitted, as a consequence of admitting Df. T, Df. F, but not LNC. In Kroon’s account, Priest’s dialetheism would try to reconcile the fictional idea that things are exactly like our classical logic says, with the idea that (maybe) everything is true, and so everything is contradictory. And it would do this, by adopting the moderate position, according to which there are some Cs, but trivialism is to be rejected, otherwise, we won’t be able to make choices, and act in the world.²⁷ Now, the crucial point is that if things stand in this way, there is no point for dialetheists in saying that there are evident Cs, in the empiricist sense of evidence, because these Cs would be only fictional or conventional, and there are plausible doubts that fictional or conventional Cs could really threaten in any sense the inviolability of LNC.

5.4 What Is Metaphysical Realism? I think all these perplexities might be eliminated, by a more accurate distinction between semantic realism (SR) and alethic realism (AR), and by specifying why AR is in fact, and fundamentally, a sort of metaphysical realism (MR). In Putnam’s account, MR requires three theses: “(1) the world consists of some fixed totality of mind-independent objects; (2) there is exactly one true and complete description of ‘the way the world is’; (3) truth involves some sort of correspondence relation between words and thought-signs and external things or set of things”.²⁸ This is a very demanding perspective. I suspect that nobody has ever endorsed such a position. Though, in a slightly different but maybe more plausible account, MR is simply the idea that: 1. 2. 3.

there are facts (for a plausible meaning of facts) there is a unique true description of these facts sometimes we can formulate true descriptions of facts, and evaluate if a certain description is true or false.

27 Kroon (2004), 244. 28 Putnam (1981), 49.

50 | Franca D’Agostini These three theses are unquestionable, if we keep to the usual (Aristotelian) meaning of predicates such as ‘being a fact’, ‘being true’ and ‘being false’. Let’s suppose I am ineffabilist, so I accept 1, and 2 but not 3: I will be forced to admit that there is at least one true description of facts accessible to me, namely: the one consisting of the theses 1 and 2. Suppose now I accept 1, and 3, but refuse 2 (relativist realism, see Putnam (2012)): I will be forced to acknowledge that 1 and 3 constitute the unique true description of facts concerning our knowledge of facts, or else I will admit that this is only one among possible descriptions (but in this case, what’s the point in defending it?). Finally, suppose nihilists, who do not accept any of the three theses. What the nihilist is intending is that the entire mechanism of truth is to be rejected, and possibly substituted by other things (other concepts). This might be interesting (and it is the basis of some continental positions toward realism). But the nihilist must justify and explain his position by using the concepts of ‘truth’ and ‘reality’, so he will be forced to accept the three theses. And if he wants to do away with them later (like ancient sceptics wanted), he will be forced to renounce arguing and reasoning, and he should live – like Nietzsche wanted – “like sheeps on the grass”. I am not sure it is a good attitude. As it seems, the only consistent position is a form of radical subversion of the entire mechanism, which will lead to renounce the usual meaning of factuality (reality), falsity and truth. But in so doing, one should get rid of all our ways of reasoning, and discussing. AR is perfectly adaptable to the three theses. So it is MR, to the extent that it postulates the occurring of facts, the existence of true descriptions of them, and the possibility of evaluating and formulating true or false descriptions of facts. The only requisite is that the field of really existing facts must be left open to further metaphysical inquiry. So truth is a metaphysical property, even if it does not convey any commitment to some specific metaphysics. In this perspective, Cs are metaphysically real. In the sense that they are Tfacts, facts of truth, and the use of truth positively requires metaphysical realism, in the above mentioned meaning. If we intend ‘semantic’ as detached from metaphysics, we must admit that truth is not only a ‘semantic’ concept, but also something else. It is more-than-semantic.

6 Conclusion Metaphysical alethic realism (in the minimal and I would say unavoidable version of the three theses specified above) isolates a specific ontological field, typically

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51

located at the intersection of metaphysics and epistemology.²⁹ What is ‘real’ there, is not preliminarily specified or restricted. It surely contains what we may call ‘real’ according to a more or less restrictive metaphysics (say naturalist, or actualist, or spiritualist), but it also contains what we may call derivate reality, with respect to the given restriction. For instance a naturalist may admit that 𝐹𝜆 is made true by the positive occurring of 𝐹 + 𝜆, where 𝐹 might be a natural property; but also a “supervenient” property, supervening on physical properties of 𝜆. This special field is the wide realm of both truthmakers and propositions (and beliefs). All this was partially clear in Aristotle’s Met. B (where “first philosophy” is called the “science of truth”), and it was somehow specified and isolated by Kant. And this was what exactly Hegel held (as far as I know), by talking about the ‘reality’ of conceptual phenomena. Calling this semantic reality, as opposed to metaphysical reality, is reductive, if not decidedly wrong, I think. First because among the real facts included there, there are also ‘real’ facts in a strong and restricted sense. Second because known facts (as Kant stated) are hybrid entities: they come from the joined efforts of reality “in itself” and human cognitive means. If our evidence of Cs is true evidence, we may say that Cs (in the various contents they may assume) are real, as located in that field, to say: they are alethically real.

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29 Possibly, also of ethics.

52 | Franca D’Agostini F. D’Agostini, “Was Hegel Noneist, Allist or Someist?”, in: A. Nuzzo (ed.), Hegel and the Analytic Tradition, New York and London, 135–157, 2009a. F. D’Agostini, Paradossi, Rome, 2009b. F. D’Agostini, Introduzione alla verità, Turin, 2011. F. D’Agostini, “Kant era noneista?”, in: Paradigmi 30/1, 91–110, 2012. P. Eldridge-Smith, “Pinocchio against the dialetheists”, in: Analysis 71, 306–308, 2011. P. Eldridge-Smith, “Pinocchio beards the Barber”, in: Analysis 72, 749–752, 2012. V. Eldridge-Smith and P. Eldridge-Smith, “The Pinocchio paradox”, in: Analysis 70, 212–215, 2010. E. Ficara, “Dialectic and Dialetheism”, in: History and Philosophy of Logic 34, 35–52, 2013. H. Field, Saving Truth from Paradox, Oxford, 2008. F. Kroon, “Realism and Dialetheism”, in: G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 245–263, 2004. W. Künne, Conceptions of Truth, Oxford, 2003. M. P. Lynch, Truth as One and Many, Oxford, 2009. E. D. Mares, “Semantic Dialetheism”, in: G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 264–275, 2004. G. Priest, In Contradiction: A Study of the Transconsistent, Dordrecht (2nd edition: Oxford 2006), 1987. G. Priest, Towards Non-Being, Oxford, 2005. G. Priest, Doubt Truth To Be A Liar, Oxford, 2006. G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 2004. H. Putnam, Reason, Truth and History, Cambridge, 1981. H. Putnam, Philosophy in an Age of Science. Physics, Mathematics and Skepticism, Cambridge, 2012. W. V. O. Quine, Ways of Paradox and Other Essays, New York, 1962. M. Sainsbury, Paradoxes, Cambridge (1st edition: 1987), 1995. R. A. Sorensen, Vagueness and Contradiction, Oxford, 2001. R. A. Sorensen, “The Art of the Impossible”, in: T. S. Gendler, J. Hawthorne (eds.), Conceivability and Possibility, Oxford, 337–368, 2003. R. A. Sorensen, Seeing Dark Things, Oxford, 2008. R. van Woudenberg, “On the Metaphysical Implications of Alethic Realism”, in: W. Alston (ed.), Realism and Anti-Realism, New York, 119–130, 2002. A. C. Varzi, “Conjunction and Contradiction”, in: G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 93–112, 2004. T. Williamson, Knowledge and Its Limits, Oxford, 2000. L. Wittgenstein, Philosophical Investigations, translated by G. E. M. Anscombe, Oxford, 1985.

Achille C. Varzi

Logic, Ontological Neutrality, and the Law of Non-Contradiction 1 Logic in the Locked Room As a general theory of reasoning, and especially as a theory of what is true no matter what is the case (or in every “possible world”), logic is supposed to be ontologically neutral. It should be free from any metaphysical presuppositions. It ought to have nothing substantive to say concerning what there is, or whether there is anything at all. For Kant, it is “pure” and “a priori”.¹ For Russell, it doesn’t deal with “mere accidents”.² For Gödel, it is “a science prior to all other”.³ This conception of logic may be illustrated with the help of the “locked room” metaphor.⁴ Logicians must pretend to be locked in a dark, windowless room, and to know nothing about the world outside. When confronted with a statement, they must try to evaluate it exclusively on the basis of their linguistic competence. If they can establish that it is true, then the statement is logically true. And if they can establish that the statement is true on the assumption that certain other statements are true, then the corresponding argument is logically valid. Logical truth and validity are based on how our language works, and on our ability to keep track of the fixed meaning of certain syncategorematic expressions such as connectives and quantifiers. They do not depend on what extralinguistic reality might look like. It is precisely because it didn’t measure up to this conception that traditional Aristotelian logic has eventually been deemed inadequate as a canon of pure logical reasoning. The relations among categorical statements that make up the traditional Square of Opposition (Figure 1) were supposed to determine valid patterns of inference.⁵ Yet some of them really rest on implicit existential assumptions concerning the extension of the subject term, 𝑆, and should not, therefore, count as valid as a matter of pure logic.⁶

1 See A53/B77, A54/B78, A131/B170, and elsewhere. 2 Russell (1919b), 205. 3 Gödel (1944), 125. 4 From Bencivenga (1999), 6–7. 5 The traditional Square emerges from Aristotle’s remarks in De Interpretatione 6–7 (17b.17–26) and in Prior Analytics I.2 (25a1–25). 6 For a history of the issue, see e.g. Church (1965).

54 | Achille C. Varzi Every S is P

No S is P

A

CONTRARIES

E

SUBALTERNS

CONTRADICTORIES

SUBALTERNS

I

SUBCONTRARIES

Some S is P

O Some S is not P

Figure 1. The traditional Square of Opposition.

For example, the inference from an A-form universal statement to its I-form particular subaltern, (1) Every 𝑆 is 𝑃. ∴ Some 𝑆 is 𝑃. depends on the existence of at least one 𝑆, since in an 𝑆-less world the conclusion would be false whereas the premise would be true, albeit vacuously. Of course, one could just reject the notion of vacuous universal truth by insisting that the non-emptiness of the subject term is presupposed in every A-form statement. After all, most ordinary-language speakers share that intuition. However, such a move would leave us with a logical theory that cannot distinguish between those arguments whose validity depends on the presupposition, such as instances of (1), and those that do not, such as instances of (2) Every 𝑆 is 𝑃. ∴ It is not the case that some 𝑆 is not 𝑃.⁷ Besides, the move would still not suffice to salvage the traditional Square. For, if ‘𝑆’ is indeed an empty term, then certainly the I-form statement, ‘Some 𝑆 is 𝑃’, must be false. But then its contradictory E-form, ‘No 𝑆 is 𝑃’, must be true, and that

7 This complaint goes back to Lambert (1967), 134.

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would imply the truth of the subaltern O-form, ‘Some 𝑆 is not 𝑃’ – contradicting the assumption that there are no 𝑆s to begin with.⁸ Modern quantification theory, as rooted in the work of Frege, Russell, and Whitehead,⁹ is much better in this respect, as it is free from all the existential commitments of Aristotelian logic. The modern interpretation of the Square of Opposition condones only the two relations of contradictoriness – along the diagonals – rejecting all other relations as strictly speaking invalid: Every S is P

No S is P

A

E

CONTRADICTORIES

I

O

Some S is P

Some S is not P

Figure 2. The revised Square of Opposition.

In order to permit, for instance, an inference of subalternation, the modern logician requires that an additional premise be added, making explicit the existential assumption that in (1) was implicit: (1󸀠 ) Every 𝑆 is 𝑃. There exists some 𝑆. ∴ Some 𝑆 is 𝑃. As it turns out, however, quantification theory cannot claim full ontological neutrality, either. For while it blocks the problematic inferences of Aristotelian logic,

8 This reasoning goes back to Kneale/Kneale (1962), 55–60. It should be noted that on some translations of De Interpretatione the argument does not go through, since the O-form is rendered as ‘Not every 𝑆 is 𝑃’. See Wedin (1990). 9 Frege (1893/1903) and Whitehead/Russell (1910/1913).

56 | Achille C. Varzi it still sanctions as valid inferential patters that are, on the face of it, ontologically committing, as in (3) and (4): (3) Everything is 𝑃. ∴ Something is 𝑃. (4) Everything is 𝑃. ∴ 𝑎 is 𝑃. Obviously, the inference in (3) rests on the implicit assumption that something must exist, since in an empty world the conclusion would be false whereas the premise would be (vacuously) true, while the inference in (4) rests on the specific assumption that 𝑎 exists, i.e., that ‘𝑎’ denotes something. Indeed, modern quantification theory also sanctions as logically true statements that carry explicit existential import, such as (5) Something is either 𝑃 or not 𝑃. (6) Something is self-identical. Even the following comes out as a logical truth: (7) Something exists. and to the extent that ‘𝑎’ is treated as a genuine singular term, so does (8) 𝑎 exists. One can tinker with the pieces, alter the reading of the quantifiers, make room for mere possibilia, get rid of singular terms, etc.¹⁰ But all this just confirms the problem. As Russell himself acknowledged a few years after the publication of Principia Mathematica, the provability of such existential theorems is a “defect in logical purity”.¹¹ Free logic, as rooted in the more recent work of Leonard, Lambert, Hintikka and others,¹² is so called precisely because it is “free” from the existential pre-

10 For example, Russell’s (1905) theory of descriptions provides the resources for disposing of (8) by rewriting it as ‘There exists exactly one thing that 𝑎-izes’, which is not a theorem of quantification theory. (See Quine (1948).) 11 Russell (1919a), 203. See also Russell (1919b), 205. In both cases, Russell was referring explicitly to (7). 12 See e.g. Leonard (1956), Hintikka (1959), and Lambert (1967). For a survey of free logic, see Bencivenga (1986) and Lehmann (2002).

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suppositions that are responsible for such remnants of logical impurity. It allows, not only for empty general terms, but also for non-denoting singular terms, and it does not rule out the possibility that the domain of quantification be empty, i.e., that there exist nothing at all.¹³ Again, the remedy lies in revising the problematic inferential patterns by making the relevant existential presuppositions explicit. For example, (3) and (4) become (3󸀠 ) Everything is 𝑃. Something exists. ∴ Something is 𝑃. (4󸀠 ) Everything is 𝑃. 𝑎 exists. ∴ 𝑎 is 𝑃. Once this is done, the contentious existential claims in (5)–(8) are no longer provable, either, and free logicians can fairly claim to have achieved greater purity in the spirit of the “locked room” metaphor. Is this the end of the story? Is free logic completely pure, universal, ontologically neutral? Today this is still an open question, as it is an open and controversial question whether there is in fact any logical theory that can claim the honor. Among other things, it may be observed that free logic shares with classical quantification theory the Square of Opposition in figure 2, which in turn is meant to retain the uncompromising patterns of inference of the traditional Square of figure 1. But are the surviving relations of contradictoriness truly neutral from an ontological perspective? If, for example, it were possible for something to be neither 𝑃 nor not 𝑃, then the A-form statement ‘Every 𝑆 is 𝑃’ and the corresponding O-form statement ‘Some 𝑆 is not 𝑃’ could both be false simultaneously. And if it were possible for there to be something that is both 𝑃 and not 𝑃, then those statements could be both true. More generally, from traditional Aristotelian logic through modern quantification theory all the way to free logic, the following two principles are assumed in the background (for any predicate ‘𝑃’): (9) Everything is either 𝑃 or not 𝑃. (10) Nothing is both 𝑃 and not 𝑃.

13 Strictly speaking, logics admitting the empty domain of quantification are called “inclusive”. While an inclusive logic for a language whose non-logical vocabulary contains singular terms must perforce be free, a free logic need not be inclusive. (The first inclusive logic – without singular terms – goes back to Jaśkowski (1934).)

58 | Achille C. Varzi Yet one might object that these principles – the law of excluded middle and the law of non-contradiction, on some terminology – betray a conception of possibility that is ultimately rooted in metaphysics, not in the linguistic competence that should guide our work in the locked room. It is the business of metaphysics, not of logic, to legislate on whether an object can ever be indeterminate, or overdeterminate, with respect to any given property or condition 𝑃. And if this objection is granted, then clearly the alleged neutrality of free logic, as of any other theory endorsing (9) or (10), founders. In fact, (9) has been especially challenged over the years, though often in terms that leave the question open. For example, it has frequently been pointed out that vagueness is a natural source of counterexamples to the law of excluded middle.¹⁴ To the extent that the extension of a predicate ‘𝑃’ may not be fully precise, it may admit of borderline cases that do not comply with (9) – things that are neither definitely 𝑃 (i.e., falling inside the extension) nor definitely not 𝑃 (i.e., falling outside). Yet it might be replied that cases of this sort do not necessarily affect the generality of (9). They may induce a violation of the semantic (metalinguistic) principle of bivalence, namely (11) Every statement is either true or false, but that need not entail a failure of the law of excluded middle as such.¹⁵ In order to have a genuine counterexample to (9), we need to make room for genuine ontological, de re indeterminacy, and according to a certain line of reasoning, that is not a coherent option.¹⁶ As Russell famously put it, to claim that linguistic vagueness is a sign of ontic indeterminacy is to incur a “fallacy of verbalism”.¹⁷ It is indeed an open question whether this sort of response is acceptable from the present perspective, i.e., whether it does not already betray a metaphysical stance that ought not to be built into the laws of logic.¹⁸ More importantly, it is an open, deep question whether there may be other legitimate sources of ontic indeterminacy over and above vagueness, hence other legitimate reasons to doubt the ontological neutrality of (9). I’m not, however, going to delve into such questions

14 The point goes back to Frege (1893/1903), vol. 2, §56, though Frege himself saw it as a reason to require that all vagueness be banned from the scope of logical theorizing. 15 This is the gist, for instance, of Fine’s (1975) supervaluational account of vagueness. For the argument that the excluded middle does entail bivalence (so that failure of the latter would entail failure of the former), see Williamson (1992), esp. 145–146. 16 See e.g. Evans (1978), Salmon (1982), 243–246, and Pelletier (1989). 17 Russell (1923), 85. 18 See Williams (2008) and Hyde (2008) for a survey of some views on this question. For my own thoughts, I refer to Varzi (2001). I’ll come back to this below, too.

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here, at least not in their own right, as they would take us to far afield. Rather, my purpose is to focus on (10) and consider the parallel question of whether the law of non-contradiction, too, is open to the charge of infringing the expected ontological neutrality of logic. Aristotle called it βεβαιοτάτη δ’ ἀρχὴ πασῶν, “the most certain principle of all”,¹⁹ and it is fair to say that this characterization has survived more or less intact until our days. Indeed, Aristotle himself viewed the incompatibility between contradictories as the most fundamental form of opposition, thus predicting the destiny of the traditional Square in our times.²⁰ Nonetheless, even this principle has occasionally been questioned on various grounds, were it only to exhibit its status as an “unshakable dogma” (Łukasiewicz’s phrase²¹) of Western thought. The development of paraconsistent logic, as grounded in the work of Vasil’év, Jaśkowski, Asenjo, da Costa, Priest, and others,²² bears witness to the determination with which the project of resisting the dogma has actually been pursued since the early twentieth century. In many cases, the original motivations had little to do with the quest for a pure, universally applicable, ontologically neutral theory: from the Liar paradox and the set-theoretic antinomies to belief revision, relevant implication, automated reasoning, and beyond. All of these are areas which, as Priest puts it, lie “at the limits of thought and language”,²³ but it is not obvious that they provide good evidence for the possibility of genuine de re counterexamples to (10), as opposed to evidence against the semantic principle of contravalence: (12) No statement is both true and false. Even the rise of dialetheism in recent times – the view according to which, not only could there be, but there are violations of the law of non-contradiction – is in principle subject to this worry,²⁴ and the step from semantics to ontology is as vulnerable to the “fallacy of verbalism” in this case as it is in the case of putative failures of the excluded middle. Still, all of this demands close scrutiny. I’ll leave it to others to assess the pros and cons of paraconsistent logic and dialetheism visà-vis the many motivations that led to their development. The specific question

19 Metaphysics, IV.3 (1005b11–12); W. D. Ross’s translation. 20 Metaphysics, IV.5 (1008a35–b12). 21 Łukasiewicz (1910a), 87, retained in the (1910b) summary, 37. 22 See e.g. Vasil’év (1912), Jaśkowski (1948), Asenjo (1966), da Costa (1974), and Priest (1979). For a survey of paraconsistent logic, see Priest (2002). 23 Priest (1995). See also Priest (1987). 24 After all, the term ‘dialetheism’ comes from di-aletheia, a two-way truth. See Priest/Routley (1989a), xx. It is worth noting, however, that Priest takes (12) to express the law of noncontradiction itself; see e.g. Priest (1998), 416.

60 | Achille C. Varzi I’m interested in, here, is whether and to what extent the pressure to relinquish such a fundamental principle as (10) may be viewed as an expression of the general need to develop logical theories in the spirit of the “locked room” conception mentioned at the beginning. Does (10) betray a genuine ontological bias? If so, what does it mean to forego such a bias in the interest of even greater neutrality?

2 A Big Deal It is, in fact, not quite accurate to frame the issue exclusively in terms of the principle of non-contradiction, as formulated in (10). Before looking at the details, however, there is a general point that needs to be clarified. For if the worry is that (10) delivers a notion of validity that is ontologically biased, one might wonder whether the worry is well grounded at all. Never mind (10) itself. Are there any other theorems or inferential patterns that depend on such a law?²⁵ In the Metaphysics, Aristotle famously says that all who are carrying out a demonstration reduce it to this as an ultimate belief; for it is naturally the starting-point even for all the other axioms.²⁶

But this sounds more like a closing flourish than a precise assessment of the role of (10) in actual arguments, as when Leibniz says that everybody – even “barbarians” – must tacitly rely on it at every moment.²⁷ In fact, the relevant section of the Posterior Analytics says explicitly that the law itself does not actually feature in the context of any interesting proof: That it is not possible to affirm and deny [the same predicate of the same subject] at the same time is assumed by no demonstration – unless the conclusion too is to be proved in this form.²⁸

The latter view became especially popular among medieval philosophers, not least through Aquinas’s reading of it: Nulla demonstratio accipit hoc principium.²⁹ So, if that view is indeed correct, then one might as well say that the worry does not bite deep. The law of non-contradiction may be an entrenched dogma, but doing away with it needn’t be a big deal.

25 26 27 28 29

This is – correctly, in my opinion – the starting point of Berto (2007), at p. 4. Metaphysics, IV.3 (1005b32–34); W. D. Ross’s translation. New Essays, I. i.4. Posterior Analytics, I.11 (77a10–11); W. D. Ross’s translation. Commentary on Aristotle’s Posterior Analytics, I.l.xix.

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The view, however, is not correct. For one thing, this is already apparent from the Square of Opposition, in the original form as well as in its modern, weaker variant. The very inference from a statement to the denial of its contradictory, as in (2) above, depends crucially on (10). For, as already mentioned, in a world where the A-form premise ‘Every 𝑆 is 𝑃’ is true, the existence of an 𝑆 that is both P and not 𝑃 would warrant the truth of the corresponding O-form statement ‘Some 𝑆 is not 𝑃’, hence the falsity of the conclusion in (2). Thus, exactly as with the move from Aristotelian logic to modern quantification theory with regard to the inference in (1), and the move from quantification theory to free logic with regard to the inference in (3), the move from any such theory to a logical theory that is not committed to the law of non-contradiction would require that the inference in (2) be revised by adding a further premise asserting the relevant instance of the law: (2󸀠 ) Every 𝑆 is 𝑃. Nothing is both 𝑃 and not 𝑃 ∴ It is not the case that some 𝑆 is not 𝑃. The same applies to other inferential patterns that make up that core of Aristotelian logic that has survived all the way to free logic, such as obversion (e.g., from the ‘Every 𝑆 is 𝑃’ to ‘No 𝑆 is not 𝑃’), exactly as some of those patters depend implicitly on the law of excluded middle (e.g., the inference from ‘No 𝑆 is not 𝑃’ back to ‘Every 𝑆 is 𝑃’). Second, and more important, modern logic is characterized by several additional patterns of reasoning that rely implicitly on the law of non-contradiction, beginning with so called indirect proofs (also known, quite aptly, as “proofs by contradiction”, though they depend just as much on excluded middle). The following inference is an obvious case in point: (13) If 𝑎 is 𝑆, then 𝑎 is 𝑃. If 𝑎 is 𝑆, then 𝑎 is not 𝑃 ∴ 𝑎 is not 𝑆. It is indeed telling that precisely this sort of inference founders in most systems of paraconsistent logic. Another obvious example is the inferential pattern known as ex contradictione quodlibet, the rejection of which is a central feature of most systems of paraconsistent logic: (14) Something is both 𝑃 and not 𝑃. ∴ 𝑎 is 𝑄. The validity of this inference, as of any inference from the same premise to any conclusion whatsoever, rests implicitly on the fact that the law of non-

62 | Achille C. Varzi contradiction completely rules out any possibility for the premise to be true. And if there is no possible circumstance under which the premise is true, then a fortiori there is no possible circumstance under which the premise is true and the conclusion false. Finally – though this is more controversial – a similar point could be made with regard to argument forms that do not, on the face of it, involve any explicit use of negation. Łukasiewicz remarked that such direct proofs do not in fact depend on the law of non-contradiction, since the law “always joins an affirmative proposition and its contradictory negative”.³⁰ But as some commentators have pointed out, what is presupposed by a pattern of inferential reasoning may not be part of that reasoning itself.³¹ Consider, for instance, the following argument: (15) 𝑎 is 𝑆 and 𝑏 is either 𝑃 or 𝑄. ∴ Either 𝑎 is 𝑆 and 𝑏 is 𝑃, or 𝑎 is 𝑆 and 𝑏 is 𝑄. On the face of it, this argument is valid, not only in standard quantification theory, but also in free logic – a mere instance of the distributivity of conjunction over disjunction. And surely enough, this is a direct argument whose validity does not require an appeal to (10) as an implicit premise. However, to the extent that the notion of validity is defined semantically in the spirit of the “locked room” metaphor – as the relation that holds between the premises of an argument and its conclusion if and only if there is no possible circumstance under which the former are true while the latter is false – one could reason as follows. Why is (15) valid? Answer: precisely because there is no circumstance under which its premise is true while the conclusion is false. But neither is there any circumstance under which the premise is false while the conclusion is true; the premise and the conclusion stand or fall together, i.e., they are equivalent, they are true exactly under the same circumstances. Thus, the answer boils down to this: (15) is valid because there is no possible circumstance under which the premise is true while the premise itself is false, which is to say, no possible circumstance under which the premise is both true and false. And isn’t this just another way of saying that (15) is valid owing to contravalence, hence to the law of non-contradiction? As I said, this third point is more controversial, among other reasons because it is not quite clear what exactly warrants the crucial central claim, to the effect that the premise and the conclusion are true under exactly the same circumstances. But never mind. Even short of this last point, we have enough good reasons to conclude that there are theorems and inferential patterns that depend

30 Łukasiewicz (1910b), 33. 31 See e.g. Wedin (2000), 117ff., though his examples are erroneous.

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strictly on the law of non-contradiction, contrary to Aristotle’s remarks in the second quote above.³² Hence, the worry on the table is not ill-grounded. On the contrary, forgoing the law is a big deal indeed, for so much depends on it. The discussion of (15), however, is also useful in relation to the other issue mentioned at the beginning of this section. For the reasoning offered in connection with (15) rests on the idea that there is an intimate link between the law of non-contradiction, as stated in (10), and the principle of contravalence, (12). It’s easy to see that in the presence of the latter, the former admits of no counterexamples, so in this respect the reasoning is not fallacious. But I have already pointed out that contravalence is, strictly speaking, the profession of a semantic principle, the dual of bivalence. And just as it may be argued that the semantic principle of bivalence, understood as in (11), is not implied by the law of excluded middle, understood strictly as in (9), one can argue that the semantic principle of contravalence is not implied by the law of non-contradiction. Aristotle himself did not seem to see any significant difference, treating (10) and (12) as expressing the same fundamental idea³³ (an attitude that is shared, more or less carelessly, by many contemporary philosophers and logicians³⁴). Indeed, he helped himself with a third way of formulating what he thought was the same idea, namely, that “it is impossible for any one to believe the same thing to be and not to be”.³⁵ We can safely set this third formulation aside here, for there are good reasons to think that it pertains the realm of psychology rather than ontology proper, or semantics.³⁶ But the relationship between (10) and the attendant semantic principle of contravalence, (12), is central to our present concerns. How does it work, exactly? And how does it play out in relation to the desideratum of an ontologically neutral logic?

32 For a full account of the role of the law in Aristotelian logic, see Cavini (2008). 33 See e.g. Metaphysics, IV.3 (1005b19–20) and IV.6 (1011b13–14), respectively. 34 Even authors who carefully draw the distinction between bivalence and excluded middle often conflate contravalence and non-contradiction; see e.g. Haack (1978), at pp. 246 and 246. In fact, there is still a pervasive tendency to conflate the former distinction, too. To give just one example, Copi’s (1953) popular textbook survived all its fourteen editions, up to Copi and Cohen (2010), treating (9) and (11) as if they expressed one and the same doctrine. (See DeVidi/Solomon (1999), for an assessment of this ubiquitous practice.) All of this over and above any differences in terminology, which in the case of (10) and (12) is especially striking: even authors who draw all the relevant distinctions tend to use ‘law of non-contradiction’ to refer to contravalence (otherwise known as biexclusion, or exclusion, or just as the dual of bivalence). 35 Metaphysics, IV.3 (1005b23–25); W. D. Ross’s translation. 36 The three formulations were clearly distinguished for the first time by Łukasiewicz (1910a) and (1910b), though he used the label “logical” for what I have called the “semantic” principle of contravalence – a terminology that is still current practice.

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3 Contravalence and Contradiction I have already remarked that, in one direction, the relationship between the law of non-contradiction and the principle of contravalence is straightforward. If we have a counterexample to (10), say (16) 𝑎 is both 𝑃 and not 𝑃, then the following must hold: (17) ‘𝑎 is both 𝑃 and not 𝑃’ is true. From this, it follows that each of the following must hold, too: (18) ‘𝑎 is 𝑃’ is true (19) ‘𝑎 is not 𝑃’ is true But (19) is equivalent to (19’) ‘𝑎 is 𝑃’ is false. Hence we can conclude that (20) ‘𝑎 is 𝑃’ is both true and false. Thus, our putative counterexample to the logical law of non-contradiction turns automatically into a counterexample to the semantic principle of contravalence. And since nothing in our reasoning depends on the specific form of the counterexample, by generalization this means that the logical law is entailed by the semantic principle. The converse entailment, however, need not stand. More precisely, if we ran the argument in reverse, i.e., from (20) to (16), our reasoning would be acceptable only under certain semantic assumptions which, in the present context, cannot be taken for granted. I am referring specifically to the semantic assumptions that govern the truth conditions of statements involving the logical operators – here, the connectives for negation, ‘not’, and for conjunction, ‘and’. Standardly, the conditions for these connectives would be formulated as follows: (21) ‘Not 𝐴’ is true if and only if ‘𝐴’ is false. (22) ‘𝐴 and 𝐵’ is true if and only if ‘𝐴’ and ‘𝐵’ are true.

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Given these conditions, there is no question that the argument could be run symmetrically in either direction. Absent contravalence, however, the validity of the truth conditions for conjunction, (22), may be questioned: from left to right, the biconditional is irreproachable, warranting the inference from (17) to (18)–(19),³⁷ but from right to left the biconditional may fail, thus blocking the inference in the reverse. Since to establish the entailment from non-contradiction to contravalence one cannot assume the latter at the start, it follows therefore that in that direction the entailment founders. When exactly does (22) fail from right to left? It depends on the relevant motivations for rejecting contravalence. Suppose, for example, that our motivations for doing so stem from the desire to model the logic of a discussion group, as in Jaśkowski’s “discursive logic”.³⁸ We want to say that a statement counts as true, in the context of a discussion, if and only if it is held true by at least one of the participants. Evidently, different participants in the discussion may disagree while being perfectly self-consistent. For instance, some may claim that 𝑎 is 𝑃 while others may claim that 𝑎 is not 𝑃, though no one will claim that 𝑎 is both 𝑃 and not 𝑃. In such a case, then, each of ‘𝑎 is 𝑃’ and ‘𝑎 is not 𝑃’ will be true, yet their conjunction will not. For another example, suppose that our motivations stem instead from the need to deal with a data bank compiled from different sources, or to explain how a useful data processor “should think”, as Belnap put it.³⁹ The data come from sources which, alas, may not always agree, though each one is on the whole trustworthy. If one source says that 𝐴 while another says the opposite, the data processor should treat both ‘𝐴’ and ‘not 𝐴’ as true. Yet, again, as long as each of the sources is self-consistent, the processor should refrain from treating ‘𝐴 and not 𝐴’ as also true. A third example comes from the need to “quarantine inconsistencies”, as Lewis put it,⁴⁰ in the context of literary fiction. We have all read the Holmes stories and we know how to put them together. Truth in Holmes’s world is truth according to at least one of the stories. Yet there are discrepancies. We are told that Dr. Watson suffered a bullet wound during the Afghan campaign in which he participated, but in A Study in Scarlet the wound is said to be located in Watson’s shoulder, in The Sign of Four it is located in his leg. It would be logical chaos if we inferred that Watson’s wound both is and is not in his shoulder (and

37 I am of course assuming, here as elsewhere, that ‘𝑎 is both 𝑃 and not 𝑃’ is shorthand for ‘𝑎 is 𝑃 and 𝑎 is not 𝑃’. 38 Jaśkowski (1948). 39 Belnap (1977). 40 See Lewis (1982), though the example that follows is from Lewis (1983). I am, in fact, just offering it as a simple example, with no intention to be dismissive of the complications discussed e.g. in Proudfoot (2006).

66 | Achille C. Varzi in his leg). But we don’t, for once again we do not infer the truth of a conjunction from the truth of its conjuncts. Of course, one might protest that none of these cases should be given much credit. That is, one might protest that a fictional story, a data bank, the record of a discussion, etc. do not constitute good examples of the sort of possible “circumstance” under which a statement can properly be said to be true or false in the sense that matters when it comes to reasoning in the logician’s locked room; there are other ways to address the relevant needs. For example, one could resort to a suitable sentential operator that maps every statement 𝐴 to a corresponding statement of the form (23) According to 𝛷: 𝐴 where 𝛷 is the story in question, the computer’s data bank, the record of a discussion, or what have you. Then the cases discussed above would provide us with good reasons to question the following biconditional: (24) ‘According to 𝛷: 𝐴 and 𝐵’ is true if and only if ‘According to 𝛷: 𝐴’ and ‘According to 𝛷: 𝐵’ are true. But this would have no bearing on the status of (22). ‘According to 𝛷’ is an operator that may introduce an intensional context, on a par with ‘Possibly’, or ‘Graham said that’, and the question of whether such intensional contexts distribute over conjunction should be kept distinct from the question of whether conjunction itself is properly governed by the truth conditions in (22). In fact, that question has no bearing on whether contravalence holds, either, for obviously a statement of the form (23) and a statement of the form (25) According to 𝛷: not 𝐴 do not contradict each other; they simply attest to the self-contradictoriness of 𝛷 (just as the statements (26) Graham said that 𝐴 (27) Graham said that not 𝐴 do not contradict each other but rather attest to the contradictoriness of Graham’s pronouncements). There is indeed nothing wrong with this line of thought, except that it misses the point. For the issue on the table is the relationship between the principle of contravalence and the law of non-contradiction, specifically whether the former

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is entailed by the latter. We may find good ways of dealing with the three cases mentioned above (and similar ones) so as to preserve (22) along with contravalence, and the use of a suitable sentential operator may well be one of them.⁴¹ In that case, the entailment would be safe and we might conclude that contravalence and non-contradiction stand or fall together. This is not an unpopular view, equally available to the friends and foes of the law of non-contradiction. But to the extent that any of those cases counts as a legitimate motivation for rejecting contravalence, to that extent we have reasons to deny the entailment and, with it, the equivalence between contravalence and non-contradiction. Since it is a fact that a variety of logical theories have been developed that violate contravalence precisely on such grounds, a dismissive attitude would not, in the present context, be of service. Besides, the very question of what constitutes a good example of the notion of “circumstance” that is relevant to the concepts of logical truth and logical validity is part of the problem. Obviously, to rule out certain options just because they would infringe contravalence would beg the question. It might be fine to insist on the use of a suitable sentential operator, as in (23). But then, again, nothing prevents us from doing the same when ‘𝛷’ stands for a possible world of the garden variety. In that case, ‘According to 𝛷’ would presumably be redundant, which is to say that the following biconditional would hold (28) [According to 𝛷: 𝐴] if and only if 𝐴. and (24) would reduce to (22). But so be it. The question is precisely whether there are any other candidates for ‘𝛷’ that behave in the same way. There is no obvious a priori reason why the logician in the locked room should answer this question in the negative. Finally, even if we kept to the idea that the only admissible “circumstances” are genuine worlds of sorts (as opposed to the “ersatz worlds” that emerge from fictional stories, data banks, etc.), the argument for (22) can hardly be that truth commutes with the truth-functional connectives.⁴² That is, that can hardly be the argument as soon as we entertain the possibility that a genuine world may be the

41 Thus, for example, Jaśkowski’s discursive logic can be embedded into modal logic through the familiar Kripkean modalities. See da Costa/Dubikajtis (1977). For a general overview of this strategy, see Arló-Costa (2005). 42 That is how Lewis (1986), 7n, draws the line. What follows draws on my response in Varzi (1997).

68 | Achille C. Varzi source of counterexamples to such semantic principles as bivalence and contravalence. If that were the case, then the rationale for (22) would also be a rationale for (29) ‘Not 𝐴’ is true if and only if ‘𝐴’ is not true. Yet clearly (29) is controversial. In classical logic, ‘not true’ just means ‘false’, so (29) is equivalent to the condition given in (21). But as soon as we allow for the possibility of sentences that are neither true nor false, or both true and false, (29) is stronger than (21). On most counts, if ‘𝐴’ is neither true nor false, then so is its negation, hence the right-to-left direction of (29) may fail. And if ‘𝐴’ is both true and false, then it is the left-to-right direction of (29) that fails. Thus, on most theories, truth does not commute with negation. Why should conjunction behave any differently? Why should (22) fare any better when we leave the terra firma of classical logic? As it turns out, failure of bivalence is harmless in this respect.⁴³ Failure of contravalence need not be, at least with respect to the right-to-left direction of (22). Why should this departure be regarded as a violence to the “normal interpretation” of the logical connectives?⁴⁴

4 Genuine Contradictions? I hope this will suffice to establish the main point so far: while there is a straightforward argument from the principle of contravalence to the law of non-contradiction, i.e., from (12) No statement is both true and false, to any instance of (10) Nothing is both 𝑃 and not 𝑃. the argument in the opposite direction is wanting. Indeed, it is worth noting that precisely the same sort of consideration may be called upon to motivate the parallel claim mentioned earlier in connection with bivalence and excluded middle, namely, that while the former, (11) Every statement is either true or false,

43 Of course, absent bivalence it becomes necessary to supplement (22) with necessary and sufficient conditions for a conjunction to be false. In itself, however, (22) stands. 44 See Priest/Routley (1989b), n. 159, where the departure is compared to that of intuitionistic negation.

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entails all instances the latter, (9) Everything is either 𝑃 or not 𝑃, the converse entailment need not hold. One can reason from, say, the denial of (30) 𝑎 is either 𝑃 or not 𝑃. to the denial of (31) ‘𝑎 is 𝑃’ is either true or false. in a way that is perfectly dual to the foregoing argument from the acceptance of (16) to the acceptance of (20), this time using the right-to-left direction of the standard truth conditions for the disjunction connective, ‘or’: (32) ‘𝐴 or 𝐵’ is true if and only if ‘𝐴’ or ‘𝐵’ is true. That is a perfectly legitimate way of reasoning. But running the argument in reverse, from the falsity of (31) to the falsity of (30), would call for the left-to-right direction of (32), and inspection shows that in that direction (32) fails in each of the three cases considered above – Jaśkowski’s discursive logic, Belnap’s computer logic, or Lewis’s logic of fiction. That is why I said that failure of bivalence need not entail genuine ontological indeterminacy, i.e., genuine counterexamples to excluded middle.⁴⁵ Likewise, the present point is that failure of contravalence need not entail genuine ontological overdeterminacy, i.e., genuine counterexamples to non-contradiction. Our question then comes to this: When is the inference legitimate, if ever? Under what conditions can we warrantably say that a dialetheia – a statement that is both true and false – is bona fide evidence of a contradiction arising in the world? After all, typically the only evidence we can rely on, in logic as elsewhere in philosophy, comes in the form of claims or intuitions to the effect that certain statements are true and others are false. But as I remarked before, this is slippery business. The fallacy of verbalism – the fallacy of mistaking facts about words for facts about worlds – is constantly lurking. Is there any way of detecting it when it comes to assessing putative infringements of logical laws? Specifically, is there any way of discriminating a merely de dicto dialetheia from a genuinely de re one? In my opinion, that is the best question we can ask if we are interested in the

45 In essence, this is my reply to Williamson’s argument mentioned in n. 15 above.

70 | Achille C. Varzi status of the law of non-contradiction vis-à-vis the desideratum of the ontological neutrality of logic. Alas, I do not have a clear and distinct answer to offer. But I do have two suggestions that, hopefully, will at least be indicative of the kind of answer that I think we should seek. Both are probably too loaded, philosophically, to be of much service. And both come with reservations, the most important of which is that in some cases they yield the wrong verdict. Let me try to outline them none the less.

5 First Suggestion The first suggestion builds directly on the foregoing. To the extent that a counterexample to contravalence results in a violation of the law of non-contradiction only insofar as it can be conjoined with its own negation to yield a single, explicit statement of the form (16) 𝑎 is both 𝑃 and not 𝑃, we can say that it counts as bona fide evidence of a contradiction arising in the world if, and only if, the logical theory assumed in the background licenses such a move. Pretty clearly, a sufficient condition for that to be the case is that the theory validate the relevant instances of conjunction introduction: (33) 𝑎 is 𝑃 𝑎 is not 𝑃 ∴ 𝑎 is both 𝑃 and not 𝑃. And we have seen that such a move need not be valid insofar as the semantic behavior of ‘and’ may run afoul of the standard truth conditions, (22). Thus, the suggestion is simply to look at the whole picture, which is to say the whole set of axioms and inferential patterns that define the logic whose neutrality we are trying to assess. After all, the meaning of a statement is at least in part determined by its logical relations to other statements, hence it is only the network of such relations that can help us answer our question. And when it comes to contradictions, the crucial relation is the one reflected in (33). A different way of putting the same point is this. There are two ways of construing the notion of a contradiction. The first is the one we have been using throughout, the “collective” sense, according to which a contradiction manifests itself in the form of a single statement, as the joint assertion of a proposition and its denial. The other is the “distributive” sense, according to which a contradiction

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arises whenever someone asserts something she is also denying, whether or not she does both things “in the same breath” (as Strawson used to put it⁴⁶). Both notions are perfectly legitimate. But it is only a contradiction in the strong, collective sense that bears witness to a circumstance in which things infringe of the law. At least, this is the suggestion I am offering: (S1) A contradiction is de re if and only if it is closed under conjunction. Contradictions that arise only in the distributive sense – contradictions that don’t conjoin – are merely evidence of discrepancies in our ways of talking about things, as with Sir Arthur’s slips of the pen. That’s why they do not imply logical chaos. Absent (33), the law of non-contradiction may still warrant the “explosive” inferential pattern in (14), ex contradictione quodlibet. It need not, however, warrant its distributive variant: (14󸀠 ) 𝑎 is 𝑃 𝑎 is not 𝑃 ∴ 𝑎 is 𝑄 If this account is accepted, then we can draw our first moral. Our initial question was whether the law of non-contradiction reflects an ontological prejudice that should not be built into our logic. We now see that it need not be so unless we endorse (33). Since classical logics (including free logic) warrant (33) unrestrictedly, it follows that something has to give. One way or the other, a paraconsistent logic has better claim to ontological neutrality.⁴⁷ Unfortunately, there is an obvious problem with the account, which is why I said it is just a “suggestion”. That is, there is an obvious problem over and above the fact that one may just not agree with the idea that distributive contradictions fall short of biting at the ontological level.⁴⁸ A simple example will suffice. Suppose the predicate ‘𝑃’ was introduced, by definition, in a way that is not quite coherent: we stipulated that, say, ‘𝑃’ is true of every individual who is at least 16 years old, and false of every individual who is less than 18 years old. Clearly, both ‘𝑎 is 𝑃’ and ‘𝑎 is not 𝑃’ will turn

46 Strawson (1952), ch. 1, passim. For further details on the distinction between collective and distributive construals of the notion of a contradiction, see Varzi (2004). 47 For the record, paraconsistent logics in which (33) does not hold are generally known as nonadjunctive. As it turns out, Jaśkowski’s discursive logic was the first of this kind. For a brief survey of other non-adjunctive logics, see e.g. Priest (2002), §4.2. 48 For example, Rescher and Brandom’s (1980) “logic of inconsistency” is non-adjunctive precisely in the sense described here. Yet they are adamant about distributive contradictions being grounded in the world itself, not just our discourse about it.

72 | Achille C. Varzi out to be true when ‘𝑎’ picks out an individual whose age is between 16 and 18. But suppose now that our logic does license the inference in (33) by conjunction introduction (as in many systems of paraconsistent logic). It follows that we can derive a genuine counterexample to the law of non-contradiction, and (S1) would confirm that the contradiction in question is genuinely de re. But that is ludicrous. Why should the world be blamed for the sloppiness of our linguistic stipulations? Even a hard-core dialetheist such as Priest would resist that conclusion.⁴⁹ Of course, one could respond that this sort of case provides further evidence against conjunction introduction. But this is a familiar predicament that leads nowhere: one philosopher’s modus ponens is another philosopher’s modus tollens. That is why I said that the suggestion on the table is too loaded, philosophically, to be of much service when it comes to applying it to actual cases. We are still missing some independent criteria for saying whether the truth conditions of a given statement suffer from our contradictory semantic practices. We need necessary and sufficient conditions for determining whether ‘𝑎 is 𝑃’ is supposed to violate contravalence because of the meaning of ‘𝑎’ and ‘𝑃’, or because of how 𝑎 and 𝑃 are. Absent such criteria, we have an account that cries for guidelines.

6 Second Suggestion It is here that the second suggestion enters the picture. And it is a suggestion that builds once again on the duality between non-contradiction vs. contravalence, on the one hand, and excluded middle vs. bivalence, on the other. As it turns out, in connection with the latter opposition there has been a conspicuous debate concerning precisely the dual of our question – namely, under what conditions can we warrantably say whether a statement being neither true nor false is bona fide evidence of an indeterminacy arising in the world? Precisely because of Russell’s influential attempt to discredit all putative ontological vagueness as a form of verbalism, several efforts have been made to explicitly address this question in its general form, at least with respect to certain varieties of indeterminacy such as indeterminacy due to vagueness. And such efforts have often included an account of what it is for an expression to lack a definite, fully determinate meaning – exactly the dual of what we are missing. The suggestion, then, is to capitalize on such efforts; to “piggy back” on what I take to be the best account that arose out of them and “dualize” it.

49 See Priest’s contribution in this volume for an explicit statement to that effect.

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Before explaining how that works, let me briefly illustrate with a concrete example the force of the duality between the two cases. Suppose someone says that the statement (34) Tibbles is white. is neither true nor false. This flies in the face of bivalence. Does it mean that we have a (purported) counterexample to excluded middle? It depends on the semantic theory assumed in the background. If we assume that the name ‘Tibbles’ picks out a unique individual, the cat Tibbles, and the predicate ‘white’ picks out a unique property, the color white (or whatever sort of entity we take the semantic value of our predicate to be – e.g., a class of individuals), then the answer is in the affirmative: we are told that it is a fact of the matter, a matter of how things are in the world, that Tibbles neither definitely is nor definitely isn’t white. On the other hand, one might resist that semantic assumption and maintain instead that the name ‘Tibbles’ fails to pick out a unique individual, or that the predicate ‘white’ fails to pick out a unique color. There are many (slightly different) cat-like individuals and many (slightly different) white-like colors out there, one for each admissible way of “sharpening” the reference of ‘Tibbles’ and the reference of ‘white’, and each of those individuals either definitely has or definitely fails to have each of those colors. If our statement turned out to be true under every such sharpening, then we could say that the statement is true. If it turned out to be false under every sharpening, then we could say that the statement is false. But if, as we may suppose, the truth value of our statement changes depending on which sharpening we consider, then there’s no way for us to settle the issue. No sharpening is better than the others, hence neither truth value will trump the other. That is why (34) lacks a truth value altogether, yielding a counterexample to bivalence.⁵⁰ But the answer to our question is in the negative. For note that a statement such as (35) Tibbles is either white or not white. would come out true under every sharpening, since every sharpening will verify one disjunct or the other. The law of excluded middle still holds. This is perfectly parallel to the case we are interested in, where someone might say that (34) is both true and false. If we assume that ‘Tibbles’ and ‘white’ have a perfectly coherent semantic connotation, then the claim in question is warranted if, and only if, it is a fact of the matter that Tibbles both is and is not white – a genuine violation of the law of non-contradiction. But one might also contend that it

50 This is the gist of the supervaluationist account mentioned in n. 15 above.

74 | Achille C. Varzi is just the word ‘Tibbles’, or perhaps the word ‘white’, that comes with a contradictory interpretation. There are several ways of clearing up the interpretation of these words, each corresponding to a (slightly different) way of extracting a genuine semantic value from their incoherent semantic behavior: a genuine individual as the referent of ‘Tibbles’ and a genuine color property as the value of ‘white’. Since each way of doing so is as legitimate as the others, each will warrant a legitimate truth-value assignment to (34), and since each of those individuals turns out to possess one of those properties while failing to possess the others, (34) turns out to be both true and false, yielding a counterexample to contravalence. However, note that a statement such as (36) Tibbles is both white and not white. would come out false and only false in each case, since every coherent interpretation of ‘Tibbles’ and ‘white’ will falsify one conjunct or the other. Hence the law of non-contradiction still holds.⁵¹ So how can we tell? How can we say whether our interlocutor’s claim should be interpreted in accordance with a definite and coherent semantics that speaks to an indeterminate and/or contradictory world, or in accordance with a semantics that is indefinite and/or incoherent, not because of the way things are in the world, but because of deficient stipulations? There is, I’m afraid, no way of telling just by looking at the statement in question. Nor would it be of any help to just ask our interlocutor what kind of semantics she has in mind, for that would leave everything up for grabs. However, we can once again rely on the fact that the meaning of an expression is determined, at least in part, by its logical behavior, hence by the network of logical relations that tie those statements in which the expression occurs, and we can try to answer our question by looking at how the claim at issue fits the rest of our interlocutor’s logic. Now, in the first case – where the claim is that (34) is neither true nor false – it seems to me that there is a good account available for this purpose. The basic idea grew out of the extensive debate triggered by Evans’s argument against vague objects, especially through Lewis’s revisitation of it,⁵² but it is independent of that argument and admits of a general formulation. It can be put thus: (S) An expression ‘𝑒’ has a definite meaning if and only if ‘𝑒’ admits of scope raising in contexts of the form ‘it is indeterminate whether . . . ’.

51 This “dualization” of supervaluationism is examined in detail in some of my earlier works, especially Varzi (1999) and (2000). 52 See Evans (1978) and Lewis (1988), respectively.

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where by “scope raising” I mean, quite generally, the move from a statement in which the expression in question has narrow scope with respect to a certain operator to a statement in which it has wide scope – thus, in particular, the inferential move in an argument of the form (37) It is indeterminate whether . . . 𝑒 . . . ∴ 𝑒 is such that it is indeterminate whether . . . it . . . Here is why (S) is a good account. If the expression ‘𝑒’ lacks a definite meaning, then clearly the inference in (37) is fallacious. For whereas the premise can be true insofar as ‘𝑒’ may admit of alternative sharpenings that do not settle the truth-value of ‘. . . 𝑒 . . . ’, precisely the variety of such sharpenings will prevent the conclusion from being true. Thus, to return to our example, and setting aside the nuances of the grammatical etiquette of English, if (34) is neither true nor false owing to some indefiniteness in the meaning of the name ‘Tibbles’, or of the predicate ‘white’, then the following arguments (respectively) are not truth-preserving, hence invalid: (38) It is indeterminate whether Tibbles is white. ∴ Tibbles is such that it is indeterminate whether it is white. (39) It is indeterminate whether Tibbles is white. ∴ White is such that it is indeterminate whether Tibbles is it. In this sense, the alternative sharpenings that come with an expression whose meaning is not fully specified play a role analogous to the alternative worlds of modal logic, ‘indeterminate’ being the analogue of ‘contingent’, and the invalidity of (38) and (39) is analogous to the invalidity of, say (40) It is contingent whether the number of planets is greater than 7. ∴ The number of planets is such that it is contingent whether it is greater than 7. (41) It is contingent whether 7 is less than the number of planets. ∴ Less than the number of planets is such that it is contingent whether 7 is it. However, if ‘𝑒’ is not a semantically deficient expression – if it definitely picks out a unique individual, a unique property, etc. – then the inference in (37) is perfectly legitimate. For in that case ‘𝑒’ behaves like a rigid designator across any sharpenings that may still be necessary in order to evaluate ‘. . . 𝑒 . . . ’. Indeed, when

76 | Achille C. Varzi ‘Tibbles’ and ‘white’ are taken to have a definite semantic value, (38) and (39) are just as valid as (42) It is contingent whether 7 is less than the number of planets. ∴ 7 is such that it is contingent whether it is less than the number of planets. (43) It is contingent whether the number of planets is greater than 7. ∴ Greater than 7 is such that it is contingent whether the number of planets is it. So why is (S) a good account? Because it pinpoints a crucial inferential pattern with respect to which the logical behavior of a well-defined expression and the logical behavior of an indefinite expression part company. Insofar as our problem was to identify such a pattern, (S) does the job. And insofar as any claim to the effect that a statement 𝐴 is neither true nor false warrants a corresponding claim of the form (44) It is indeterminate whether 𝐴, the pattern in question is central enough for (S) to count as useful in relation to the general question of determining the conditions under which failure of bivalence entails failure of the law of excluded middle. As with the distinction between collective and distributive readings of a contradiction, the entailment holds to the extent that we are willing to buy into a certain pattern of reasoning. Let us, then, return to the case we are interested in, where the general question concerns instead the conditions under which failure of contravalence entails failure of the law of non-contradiction. I have already said that the two cases are fundamentally parallel – or rather, dual. And I take it that the duality extends to the point of saying that any claim to the effect that a statement 𝐴 is both true and false warrants a corresponding claim of the form (45) It is overdeterminate whether 𝐴 My suggestion, then, is simply to exploit the duality all the way and dualize the account in (S) to fit the case: (S2) An expression ‘𝑒’ has a coherent meaning if and only if ‘𝑒’ admits of scope raising in contexts of the form ‘it is overdeterminate whether . . . ’.

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7 Concluding Remarks Does (S2) do the job? Unfortunately, it is once again only a suggestion – and a tentative one at that. For there are at least two important respects in which (S2) is deficient. The first is that it hinges on shaky philosophical assumptions. In particular, it might be objected that it rests too heavily on contentious doctrines about reference. This is already apparent with (S). If, for example, one holds that every singular term has its reference fixed by descriptive means that invoke a sortal, and that all sortals are somewhat indefinite in meaning, then no singular term will have a definite meaning in the relevant sense. Hence, our strategy will imply that there are no good reasons to posit indeterminate objects – a conclusion that can hardly be justified on such grounds.⁵³ Indeed, the whole idea of deriving ontic indeterminacy from violations of bivalence that do not involve indefinite language is in jeopardy, for it may leave us with no genuine ontic indeterminacy just because of widespread linguistic indeterminacy. This problem, and any variant thereof, are imported into (S2) holus bolus. The second respect in which reference to (S2) won’t take care of the problem in its generality is that failure of contravalence may come in the form of a statement that contains both expressions with a coherent meaning and expressions whose meaning has not been fixed in a coherent way. Accordingly, while (S2) itself provides both necessary and sufficient conditions for telling such expressions apart, knowing that a dialetheia involves expressions of the former sort may be necessary but not sufficient for classifying it as a sign of a genuine de re contradiction, just as knowing that it contains expressions of the latter sort may be insufficient for classifying it as a mere de dicto discrepancy. For instance, suppose that ‘𝑃’ turns out to be an incoherent predicate, and suppose someone holds that (46) The round square is 𝑃 is both true and false. Insofar as both ‘round’ and ‘square’ are perfectly coherent predicates, (S2) would license the inference (47) It is overdeterminate whether the round square is 𝑃. ∴ The round square is such that it is overdeterminate whether it is 𝑃. Yet it is far from obvious that this should count as evidence of a contradiction arising in the world. The round square may be an excellent candidate for the real 53 This point draws on Sainsbury (1989), 99–100, mutatis mutandis.

78 | Achille C. Varzi content of Sylvan’s box⁵⁴ – a genuine, authentic, truly contradictory object. But the overdeterminacy of (46) may have nothing to do with this. It may still be a mere dialetheia ex vi terminorum due entirely to the incoherence of ‘𝑃’. I’m afraid I don’t have much to offer in response to these concerns. As with (S1), (S2) turns out to be philosophically loaded, and prone to misjudgment. I wish I could say that while neither account does the job properly, both of them (collectively) do. But that is just not true. Let me simply say that in spite of the limits and defects of each, I hope that (S1) and (S2) provide at least a rough indication of the kind of criterion that I think is required in order to address the difficult question that has been the main concern of this paper, namely, whether the law of noncontradiction is yet another instance of the sort of prejudices from which logic has tried to free itself throughout its history in the spirit of ever greater ontological neutrality. The answer to that question may well be in the negative, since any evidence against the law may require that we deploy further principles to make the case, and it is those principles that may be deemed inadequate as canons of pure logical reasoning. Precisely for this reason, however, there seems to be no option short of confessing our narrow ontological horizons: something – if not the law, one of those principles – has gotta give.⁵⁵

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80 | Achille C. Varzi F. J. Pelletier, “Another Argument against Vague Objects”, in: Journal of Philosophy 86: 481– 492, 1989. G. Priest, “The Logic of Paradox”, in: Journal of Philosophical Logic 8, 219–241, 1979. G. Priest, In Contradiction: A Study of the Transconsistent, Dordrecht (2nd expanded edition: Oxford 2006), 1987. G. Priest, Beyond the Limits of Thought, Cambridge (2nd expanded edition: Oxford 2001), 1995. G. Priest, “Sylvan’s Box: A Short Story and Ten Morals”, in: Notre Dame Journal of Formal Logic 38, 573–582, 1997. G. Priest, “What Is So Bad About Contradictions?”, in: Journal of Philosophy 95, 410–426, 1998. G. Priest, “Paraconsistent Logic”, in: D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd edition, vol. 6, Dordrecht, 287–393, 2002. G. Priest, R. Routley, “Introduction”, in: G. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Munich, ixx–xxi, 1989a. G. Priest, R. Routley, “First Historical Introduction. A Preliminary History of Paraconsistent and Dialectic Approaches”, in: G. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Munich, 3–75, 1989b. D. Proudfoot, “Possible Worlds Semantics and Fiction”, in: Journal of Philosophical Logic 35, 9–40, 2006. W. V. O. Quine, “On What There Is”, in: Review of Metaphysics 2, 21–38, 1948. N. Rescher, R. Brandom, The Logic of Inconsistency. A Study in Non-Standard Possible-World Semantics and Ontology, Oxford, 1980. B. Russell, “On Denoting”, in: Mind 14, 479–493, 1905. B. Russell, Introduction to Mathematical Philosophy, London, 1919a. B. Russell, “The Philosophy of Logical Atomism” [Parts V–VI], in: The Monist 29, 190–222, 1919b. B. Russell, “Vagueness”, in: Australasian Journal of Philosophy and Psychology 1, 84–92, 1923. M. Sainsbury, “What Is a Vague Object?”, in: Analysis 49, 99–103, 1989. N. Salmon, Reference and Essence, Oxford, 1982. P. F. Strawson, Introduction to Logical Theory, London, 1952. A. C. Varzi, “Inconsistency without Contradiction”, in: Notre Dame Journal of Formal Logic 38, 621–638, 1997. A. C. Varzi, An Essay in Universal Semantics, Dordrecht, 1999. A. C. Varzi, “Supervaluationism and Paraconsistency”, in: D. Batens, C. Mortensen, G. Priest, J. P. Van Bendegem (eds.), Frontiers of Paraconsistent Logic, Baldock, 279–297, 2000. A. C. Varzi, “Vagueness, Logic, and Ontology”, in: The Dialogue 1, 135–154, 2001. A. C. Varzi, “Conjunction and Contradiction”, in G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford, 93–110, 2004. N. A. Vasil’év, “Logica i Métalogica”, in: Logos 1–2, 53–81, 1912. M. V. Wedin, “Negation and Quantification in Aristotle”, in: History and Philosophy of Logic 11, 131–150, 1990. M. V. Wedin, “Some Logical Problems in Metaphysics Gamma”, in: Oxford Studies in Ancient Philosophy 19, 113–162, 2000. A. N. Whitehead, B. Russell, Principia Mathematica, 3 vols., London, 1910/1913. R. G. Williams, “Ontic Vagueness and Metaphysical Indeterminacy”, in: Philosophy Compass 3, 763–788, 2008. T. Williamson, “Vagueness and Ignorance”, in: Proceedings of the Aristotelian Society 66 (Suppl.), 145–162, 1992.

Francesco Berto

Representing the Contradictory* 1 Overview Relevant logics are perhaps the most developed among paraconsistent logics, these being logical systems rejecting the principle Ex contradictione quodlibet (ECQ), according to which a contradiction entails everything (in object language’ version, (𝐴 ∧ ¬𝐴) → 𝐵). Arguably, the most discussed kinds of formal semantics for relevant logics are world semantics. As specialists know, these include so-called non-normal or impossible worlds, often thought of as situations where the truth conditions of logical operators are different. Non-normal worlds are crucial for providing model-theoretic counterexamples to ECQ as well as to other irrelevant entailments, such as 𝐴 → (𝐵 ∨ ¬𝐵) and 𝐴 → (𝐵 → 𝐵).¹ They can thus help in modeling our capacity of reasoning non-trivially also in the face of inconsistent information or full-fledged contradictions. And such a capacity is widely attested, thus providing counterexamples to ECQ. For an often mentioned case: Bohr’s atomic theory includes both the assumption that energy has the form of quanta, that is, discrete packs, and Maxwell’s usual electromagnetic equations, which are inconsistent with that assumption.² Nevertheless, Bohr provided quite a successful theory. More importantly for our purposes: he did not infer arbitrary conclusions from his contradictory assumptions – for instance, that electrons have the same electric charge as protons.

* A version of this paper has appeared also in The Logica Yearbook 2011 (College Publications, London) with the title “Non-Normal Worlds and Representation”. Thanks to the organizers of the Logica conference 2011 for allowing me to draw on that material here. 1 Intuitively, a premise or conditional antecedent is irrelevant within an inference or a conditional, if it is of no utility in getting to the conclusion, or in grounding the consequent. The research program of relevant logic is based on the positive view that the intuition of relevance can be given formal substance, together with the negative view that classical logic legitimates irrelevant inferences – on the ground, for instance, of its admitting logically valid conditionals with no content connection between antecedent and consequent. At least part of the formal substance to the idea of relevance as content-connection is provided by the so-called Variable Sharing Property (VP), also called weak or necessary condition of relevance. As far as the conditional goes, this states that if 𝐴 → 𝐵 is logically valid, then 𝐴 and 𝐵 must share some sentential variable. On this ground, ECQ and the two aforementioned formulas count as fallacies of relevance, not passing the VSP test. For a short and accessible introduction to relevant logic, see Mares (2004). 2 For an account of this story, see Brown (1993).

82 | Francesco Berto The main philosophical issue concerning world semantics for relevant logics has traditionally been the one of the intuitive reading of its worlds, and of the relations and operations defined on them: what does it mean that a world is such that contradictions can be true at it, for instance? Some well-known views interpret these worlds precisely as information states, or conduits thereof (see e.g. Mares (2004)). Given such an epistemically-driven reading, non-normal worlds may model our ability of conceiving or representing contradictions, and broadly logical impossibilities. This is tightly connected to our aforementioned capacity of reasoning efficiently in contradictory informational circumstances – if not a precondition of it. As Bohr knew he was making incompatible assumptions in his theory, for instance, he was arguably able to conceive those contradictory hypotheses as holding together. This did not lead him astray, though. Supposing the nonnormal worlds of relevant semantics are essentially realizations of intentional states, such as conceiving or representing,³ this paper explores the phenomenon by combining a formal setting with philosophical discussion. I proceed as follows: in Section 2, I introduce the syntax of a first-order intensional language 𝐿 and, in Section 3, I present a model-theoretic semantics for it, which draws upon the relevant logic 𝑁4 proposed in Chapter 9 of Priest (2001). This combines techniques of many-valued and modal logics, including locally contradictory and incomplete non-normal worlds, but has standard definitions of logical consequence and validity. Despite being simpler than the mainstream world semantics for relevant logics, the 𝑁4 setting allows to model all the features of relevant systems that are significant for our purposes in a friendly formal setting. The language includes a representation operator, whose role is to capture our capacity of representing or conceiving contradictions and logical impossibilities. Section 4 provides a brief discussion of the distinction, embedded in the model, between two kinds of nonnormal worlds, displaying different degrees of logical lawlessness and labeled, for reasons to be explained, as extensionally and intensionally impossible worlds. In Section 5, it is shown that the semantics makes of 𝐿’s conditional a fully relevant (albeit weak) one, invalidating the fallacies of relevance and, in particular, ECQ: contradictions do not entail anything whatsoever. Section 6 explains how the representation operator invalidates (the formulations in terms of it of) typical unwelcome inferences of epistemic logic gathered under the rubric of “logical omniscience”, such as the non-contradictoriness of our beliefs, or their closure under entailment. It is well known that logical omniscience phenomena make for

3 I employ these two terms as generics for a range of broadly cognitive human activities, all involving the depiction of scenarios, situations, or circumstances, which count as their contents. I take a dim view on such intentional phenomena, and leave their serious investigation to philosophers of mind, cognitive scientists, or neuroscientists.

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highly idealized epistemic notions, not mirroring the actual condition of human beings as finite, fallible, and occasionally self-contradicting cognitive agents. If we can conceive contradictions and other absolute impossibilities, non-normal worlds are natural candidates to model this human condition: the content of a representational state is the set of worlds that make the representation true, that is, where things are as they are conceived or represented to be. This may include non-normal worlds where those inferences fail. Finally, some open questions are raised in Section 7, as to the best strategies to regiment the representation operator in order for it to express specific and more vertebrate kinds of conceivability; these should intuitively be closed under some (albeit weaker-than-classical) logical consequence relation and, more importantly, allow for ceteris paribus import of information from actuality.

2 Syntax of 𝐿 𝐿 consists of a fully standard first-order vocabulary with individual variables 𝑥, 𝑦, 𝑧 (and, if more are needed, indexed ones, 𝑥1 , . . . , 𝑥𝑛); individual constants: 𝑚, 𝑛, 𝑜 (if more are needed, 𝑚1 , . . . , 𝑚𝑛); 𝑛-place predicates: 𝐹, 𝐺, 𝐻 (𝐹1 , . . . , 𝐹𝑛); the usual connectives, negation ¬, conjunction ∧, disjunction ∨, the conditional →; the two quantifiers, ∀ and ∃; the two standard alethic modal operators for necessity ◻ and possibility ⬦; a unary sentential operator ®; round brackets as auxiliary symbols. Individual constants and variables are singular terms. If 𝑡1 , . . ., 𝑡𝑛 are singular terms and 𝑃 is any 𝑛-place predicate, 𝑃𝑡1 . . .𝑡𝑛 is an atomic formula. If 𝐴 and 𝐵 are formulas, ¬𝐴, (𝐴 ∧ 𝐵), (𝐴 → 𝐵), (𝐴 ∨ 𝐵), ◻𝐴, ⬦𝐴, and ® 𝐴 are; outermost brackets are normally omitted in formulas. If 𝐴 is a formula and 𝑥 is a variable, then ∀𝑥𝐴 and ∃𝑥𝐴 are formulas, closed and open formulas having their standard definitions. The only piece of notational novelty is ®, which I shall call the representation operator. The intuitive reading of ‘® 𝐴’ will be “It is represented that 𝐴”, or “It is conceived that 𝐴”.

3 Semantics for 𝐿 The semantics for 𝐿 is largely down to Priest’s work in non-standard intensional logic (see Priest (2001) and (2005)), with a few modifications. An interpretation is an ordered septuple ⟨𝑃, 𝐼, 𝐸, @, 𝑅, 𝐷, 𝑣⟩ the intuitive reading of whose members is as follows. 𝑃 is the familiar set of possible worlds; 𝐼 and 𝐸 are two sets of non-normal or impossible worlds of two kinds, the intensionally and extension-

84 | Francesco Berto ally impossible ones respectively (what this means, we will see soon); 𝑃, 𝐼 and 𝐸 are disjoint, 𝑊 = 𝑃 ∪ 𝐼 ∪ 𝐸 is the totality of worlds simpliciter. @ is the obtaining world (or, better, its foster in the formalism). I assume, for prudence, that @ ∈ 𝑃, the actual world is possible. 𝑅 is a binary relation on worlds, 𝑅 ⊆ 𝑊 × 𝑊; if ⟨𝑤1 , 𝑤2 ⟩ ∈ 𝑅(𝑤1 , 𝑤2 ∈ 𝑊), I write this as ‘𝑤1 𝑅𝑤2 ’ and claim that world 𝑤2 is representationally accessible (R-accessible), from world 𝑤1 (what this means, we will also see soon). 𝐷 is a non-empty set of objects. 𝑣 is a function assigning denotations to the descriptive constant symbols of 𝐿, as follows: If 𝑐 is an individual constant, 𝑣(𝑐) ∈ 𝐷 . If 𝑃 is an n-place predicate and 𝑤 ∈ 𝑊, 𝑣(𝑃, 𝑤) is a pair:

⟨𝑣+ (𝑃, 𝑤); 𝑣− (𝑃, 𝑤)⟩ ,

+

𝑛

−

𝑛

with 𝑣 (𝑃, 𝑤) ≤ 𝐷 , 𝑣 (𝑃, 𝑤) ≤ 𝐷 .

𝐷𝑛 = {⟨𝑑1, . . ., 𝑑𝑛⟩|𝑑1 , . . ., 𝑑𝑛 ∈ 𝐷}, and ⟨𝑑⟩ is stipulated to be just 𝑑, so 𝐷1 is 𝐷. To each pair of 𝑛-place predicate 𝑃 and world 𝑤, 𝑣 assigns a (positive) extension 𝑣+ (𝑃, 𝑤) and an anti-extension or negative extension, 𝑣− (𝑃, 𝑤). The extension of 𝑃 at 𝑤 is to be thought of as the set of (𝑛-tuples of) things of which 𝑃 is true there, the anti-extension as the set of (𝑛-tuples of) things of which 𝑃 is false there. Such double extensions are to model inconsistencies -things being both true and false (truth value gluts; or also, neither true nor false – truth value gaps). On the other hand, one may sensibly want truth and falsity to be exclusive and exhaustive at possible worlds (this is part of what makes them possible, after all). We can recover the classical setting by imposing the following double clause – let us call it the Classicality Condition: +

−

(CC) If 𝑤 ∈ 𝑃, for any 𝑛-ary predicate 𝑃: 𝑣 (𝑃, 𝑤) ∩ 𝑣 (𝑃, 𝑤) = 0 ,

𝑣+ (𝑃, 𝑤) ∪ 𝑣− (𝑃, 𝑤) = 𝐷𝑛 . At possible worlds, extensions and anti-extensions are exclusive and exhaustive. We need the usual assignments of denotations to variables. If 𝑎 is an assignment (a map from the variables to 𝐷), then 𝑣𝑎 is the suitably parameterized denotation function, so that we have denotations for all singular terms: (1)

If 𝑐 is an individual constant, 𝑣𝑎 (𝑐) = 𝑣(𝑐) .

(2)

If 𝑥 is a variable, 𝑣𝑎 (𝑥) = 𝑎(𝑥) .

Let us read ‘𝑤 ⊩+𝑎 𝐴’as “𝐴 is true at world 𝑤 (with respect to assignment 𝑎)”, and ‘𝑤 ⊩−𝑎 𝐴’ as “𝐴 is false at world 𝑤 (with respect to assignment 𝑎)” (and an interpretation, but I will omit to mention it when no confusion arises). The truth and falsity conditions for atomic formulas are:

𝑤 ⊩+𝑎 𝑃𝑡1 . . .𝑡𝑛 iff ⟨𝑣𝑎 (𝑡1 ), . . . , 𝑣𝑎 (𝑡𝑛)⟩ ∈ 𝑣 + (𝑃, 𝑤)

𝑤 ⊩−𝑎 𝑃𝑡1 . . .𝑡𝑛 iff ⟨𝑣𝑎 (𝑡1 ), . . . , 𝑣𝑎 (𝑡𝑛)⟩ ∈ 𝑣 − (𝑃, 𝑤) .

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The extensional vocabulary has straightforward clauses at all 𝑤 ∈ 𝑃 ∪ 𝐼:

𝑤 ⊩+𝑎 ¬𝐴 iff 𝑤 ⊩−𝑎 𝐴

𝑤 ⊩−𝑎 ¬𝐴 iff 𝑤 ⊩+𝑎 𝐴

𝑤 ⊩+𝑎 𝐴 ∧ 𝐵 iff 𝑤 ⊩+𝑎 𝐴 and 𝑤 ⊩+𝑎 𝐵 𝑤 ⊩−𝑎 𝐴 ∧ 𝐵 iff 𝑤 ⊩−𝑎 𝐴 or 𝑤 ⊩−𝑎 𝐵

𝑤 ⊩+𝑎 𝐴 ∨ 𝐵 iff 𝑤 ⊩+𝑎 𝐴 or 𝑤 ⊩+𝑎 𝐵

𝑤 ⊩−𝑎 𝐴 ∨ 𝐵 iff 𝑤 ⊩−𝑎 𝐴 and 𝑤 ⊩−𝑎 𝐵

𝑤 ⊩+𝑎 ∀𝑥𝐴 iff for all 𝑑 ∈ 𝐷, 𝑤 ⊩+𝑎(𝑥/𝑑) 𝐴 𝑤 ⊩−𝑎 ∀𝑥𝐴 iff for some 𝑑 ∈ 𝐷, 𝑤 ⊩−𝑎(𝑥/𝑑) 𝐴

𝑤 ⊩+𝑎 ∃𝑥𝐴 iff for some 𝑑 ∈ 𝐷, 𝑤 ⊩+𝑎(𝑥/𝑑) 𝐴 𝑤 ⊩−𝑎 ∃𝑥𝐴 iff for all 𝑑 ∈ 𝐷, 𝑤 ⊩−𝑎(𝑥/𝑑) 𝐴 ‘𝑎(𝑥/𝑑)’ stands for the assignment that agrees with 𝑎 on all variables, except for its assigning 𝑑 to 𝑥. As for the modals, we have the following for all 𝑤 ∈ 𝑃:

𝑤 ⊩+𝑎 ◻ 𝐴 iff for all 𝑤1 ∈ 𝑃, 𝑤1 ⊩+𝑎 𝐴

𝑤 ⊩−𝑎 ◻ 𝐴 iff for some 𝑤1 ∈ 𝑃, 𝑤1 ⊩−𝑎 𝐴

𝑤 ⊩+𝑎 ⬦ 𝐴 iff for some 𝑤1 ∈ 𝑃, 𝑤1 ⊩+𝑎 𝐴

𝑤 ⊩−𝑎 ⬦ 𝐴 iff for all 𝑤1 ∈ 𝑃, 𝑤1 ⊩−𝑎 𝐴

(Unrestricted) necessity/possibility is truth at all/some possible world(s) (I am not making much use of the box and diamond in this work, but they can be usefully contrasted, within the model, with the behavior of the representation operator). While we have the normal material conditional, say 𝐴 > 𝐵 =𝑑𝑓 ¬𝐴 ∨ 𝐵, our more vertebrate intensional conditional is the following. At all 𝑤 ∈ P:

𝑤 ⊩+𝑎 𝐴 → 𝐵

𝑤 ⊩−𝑎 𝐴 → 𝐵

+

+

iff for all 𝑤1 ∈ 𝑃 ∪ 𝐼 such that 𝑤1 ⊩𝑎 𝐴, 𝑤1 ⊩𝑎 𝐵 . +

−

iff for some 𝑤1 ∈ 𝑃 ∪ 𝐼, 𝑤1 ⊩𝑎 𝐴 and 𝑤1 ⊩𝑎 𝐵 .

So far everything works familiarly enough as far as worlds in P are concerned, the main change with respect to standard modal semantics being that truth and falsity conditions are spelt separately. But even this does not change much at possible worlds. The CC dictates that, at each possible world, any predicate is either true or false of the relevant object (or 𝑛-tuple thereof), but not both. That no atomic formula is both true and false or neither true nor false entails that no formula is, as can be checked recursively. Overall, there are no truth value gluts or gaps at

86 | Francesco Berto possible worlds.⁴ In particular, for instance, if 𝑤 ∈ 𝑃 then 𝑤 ⊩+𝑎 ¬𝐴 if and only if it is not the case that 𝑤 ⊩+𝑎 𝐴: at possible, contradiction-free worlds negation works “homophonically”, the classical way. And since @ ∈ 𝑃, the actual world is possible, truth simpliciter, truth at the actual world, behaves in an orthodox way with respect to negation. Things get more exciting at non-normal worlds. At points in I, 𝑣 treats formulas of the form 𝐴 → 𝐵, 𝐴, and ⬦𝐴 essentially as atomic: their truth values are not determined recursively, but directly assigned by 𝑣 in an arbitrary way. At points in E, all formulas can be treated as atomic and behave arbitrarily: 𝐴 ∨ 𝐵 may turn out to be true even though both 𝐴 and 𝐵 are false, etc. Hence the denominations for the two kinds of worlds: at intensionally impossible worlds, only the conditional and the modals are anarchic; at the extensionally impossible ones, also the extensional vocabulary behaves arbitrarily.⁵ The idea of having complex formulas behave as atomic at some worlds comes from the classic Rantala (1982), where non-normal worlds were introduced to make logical omniscience fail for epistemic operators. I use non-normal worlds for similar, but more general, purposes. Such worlds are to be accessible via the binary 𝑅 when the truth conditions for ® are at issue. At 𝑤 ∈ 𝑃:

𝑤 ⊩+𝑎 ® 𝐴 iff for all 𝑤1 ∈ 𝑊 such that 𝑤𝑅𝑤1 , 𝑤1 ⊩+𝑎 𝐴

𝑤 ⊩−𝑎 ® 𝐴 iff for some 𝑤1 ∈ 𝑊 such that 𝑤𝑅𝑤1 , 𝑤1 ⊩−𝑎 𝐴

The semantics for ® is similar to the ordinary binary accessibility semantics for the standard modal operators. ‘𝑤𝑅𝑤1 ’ (“world 𝑤1 is R-accessible from world 𝑤”), should be read as the claim that, at world 𝑤1 , things are as they are conceived or represented to be at world 𝑤. So it is represented that 𝐴 (at 𝑤) just in case 𝐴 is true at all 𝑤1 where things are as they are represented to be. For instance, if ® 𝐴 is your dreaming that you win the lottery, (an R-accessible) 𝑤1 is a fine world at which your dream comes true. The difference with the usual binary accessibility for modalities is in the broader set of accessible worlds: representation allows us to imagine contradictions and impossibilities.

4 One would need a couple of technical additions to rule out gaps and gluts when operators involving non-normal worlds are included, but we can skip them for simplicity. 5 Priest (2005) calls our extensionally impossible worlds open worlds, meaning that they are not closed under any non-trivial consequence relation; but they deserve to be called impossible if any world does.

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The definitions of logical consequence and validity are standard. If 𝑆 is a set of formulas:

𝑆 ⊨ 𝐴 iff for every interpretation ⟨𝑃, 𝐼, 𝐸, @, 𝑅, 𝐷, 𝑣⟩, and assignment 𝑎, +

+

if @ ⊩𝑎 𝐵 for all 𝐵 ∈ 𝑆, then @ ⊩𝑎 𝐴 . As for logical validity:

⊨ 𝐴 iff 0 ⊨ 𝐴, i.e., for every interpretation ⟨𝑃, 𝐼, 𝐸, @, 𝑅, 𝐷, 𝑣⟩, +

and assignment 𝑎, @ ⊩𝑎 𝐴 .

4 Two Kinds of Worlds There are collateral, but philosophically interesting, reasons for adding items in I among the non-normal worlds, that is, worlds less anarchic than those in E, where only the intensional logical vocabulary behaves in a deviant fashion. The distinction between intensionally and extensionally impossible worlds mirrors the presence of two positions in the current debate on the subject. The first may be labeled as the “Australasian stance”. In the Australasian approach, worlds are constituents of interpretations of some relevant logic or other, which imposes to them some logical structure: they are closed under a relevant consequence relation, weaker than classical consequence relation (see e.g. Mares (1997), Restall (1997)). Since this position draws especially on the conception of non-normal worlds as worlds where “logical laws may fail or be different”, it is naturally allied to the idea that, at the (admissible) non-normal worlds, only intensional operators, such as a relevant conditional, behave in non-standard fashion. After all, it is the conduct of such operators that concerns the laws of logic. The truth conditions for conjunction, disjunction, or the quantifiers, should thus remain the same as in ordinary, possible worlds.⁶ The more radical view may be labeled the “American stance”, since it reflects the opinion of some north-American impossible worlds theorists. The American stance focuses on the definition of non-normal worlds as “ways things could (absolutely) not be”, and adopts what we may call an unrestricted comprehension principle for them. Roughly: for any way the world could not be, there is some impossible world which is like that. This can deliver particularly anarchic worlds, not closed under any non-trivial notion of logical consequence (see e.g. Vander Laan (1997), Zalta (1997)).

6 For similar considerations, see e.g. Priest (2001), ch. 9.

88 | Francesco Berto

5 Relevant Conditional Having world quantifiers range on 𝑃 ∪ 𝐼 in the semantic clauses for → makes of it a relevant conditional, in the sense of fulfilling the aforementioned Variable Sharing Property. In particular, the arrangement above makes irrelevant entailments like 𝐴 → (𝐵 → 𝐵) fail – take a world 𝑤 ∈ 𝐼 where 𝐴 is true but 𝐵 → 𝐵 is not. The failure is in the spirit of the “illogical” features of non-normal worlds: these are situations where laws of logic, like the law of sentential identity, may fail. EFQ as (𝐴 ∧ ¬𝐴) → 𝐵, and 𝐴 → (𝐵 ∨ ¬𝐵), also fail (take a non-normal 𝑤 ∈ 𝐼 where a contradiction obtains, i.e., 𝐴 is both true and false but 𝐵 is untrue for the former, one where 𝐴 is true but 𝐵 is neither true nor false for the latter). The conditional counts as a weak one by relevantist standards (it does not satisfy minimal contraposition, for instance). This may or may not be a problem, depending on what one expects from a conditional. A stronger setting can be obtained by adding to the interpretations for 𝐿 a ternary relation on worlds and providing the semantics for a conditional in terms of it, as per the classical approach of Routley/Meyer (1973). This would complicate matters here, though. Our main concern is the representation operator ®, to which I now turn.

6 The (Non-)Logic of Representation The traditional debate in epistemic logic concerns the logical principles that should characterize the epistemic operators at issue, so as to mirror at best the corresponding intuitive notions. Some views are straightforward, for instance, knowledge being factive: if ‘K 𝑐’ stands for cognitive agent 𝑐 knows that, it should sustain the entailment from K 𝑐𝐴 to 𝐴 for any 𝐴. Other inferences are more controversial. Must K 𝑐 allow the entailment from K 𝑐𝐴 to K 𝑐 K 𝑐𝐴, i.e., must one always know that one knows that 𝐴? While this turns on issues concerning our intuitions about knowledge, it is not difficult to vindicate the inference, if we like it, by tampering with accessibility between worlds (in this case, just have it be transitive). But the failure of some basic logical inferences in epistemic and intentional contexts is more difficult to handle. This is the cluster of problems gathered under the well-known label of “logical omniscience”. When modeled in standard possible world semantics, knowledge (or belief) turns out to be closed under entailment: (Cl)

𝐴 → 𝐵,

K 𝑐𝐴 ⊨ K 𝑐𝐵

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Also, all valid formulas turn out to be known (believed): (Val) If ⊨ 𝐴, then ⊨ K 𝑐𝐴. And, most interestingly for our purposes, beliefs form a consistent set: (Cons)

⊨ ¬(K 𝑐𝐴 ∧ K 𝑐¬𝐴)

Taken together, these principles deliver an idealized notion of knowledge (belief), not mirroring the status of fallible and occasionally inconsistent cognitive agents.⁷ Now Rantala’s non-normal worlds were proposed to deal with these phenomena: despite being logically impossible, and not closed under any non-trivial consequence relation, they can be seen as viable epistemic alternatives by imperfect or inconsistent cognitive agents. A similar story is to be told for ®. If we can conceive and represent contradictions and impossibilities, the content of our representational state is the set of worlds that make our representation true, that is, where things are as they are conceived or represented to be; and this has to include non-normal worlds. Given the way things were set up above, non-normal worlds have no effect at the actual world @ on formulas not including ®. By allowing such worlds to be R-accessible in the evaluation of formulas including it, though, one can eliminate any unwelcome closure feature, thereby dispensing with (the formulations with ® in place of K 𝑐 of) (Cl), (Val), and (Cons). As for (Cl), for instance: assume ⊨ 𝐴 → 𝐵. Then at all worlds in 𝑃 ∪ 𝐼 where 𝐴 holds, 𝐵 holds. But there can be a non-normal world, 𝑤, at which 𝐴 holds and 𝐵 fails. If @ 𝑅𝑤, then we can have that @ ⊩+𝑎 ® 𝐴, but it is not the case that @ ⊩+𝑎 ® 𝐵 . Similarly for consistency, or our believing contradictions: when the relevant R-accessible worlds are inconsistent worlds where both 𝐴 and ¬𝐴 are true, we can have @ ⊩+ ® 𝐴 ∧ ® ¬𝐴.

7 Constraints By accessing non-normal worlds of any kind on the one hand, and by not having constraints on its R-accessibility relation on the other, ® has quite a poor logic – one may indeed wonder whether it is worth being called a logic at all. What is doing the interesting work here, though, is not the logic but the semantics. I am interested in the general form of the latter, and representability or conceivability

7 E.g., I know Peano’s axioms as basic truths of arithmetic, and Peano’s axioms entail (let us suppose) Goldbach’s conjecture; but I do not know whether Goldbach’s conjecture is true. With other intentional states such as belief or desire, also broad consistency is at stake.

90 | Francesco Berto had better be, generally speaking, quite anarchic. In order to have ® express specific intentional operators under the generic umbrella of conceivability, say, mentally representing a scenario as opposed to hallucinating, we may nevertheless demand more structure. When one mentally represents a scenario, say, engaging in speculations on the next move of the financial markets, one’s representation must have some more or less minimal coherence, that is, be closed under some, however weaker-than-classical, notion of logical consequence. This is proved by the fact that people meaningfully argue on how things are, and on what follows from what, in the relevant scenarios, that is, they accept or reject some things as holding in the situations at hand. Even when we represent to ourselves the impossible, we generally believe that we can draw inferences from what we explicitly represented. One way to achieve this would be to place appropriate constraints on R-accessibility. We could then have ® model different species of representation depending on the constraints at issue. If there is something like truthful representation which is factive, we stipulate its 𝑅 to be reflexive. Conversely, we may have make-believe representations such that the world 𝑤 where the representing takes place is ruled out as a candidate for realizing them (as per the proviso to much function: “Any resemblance with real people or actual facts is merely accidental”). To have ® express something like “It is represented as holding purely fictionally that 𝐴”, we stipulate R to be irreflexive. Another way would be to make sub-distinctions between non-normal worlds of various kinds. One may then allow only worlds that are closed under some form of entailment to be R-accessible, for instance, worlds in 𝐼. This gives us interesting results: representation then only accesses “typical” worlds of relevant logics, which are occasionally contradictory or incomplete, and can also violate some logical laws, but are nevertheless adjunctive and prime (conjunction and disjunction behave standardly there). Then ® becomes closed under relevant entailment. Thus, this kind of “relevant conceivability” brings a form of logical omniscience for relevant consequences of what is represented. However, inconsistent representation, that is, the conceiving of contradictions, is still allowed, i.e., (Cons) fails, as well as (Val), i.e., not all logically valid formulae are represented.⁸ The need for further constraints is apparent when the representational act at issue is fictional representation, that is, the conceiving of situations described in fictional works, tales, stories, myths, etc. Sherlock Holmes is represented (at @), by Doyle and his readers, as a detective living in Baker Street, gifted with acute observational and logical skills, etc. Things are as they are represented at the worlds that

8 The closest antecedent to this in the literature, as far as I know, is Levesque’s logic of explicit and implicit belief – see Levesque (1984).

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make the relevant representational characterization true. But which are the relevant R-accessible worlds? That is: under which conditions does a world count as such that things are at it as they are represented? We want the relevant representations to be closed under some notion of logical consequence, so that if ® 𝐴, and 𝐵 is a consequence of 𝐴, then ® 𝐵. In general, then, things represented in a certain way may well have further properties besides those they are explicitly represented as having. Some such properties will just follow on the basis of the entailments mandated by the logic for ®. For instance, from the fact that Tolkien represents Gandalf as a friend of Bilbo and Bilbo as a pipe-smoker, we can infer that Gandalf is represented as being friends with a pipe-smoker even though (let us suppose) Tolkien never says that explicitly. On the other hand, what holds in a representation in many cases goes beyond both what is explicitly represented and what is entailed by logical implication. For while making inferences on what does or does not hold in a representation, we often import information from actuality, which we want to retain when assessing what goes on in a certain represented situation. What the relevant information is depends on our background knowledge of reality; but may also depend on our beliefs (even contradictory beliefs!). The import can rely on ceteris paribus and default clauses. Again, the case of fictional representation makes the point evident, and has been extensively studied, e.g., in Lewis (1978), Proudfoot (2006). Doyle never explicitly represents (let us suppose) Holmes as living in Europe, or as having lungs. We are inclined to take these things as holding at all worlds that realize Doyle’s characterization of Holmes, though, for we integrate the explicit representation with information imported from actuality. Now Doyle certainly characterizes Holmes as a man living in London. At the actual world, London is in Europe and, if something is a normally endowed man, then it has lungs. Doyle says nothing against this, so, absent contrary indications from the author, the import is legitimate. Intuitively, we should exclude from the R-accessible worlds that matter in evaluating what holds in the representation those worlds that, despite making true what is explicitly represented, add gratuitous changes with respect to actuality: we must exclude worlds that differ from @ more than required. Holmes is represented by Doyle as walking through London; we infer that Holmes is represented as walking through a European city. All worlds where Holmes walks through London but London is in Africa must be ruled out, for that would be a departure from actuality not mandated by what Doyle explicitly represents. London’s being in Europe has to be held fixed across the worlds where things are as they are represented. This means that, to some extent, representations (of this kind) are about the real world as well. For what holds in a representation depends on what holds at the R-accessible worlds, where things are as represented. And which worlds these are depends also, to some extent, on how our reality is. Even if this is worked out in a satisfactory way, it does not

92 | Francesco Berto mean that we can expect precise answers to all the questions we may ask concerning a represented situation. Is Holmes, as characterized in Doyle’s stories, righthanded or left-handed? Doyle does not say. And, intuitively, it is not the case that worlds where Holmes is left-handed in general differ gratuitously from @ more than worlds where he is right-handed, or vice versa. Representation typically under-represents. Providing a detailed account of the workings of the representation operator, especially of how one is to select the worlds that are relevant to address what holds in a certain representation, is overall a difficult issue. Part of the difficulty is similar to the one of the standard treatment of counterfactuals à la Stalnaker-Lewis, where a counterfactual “If it were the case that 𝐴, then it would be the case that 𝐵” is true just in case the world(s) most similar to the actual world that make(s) the antecedent true, make(s) the consequent true as well. We need to invoke some notion of similarity between worlds, having to take into account worlds with minimal differences from actuality in certain respects. And this notion is notoriously slippery. The task becomes exceptionally tricky when we have to consider the intentions and beliefs of those who do the representing. Sometimes, for instance, an author of a work of fiction can make claims that, later on, turn out to be false in the story, or can make claims that are subtly ironic, etc. What the appropriate constraints on R-accessibility are to be for the various species of representational activities is a difficult issue, and I am happy to leave it open here. Besides the similarities there is, in fact, a philosophical dis-analogy between ® and more traditional epistemic and intentional notions. That we are fallible as cognitive agents, and sometimes inconsistent in our cognitive activity so that not only we can conceive contradictions, but also believe them, may be seen as a defect due to our finite and imperfect nature – when it’s about knowing and, perhaps, believing. This is not so when it’s about imagining and conceiving: in this case, logical fantasy is, generally speaking, a gift (or so I view it).

References F. Berto: “Non-Normal Worlds and Representation”, The Logica Yearbook 2011, College Publications, London, 15–30, 2012. B. Brown: “Old Quantum Theory: A Paraconsistent Approach”, in: Proceedings of the Philosophy of Science Association 2, 397–441, 1993. H. Levesque: “A Logic of Implicit and Explicit Belief”, in: Proceedings of the National Conference on Artificial Intelligence (AAAI-84), 198–202, 1984. D. Lewis: “Truth in Fiction”, American Philosophical Quarterly 15 (1978), 37–46. E. Mares: “Who’s Afraid of Impossible Worlds?”, in: Notre Dame Journal of Formal Logic 38 (1997), 516–526 E. Mares: Relevant logic. A philosophical interpretation. Cambridge, 2004.

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G. Priest: An introduction to non-classical logic. Cambridge, 2001. G. Priest: Towards non-being. The logic and metaphysics of intentionality, Oxford, 2005. D. Proudfoot: “Possible Worlds Semantics and Fiction”, Journal of Philosophical Logic 35 (2006), 9–40. V. Rantala: “Impossible Worlds Semantics and Logical Omniscience”, in: Acta Philosophica Fennica 35 (1982), 106–115. G. Restall: “Ways Things Can’t Be”, Notre Dame Journal of Formal Logic 38 (1997), 583–596. R. Routley, R. Meyer: “The Semantics of Entailment”, in: H. Leblanc (ed.), Truth, syntax and modality, Amsterdam, 194–243, 1973. D. A. Vander Laan: “The Ontology of Impossible Worlds”, Notre Dame Journal of Formal Logic 38 (1997), 597–620. E. N. Zalta: “A Classically-Based Theory of Impossible Worlds”, Notre Dame Journal of Formal Logic 38 (1997), 640–660.

| Part II: History

Enrico Berti

Objections to Aristotle’s Defence of the Principle of Non-Contradiction 1 The Main Objections In this paper, I recall the main objections to Aristotle’s defence of the Principle of Non-Contradiction (PNC), in order to show that they exclude the possibility of one of the most frequent arguments used by dialectic, conceived in the ancient meaning of the word, i.e. as a technique of discussion in general, and consequently also of the philosophical discussion. I will not mention the position of Hegel, because it is not properly a criticism of Aristotle’s defence of the PNC, but perhaps of the PNC itself, although in my opinion it is rather a criticism of the modern principle of identity, as formulated by Leibniz and by Kant.¹ As is well known, the first important criticism of Aristotle’s defence was the book of Jan Łukasiewicz (1910), resumed by himself in German in an article, which was translated into English (twice), French and also Italian: On the Principle of Contradiction in Aristotle (1971). (The book was also translated into German, French, and Italian, but – as far as I know – not yet into English.) Łukasiewicz distinguishes, like Heinrich Maier in Die Syllogistik des Aristoteles (1896–1900), an ontological, a logical, and a psychological formulation of the PNC, and he affirms that not one of these three formulations was really proved by Aristotle. Even the proof by refutation, which Aristotle develops in the IV book of his Metaphysics is, according to Łukasiewicz, inadequate, because it also falls in the petitio principii which Aristotle attributes to the adversaries of the PNC. Concerning the PNC itself, Łukasiewicz maintains that it is in no way demonstrable that it is not the first principle of logic, because it is preceded by other principles, like the principle of identity, and finally that its psychological formulation is false, because it is possible to have contemporary contrary beliefs, i.e. it is possible to profess a contradiction. Łukasiewicz however never affirms that the PNC, in its ontological formulation, is false. On the contrary, he says that “we do not know of a single example of a contradiction existing in reality” and that “the Law of Contradiction [as he calls it] has no logical value, since it only has the status of an assumption; but it does have a practical and ethical value”, because “the

1 Cfr. Berti (1987), 177–222.

98 | Enrico Berti Law of Contradiction is our only weapon against error and falsehood”.² Faced with these words, one could wonder whether error and falsehood have only a practical meaning, and not also a logical and ontological one. Many interpreters of Aristotle have replied to Łukasiewicz that the Greek philosopher has never tried to demonstrate the PNC, that his defence of this principle aims only to show that it cannot be explicitly denied, that perhaps this defence is inadequate (we will see why), and that in fact it is possible to profess some contradictions, but only in an implicit way, i.e. without having a perfect consciousness of them.³ On the other hand Łukasiewicz himself mentioned, like Husserl, the case of people deceived by fallacies, who contrive at times to believe contradictories together, or the case of the insane, hypnotic states, delirium tremens, etc. To all of this one could add the case of the unconscious, described by Ignacio Matte Blanco in his “bilogic”.⁴ An interesting criticism of the adequacy of the defence of the PNC has been made by an American scholar specialized in ancient philosophy, Robert Dancy.⁵ He observed that Aristotle’s defence depends on a view of sense that may well be wrong: it depends on saying that where a word has a sense, we can give its sense in other words, and that this is a source for non-trivial necessary truths. Moreover, Dancy says that Aristotle’s arguments are directed against a denier of the PNC which is supposed to formulate a strong negation of it, i.e. a negation following which the PNC falls into pieces in every case. But these arguments do not hold against a weak negation of the PNC, following which the PNC breaks down only in some cases. In other words, Aristotle supposes that the denier, called “Antiphasis” by Dancy, maintains that all things are contradictory, and consequently his defence does not hold if Antiphasis would maintain that only something is contradictory. In conclusion – says Dancy – Aristotle often acts as if the Antiphasis’ thesis were not simply that the PNC is false, i.e. that something somewhere does or could have and lack some predicate or other, but that the principle breaks down all the time, that everything that has a predicate also lacks it. Dancy’s criticism has provoked an interesting debate among the specialists of Aristotle, some of whom have objected to his theses⁶, while others have approved them⁷. In the meantime some contemporary logicians formulated the first systems

2 Łukasiewicz (1975), 61–62. The other English translation is Łukasiewicz (1971), 485–509. 3 One of the most recent and rigorous replies to Łukasiewicz is Severino (2005), 39–60. 4 Matte Blanco (1975). I wrote about this in Berti (2002), 22–32, repr. in Berti (2010), 485–494. 5 Dancy (1975). 6 See for instance Code (1986), 341–358; Cohen (1986), 359–370; Furth (1986), 371–382; Gottlieb (1994), 183–209. 7 Mignucci (1996), 53–60.

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of “paraconsistent logic”, which show the possibility of avoiding the Pseudo-Scotus’ theorem, according to which everything can follow from a contradiction, what makes the system containing the contradiction trivial. In particular the system developed by Newton da Costa shows the possibility that from a contradiction not all the consequences can be deduced, but at least one can be avoided,⁸ while Richard Routley (later Sylvan) and Robert Meyer’s system, thanks to the “logic of relevance”, shows that a contradiction contained in it can be in some way isolated, so that it cannot make the whole system trivial.⁹ The birth of paraconsistent logics confirms, in my opinion, Dancy’s criticism of Aristotle’s defence of the PNC, i.e. that this defence proves only the impossibility of a theory which admits that “all things are contradictory” (like, for instance, the philosophy of Hegel), but not the impossibility of a theory which admits that only some things are contradictory. Besides, paraconsistent logics seem to concern only the possible worlds, not the real world, because they show the possibility of avoiding the pseudo-Scotus theorem only in logical systems.¹⁰ The strongest objection which has been made not only against Aristotle’s defence of the PNC, but against the PNC itself, is in my opinion the so-called “dialetheism”, i.e. the theory elaborated by Richard Routley and Graham Priest, which maintains that some contradictions are not only possible, but also true, i.e. really existing, in the sense that the same sentence is contemporarily true and false or that contradictory sentences are both true. The examples of true contradictions made by the supporters of dialetheism are the paradoxes of selfreference (e.g. Russell’s paradox), the paradox of the Liar, the transition states, Zeno’s paradoxes, the borderline cases of vague predications, the multi-criterial predicates, certain legal situations.¹¹ They also claim that in the history of philosophy there were many dialetheists, among whom they mention Heraclitus, St. Pier Damiani (who attributes to God the power of making what is done undone), Nicholas of Cusa (who said that God is a coincidentia oppositorum), Hegel (who maintained however that everything is contradictory, but that contradictions firstly are necessary and then must be removed, although in the sense of Aufhebung) and Buddhist logicians. Concerning Aristotle in particular, Priest repeats Łukasiewicz’s and Dancy’s objections, and adds some other objections of his own, concluding that Aristotle’s defence does not provide any kind of arguments against dialetheism, nor does it give any transcendental reason for the PNC; it shows, however, that a rejection of triviality (i.e. the deducibility of everything 8 Da Costa (1997). 9 Routley/Meyer (1976), 1–25. 10 I have discussed the paraconsistent logics in Berti (1987), 264–279. 11 See Priest/Routley/Norman (1989); Priest (1987); Priest (2004), 23–40; Berto/Priest (2013).

100 | Enrico Berti from the contradiction) is a condition for reflective purposive activity, especially for the institution of communication.¹² Obviously, dialetheism has also been discussed, from a general point of view – and some philosophers have approved it¹³, while others have criticised it¹⁴ – and with particular regard to Aristotle, the majority of scholars have defended the Greek philosopher¹⁵. Now I am not interested in this general discussion, which has been greatly developed, but only in one particular aspect, i.e. in the relationship between dialetheism and Aristotle’s dialectic, particularly Aristotle’s theory of refutation. This has nothing to do with the defence of PNC, although Aristotle called this defence a “demonstration by refutation”, because the refutation presupposes the PNC and therefore cannot be a demonstration of it. But refutation, precisely because it presupposes the PNC, uses it and is the major use of it, i.e. the only use where PNC works as a premise, although not explicitly formulated.

2 The Refutation according to Aristotle Aristotle’s classical definition of refutation (elenchos) is Prior Analytics II 20: If what is laid down (to keimenon) is contrary to the conclusion, a refutation must take place; for a refutation is a deduction which establishes the contradictory (sullogismos antiphaseôs).¹⁶

In this definition “what is laid down” (to keimenon) is the thesis of the interlocutor of a dialectical discussion, i.e. the proposition supported by the respondent, as was suggested by W. D. Ross and accepted by all the interpreters.¹⁷ The word “contrary” (enantion) has the value of “opposite”, so that the conclusion of the “deduction” is the opposite, i.e. the contradictory proposition of the thesis proposed by the respondent. The “deduction” (sullogismos), whether it is used in the technical sense of “syllogism”, as it is described in the Analytics, or whether it is used in the larger sense introduced in Topics and Sophistical Refutations, indicates an

12 Priest (1998), 91–130. 13 See for instance Beall (2004), 197–216; Mares (2004), 264–275. 14 See Littmann/Simmons (2004), 314–335; Shapiro (2004), 336–354; but also Berto (2006); Berto (2007), 45–62. See on this debate also Gaio (2006), 69–92. 15 Wedin (2004), 225–265; Tahko (2009), 32–47; Gottlieb (2011). 16 Aristotle (1984a), An. Pr. II 20, 66 b 9–11. 17 A complete status quaestionis and a convincing interpretation of the subject have been given by Gobbo (1997), 309–357.

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argumentation in which the conclusion necessarily follows from the premises.¹⁸ Consequently, the conclusion established by the deduction, which Aristotle simply calls “contradiction” (antiphasis), must be intended as the proposition which is contradictory in respect to the interlocutor’s thesis, i.e. which denies what it affirms or which affirms what it denies. In Sophistical Refutations, the work dedicated to unmask the false refutations used by the Sophists, Aristotle explains what he means when speaking of contradiction (antiphasis) about the refutation: To refute is to contradict one and the same attribute – not the name, but the object (pragma) and one that is not synonymous but the same – and to confute it from the propositions granted (ek tôn dothentôn), necessarily (ex ananchês), without including in the reckoning the original point to be proved, in the same respect and relation and manner and time in which it was asserted.¹⁹

Here Aristotle’s intention to recall exactly the definition of contradiction given in the formulation of the PNC is evident, in order to show that the refutation is the deduction not of a simple contrariety or opposition to the interlocutor’s thesis, but a real contradictory proposition, with all the precisions given in that formulation. The “object” is the predicate of a subject which can be affirmed or denied: if the interlocutor affirms it, the refuter tries to deny it, and if the interlocutor denies it, the refuter tries to affirm it.²⁰ The observation that it must not be synonymous but the same, means that this predicate must be one and the same thing which is affirmed or denied, not another thing with the same name. There are not many formulations of PNC; the true formulation is only one, the ontological formulation. The others are only applications of it. The so-called psychological formulation affirms the impossibility of believing in a contradiction, not of conceiving it, where to believe means to consider something as true, not only to think or to understand it. However, if Aristotle says that the contradiction can be deduced, this means that, according to him, the contradiction can be thought and said. Before the refutation, the contradiction is only implicit in the position of the interlocutor, who is perhaps unconscious of it, but after the refutation the contradiction becomes explicit, therefore it is recognised by both the discussants. This means that the interpreters who attribute to Aristotle the thesis of the impossibility of thinking and saying the contradiction, on the basis of the affirmation that it is impossible

18 Crubellier (2011), 17–36. 19 Aristotle (1984b), El. Soph. 5, 167 a 23–27. 20 See Fait (2007), 120.

102 | Enrico Berti to be in error about the PNC, have not well understood the intention of Aristotle. If he considers the contradiction to be essential to the refutation, and the refutation to be the argument most frequently used in dialectical discussions, he admits the possibility of thinking and expressing the contradiction, so that the so-called logical and psychological formulations of the PNC do not mean the impossibility of thinking and saying the contradiction. But the contradiction is not only thought and expressed by the interlocutor; it must also be recognised as a contradiction, i.e. an opposition between two contradictory propositions that forms the thesis of the interlocutor and the conclusion which is deduced, which is accepted by him, because the premises from which it is deduced are admitted by him himself (ek tôn dothentôn). Consequently, the interlocutor, thanks to the refutation, discovers he is in contradiction with himself, and this authorises one to suppose that he abandons his thesis, not yet because he recognises it as false, but because he recognises it as contrasting with the conclusion that he himself has accepted. From a point of view which is only dialectical, i.e. not yet implied in questions of true and false, the refutation of a thesis is sufficient to determine the refusal of this thesis. If there is no refusal, the refutation is useless and the whole discussion is in vain. The possibility of thinking and expressing the contradiction is confirmed by a third definition of the refutation given in the Rhetoric, where Aristotle says: The significance of contrasted ideas (tanantia) is easily felt (gnôrimôtata), especially when they are thus put side by side (par’allêla), and also because it has the effect of a logical argument (sullogismos); it is by putting two opposing conclusions side by side (sunagôgê tôn antikeimenôn) that you prove one of them false (elenchos).²¹

The Oxford translation of this passage, although revised, is too free, it is nearly a paraphrase of Aristotle’s text, which in its concision is much more efficacious: refutation is a collecting, or a bringing together, of opposites, i.e. of two contradictory propositions, whose meaning in this way is grasped much more easily. This passage shows that the refutation not only uses the contradiction, but also emphasises it and permits one to understand it better. In the definition of the Rhetoric, in spite of its free Oxford translation, the true and the false are not yet mentioned. They are introduced in another passage of the Sophistical refutations, where Aristotle says: Refutations may be true as well as false (kai alêtheis); for whenever it is possible to demonstrate something, it is also possible to refute the man who maintains the contradictory of the truth (tên antiphasin tou alêthous); e.g. if a man has stated that the diagonal is com-

21 Aristotle (1984c), Rhet. III 9, 1410 a 21–23.

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mensurate with the side of the square, one might refute him by demonstrating that it is incommensurate.²²

Also in this case the Oxford translation is too free, because Aristotle says that the refutations can be “also true” (kai alêtheis), that is they do not serve only in dialectical discussions, where at stake is not truth, but only success: they serve also in scientific discussions, where the contradiction concerns propositions which can be either true or false. In this case, for Aristotle, the contradictory of a sentence which is true, for instance the contradictory to “the diagonal is incommensurate”, i.e. “the diagonal is commensurate”, is false. Evidently, Aristotle was not a dialetheist, and he believed that two contradictory sentences cannot be both true (thanks to the PNC), but one of them must be true and the other false (thanks to the principle of the third excluded, PTE). In conclusion the Aristotelian theory of the refutation shows: 1) that an implicit and perhaps unconscious contradiction can be made explicit and consequently can be thought and expressed in an intelligible way, which means that the PNC does not exclude the possibility of thinking and of saying contradictions; 2) that Aristotle considers the contradiction existing in the thought and the speech as a sign of falsity, i.e. of non-conformity of the thought and the speech to reality.

3 Is Refutation Still Possible? My aim in this presentation is not to discuss the value of the PNC and of the objections which have been addressed to it: I am not a specialist of logic and I do not have the necessary competence to evaluate, from a logical point of view, the paraconsistent logics and the dialetheism. My aim is to compare the Aristotelian theory of refutation in particular with dialetheism, in order to decide whether from a dialetheist point of view the refutation is still possible. At first sight I should say that it is possible no more, because it implies the falsity of the contradiction, while the dialetheism admits that at least some contradictions can be true. This could mean that a dialetheist can never refute an interlocutor with whom he is discussing, and, as the refutation is the best instrument to criticize a theory, he cannot criticize any theory. This was already remarked by Karl Popper in his famous paper What is Dialectic?, where, speaking about the Hegelian dialecticians, he writes:

22 Aristotle (1984b), El. Soph. 9, 170 a 23–26.

104 | Enrico Berti They observe, correctly, that contradictions are of the greatest importance in the history of thought – precisely as important as is criticism. For criticism invariably consists in pointing out some contradiction; either a contradiction within the theory criticized, or a contradiction between the theory and another theory which we have some reason to accept, or a contradiction between the theory and certain facts – or more precisely, between the theory and certain statements of facts. Criticism can never do anything except either point out some such contradiction, or, perhaps, simply contradict the theory (i.e. criticism may be simply the statement of an antithesis). But criticism is, in a very important sense, the main motive force of any intellectual development. Without contradictions, without criticism, there would be no rational motive for changing our theories: there would be no intellectual progress.²³

And afterwards: If we [. . . ] decide to put up with contradictions, then contradictions must at once lose any kind of fertility. They would be no longer productive of intellectual progress. For if we were prepared to put up with contradictions, pointing out contradictions in our theories could no longer induce us to change them. In other words, all criticism (which consists in pointing out contradictions) would lose its force. Criticism would be answered by ‘And why not?’ or perhaps even by an enthusiastic ‘There you are!’; that is, by welcoming the contradictions which have been pointed out to us. But this means that if we are prepared to welcome contradictions, criticism, and with it all intellectual progress, must come to an end.²⁴

To these observations it could be added that, if the contradiction were not a sign of falsity, but of truth, we should not have a criterion to distinguish truth from falsity, true theories from false theories, therefore all theories would have the same value, and we should be infallible. Obviously dialetheists have considered this objection and have replied to it. Graham Priest, who is the most important representative of this position, writes: The most obvious failing of this argument is that it makes the familiar and illicit slide from ‘some’ to ‘all’. The mere fact that some contradictions are rationally acceptable does not entail that all are. The charge ‘you accept some contradictions to be true, so why shouldn’t you believe any contradiction to be so?’ is as silly as the charge ‘you believe something to be true, so why shouldn’t you believe anything to be so?’²⁵

This reply is right, but how are we to distinguish the contradictions that are true from all the others? Even for this question Priest has an answer: I am frequently asked for a criterion as to when contradictions are acceptable and when they are not. It would be nice if there were a substantial answer to this question–or even if one

23 Popper (2002), 424. 24 Ibid. 25 Priest (2004), 34.

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could give a partial answer, in the form of some algorithm to demonstrate that an area of discourse is contradiction-free. But I doubt that it is possible.²⁶

However, perhaps to console us for this difficulty, Priest adds: I think that there are general reasons as to why contradictions are a priori improbable [. . . ]. The statistical frequency of true contradictions in practice is low. This low frequency suffices to determine a low probability [. . . ]. The counter-examples to the universality of the LNC [=PNC] are of very particular sorts (involving self-reference, or states of affairs that are but instantaneous, etc.), and we do not deal with these kinds of situations very often. As a measure of this fact, recall the disjunctive syllogism (𝑎, ¬𝑎 ∨ 𝑏 ⊢ 𝑏). This is not valid in the semantics we looked at. Yet we use it all the time in practice, and rarely does it lead us astray [italics mine].²⁷

I wonder what the expression “in practice” means in this passages, which recurs twice. It seems to me that it means the same as what Łukasiewicz said at the end of the article I quoted at the beginning of this paper, that is: The Law of Contradiction has no logical value, since it only has the status of an assumption; but it does have a practical and an ethical value, which is all the more important for that. The Law of Contradiction is our only weapon against error and falsehood. [emphasis in the original]²⁸

But Priest in his article on Aristotle said in a footnote: The end of Łukasiewicz’ essay is a little disappointing, though. After demolishing Aristotle’s arguments, he nonetheless seems to think that Aristotle was justified in entrenching the law as ‘unassailable dogma’, for the sketchiest of reasons.²⁹

Regarding the rare counter-examples indicated by him, it is well known that the paradoxes “involving self-reference” have been considered by many logicians as problems concerning language, not reality,³⁰ and “the states of affairs that are but instantaneous” depend on a conception of time as composed by separate instants, so that the problems concerning the notion of corporeal “limit” depend on a conception of space as composed by separate points. But when discussing the arguments of Zenon of Elea, Aristotle demonstrated that time, like space, is a continuous magnitude to which the arguments of Zeno cannot be applied. If they

26 27 28 29 30

Priest (2004), 35. Ibid. Łukasiewicz (1971), 509. Priest (1998), 92, note 1. D’Agostini (2011), 128–137.

106 | Enrico Berti were valid, the examples of contradiction would not be so rare, because every object of experience is in space or in time, and in this case Hegel, who says that “all things are in themselves contradictory”³¹, was right. But this is not the position of dialetheism. More recently Priest has given us a criterion to distinguish true contradictions from others, the criterion which he calls “The Rationality Principle”, that is: (RP) If you have good evidence for (the truth of) 𝐴, you ought to accept 𝐴.³²

And: Belief, acceptance, and assertion have a point: when we believe and assert, what we aim at is believing and asserting what is the case or, equivalently, the truth. Therefore, the dialetheist will accept and, sometimes, assert both 𝐴 and ¬𝐴, if she [or he] has evidence that 𝐴 is a dialetheia – that both 𝐴 and ¬𝐴 are true, as it happens, for instance, with the Liar sentences.³³

I would like not to be too obstinate, but I observe that also in this case the only dialetheia which is produced as an example of evident contradiction is the Liar, i.e. a linguistic paradox. I must admit that I do not understand the advantage of admitting local contradictions, because either the contradictions are impossible, and in this case this impossibility concerns all the contradictions, or they are possible, and in this case why should we admit only some of them and not all? We have to choose between Aristotle and Hegel, I cannot see a third way. The contradiction, in my opinion, cannot be local. If there is a local contradiction, there must be an error or an inadequacy of language or even something that is not real. We must remember that our language is wider than reality, because it can express not only truth, i.e. the real, but also falsity, i.e. the not real. Contradictions belong to falsity, i.e. to the not real.

References Aristotle, Analytica Priora, trans. by A. J. Jenkinson, revised by J. Barnes, in: The Complete Works of Aristotle, the Revised Oxford Translation (ROT), ed. by J. Barnes, Princeton, 1984a. Aristotle, Sophistici Elenchi, trans. by W. A. Pickard-Cambridge, revised by J. Barnes, in: The Complete Works of Aristotle, the Revised Oxford Translation (ROT), ed. by J. Barnes, Princeton, 1984b. 31 Hegel (1969), book 2, sect. I, ch. II, C, footnote 3. 32 Priest (2006), 109, and Berto/Priest (2013). 33 Berto (2008), 169.

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Aristotle, Rhetorica, transl. by W. R. Roberts, revised by J. Barnes, in: The Complete Works of Aristotle, the Revised Oxford Translation (ROT), ed. by J. Barnes, Princeton, 1984c. JC Beall, “True and False–As If”, in: G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of NonContradiction, Oxford, 197–216, 2004. E. Berti, Contraddizione e dialettica negli antichi e nei moderni, Palermo, 1987. E. Berti, “Il principio di non contraddizione. Storia e significato”, in: P. Bria, F. Oneroso (eds.), Bilogica e sogno. Sviluppi matteblanchiani sul pensiero onirico, Milan, 22–32, 2002. E. Berti, Nuovi studi aristotelici IV/2, Brescia, 485–494, 2010. F. Berto, Teorie dell’assurdo. I rivali del Principio di Non-Contraddizione, Rome, 2006. F. Berto, “Non dire non! (Una proposta che Priest non può rifiutare)”, in: F. Altea and F. Berto (eds.), Scenari dell’impossibile. La contraddizione nel pensiero contemporaneo, Padua, 45–62, 2007. F. Berto, “Adynaton and Material Exclusion”, in: Australasian Journal of Philosophy, 86(2), 165– 190, 2008. A. Code, “Aristotle’s Investigation of a Basic Logical Principle”, in: Canadian Journal of Philosophy 16, 341–358, 1986. S. M. Cohen, “Aristotle and the Principle of Non-Contradiction”, in: Canadian Journal of Philosophy 16, 359–370, 1986. M. Crubellier, “Du sullogismos au syllogisme”, in: Revue philosophique de la France et de l’étranger 136, 17–36, 2011. N. da Costa, Logique Classique et Non-Classique, Paris, 1997. F. D’Agostini, Introduzione alla verità, Turin, 2011. R. M. Dancy, Sense and Contradiction. A Study in Aristotle, Dordrecht, 1975. P. Fait (ed.), Aristotele, Le confutazioni sofistiche, Rome and Bari, 2007. M. Furth, “A Note on Aristotle’s Principle of Non-Contradiction”, in: Canadian Journal of Philosophy 16, 371–381, 1986. S. Gaio, “Sul principio di non contraddizione. Il dibattito sul Dialetheism”, in: Verifiche 35, 69–92, 2006. E. Gobbo, “La concezione ‘diretta’ dell’elenchos negli Analitici primi e nelle Confutazioni sofistiche”, in: Elenchos 18, 309–357, 1997. P. Gottlieb, “The Principle of Non-Contradiction and Protagoras: The Strategy of Aristotle’s Metaphysics IV 4”, in: Proceedings of the Boston Area Colloquium in Ancient Philosophy 8, 183–209, 1994. P. Gottlieb, “Aristotle on Non-contradiction”, in: Stanford Encyclopedia of Philosophy (Summer 2013 Edition), E. N. Zalta (ed.), http://plato.stanford.edu/archives/spr.2013/entries/ aristotle-noncontradiction/, 2011. G. W. F. Hegel, Science of Logic, trans. by A. V. Miller, London, 1969. G. Littmann, K. Simmons, “A Critique of Dialetheism”, in: G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 314–335, 2004. J. Łukasiewicz, “Über den Satz des Widerspruchs bei Aristoteles”, in: Bulletin international de l’Académie des sciences de Cracovie, Classe d’histoire et de philosophie, 1/2, 15–38, 1910. J. Łukasiewicz, “On the Principle of Contradiction in Aristotle”, in: Review of Metaphysics 24, 485–509, 1971. J. Łukasievicz, “Aristotle and the Law of Contradiction”, in: J. Barnes, M. Schofield, R. Sorabji (eds.), Articles on Aristotle, 3. Metaphysics, London, 61–62, 1975.

108 | Enrico Berti E. Mares, “Semantic Dialetheism”, in: G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 264–275, 2004. I. M. Blanco, Unconscious as Infinite Sets. An Essay in Bi-Logic, London, 1975. H. Maier, Die Syllogistik des Aristoteles, Tübingen, 1896/1900. M. Mignucci, “Consistenza e contraddizione in Aristotele”, in: Dianoia 1, 53–60, 1996. K. Popper, Conjectures and Refutations. The Growth of Scientific Knowledge, London and New York, 2002. G. Priest, In Contradiction, Dordrecht (2nd edition: Oxford 2006), 1987. G. Priest, “What’s So Bad About Contradictions?”, in: G. Priest, JC Beall, B. Armour-Garb, The Law of Non-Contradiction, Oxford, 2004. G. Priest, “To be and not to be – that is the answer. On Aristotle on the Law of NonContradiction”, in: A. Newen, U. Meixner (eds.), Philosophiegeschichte und logische Analyse, Paderborn, 91–130, 1998. G. Priest, Doubt Truth to Be a Liar, Oxford, 2006. G. Priest, JC Beall, B. Armour-Garb (eds.), The Law of Non-Contradiction, Oxford, 2004. G. Priest, R. Routley, J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Munich 1989, 1989. G. Priest and F. Berto, “Dialetheism”, in: The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), E. N. Zalta (ed.), http://plato.stanford.edu/archives/sum2013/entries/ dialetheism/, 2013. R. Routley, R. Meyer, “Dialectical Logic, Classical Logic and the Consistency of the World”, in: Studies in East European Thought 16, 1–25, 1976. E. Severino, Fondamento della contraddizione, Milan, 39–60, 2005. S. Shapiro, “Simple Truth, Contradiction, and Consistency”, in: G. Priest, JC Beall, B. ArmourGarb (eds.), The Law of Non-Contradiction, Oxford, 336–354, 2004. T. E. Tahko, “The Law of Non-Contradiction as a Metaphysical Principle”, in: Australasian Journal of Logic 7, 32–47, 2009. M. V. Wedin, “Aristotle on the Firmness of the Principle of Non-Contradiction”, in:Phronesis 49, 225–265, 2004.

Angelica Nuzzo

The Justice of Contradiction Logical Advancement and Historical Transformations In this essay I look at the implications that the systematic foundation of Hegel’s philosophy of objective spirit in the Logic and the logical method has for his idea of freedom and for his conception of history as the culmination of the movement of freedom’s realization within the sphere of ethical life. In particular, I am interested in the role that contradiction and negativity play in structuring logical, practical, and historical processes as processes. On the basis of an analysis of this issue and in contrast with a long-standing interpretation of Hegel’s idea of history, I claim that the most innovative and for us today useful features of such an idea must be brought back precisely to history’s logical foundation. My overall claim regards the fundamental solidarity between Hegel’s logical thought of contradiction and his awareness of its practical and historical relevance. I begin with a discussion of the Frankfurt fragment “Der immer sich vergrössernde Widerspruch [. . . ]” (1799/1800)¹ which testifies of the complex constellation of problems that occupies Hegel’s reflection on contradiction in his early years. After having shown how Hegel uses the dialectical idea of contradiction against traditional and Kantian Verstandeslogik, I turn to the philosophy of spirit and to the practical significance of the idea of contradiction at work in the dialectic-speculative logic. Here I offer a new account of Hegel’s critique of Kant’s moral formalism – an account that is based on the function of contradiction in relation to action. I argue that contradiction is what grounds the crucial transition from Moralität to Sittlichkeit in the Philosophy of Right. At this point, laying out the framework for an interpretation of the idea of history that concludes the sphere of ethical life, I move back to the logical use of contradiction, offering a brief account of the second moment of the “absolute method” in the Science of Logic, the moment of the “advancement”. Finally, I bring this analysis to bear on Hegel’s idea of Weltgeschichte and on its placement as conclusion of the sphere of objective spirit. I argue that Hegel’s choice for this position, which has often been disputed and variously challenged, is the direct and coherent consequence of the claim that historical processes are structured according to the dialectical logic of contradiction.

1 Hegel (1969ff.), TW 1, 457–460.

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1 Contradiction and Verstandeslogik There is a fundamental continuity between the task that Hegel assigns to his practical philosophy or philosophy of objective spirit and the thought that leads him from early on to the idea of a dialectic-speculative logic that replacing the unmoved fixity of traditional Verstandeslogik (of which Kant is one of the latest representatives) is able to account for change and transformation – in reality as well as in thinking. In short, in Hegel’s view, the most pressing issue of the modern, post-revolutionary world is understanding how to live with and how to practically overcome the contradiction present in the world of spirit’s objective reality, i.e., ultimately, how to change practical norms with the changing of historical conditions. This is the fundamental task that he assigns to a new type of logic and to a practical philosophy based on that logic. Hegel’s concept of freedom, his systematic articulation of the relation between Moralität and Sittlichkeit, and the conclusion of the Philosophy of Right with “world history” should all be brought back to that core issue. Contradiction sums up for Hegel the chief question of the present age and defines, at the same time, the structure of logical processes and the space of freedom’s realization. Hegel’s concern with the historical present and the idea that its fractured actuality poses to philosophy a fundamental task – that this is indeed the fundamental task of practical philosophy – can already be detected in the fragment that opens the Verfassung Deutschlands (1799/1800).² As will be the case in 1807 and, albeit under different conditions, in 1820, the starting point is the apparent evidence of “what is there” and seems “not difficult to see”, the deceitful transparency of immediate facts that pose to the philosopher the much more difficult problem of recognizing the relevant issue of the time – “die Vernunft als die Rose im Kreuze der Gegenwart”,³ as Hegel eloquently puts it in 1820. This is the contradictory reality of historical change. As Hegel registers in the preface to the Phenomenology, “it is not difficult to see that our time is a time of birth and transition (Übergang) to a new era”.⁴ It has been observed that a confrontation between the Verfassung Deutschlands and Hegel’s works on political philosophy of this period

2 Hegel (1969ff.), TW 1, 451–610. 3 Hegel (1969ff.), Grundlinien der Philosophie des Rechts (henceforth RPh), preface, TW 7, 26. 4 Hegel (1969ff.), TW 3, 18; see also the “Anstrengung und Bemühung” at 19. Many are the contemporary voices that express a similar assessment of the present time. See, among them, Goethe’s passage at the end of Hermann und Dorothea (written between 1796 and 1797) where a German revolutionary says: “Alles bewegt sich/ auf Erden einmal, es scheint sich alles zu trennen./ Grundgesetze lösen sich auf der festen Staaten,/ [. . . ] Alles regt sich, als wollte die Welt, die gestaltete, rückwärts/ lösen in Chaos und Nacht sich auf und neu sich gestalten”. Goethe (1988),

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(System der Sittlichkeit, Naturrechtsaufsatz) yields radically conflicting views. For, while philosophical reflection leads Hegel to attempt overcoming the contradictions found in the historical world, in the Verfassung Deutschlands all the contradictions are left un-reconciled as plain and hard facts – as facts that “should remain”, as it were, in their contradictory, unmediated character.⁵ This important observation supports, in my view, the opposite conclusion, namely, the idea of the fundamental continuity and solidarity between Hegel’s occasional political writings and his dialectic-speculative philosophy. Neither could be understood without the other. As the comprehension of the present world leads to a contradiction that can neither be healed nor overcome, the effort of philosophy struggling for a conceptual comprehension of the dynamics of change leads to the thought of a possible conciliation and to the conditions thereof. In both cases the central question of the time concerns the reality of contradiction – the logical problem of its conceptualization and the practical problem of living with it and overcoming it. The project of Hegel’s dialectic-speculative logic as a logic of contradiction and, as I have claimed elsewhere, as a “logic of transformative processes” arises, from early on, from the need to learn how to live with and give a philosophical account of the fundamental contradictions and transformations of modernity.⁶ The fragment “Der immer sich vergrössernde Widerspruch [. . . ]”,⁷ offers at the same time a philosophical diagnosis of the historical crisis faced by Germany at the end of the 18th century, the first emergence of Hegel’s dialectical logic, and one of the central tenets of his practical philosophy. The problem herein is: What is change? How shall the philosopher conceptualize the moment of historical transition, the unrest that everyone feels as the prevailing dimension of the present, the necessary pull (Trieb, Drang) toward the unknown and the new which one must grasp and embrace in order to withstand its unstoppable affirmation? Unlike the dead fixation of life in “positive” institutional forms and in their destructive, blocked contradictions, the contradiction that shapes transformative processes is the condition of survival – individual and collective, personal and national. For, contradiction bears within itself the possibility of a way out and the conditions of a new beginning. Significantly, Hegel does not point to any guaranteed solution to the “growing contradiction”. Insecurity and the striving for the unknown

vol. 2, 512f.) The political diagnosis turns here into a metaphysical view of the development of history out of and back to the original Chaos. 5 Maier (1963), 340; this observation is supported by Cesa (1972), vii–lii, xxii. 6 See Nuzzo (2006), 85–104. 7 In Hegel (1969ff.), TW 1, 457–460. With regard to the period of its composition and its editorial history, see the remarks by Baum/Meist (1998). A commentary of this fragment is in Luporini (1972), 440–450.

112 | Angelica Nuzzo are the predicament of the age.⁸ He indicates in the “growing contradiction” and the “need” for its “Aufhebung” or “Widerlegung”⁹ both the logical and practical structure of change.¹⁰ Contradiction is a real force operating in history, a force moved by its own inner logic, which is a logic of immanent development. Contradiction defines the relation between the ideal and the real, nature and life,¹¹ between what political and juridical institutions have to offer to their citizens and what individuals more or less consciously seek and desire but cannot see fulfilled by those institutions. The tension catalysed in contradiction is the mark of an epoch in which all certainty and security has been shattered and the only hope for survival – individual and collective – lies in the acceptance of transformation, in the capacity to face the negativity to which life has been reduced. Knowledge by itself cannot produce transformation, although it may be one of its conditions. And neither a pure act of the “will” [(individual or collective)], nor a social contract or mere revolutionary “violence”¹² can overcome contradiction and bring change about. Rather, Hegel seems to suggest that transformation lies in the nature of things, in the inner logic of the contradiction that animates the present time once the obstacles to its radicalization and free development are removed and contradiction is let grow to its extreme consequences without being fixated or hypostatized into something self-standing and “absolute”.¹³ Contradiction is a force independent of human cognition and will. It is rather the force within which all human action is inscribed. Only the recognition and expression of real needs and desires can lead to the articulation and thereby (dis)solution of the growing contradiction.¹⁴ Change takes place as contradiction gives rise to a “need” and thereby to the movement of its own “refutation”. For, the need that contradiction be overcome – a need that arises once life has met pure negativity and has recognized that it can no longer live with it and in it – is already in itself change. In sum, contradiction is for Hegel the sign of historical crises; practical transformation and change are the manifestation and internal development of the reality of contradiction, the movement that contradiction necessarily marshals in once it is not taken as static and absolute, once it is not fixed within illusory limits or repressed.

8 See also the “Unbekannte(s)” in Hegel (1969ff.), TW 3, 18. 9 Hegel (1969ff.), TW 1, 458 and 459 respectively. 10 Hegel (1969ff.), TW 1, 457f. 11 Hegel (1969ff.), TW 1, 458 and 457 respectively. 12 Hegel (1969ff.), TW 1, 459. 13 Hegel (1969ff.), TW 1, 457. 14 See Bodei (1987), 19.

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Hegel’s dialectic-speculative logic elaborates this seminal thought in opposition to the Verstandeslogik of which Kant’s transcendental logic is one of the most recent examples. If unforeseeable change, the unrest of transition, and the violence of contradiction are essential features of the historical present and not merely contingent aspects of it, they are also the stumbling-block that philosophy encounters in its attempts at a comprehension based on formal logic, on Kant’s transcendental philosophy, and on contemporary epistemologies more generally. Hegel brings together all these approaches under the designation of Verstandeslogik. Thereby he indicates the logic that makes of the principle of non-contradiction the first and foremost law of thinking and proceeds by applying fixed concepts (taken from an allegedly complete table of categories), which in their empty formality have no grip on reality. Herein lies Hegel’s critique: the present world is not understandable assuming traditional logic and metaphysics as paradigm of comprehension because the present is contradictory, has no fixed features, and being characterized by change cannot be held fast and pinpointed by any given definition or a priori concept. Hence, on Hegel’s account, it is also not surprising that philosophy has yielded in recent years either skepticism or various forms of irrationalism and Schwärmerei. Common to these positions is the confessed defeat that radically disengages philosophy from the comprehension of the contemporary world and from active participation in it. The need for a new method of understanding the contradiction proper to the historical present is also, at the same time, the practical need for what Hegel calls, in that early fragment, a “better life”,¹⁵ the striving toward different conditions of life. Verstandeslogik is characterized by two interconnected flaws. First, it is a logic that unable to cope with contradiction reduces reason to the understanding, whose chief activity is to avoid contradiction but whose main predicament is ironically to remain trapped in it – for the understanding is the very source of the contradiction it tries so hard to avoid. Second, since the categories of Verstandeslogik “as fixed determinations fall outside one another and are not held together in organic unity, they are dead forms that do not have in themselves the spirit which alone constitutes their living unity”.¹⁶ As dead, unmoved forms the categories of formal and transcendental logic have the same status as those political and juridical institutions from which life has forever departed. They are forms with no actual relevance, no normativity, no real grip on reality. They are “dead” insofar as they are irrelevant to human practices: their consecrated authority or alleged “ideality” is no longer authority over people’s lives nor guar-

15 Hegel (1969ff.), TW 1, 458. 16 Hegel (1969ff.), TW 5, 41.

114 | Angelica Nuzzo antee of meaningfulness in relation to lived practices and beliefs. In their dead fixity and unmoved abstract existence, they are useless relicts of a long gone past. Importantly, the two flaws of Verstandeslogik are connected: its forms are dead and meaningless or irrelevant precisely because they are set to avoid the contradiction that would put them at odds with reality but would also make them alive in interaction with reality; and since they refuse to embrace contradiction and thereby change, they remain locked into the unmoved ideality of their a-historical a priori status. Significantly, for Hegel, the Verstandeslogik perfectly corresponds to the “dürre[s] Verstandesleben”¹⁷ of Kantian morality, which goes hand in hand with the arid and egoistic economic existence of modern civil society.¹⁸ Contrary to Kant’s reassurance, pure practical reason is unable to overcome the limits – and the contradictions – that undermine the understanding and an impotent, merely antinomic reason. Unable to sustain the force of real contradiction, in fact utterly destroyed by it, pure practical reason and its highest a priori principle, the categorical imperative, follow the same logic of non-contradiction or abstract identity prescribed by the understanding. The consequence is the impossibility of the “transition” from morality to ethical life, just as the implication of the Verstandeslogik is the incapacity to conceptualize the predicament of the time. Herein we meet the critique of Kant’s morality that Hegel articulates in the Philosophy of Right. Morality is condemned to be ineffectual, i.e., to have no grip on reality as long as it assumes a practical version of the logic of non-contradiction as its highest principle. If, however, morality (or better the “moral standpoint”) does resolve to embrace contradiction, we are ipso facto led “outside” of morality into the sphere of ethical life. From here on, fuelled by the unavoidable conflicts met within ethical life, freedom’s realization proceeds into world history and into the development of art, religion, and philosophy in the successive sphere of absolute spirit. Let’s see now how Hegel, on the basis of his dialectical understanding of contradiction, moves freedom “outside” of morality.

17 Hegel (1969ff.), TW 1, 458. 18 In the historical sequence of the Phenomenology, later reversed by the systematic of the Philosophy of Right, the loss of ancient Sittlichkeit is followed by the “becoming of Moralität” that characterizes modernity.

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2 Contradiction: Kant’s Moralität and Hegel’s Sittlichkeit In the Philosophy of Right as the historical situation has changed, Hegel’s rhetoric is more restrained than in his early years. The diagnosis is not as dramatic and is now filtered through and reflected by the complex systematic construction of the work. Although contradiction plays a crucial role at many junctures of the development of freedom in the ethical world (in the family, civil society, and the state) being precisely the inner force of such development, I shall limit my analysis to two places in which contradiction displays a systematic and practical function, namely, to the critique of Kant’s concept of morality which leads to the “transition” to Sittlichkeit, and to the conclusion of the sphere of objective spirit with the moment of “world history”. Although Hegel praises Kant for introducing the idea of the “infinite autonomy” of the will, the crucial point of his critique is that Kant ultimately revokes this gain by “holding fast to the merely moral standpoint that does not make the transition to the concept of ethical life” but remains instead an “empty formalism”. In fact, the “transition” (Übergang) it makes is rather in the opposite direction, namely, toward the “unconditioned”.¹⁹ The only determination duty attains is to be “abstract universality”, indeterminate “identity with no content”, which “lacking contradiction” is only the will’s “formal correspondence with itself”. What interests me in particular in Hegel’s objection is the connection between the idea that Kant’s duty is based on the principle of non-contradiction (hence is formal, lacking content, merely tautological, etc.) and the notion that from the standpoint of morality so construed the transition to Sittlichkeit (to its “concept” and its “standpoint”)²⁰ is made impossible (hence the realization of freedom is blocked). While Hegel seems to criticize the idea that the mere lack of contradiction cannot be principium dijudicationis for moral action (it implies the justification of all actions indiscriminately, even of wrong and immoral ones),²¹ the crux of his attack is rather the idea that it cannot be principium executionis. This explains the misconstruction to which Hegel subjects Kant’s formulation of the moral law. In the Metaphysik der Sitten Kant’s formulation is: “Act according to a maxim that

19 RPh §135 and Anm. respectively. 20 RPh §135 Anm. for the former, §33 Anm. for the latter. 21 RPh §135 Anm.

116 | Angelica Nuzzo can, at the same time, be valid as universal law”.²² Hegel renders it as “Kant’s further formulation that presents an action as a universal maxim”.²³ At issue for Kant is not the possibility for an action to be represented as a universal maxim; but the possibility for a maxim to become (or to be willed as) a universal law valid for all rational agents. What Hegel thereby misconstrues is the place where contradiction (or, respectively non-contradiction) occurs. For Kant what ought not to contain contradiction is the maxim (or, alternatively, the will determined by the maxim);²⁴ in Hegel’s rendering of the position of morality it is instead, directly, the action itself. This is a crucial shift. How are we to understand the occurrence of contradiction in the action itself (or contradictory action)? While the idea that an action (as opposed to a maxim) may or may not contain contradiction is meaningless for Kant (for whom contradictory are propositions not actions), it is for Hegel the condition of realization or actualization that may characterize an action as free by leading from the inner ineffectual world of subjective intentions to the outer objective world of a shared intersubjective and always conflictual actuality.²⁵ Recall that in the 1799/1800 fragment discussed above Hegel placed the “growing contradiction” at the intersection of the inner and the outer world of consciousness. This is precisely the transition that leads outside the sphere of morality – and outside the subject-centered idea of the good – into the complex social world of Sittlichkeit. To actualized freedom contradiction belongs as a necessary dimension since to realized action necessarily belongs the possibility to be intersubjectively challenged. In the 1797 treatise Verkündigung des nahen Abschlusses eines Traktats zum ewigen Frieden in der Philosophie Kant contends that the principle of non-contradiction, under certain conditions to be specified, can indeed become the principle from which duties can be cognized. “The following is clear”, says Kant, “that this is an unmistakable sign of moral impossibility of an action, not that, if the maxim of my will is made into a universal law, it contradicts the maxim of someone else, but if it contradicts itself (which I [. . . ] can judge according to the principle of con-

22 Kant (1900ff.), AA VI, 226: “Handle nach einer Maxime, die zugleich als allgemeines Gesetz gelten kann”. 23 RPh §135 Anm.: “die weitere Kantische Form, die Fähigkeit einer Handlung, als allgemeine Maxime vorgestellt zu werden”. For a punctual reconstruction of the discussion in a Kantian perspective, see Baum (1987), 238f. 24 Given the examples offered by Kant in the Grundlegung (chapters 1–2), the former is the case of perfect duties the latter of imperfect duties. 25 To this extent, I agree with Pippin’s reconstruction of Hegel’s account of rational agency. Unlike Pippin, however, I insist on the crucial importance of the moment of contradiction (see Pippin (2008), ch. 3 dwells on the Hegelian inheritance of the Kantian idea of self-legislation; with regard to the Phenomenology, Pippin (2010), 413f.).

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tradiction)”.²⁶ On the basis of the principle of contradiction one knows that not to commit such an action, namely, acting according to the opposite maxim from the one that has been tested, is a duty. Significantly, Kant insists that at stake is the contradiction of the subjective maxim with itself, not the contradiction of my maxim with the maxims of others. This latter, by contrast, is what interests Hegel from the outset, and drives his shift from a contradiction in the maxim to a contradiction in the action itself. For, when action (and not a subjective maxim) is directly at stake, since action is the unfolding of a realization process in the objective and intersubjective world, it unavoidably comes into conflict with others or is challenged by others. Maxims can be considered in their utter abstraction, laws may be entirely formal, but actions being effectual cannot. The way in which Hegel raises the problem of content against the formalism of Kant’s idea of duty is connected precisely to this shift. Now, the idea that contradiction can occur only in relation to a content perfectly corresponds to Kant’s own view – to the notion that what is tested for contradiction is a subjective maxim, which as such always provides the “moral content” of the action; but also to Kant’s claim concerning the ontological argument (existence as real predicate must be assumed for the definition of a necessary being to be possible).²⁷ Hegel’s point, however, is a different one. He claims: “a contradiction can only occur with a content that already constitutes the basis as an established principle”.²⁸ On Hegel’s account, what makes contradiction a principle that can indeed meaningfully discriminate among actions (and not, notice, among maxims) with regard to their rightfulness, justice, and freedom, is not just the necessary assumption of a content but of “a content that already constitutes the basis as an established principle”. For, Hegel continues, it is only “in relation to such a principle that an action is ei-

26 Kant (1900ff.), AA VIII, 420f.: “Es is aber offenbar: [. . . ] dass nicht, wenn die Maxime meins Willens zum allgemeine Gesetzt gemacht, der Maxime eines Anderen, sondern wenn sie sich selbst widerspricht (welches ich [. . . ] nach dem Satz des Widerspruchs beurteilen kann), dieses ein unfehlbares Kennzeichen der moralische Unmöglichkeit der Handlung sei”. 27 See Baum (1987), 240 who refers to Kant’s critique of the ontological proof. It is interesting that at RPh §141 Anm., with regard to the “Übergang des Begriffs” into actuality that is the transition taking place between Moralität and Sittlichkeit, Hegel refers back to the Logic, to the “idea of the good” in which reference to the ontological proof is made. Now, the ontological proof is often used by Hegel to indicate the necessity of the transition to objectivity which takes place through action (see Hegel (1969ff.), TW 6, 404f.: just like the subjective will (RPh §124), god “can be known only through his action (Tun)”. See Cesa (1981), 174). 28 RPh §135 Anm. (my emphasis): “ein Widerspruch kann sich nur mit etwas ergeben, das ist, mit einem Inhalt, der als festes Prinzip zum voraus zugrundeliegt”.

118 | Angelica Nuzzo ther adequate or contradictory”.²⁹ In other words, Hegel’s charge against Kant is that what his moral principle lacks is not simply content but a content capable of being intersubjectively, i.e., ethically relevant and normative, a content that being valid as a principle can determine not just subjective maxims but the actual realization of actions. In other words, Kant’s formalism is undermined not by its lack of content but by its lack of actual relevance. His moral principle is noncontradictory because it has no traction in the objective world of action. Hegel’s point is that Sittlichkeit needs to be Grundlage of Moralität: when the relation is reversed the moral principle looses normativity and relevance (not just content). It becomes a principle that can neither be implemented nor applied but remains a dead, ineffectual “positive”. Such is, for Hegel, the status of Kantian morality – the “dürres Verstandesleben” corresponds to an ineffectual reason that, unable to sustain contradiction, is ultimately identical with abstract understanding. Thus, Hegel’s critique of Kant’s formalism is not simply that the form of duty lacks content, hence that from it particular duties cannot be derived. His charge is that the mere form of duty lacks normativity over actual actions because it flees the contradiction that alone anchors the will’s determination to the action’s realization, the latter always and necessarily occurring in a social context. Ultimately, what is not formal, for Hegel, is contradiction. Contradiction does reveal the nature of an action because it occurs “with a content that already constitutes the basis as an established principle”, that is, is ethical hence normative content. If free action is identical with moral action and moral action is action in which the will is determined by a principle from which contradiction must be excluded, then free action becomes impossible. For, lack of contradiction and formal self-identity cannot provide the will with a ground for determination – after all, since all determination implies negation, on this path conflict is unavoidable. By contrast, the transition to Sittlichkeit requires the acceptance that free action is not the action that paralyzed by contradiction is determined only by the injunction to avoid it at all costs; an action is free when it embraces contradiction and the confrontation with others, and eventually is “at home” in it – freedom is a movement of externalization (Äusserung and Entäusserung) that is formally characterized as bei-sich-selbst-sein-im-Anderssein. While for Kant non-contradiction sustains and guarantees the purity of the moral principle, i.e., its formality, for Hegel it blocks the development of freedom and makes the transition to the concept of ethical life impossible. For both Kant and Hegel, however, contradiction is the force that

29 RPh §135 Anm. (my emphasis): “In Beziehung auf ein solches [Prinzip, a.n.] ist erst eine Handlung entweder damit übereinstimmend oder im Widerspruch”; see Baum (1987), 240f. On his view, Hegel’s misconstruction of Kant’s position is no more than a sheer misunderstanding.

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ultimately leads “outside” morality – to non-moral maxims for Kant; to the realization of freedom in the ethical world for Hegel. I now turn to the connection between Hegel’s Logic and the idea of world history.

3 Contradiction, Logical “Advancement”, and Historical Justice Hegel’s idea of a dialectic-speculative logic (in contrast to the un-dialectical Verstandeslogik) constitutes the most adequate basis for the introduction and presentation of history in the systematic of spirit and for the understanding of the specific developmental structures of history itself. To claim that history has its systematic foundation in the Logic means that it is dialectical logic and not some metaphysical or theological or even moral assumption or goal that guides its development. Herein, I suggest, we should recognize the contemporary relevance of Hegel’s idea of history. My thesis can be summarized by the following three claims.³⁰ Hegel’s Logic is the best-suited tool for articulating the structures of history, first, because it is the logic of the transformative process that pure thinking itself undergoes when considered in its immanent activity; second, because such logic replaces the metaphysical (ontological, cosmological, theological) problem of origin with the methodological problem of the beginning of thinking’s most proper activity; and third, because the logical movement is a movement of transformation and advancement fuelled by the dynamic of contradiction and the practice of judgment. Hegel’s specific conception of history directly follows from and is shaped by these three programmatic logical objectives. Presently, I can dwell only on the latter claim. History is the immanent development of real transformative processes, which display human, worldly beginnings, advancements and epochal transitions but is not the search for metaphysical first ‘origins’ or ultimate, unreachable or transcendent final ends. On Hegel’s idea of history, the latter are not properly ‘historical’ and do not belong to a dialectic philosophy of history. Finally, the motor of history and the authority to which history is subject is the justice done by the power of contradiction, the same immanent contradiction that determines historical advancements: Weltgeschichte is Weltgericht.³¹

30 I have argued for these claims extensively in Nuzzo (2012); see in particular ch. 4. 31 RPh §340; Enz §548 (Enz refers to Hegel (1969ff.), Enzyklopädie der philosophischen Wissenschaften, TW vol. 8–10).

120 | Angelica Nuzzo In the last chapter of the Logic, Hegel presents the three moments of the “absolute method”: beginning, advancement, and end.³² The moments that account for the development of logical truth are, at the same time, the crucial structures of the historical realization of freedom. For, in the first case the method discloses the generative forms of thinking’s pure activity, while in the second case history brings to light the structures of spirit’s own realization. Here I can only discuss the intermediary moment, the moment of advancement (Fortgang). Methodologically, dialectical contradiction is the fundamental structure of the advancement – of the purely immanent movement advancing out of the beginning. The second moment of the logical method considered in its formality is the action (of thinking) that advances – Fortgehen. This is immanently developed from the first moment because Anfang is the “beginning of a process and a development”.³³ And yet advancing is not a mere “Überfluß” over and above the beginning.³⁴ Advancing is the activity of dialectical contradiction. What characterizes the advancement is the intervention of “difference” (Unterschied, Differenz) and negativity, the transition to otherness with the split that this implies, and the “judgment” (Urteil) that draws differences and acknowledges, reflectively, that the simplicity of the beginning is re-visited in the advancement as the unity of that which is in itself different or which carries difference in itself.³⁵ In the second moment advancement is made because the first moment, in its immanent development, shows itself as contradictory: the simple is in itself different, the immediate entails mediation. Although the advancement in its negativity seems to do violence to the beginning and betray its simplicity, it is truly the act that does justice to it, bringing the beginning to completion, making it real, and thereby manifesting what the beginning truly is. Thus, the second moment of the method brings to the fore its properly dialectical negativity. Methodologically, dialectic is the “standpoint in which a universal first, considered in and for itself reveals itself as the other of itself”.³⁶ This standpoint is crucial to Hegel’s notion of freedom as self-actualization in (relation to) otherness. In the final perspective offered by the method dialectic discloses that the process of the whole is both continuous (the method is analytic, difference is immanent) and fundamentally discontinuous (the method is synthetic, difference is in the gap that produces the transition

32 See Nuzzo (2005), 187–205; see also Nuzzo (2011), 111–139. 33 It is “Anfang des Fortgehens und der Entwicklung” (Hegel (1969ff), TW 6, 556). 34 Hegel (1969ff), TW 6, 555; see the corresponding passage on the relationship between Anfang and Fortgang in Hegel (1969ff.), TW 5, 71. 35 Hegel (1969ff.), TW 6, 556. 36 Hegel (1969ff.), TW 6, 561.

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to the other).³⁷ This is the fundamental logical structure that underlies all historical transition and epochal transformation – it is the ground of historical continuities and discontinuities, the basis of the negativity and destructiveness but also of the recovery from such destructiveness that characterizes historical development. The difficulties met by the conclusion of the sphere of objective spirit with the moment of Weltgeschichte are well known. The field of world history seems to represent an abrupt interruption – even a reversal – in the ascending structure of the progress of freedom from “abstract right” through “morality” up to the different moments of “ethical life”. Already in the confrontation among autonomous states (Völkerrecht) right loses its power of actuality, sinks back to the level of the dreaded Kantian Sollen,³⁸ and is constantly undermined by contingency,³⁹ while the anarchy of a renewed state of nature seems to propose, yet again, the resurgent condition of abstract right. How then can Hegel attribute to world history the function of establishing the last “judgment” on what is the highest and absolute level of right, the most advanced development of freedom – the famous claim: Weltgeschichte is Weltgericht? How can the impasse of an un-reconciled confrontation between nature and freedom be proposed as closure for the ascending realization of freedom and considered the ultimate Weltgericht? Hegel’s systematic choice has often been discussed (and rejected) on the ground of its political and ideological implications. Leaving this discussion aside, I am interested in the conceptual nature of the figure of world history introduced by Hegel at this point. What can we infer with regard to Hegel’s idea of world history from its systematic placement, and from the logic that such placement suggests history follows? In short, my contention is that framed as Weltgericht world history fulfills the same function in the conclusion of the sphere of objective spirit that the second moment of the method fulfills in the conclusion of the Logic. The account of the second moment of the logical method offers a crucial insight into the connection between contradiction, judgment, and justice that becomes relevant in Hegel’s thinking of history. As the result of the logical activity of judgment, justice – which discloses the “truth” of the beginning and its necessary implications but also subverts it by negating and mediating its simplicity and immediacy – is neither the starting point nor the conclusion of a process. It is neither the absolute value positioned in an original moment before the beginning of history (the Absolute, the Garden of Eden, an alleged mythical Golden Age)

37 Hegel (1969ff.), TW 6, 557. 38 RPh §§330, 333. 39 RPh §334 Anm., §335.

122 | Angelica Nuzzo nor the final goal beyond history to which the process approximates (the Himmelreich, Perpetual Peace). Justice is instead the intermediary, ‘critical’ moment of the advancement – a moment of fragmentation and split in which contradiction is responsible for continuing the overall movement and orienting it. Logical advancement is the dynamic structure of the dialectical process of history. Justice is the loss of the innocence of immediacy that advances historical processes and thereby brings freedom to actualization. Justice is neither a first origin nor a final end; it rather lies in the middle and constitutes the dynamic form of the process itself. Viewed on this logical basis, the historical movement is carried on neither by an absolute origin nor by a final goal (both placed beyond history – before or after it) but by the capacity that the middle, mediating force of contradiction has to produce difference and thereby to discriminate or judge – the capacity to be both the crisis in the process and the critic thereof. Justice is precisely the intermediary ‘critical’ moment that immanently moves on the process of transformation – the logical as well as the historical process. At issue are the conditions that structure a process as historical, making the movement of Entwicklung, which both in the Logic and all along in the Philosophy of Right was a-temporal and non-historical, into the development in time that is world history. What is it that transforms, alternatively, a logical Stufe or a discrete number of successive empirical events within the development of the concept of right or freedom into an epoch of world history? What is the systematic principle of history? My claim is that the idea of historical justice whereby Weltgeschichte in its contradictory tensions is framed as Weltgericht (and placed above international justice) provides the answer in Hegel’s late system.⁴⁰ As the political state becomes the agent and the subject of history the traditional idea of God’s final judgment is secularized in the idea of historical justice,⁴¹ which now becomes the principle responsible for the immanent generation and “partition” of the historical process, that is, for the historical periodization that concludes the Philosophy of Right.⁴² On the basis of the dialectical method, the immanent partition/periodization of the process generates the process itself as the totality

40 The extensive argument in support of this claim is in Nuzzo (2012), ch. 4. 41 Assmann (2001), 302f., traces the beginning of history in the move taking place from Egypt to Mesopotamia and ancient Israel whereby the idea of a “tribunal of the dead” judging of one’s individual life (before the life’s end) is replaced by the idea of a worldly responsibility of the kings toward the gods and then by the Jewish idea of a historia sacra in which God himself participates. In Hegel’s idea of world history there is a parallel move from the idea of divine justice taking place after the end of history to the idea of an intra-historical judgment that falls within history itself. The tribunal of justice is now history itself. 42 See RPh §§354–360.

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of history. Significantly, such periodization does not presuppose history but first establishes a temporal sequence as world history. The tribunal that judges of the actions of the states on the world scene, is no longer placed beyond history but is now history itself. Historical justice is the immanent principle of historical judgment, i.e., is the principle on which the advancement of the process is made. Here again, the structure of history leads us back to the logic of the process. For, the tribunal of history neither reflects a divine providential order nor dictates ideal conditions of ethical or international justice (for the pursuit, for example, of perpetual peace, which always remains for Hegel an unreal Sollen). Its function is rather to indicate the conditions under which alone the historical process can advance as the immanent movement of freedom’s realization (and is not stalled, for example, or pushed back to preceding stages or forced to sterile repetitions of the same errors). Because of its logical basis, history’s justice is neither theological nor moral but is pragmatic worldly justice. Just is that stage of the process which allows for and actually accomplishes historical advancement within the totality of Weltgeschichte. Just is the stage in which freedom is brought to its advancement.⁴³ As we have seen, the idea of dialectical contradiction is directly connected for Hegel to the task of thinking transformation in its logical forms. In this regard, Hegel’s Logic is framed as the last chapter in the history of dialectic that begins with ancient Greek philosophy. “One must realize that war is common and conflict is justice, and all things come about by way of conflict and necessity”, reads a famous fragment by Heraclitus.⁴⁴ On his view, constant transformation constitutes the very essence of reality, the principle to which everything existing is subject. Change, however, is generated by conflict, i.e., by the clash of opposites and their coexistence. War is a universal all-pervading principle to which nothing escapes. To this extent, Conflict is promoted to the dignity of a first metaphysical principle next to Necessity. Opposing Pythagoras who proposed the ideal of a peaceful and harmonious universe, and Anaximander who saw the warfare of opposites as outright injustice, Heraclitus identifies Conflict and its necessity with Justice (dike).⁴⁵ On his view, justice is not harmonious and changeless balance but the restless tension of strife. Contradiction does not lead to chaos but to a just order that is the necessary dynamic order of universal transformation. The Pythagorean tradition is continued in Plato and Aristotle. In their view, conflict – political, social, but also psychological as imbalance and disharmony of the different parts of

43 I want to insist that the criterion that measures advancement is neither moral nor theological or providential but merely logical. 44 Heraclitus D. 80, M 28 in Kahn (1981), 66f. 45 Kahn (1981), 206, says that such identification “is at first sight utterly perverse” (see his further commentary on this fragment at 207).

124 | Angelica Nuzzo the soul – is considered the great evil to be corrected by the harmonious force of reason which is itself justice. On this crucial point, Hegel follows Heraclitus. Reason is justice because reason is fundamentally dialectical, i.e., because it bears in itself the necessity of conflict. But reason is also, at the same time, the power able to overcome contradiction. Unlike Kantian reason, which is truly understanding, Hegelian reason does not remain stuck in the still stand of unresolved antinomies. As the dynamic unity of conflict and its resolution, Hegel’s Vernunft is justice. The verse from Schiller’s poem Resignation that Hegel appropriates in introducing the idea of world history has, after all, a pre-Socratic root in Heraclitean dialectic. Conflict is Justice: Weltgeschichte is Weltgericht because historical change is produced by strife and strife is justice. Ultimately, Hegel’s rejection of Kant’s ideal of perpetual peace has the same metaphysical motivation as Heraclitus’ polemic stance toward Pythagoras’ harmonious universe. Contradiction determines the ongoing movement of the historical process the justice of which lies in the self-regulating development of contradiction. The order of justice is the very order of (historical) change, not a changeless state beyond transformation and conflict. Contradiction is ‘critical’ in the sense of discriminative and ordering; it does lead neither to chaos nor to nothingness but to epochal transformation.

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H. Maier, “Hegels Schrift über die Rechtsverfassung”, in: Politische Vierteljahrsschrift, 1963, 334–349, 1963. A. Nuzzo, “The End of Hegel’s Logic: Absolute Idea as Absolute Method”, in: D. G. Carlson (ed.), Hegel’s Theory of the Subject, London, 187–205, 2005. A. Nuzzo, “Dialectic as Logic of Transformative Processes”, in: K. Deligiorgi, Hegel. New Directions, Chesham, 85–104, 2006. A. Nuzzo, “Thinking Being: Method in Hegel’s Logic of Being”, in: S. Houlgate (ed.), A Companion to Hegel, Oxford, 111–139, 2011. A. Nuzzo, Memory, History, Justice in Hegel, New York and London, 2012. R. Pippin, Hegel’s Practical Philosophy. Rational Agency as Ethical Life, Cambridge, 2008. R. Pippin, “Hegel on Political Philosophy and Political Actuality”, in: Inquiry 53/5,401–416, 2010.

Luca Illetterati

Limit and Contradiction in Hegel 1 Introduction At the beginning of the second book of Hegel’s Science of Logic, and more precisely in chapter II of section I, Hegel analyses the so-called essentialities or the determinations of reflection. These determinations are: A) Identity, B) Difference and C) Contradiction. In the remark preceding this analysis Hegel claims: The categories of reflection used to be taken up in the form of propositions, in which they were asserted to be valid for everything. These propositions ranked as the universal laws of thought that lie at the base of all thinking, that are absolute in themselves and incapable of proof, but are immediately and incontestably recognized and accepted as true by all thinking that grasps their meaning.¹

In these lines Hegel discusses the determinations of reflection: identity, difference, opposition and contradiction. Nevertheless, by making explicit the logical structure of these determinations, Hegel casts doubt on their propositional form as universal laws of thought such as to be immediately and incontestably recognized and accepted as true. Therefore the critical analysis of identity, difference and contradiction is also a critical discussion of the law of identity “which is usually adduced as the first law of thought”,² of the law of contradiction (considered by Hegel as an expression of the principle of identity), of the law of identity of indiscernibles and of the law of the excluded middle. The critique of the universal laws of thought depends on the impossibility to reduce the determinations of identity, difference and contradiction to these universal laws. Such impossibility should not be underrated in the analysis of the problem I am to discuss. Hegel’s focus does not seem to be the status of the propositional structure of the determinations as universal laws of thought. The main issue seems to lie at an antecedent stage, namely the function performed by these determinations in the process through which everything “realizes” its essence, that is, the role they play in the development of determinateness itself. In the third remark on the determination of contradiction, Hegel explains some features of his conception of contradiction. This conception represents a

1 Hegel (1969), 409. (Ger. orig.: Hegel (1968ff.), GW XI, 258). 2 Hegel (1969), 413. (Ger. orig.: Hegel (1968ff.), GW XI, 262).

128 | Luca Illetterati breaking point of Hegel’s philosophy with respect to the classic pattern of thought by making room for an account of contradiction that sounds scandalous from the standard philosophical perspective. Hegel explicitly refers to this perspective when he claims: “one of the fundamental prejudices of logic as hitherto understood [bisherige(n) Logik] and of ordinary thinking [gewönliche(s) Vorstellen]” is “that contradiction is not so characteristically essential and immanent a determination as identity”.³ On the one hand, the expression logic as hitherto understood is referred to formal logic, namely the logic of the Aristotelian tradition as it got developed in the Wolffean logic studied in German universities at the end of the eighteenth century; on the other hand, ordinary thinking is common thought, that is the way we usually conceive of thought and reality. Both of them are ways of thinking whose basis lies on a certain set of unjustified presuppositions. A common and fundamental presupposition of the logic as hitherto understood and of ordinary thinking is the idea that contradiction is something that we need to get rid of within any thought and discourse concerning reality and truth. This ways of thinking are characterized by what Hegel describes as a horror towards contradiction.⁴ More specifically, in the logic as hitherto understood and in ordinary thinking reality and truth are thought of as immune to contradiction. The contradictions we meet in reality are not contradictions that actually are in reality. In actuality, contradiction has its place only in the experience of error and misunderstanding depending on the finitude of thought insofar as it cannot think reality the way it is: [W]hether it occurs in actual things or in reflective thinking, it ranks in general as a contingency, a kind of abnormality and a passing paroxysm of sickness.⁵

Hegel endorses a provocative approach with respect to both logic as hitherto understood and ordinary thinking. He claims that contradiction is the root of all movement and vitality.⁶ Everything we experience in reality as characterized by an intrinsic dynamic, by an internal movement and by life is not conceivable at all outside of contradiction. Contradiction, as an absolute determination of essence,

3 Hegel (1969), 439. (Ger. orig.: Hegel (1968ff.), GW XI, 286). 4 With respect to the speculative value of contradiction, Hegel remarks that “ordinary – but not speculative – thinking, which abhors contradiction, as nature abhors vacuum, rejects this conclusion”. Hegel (1969), 442. (Ger. orig.: Hegel (1968ff.), GW XI, 289). 5 Hegel (1969), 440. (Ger. orig.: Hegel (1968ff.), GW XI, 287). 6 “Contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity”. Hegel (1969), 439. (Ger. orig.: Hegel (1968ff.), GW XI, 286).

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must be present – Hegel claims – in every experience, in everything actual, as well as in every notion.⁷ Contradiction – and this is a central point in Hegel’s view – is not a local phenomenon, a structure typical of certain exceptional situations which are inexplicable regardless of a reference to contradiction: [Contradiction] is not to be taken merely as an abnormality which only occurs here and there, but is rather the negative as determined in the sphere of essence, the principle of all selfmovement, which consists solely in an exhibition of it.⁸

Speculative thinking is that kind of thought aimed at sublating both logic as hitherto understood and ordinary thinking. It is a new paradigm of thought insofar as it does not think reality through a given logical apparatus. Therefore, speculative thinking does not presuppose the universal and necessary validity of the laws of thought. Quite the contrary, its approach to contradiction – if compared with the standard logical paradigm based on the principle of non-contradiction (from now on PNC) – is revolutionary: [S]peculative thinking consists solely in the fact that thought holds fast contradiction, and in it, its own self, but does not allow itself to be dominated by it as in ordinary thinking, where its determinations are resolved by contradiction only into other determinations or into nothing.⁹

From this point of view, contradiction is not the evidence of anything lacking or of something having mislead us. Rather contradiction represents the essential structure of every determination in its concrete nature, namely in its truth. Hegel resumes all these considerations in a propositional form that mirrors the structure of the universal laws of thought: [E]verything is inherently contradictory, and in the sense that this law in contrast to the others expresses rather the truth and the essential nature of things.¹⁰

Despite the ironical tone¹¹ depending on the approach Hegel wants to endorse against the universal laws of thought – something to which thought should al-

7 “Now as regards the assertion that there is no contradiction, that it does not exist, this statement need not cause us any concern; an absolute determination of essence must be present in every experience, in everything actual, as in every notion”. Hegel (1969), 440. (Ger. orig.: Hegel (1968ff.), GW XI, 287). 8 Hegel (1969), 440–441. (Ger. orig.: Hegel (1968ff.), GW XI, 287). 9 Hegel (1969), 440–441. (Ger. orig.: Hegel (1968ff.), GW XI, 287). 10 Hegel (1969), 439. (Ger. orig.: Hegel (1968ff.), GW XI, 286). 11 “To my knowledge, no commentators who quote this remarkable passage have paid attention to the quotation marks, the conditional form of the sentence that introduces it, or the larger con-

130 | Luca Illetterati ways obey – this sentence could be defined by Hegel as the fundamental law of speculative thinking. Such a proposition could be read as the evidence of the absolute inconsistency of Hegel’s account. Nevertheless, according to Hegel, the necessity of acknowledging the objective value and the truth of contradiction does not entail the possibility of ascribing any predicate to any subject. The scandalous Hegelian claim “contradictio regula veri, non contradictio falsi”,¹² namely the first thesis Hegel discussed in Jena in order to get his teaching habilitation, cannot be translated as “anything goes”, that is the conclusion of the ex falso quodlibet inference.¹³ How is it possible to avoid the explosive consequences of the ex falso quodlibet in such an account that is meant to make room for the truth of contradiction? This problem has given rise to different interpretative strategies toward the notion of contradiction in Hegel’s thought: 1. 2. 3.

The metaphorical interpretation. The interpretation of contradiction as a critical moment in the dialectical process. The interpretation of contradiction as principle of determination.

Each interpretation explains an important aspect of Hegel’s notion of contradiction. In the following pages I will briefly analyse the first two interpretative strategies and then I will focus on the third one. More specifically, I will test it by investigating Hegel’s dialectic of the limit and the way it implies an essential determining contradictory structure. I will finally work on the correspondence between this concrete and contradictory conception of the limit with the conception of true in-

text of Hegel’s account. In my view, Hegel here ironically couches his conception of contradiction in the metaphysical language he is intending to overcome”. De Boer (2010), 364. 12 Hegel (1968ff.), GW V, 227. 13 Criticism like Popper’s refers to the ex falso quodlibet inference in order to show the nonscientific character of Hegel’s dialectic: “if a theory contains a contradiction, then it entails everything, and therefore, indeed, nothing [. . . ]. A theory which involves a contradiction is therefore entirely useless as a theory”. Popper (2002), 429. In a logical system containing true contradictions everything is true as well as false. This system cannot say anything scientifically relevant. Horstmann writes: “Wenn Hegel also Widersprüche für notwendig und demnach unvermeidbar hält und insofern die Gültigkeit des Satzes vom Widerspruch bestreitet, dann liefert er seine eigene Theorie offensichtlich der Irrationalität und Unwissenschaftlichkeit aus”. Horstmann (1978), 19.

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finity on the one hand, and the strong connection between the notion of limitation and the bad infinite on the other. In the final part of the paper I will try to show to what extent this ontological reading allows a dialetheistic reading of Hegel’s notion of contradiction.

2 The Metaphorical Strategy The first kind of reading considers Hegel’s notion of contradiction in a metaphorical way. In this interpretation, the idea that contradiction is inherent in everything does not mean that logical contradictions exist in reality. Contradiction should rather be meant as a strong symbolic expression able to represent a whole system of notions like ‘division’, ‘separation’, ‘struggle’, ‘opposition’, and everything that can be included in what can be generally defined as ‘the negative’. Hegel uses this kind of notions throughout all his works. In Hegel’s view, these notions express the relation between the conflicting elements characterizing the essence of reality and historical experience. This conflicting essence does not find any room within an abstract and one-sided way of conceiving reality and history. Such an abstract conception is built on the paradigm of the fixed identity of everything with itself, independently from the relation to what is other than itself. Instead, a concrete way of thinking of reality and of historical development acknowledges the constitutive and determining value of the relation between opposed elements. This kind of relation sounds ‘contradictory’ when compared with the fixed identity paradigm. Nevertheless, it turns out not to imply the presence of true logical contradictions in thought or of real ontological contradiction in reality. As J. N. Findlay clearly claims: We may, however, maintain that, whatever Hegel may say in regard to the presence of contradictions in thought and reality, the sense in which he admits such contradictions is determined by his use of the concept, and not by what he says about it. And since he uses ‘contradiction’ to illuminate the workings of ordinary notions, and things in the world, and not to cast doubt on their meaning or reality, it is plain that he cannot be using it in the self-cancelling manner that at first seems plausible. By the presence of ‘contradictions’ in thought or reality, Hegel plainly means the presence of opposed, antithetical tendencies, tendencies which work in contrary directions, which each aim at dominating the whole things and worsting their opponents, but which each also require these opponents in order to be what they are, and to have something to struggle with.¹⁴

14 Findlay (1958), 77. In the same way, Popper remarks: “instead of the terminology we have used in speaking of thesis, antithesis and synthesis, dialecticians often describe the dialectic triad by using the term ‘negation (of the thesis)’ instead of ‘antithesis’ and ‘negation of the negation’

132 | Luca Illetterati In this perspective, a claim like “everything is inherently contradictory”¹⁵ can hence be read as a provocative statement against an abstract and one-sided conception of thought determinations.¹⁶ Moreover, such a sentence is meant to highlight the relational nature of thought determinations.¹⁷ Such reading has some clear advantages. First of all, it defuses the explosive consequences of the truth of contradiction. Furthermore, it defends Hegel’s account against the classic objections addressed to his conception of contradiction as an objective contradiction. The focus of these objections is the notion of ‘real contradiction’. Contradiction – this is the thesis of this criticism – can only be logical contradiction, namely something belonging to the sphere of thought.¹⁸ The notion of real contradiction would be a nonsense. This does not mean that there are not oppositions, struggles, and conflicts in reality, but that all these kinds of things do not deal with logical contradiction, but with what Kant has defined as “real opposition”.¹⁹

instead of ‘synthesis’. And they like to use the term ‘contradiction’ where terms like ‘conflict’ or perhaps ‘opposing tendency’ or ‘opposing interest’, etc., would be less misleading”. Popper (2002), 433. 15 Hegel (1969), 439. (Ger. orig.: Hegel (1968ff.), GW XI, 286). 16 “Si donc, en appelant ‘contradiction’ la relation essentielle, Hegel veut dire que, par suite de la dualité qu’elle implique, elle peut paraître à première vue logiquement contradictoire au point de vue partiel et provisoire de l’entendement, il s’ensuit que l’expression ‘contradiction’ est employée ici par métaphore. Et cette métaphore est d’intention polémique”. Gregoire (1958), 92. An interpretation which follows this guideline is Berti’s. Berti conceives of Hegel’s notion of contradiction as an effort to highlight the constitutive role of difference and opposition within a conceptual framework built on the pattern of the fixed identity. In such a context, everything not reducible to this identity, and therefore difference and opposition too, sounds contradictory. See Berti (1980), 629–654; Berti (1983); Berti (1987); Berti (1977a and 1977b). 17 The interpretations of dialectic as a kind of semantic holism are based precisely on the relational nature of thought determinations: the relation in question is an internal relation, that is, a necessary condition in order to define the determination in question. See Berto (2007), 19–39; Brandom (2002), 178–209. 18 “La contradiction, par son essence, appartient a la sphère des pensées et des concepts. Pour ‘contredire’ il faut ‘dire’: la contradiction, en bonne logique, suppose le jugement. Des concepts et des jugements peuvent se contredire [. . . ]. Mais des choses, des événements, des rapports réels ne le peuvent pas, a la rigueur. [. . . ] Ce qu’on appelle, très improprement, contradiction dans la vie et dans la réalité n’est pas le moins du monde une contradiction, mais, a la vérité, un conflit”. Hartmann (1931), 314–315. 19 Kant distinguishes real opposition from logical opposition (contradiction) because: 1. it does not imply any kind of contradiction, it is ohne Widerspruch, it does not deal with logic; 2. it is an opposition between real determinations that are not positive or negative in themselves (the negativity characterizing their opposition is not inherent in these determinations); 3. the oppositions rise from their being characterized by a functional homogeneity, namely their being applied to

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This criticism is based on the semantic definition of the notion of contradiction, according to which contradiction is the conjunction of two propositions, one of which is necessarily true, while the other is necessarily false. Therefore, contradiction does not pertain to ontology and to states of affairs, but to propositions. Moreover, given the standard definition of negation and conjunction, it can never be the case that contradiction is true and there cannot be a state of affairs verifying a contradiction. Objective contradictions cannot exist. Only real oppositions exist, yet real oppositions are not logical contradictions.²⁰ The metaphorical interpretation of the notion of contradiction blunts the power of the objection based on the ex falso quodlibet by getting rid of the core of the objection itself, namely the notion of logical contradiction. In this way, Hegel’s pretence of casting doubt on the standard conception of contradiction and on the PNC fades away. Finally, the bomb is defused insofar as the possibility for Hegel’s account to be aimed at an acknowledgement of the presence of contradiction in reality falls down.

3 Contradiction as a Necessary Error of the Understanding There is chance to avoid the weakening of Hegel’s conception of contradiction and at the same time to save it from the inconsistency raised by the claim of an ontological value and of the truth of contradiction. This chance can be found in the conception of contradiction as a logical contradiction (and not as a metaphor) that corresponds to a necessary moment in the dialectical process: contradiction is supposed to bring about the passage from an abstract and one-sided way of considering reality – namely understanding (Verstand) – to the complex and concrete consideration of reality, which is reason (Vernunft). In this kind of interpretation, contradiction can be thought of as the necessary result of the understanding’s abstract consideration of the world. The contradic-

the same object in which each one act in a way that is the opposite of the other; 4. the two opposite determinations are not nullified in this opposition, because they simply tend to annul the effects of their opposite. Take for instance two forces acting on the same body in opposite directions. See Kant (1968), KW II, 86; Kant (1968), KW II, 171; Kant (1968), KW III, 222. 20 “Non esistono ‘contraddizioni reali’, fatti contraddittori tra loro, ‘contraddizioni’ oggettive. La contraddizione è solo ed esclusivamente ‘logica’, del pensiero. Parlare di realtà contraddittorie è un non senso. [. . . ] Ciò non significa, ovviamente, che nella realtà non si diano opposizioni, lotte, scontri. Si danno e come! Ma, in questo caso, si tratta di ciò che Kant ha chiamato ‘opposizione reale”’. Colletti (1981), 7.

134 | Luca Illetterati tory nature of things would be the outcome of the understanding’s abstractive way of determining things in themselves. The acknowledgement of understanding’s contradiction would imply the acknowledgement of the necessity to overcome its abstract paradigm. The awareness of the presence of contradiction would imply the passage from understanding’s abstract approach to the rational (vernünftig) conception of reality. In other words, the task of reason, which is the task of philosophy, is to acknowledge the contradictoriness of the contradiction of the understanding, that is to make it explicit in order to resolve it. Understanding conceives of everything as simply and immediately identical to itself and as independent from the relation to what is other than itself. This one-sided conception of reality contradicts the intrinsic nature of everything there is, which is inherently relational. The task of reason is to make explicit this contradiction and to solve it by developing a concrete comprehension of the determinateness that necessarily involves the relatedness which constitutes the way everything is what it is. Consequently, the acknowledgement of the necessary and constitutive value of logical contradictions in the dialectical process, which brings to light the limitedness of the comprehension of the understanding and the necessity to overcome it in a concrete and complete comprehension of every kind of determination, does not imply any denial of the PNC: making the contradictions of the understanding explicit does not mean claiming their truth. Quite the contrary, since contradiction arises from a sort of abstract and atomistic conception of reality, contradiction can and does need to be solved by overcoming this abstract conception in a sort of holistic comprehension of determinateness. In such a kind of conception everything is characterized by a relational nature insofar as every element is a moment of a whole, within which only it gains its own consistency and its specific determinateness. This does not mean that contradiction is a simple accident or an arbitrary mistake of thinking activity. Contradiction is not something that can be simply avoided. In this kind of reading contradiction plays a constitutive role because it allows the overcoming of a one-sided and abstract view of reality in a concrete and true comprehension of the way everything articulates itself. Actually, contradiction is the necessary condition for moving toward a different level of discourse, i.e. the speculative one. Nevertheless, at the speculative level of discourse where we experience the contradiction as affecting understanding’s comprehension, contradiction itself is not only made explicit but also removed (aufgehoben). Hence, in this interpretative approach, contradiction does not affect what exists as such. Therefore, the fact that everything is inherently contradictory does not mean that everything is actually nothing. Contradiction does not characterize reality in itself, but the abstract conception of it developed by the understanding. This very experience of

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contradiction is what leads to the necessary overcoming of the point of view of the understanding. In this way, the solution of contradiction does not imply the inconsistency of things in themselves, that is to say the elimination of their existence in the world in front of us. In this perspective, the solution of contradiction implies the overcoming of the necessary contradiction of an abstract thought determination. The result of this overcoming is the unity of opposites, i.e. the necessary link between opposite determinations that constitutes their relational nature. If contradiction is raised by the omission of the understanding of the necessary conditions for defining something in the very pretence of defining this something – namely the relations that connect and distinguish this something from what it is not – the solution of contradiction consists in the reintegration of these relations in the definition of the something in question. Hence, the true discourse, that is the discourse of reason, does not imply the necessity of making room for some kind of true contradiction. The only contradiction acknowledged in the discourse of reason as a constitutive contradiction is the one that has to be removed. Contradiction plays a constitutive role with respect to the concrete truth only insofar as it brings to light the necessity of its own overcoming and then the necessity to develop a consideration of reality that cannot depend anymore on the fixity and abstractness of the understanding. This way of getting rid of the scandal of Hegel’s conception of contradiction is quite common in a lot of contemporary readings of Hegel’s dialectic. This interpretative approach, as we have seen, is based on the presupposition of a sharp distinction between the level of reason and the level of understanding. This distinction allows showing how dialectic does not involve a denial of PNC, as it is claimed in the classic objection against Hegel’s dialectic. This process is rather based on a radicalization of the value of this principle. As Robert Brandom claims in Tales of the Mighty Dead: “far from rejecting the law of non-contradiction [. . . ] Hegel radicalizes it, and places it at the very center of his thought”.²¹ Francesco Berto combines in a very effective way different interpretative paths. According to his interpretation, the cause of contradiction in Hegel’s dialectic is basically the indeterminateness (both semantic and syntactic) of understanding’s determina-

21 Brandom (2002), 179. In the same way, Gregoire claims: “Loin de supposer le rejet du principe de non-contradiction, ce processus est, tout au contraire, entièrement et visiblement appuyé sur lui”. Gregoire (1958), 61; according to McTaggart (2000), 15: “If [. . . ] the dialectic rejected the law of contradiction, it would reduce itself to an absurdity, by rendering all argument, and even all assertion, unmeaning [. . . ] In fact, so far is the dialectic from denying the law of contradiction, that it is especially based on it”; and Marconi (1980), 168, writes: “it is a basic principle of Hegelian dialectic that there be an urge [. . . ] to get away from contradiction –or, rather, over it”.

136 | Luca Illetterati tion: dialectic is a process of critical analysis of language through language itself, namely a process of re-definition of conceptual terms of our natural language on the basis of the inconsistencies arising from the fact that these terms assume incompatible meanings or incompatible syntactic roles.²² In this way, the authentic result of the dialectical process is the removal of the contradiction of the finite determinations of thought (determination of the understanding), that is the contradiction of the abstract comprehension of the understanding.²³ Focusing one more time on the scandalous Hegelian sentence claiming that “contradictio regula veri, non contradictio falsi”, these readings seem to emphasize the meaning of the word regula, which is “way” or “path”. In this sense, claiming that “contradictio regula veri” does not imply the claim of the truth of contradiction. It rather means that contradiction is a decisive moment in the process that leads towards the truth. Reason can grasp the truth of things only insofar as understanding gets entangled in a contradiction whose solution allows the development of a concrete, complete, and non-contradictory way of understanding reality. In this perspective, contradiction is not a metaphor, nor an accident that can be avoided. It rather represents a decisive and essential moment in the process of thought self-determination developed in its most complete form, namely as reason. By going through the experience faced by the abstract approach of the understanding, reason is not affected by contradiction, because it constitutes itself on a level of discourse within which the PNC finds its more radical confirmation. In this sense the sentence everything is inherently contradictory does not involve any ontological commitment. The rising of contradiction has only an epistemological character. More precisely, it is the product of an inadequate and onesided consideration of reality and then it is in no way constitutive of the way reality is in itself.

22 Important antecedents of Berto’s idea are Fulda (1973) and Marconi (1980). Fulda claims: “die dialektische Logik soll nicht nur die Gebrauchs-bedeutungen vorhandener Ausdrucke analysieren. Sie soll diese Bedeutungen korrigieren und damit die Mittel für neue propositionale Gehalte bereitstellen”. Fulda (1973), 241. Marconi shares the same interpretative approach: “natural language, with its intensional contents (meanings) and syntactic structure, is the starting point of philosophical discourse. Philosophy cannot do without natural language, though it may go beyond it”. Marconi (1980), 174. This idea recently had further development in the work of Nuzzo, more precisely in Nuzzo (2010). 23 Berto (2005), 189–224.

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4 Contradiction and Determination The thesis I want to argue for is the idea that Hegel’s sentence “everything is inherently contradictory”²⁴ expresses an ontological commitment. This claim does not imply the dismissal of the first two interpretations. The metaphorical interpretation as well as the one considering contradiction as a result ofthe understanding’s comprehension of reality are supported by some passages of Hegel’s works. Nevertheless, by trying to get rid of the scandalous import of Hegel’s theory of contradiction in order to make it acceptable and substantially reducible to the paradigm of standard logic, both interpretative approaches lose the most decisive aspect of this theory, that is the idea that contradiction is the root of the constituting process of the determinateness of things. My claim is that, according to Hegel, the way things determine themselves is articulated through contradictory structures. Therefore, if the process of self-articulation of everything determinate is considered to be non-contradictory, the very nature of determinateness itself is misunderstood. The removal of contradiction gives rise to a one-sided and abstract picture of the status of things. This picture does not provide a good account of their way of being. It is no accident that the structure of contradiction comes out already in the first and more basic levels of articulation of the logic, that is the Doctrine of Being, and more precisely in the dialectical development of Determinate Being (Dasein). The place where contradiction comes out in this basic level of the logical structures of reality is the determination of the limit. The limit is not a marginal determination with respect to our cognitive practices and our relation with the world. The limit is a structure that is the necessary condition for something to be determinate. It is a structure that allows us to deal with things in their being determinate. Given its capacity to delimit something from what is other than itself, the limit constitutes the principle of determination of everything. It is the locus where something comes out from indeterminateness in order to realize its own nature, i.e. its being itself and what is other than itself. Using Aristotle’s words with respect to the notion of ‘peras’: The limit is the terminus of everything, e.g., the first thing outside which there is nothing to be found and the first thing inside which everything is to be found.²⁵

24 Hegel (1969), 439. (Ger. orig.: Hegel (1968ff.), GW XI, 286). 25 Cfr. Aristotle, Metaph., V, 17, 1022 a 4–6.

138 | Luca Illetterati This is why the limit – in Hegel’s view – shows an inherently contradictory structure. This contradiction is at once to be found in the circumstance that the limit, as something’s negation reflected into itself, contains ideally in it the moments of something and other, and these, as distinguished moments, are at the same time posited in the sphere of determinate being as really, qualitatively distinct.²⁶

The peculiar status of the limit was already highlighted by Kant. According to Kant, reason’s disposition to understand what is beyond the realm of experience is grounded in the fact that reason itself is beyond the limit of this realm in the very act of determining its limits. The limit, as a principle for determining what is limited, is in contact with what is other than the limited too. In determining the phenomenal dimension as the dimension of what is knowable and the noumenal dimension as the dimension of what is not knowable, reason is placed under a limit. As Kant writes at the end of § 57 of the Prolegomena: “this boundary belongs just as much to the field of experience, as to that of beings of thought” (“diese [die Grenze] gehört eben so wohl zum Felde der Erfahrung, als dem der Gedankenwesen”).²⁷ According to Hegel, the limit plays a mediating role between what it determines and what it negates. In the very act of delimiting and determining the way of being of something, the limit (that is: Kant’s Grenze, which is to be distinguished from the notion of Schranke) shows to be “the mediation through which something and other both is, and is not” (“wodurch Etwas und Anderes sowohl ist als nicht ist”).²⁸ The limit is the structure where something as well as its other starts and ceases to be what it is. In being the structure where something and the other both gain and lose their being, the limit is – to use Hegel’s words – “the other of both” (“das Andere von beiden”).²⁹ In order to explain the structure of the limit, Hegel refers to some examples taken from Euclidean geometry. The same examples have been used also by Kant just with respect to the notion of limit. In the Prolegomena to Any Future Metaphysics Kant assumes the Euclidean definitions according to which the limit of a solid is a surface, the limits of a surface are lines, the limits of a line are points, in order to show that in limits (Grenzen) there is always something positive. Limits

26 27 28 29

Hegel (1969), 126. (Ger. orig.: Hegel (1968ff.), GW XXI, 113). Kant (1968), KW IV, 356–357. Hegel (1969), 127. (Ger. orig.: Hegel (1968ff.), GW XXI, 114). Hegel (1969), 127. (Ger. orig.: Hegel (1968ff.), GW XXI, 114).

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are not simple negations (as in the case of that form of limitation which Kant calls Schranke): [A] surface is the boundary of corporal space, yet it is nonetheless itself a space; a line is a space, which is the boundary of the surface; a point the boundary of a line, yet is nonetheless a locus in space.³⁰

30 Kant (1968), KW IV, 354. In Kant’s philosophy there is an explicit distinction between the structure of the limit as Grenze and the structure of the limit as Schranke. More specifically, in the Prolegomena to Any Future Metaphysics Kant shows that both expressions involve a form of negation. Nevertheless, whereas Schranken “sind bloße Verneinungen, die eine Größe afficieren, so fern sie nicht absolute Vollständigkeit hat” (Kant, ibid., 352), Grenzen are negations that have also a positive value insofar as their limiting confers determinateness to the way things are, i.e., they are what allows to grasp things in their concreteness: “denn in allen Grenzen ist auch etwas positives” (ibid., 354). The starting condition of this distinction between the function of Schranke and the function of Grenze lies in the different basis on which these two different limiting structures lie. Schranke is always set in a context of continuity: what is beyond Schranke is characterized by the same features of what is be-schränkt. Instead, Grenze is a limiting structure which distinguishes things or areas of reality that are not homogeneous. Therefore, precisely because of Grenze’s being at the origin of this not-homogeneity, Grenze itself provides the possibility of grasping the area begrenzt in its completeness. On the one hand, even if Schranke can always be shifted on and on, it never reaches a point in which it encounters something not homogeneous that marks the end of the area within which what is be-schränkt is developed. On the other hand, Grenze is posited just on this distinguishing point and thus it can determine what is be-grenzt in its completeness. According to Kant, the difference between these two limiting structures is not merely formal; rather, it is a substantial difference which has fundamental implications. This is testified by the fact that the two structures play a crucial role in the distinction of scientific and philosophical knowledge. The first one never deals with Grenzen: “In der Mathematik und Naturwissenschaft erkennt die menschliche Vernunft zwar Schranken, aber keine Grenzen, d. i. zwar daß etwas außer ihr liege, wohin sie niemals gelangen kann, aber nicht daß sie selbst in ihrem innern Fortgange irgendwo vollendet sein werde” (ibid., 352). Hence, scientific knowledge is an infinite knowing process. It always reaches new results, but these results never reach a level of completeness, because they always have the possibility to be extended just like the skyline always shifts if the observing subject tries to come up to it: “Die Erweiterung der Einsichten in der Mathematik und die Möglichkeit immer neue Erfindungen geht ins Unendliche” (ibid.). This happens because mathematic and natural sciences are developed in a context which is homogeneous. On the one hand, this is their strong point because it is what allows them to continuously advance their knowledge. On the other hand, this is also what prevents them to reach any kind of completeness: “So lange die Erkenntniß der Vernunft gleichartig ist lassen sie von ihr keine bestimmte Grenzen denken” (ibid.). Differently from scientific knowledge, philosophy deals with areas of thought that are not homogeneous. Philosophy searches for the condition of possibility of experience that necessarily need to be different from what is conditioned. The conditions of intelligibility of a certain field of experience cannot share the same features of the field of experience itself. In this sense, philosophy deals with Grenzen, that are not simply negations pertaining to a quantity, but also positive

140 | Luca Illetterati In these definitions, the limits – surface with respect to solid, line with respect to surface, point with respect to line – are not only the locus where something is not, namely the locus where something ceases to be, but also the locus where something starts to be what it is. Starting from Kant’s definitions, Hegel wants to shed light on these two different conceptions of the limit. According to Hegel, the claims that ‘the point is the limit of the line’, that ‘the line is the limit of the surface’ and that ‘the surface is the limit of the solid’ do not have to be meant as if the line appeared (erscheint) as such only out of the point, that surface showed its way of being only out of the line and the solid only out of the surface. This conception of the limit and of what is limited as having their being out of one another, beyond one another, focuses on the aspect of the limit which is sized by pictorial thought (Vorstellung) especially in reference to spatial objects: “it is primarily this aspect of limit which is seized by pictorial thought – the self-externality of the Notion – and especially, too, in reference to spatial objects” (“Dies ist die Seite, von welcher die Grenze zunächst in die Vorstellung – das Außersichsein des Begriffs – fällt, als vornehmlich auch in den räumlichen Gegenständen genommen wird”).³¹ Vorstellung is not able to grasp the essential structure of the limit, namely the fact that, with respect to what is limited, the limit is, however, equally their common distinguishedness, their unity and distinguishedness, like determinate being (ist aber ebenso ihre gemeinschaftliche Unterschiedenheit, die Einheit und Unterschiedenheit derselben wie das Dasein).³²

As a matter of fact, the limit is not something external or something that is other with respect to what is limited. On the contrary, it is its constitutive element. Therefore, coming back to the Euclidean definitions, claiming that ‘the point is the limit of the line’ does not merely mean that in the point the line ceases to be what it is and finds its being only outside of it. It means also that “in the point

determinations that allow us to grasp a certain field of knowledge in its completeness. In Kant’s transcendental dialectic, what is experienced by reason are not only negative limits making the line beyond which reason cannot venture, but Grenzen. In the effort of showing the insuperable difficulties rising from pure reason’s pretense of determining the inherent constitution of the object of transcendental ideas, dialectic gets entangled in contradictions which depend on the nature of human reason itself: what is reached in the conflicting experience of dialectic is the unavoidability of these situations and, in this unavoidability, – this is Kant’s thesis that Hegel is not willing to support – the constitutive limit of human reason. 31 Hegel (1969), 127. (Ger. orig.: Hegel (1968ff.), GW XXI, 114). The term ‘pictorial thought’ is the translation of the German term Vorstellung. The same term was before translated with ‘ordinary thinking’. 32 Hegel (1969), 127. (Ger. orig.: Hegel (1968ff.), GW XXI, 115).

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the line also begins”, namely that point is “absolute beginning” (“absoluter Anfang”)³³ of the line. In this sense limits are not only the locus where something ceases to be what it is, but at the same time “these limits are the principle, of that which they limit” (“diese Grenzen sind Prinzip dessen, das sie begrenzen”).³⁴ By being the determining principle of something determinate, the dialectical development of the limit is lead to the concrete and dynamic articulation of its structure. Insofar as it is the principle of something that is both different and identical to this something, the limit is not only a simple element of something, but also its generative component: [T]hat point, line and plane by themselves are self-contradictory, are beginnings which spontaneously repel themselves from themselves, so that the point, through its Notion, passes out of itself into the line, moves in itself and gives rise to the line, and so on, lies in the Notion of limit which is immanent in the something (Daß Punkt, Linie, Fläche für sich, sich widersprechend, Anfänge sind, welche selbst sich von sich abstoßen, und der Punkt somit aus sich durch seinen Begriff in die Linie übergeht, sich an sich bewegt, und sie entstehen macht u.s.f. – liegt in dem Begriff der dem Etwas immanenten Grenze).³⁵

Limit’s being immanent to the thing itself, namely its belonging to this thing but also to everything that is other than such thing, allows to say that the thing in question, in its limit points beyond itself to its non-being, declaring this is to be its being and thus passing over into it (über sich hinaus auf sein Nichtsein weist und dies als sein Sein ausspricht und so in dasselbe übergeht).³⁶

Limit, in being both a constitutive component of what is limited and something which points beyond itself to its not being, turns out both to be and not to be part of what is limited at the same time and under the same respect. This is why the limit is characterized by a contradictory structure and is defined by Hegel as the unrest of the something (“die Unruhe des Etwas”). The limit is the contradiction

33 Hegel (1969), 128. (Ger. orig.: Hegel (1968ff.), GW XXI, 115). 34 Hegel (1969), 128. (Ger. orig.: Hegel (1968ff.), GW XXI, 115). 35 Hegel (1969), 128. (Ger. orig.: Hegel (1968ff.), GW XXI, 115–116). On the development of the dynamical conception of the limit within Hegel’s thought, on the philosophical roots of this conception especially on Plato’s speculative background and on the implications of this conception in the debate on the infinitesimal method during modern age, see Moretto (1984) and Moretto (1988). 36 Hegel (1969), 127–128. (Ger. orig.: Hegel (1968ff.), GW XXI, 115).

142 | Luca Illetterati inherent in the structure of something, “which impels the something out beyond itself” (“der es über sich selbst hinausschickt”).³⁷ In this way, the dialectical development of the limit brings about the first definition of the finite: [S]omething with its immanent limit, posited as the contradiction of itself, through which it is directed and forced out of and beyond itself, is the finite (Etwas mit seiner immanenten Grenze gesetzt als der Widerspruch seiner selbst, durch den es über sich hinausgewiesen und getrieben wird, ist das Endliche).³⁸

This definition of the finite is meant to show, in Hegel’s view, how the structure of the finite is inherently contradictory, because it has the limit as its determining principle. In this way we have achieved a first conclusion: since everything is what it is in its limit, and since the limit is a contradictory structure, “everything is inherently contradictory”.³⁹ This thesis is stated in the doctrine of essence, but it is first articulated in the doctrine of being, and more specifically in the dialectic of the limit. In this sentence and in the analysis of the limit the meaning of the term ‘contradiction’ is not metaphorical, and it cannot perform the epistemological function of making explicit the limited perspective of the understanding. Rather, contradiction has an ontological value with regards to the structure of every determinate being, or, it could be said, it is the constitutive structure of determinateness itself.

5 What Is the Finite? The conclusions I drew might not be sufficiently convincing for those who claim that the true result of the dialectical movement of determinate being is not the contradiction as constitutive of what is real, but the removal of contradiction itself. In the third remark after the analysis of the determination of contradiction, Hegel explicitly acknowledges that finite things are those very things that are “contradictory and disrupted within themselves”.⁴⁰ This feature of the finite constitutes the transitoriness of the finite, its “non-being”. The main thesis of those interpreters who try to underline how contradiction is only a passing moment of

37 Hegel (1969), 128. (Ger. orig.: Hegel (1968ff.), GW XXI, 115). 38 Hegel (1969), 129. (Ger. orig.: Hegel (1968ff.), GW XXI, 116). 39 Hegel (1969), 439. (Ger. orig.: Hegel (1968ff.), GW XI, 286). 40 Hegel (1969), 443. (Ger. orig.: Hegel (1968ff.), GW XI, 289).

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the dialectical process is that the passage towards the absolute, namely towards the speculative dimension which is the discourse of reason, is the passage towards a dimension of discourse where the contradiction of the finite is finally removed.⁴¹ In other words, in the discourse of reason the contradiction is removed because the main feature of its dimension – the absolute – is precisely the resolution of the contradictory dimension of finitude. In this interpretation the absolute is meant to be the overcoming of the finite since it belongs to a dimension that is radically other than the finite one. The risk implied by this interpretation is falling back into a conception of the absolute affected by the aporia of bad infinity. It is no accident that the analysis of bad infinity follows precisely the analysis of finitude. In effect, bad infinity is a finite infinity, and the first goal Hegel seems to aim at in the infinity section is getting rid of such a limited conception of infinity. In order to better understand this point it is necessary to focus on Hegel’s conception of the finite. Given the conception of the finite arisen from the analysis of the notion of limit, namely the finite as something with its immanent limit, posited as the contradiction of itself, through which it is directed and forced out of and beyond itself, Hegel’s path does not immediately move towards infinity. The achievement of the definition of the finite clears the way for the dialectical development of the so-called finitude (Endlichkeit). In Hegel’s analysis, there seems to be a distinction between the finite (das Endliche) and finitude (die Endlichkeit). On the one hand, the finite, as we have seen, is brought about through the dialectic of limit as the “unrest of the something”, as “the contradiction of itself”. Because of this contradiction, the something in question “is directed and forced out of and beyond itself”. On the other hand, finitude “is the negation as fixed in itself ”, that “stands in abrupt contrast to its affirmative” (“ist die als an sich fixierte Negation und steht daher seinem Affirmativen schroff gegenüber”).⁴² What Hegel calls finitude “is the most stubborn category of the understanding” (“die hartnäckigste Kategorie des Verstandes”).⁴³ This conception of finitude implies an absolute opposition between the finite and infinity. It could be said that what Hegel calls finitude (Endlichkeit) is not the real nature of what Hegel calls the finite (das Endliche). It rather corresponds to the way the understanding fixes the finite (das Endliche). Insofar as finitude is meant to be

41 Berto (2005), 223–224. 42 Hegel (1969), 130. (Ger. orig.: Hegel (1968ff.), GW XXI, 117). 43 Hegel (1969), 129. (Ger. orig.: Hegel (1968ff.), GW XXI, 117).

144 | Luca Illetterati the most stubborn category of the understanding, the limit (Grenze) turns into a limitation (Schranke).⁴⁴ There’s a substantial difference between limit and limitation. The limit – as constituted by the contradictory structure within which only it fully articulates its way of being – could be said to correspond to the way in which reason articulates the separating structure in question. The specific feature of the limit (Grenze) is to belong both to what is limited and to the other of what is limited (the limit is in general what is common to both something and the other), that is to say, to be the structure of the “common distinguishedness” (“gemeinschaftliche Unterschiedenheit”) in which the thing limited and its other both meet and get separated. Instead, the limitation or restriction (Schranke) is the way through which understanding fixes the limit.⁴⁵ Even if the limitation represents a further development of the dialectic of the limit, in this determination the something is still opposed to its other. More precisely, even if the other of what is limited rises from its own movement (and this is the element reached through the dialectic of the limit), this other still stands beyond the something as what the something could never reach, i.e. the Ought: [T]he other of a limitation (Schranke) is precisely the being beyond it (das Andere einer Schranke ist eben das Hinaus über dieselbe).⁴⁶

In the limitation (Schranke), the other of the finite is something that is beyond the finite itself. Therefore, on the one hand the limit is articulated and can be thought of only by making room for the contradiction of the identity and distinction of something and its other. As we have seen, this contradiction is their common generative element. On the other hand, limitation is built on the fixation of the movement which leads the finite to pass over into its other, that is, its not-being.

44 Miller translates the German word Schranke as limitation. Di Giovanni uses ‘Restriction’, others use ‘Barrier’. 45 It must be said that there is a proper intellectualistic account of the limit at the beginning of the dialectic of the limit (Grenze). It is the limit that has not fully developed its inherent and contradictory articulation. It is the first immediate articulation of the limit, according to which limit is simply a separating point, a ‘third’ between something and its other. In such a conception of the limit, the something remains simply external to its other. Instead, in limitation, the other rises from the movement of the something itself, but it is also an other that the something can never reach. Therefore, in a certain sense, there is still a kind of exteriority between the something and its other. This is why I think limitation can still be conceived as an intellectualistic conception of the limiting structure. 46 Hegel (1969), 134. (Ger. orig.: Hegel (1968ff.), GW XXI, 121).

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Therefore, since limit (Grenze) and limitation (Schranke) respectively represents understanding’s and reason’s conception of the limiting structure, it could be said – playing with the terminology Hegel uses in the dialectic of the infinite and more precisely with the distinction between bad and true infinity – that the limit (Grenze) is the true limit, while the limitation (Schranke) is a sort of bad limit. The structure of limitation (Schranke) is characterized by some fundamental features defining the structure of bad infinity.⁴⁷ First, the structure of bad infinity is grounded on the fixed opposition of infinity with respect to the finite as well as the limitation is rooted on a fixed opposition to its Ought. Second, bad infinity is condemned to an undefined and reiterated re-emergence of the finite itself as well as the overcoming of a limitation is condemned to an undefined and reiterated reemergence of another limitation that always and necessarily prevents to touch what is beyond the limitation itself. Finally, as I have already pointed out, bad infinity corresponds to the conception of the limit of the understanding just like limitation can be said to represent an intellectualistic conception of the limit. This is why I think of limitation as essentially connected to bad infinity.⁴⁸ Correspondently, true infinity is essentially connected with the structure of the finite and, moreover, with the structure of the limit at the basis of the finite itself. In fact, true infinity and the limit share crucial and essential features. True infinity is not simply the opposite of the finite or what is beyond the finite. True infinity is the sublation of the finite, but not as the simple negation within which the finite is nullified. Rather, true infinity is the process through which the finite passes over into its other. Therefore, true infinity consists of the contradictory dynamic of such passing over: in being itself the finite ceases to be itself and it is its not-being; but in passing over into its not-being the finite fully realizes itself as finite, or it concretely realizes its finitude.⁴⁹ True infinity, in rising from this very process of the passing over of the finite, is both identical to and different from the being and not-being of determinate being. This contradiction is nothing but

47 The relation to Kant’s conception of Schranken is clear. In fact, Kant’s conception of Schranken and of mathematical and scientific knowledge is such that their development always meets new limitations, new Schranken, in an indefinite process that never reaches any kind of completeness or exhaustiveness. 48 It is important to highlight that just as Schranken and Grenzen are forms of finitude that are distinct, but not completely separated, the infinite of the understanding and the infinite of reason are not two completely different determinations either. They are not two mutually exclusive notions insofar as the true infinite include in itself the bad infinite and, in a certain sense, it is that infinite. 49 “The finite thing is something, or the negation of negation, not as the explicit negation of negation but as the explicit negation of its own being. Here lies the basic contradiction at the core of all finitude – the real contradiction that every finite thing itself is”. Houlgate (2006), 377.

146 | Luca Illetterati a further explicitation of the contradiction of the limit, which is identical to and different from the something and its other.⁵⁰ Therefore, true infinity realizes itself not in the sublatedness of the finite, but in the very unrest of the sublation, namely, in the self-sublating of the finite that is structured on the contradictory dynamic according to which being and not-being of determinate being are both identical and different. This contradiction is the structure of the moment of the passing over of the finite, and it turns out to be the concrete realization of the dynamical and contradictory structure of the limit. The structure of true infinity is based on the unrest of the sublating that is, as we have seen, the true nature of the finite which rises from the dialectic of the limit itself: the articulation of infinity is the proper explication of the limit meant as the constitutive element through which something points beyond itself. If we assume the limit as a structure determined as the unrest of the something, as the absolute contradiction that points beyond itself, it is possible to grasp a fundamental connection between the limit and true infinity (wahre Unendlichkeit). This connection has its basis in the self-contradictory structure that these determinations share. Therefore, on the one hand, the structure of bad infinity mirrors the structure of limitation (Schranke) because both are articulated on the basis of the fixed opposition to their opposite: bad infinity is opposed to the finite, while limitation (Schranke) is understanding’s fixation of finitude with respect to infinity. On the other hand, true infinity (wahre Unendlichkeit) is the concrete development of the structure of the limit (Grenze) and therefore they are inherently related: both are articulated on the basis of the overcoming of the fixed opposition between opposed determinations. True infinity gets realized in the sublation of the abstract opposition between the finite and infinity, while limit is a constitutive structure inherent in the “something”, and it is the locus where this something realizes its being and at the same time is pushed towards its other.

50 In the Jena System (Hegel (1968ff.), GW VII) the true infinity is defined with the same words used in the Science of Logic in order to highlight the structure of the finite: as “absolute contradiction” (“der absolute Widerspruch”) (35, 34), “the absolute unrest of sublating itself (the opposition)” (“die absolute Unruhe, sich selbst (der Gegensatz) aufzuheben”) (34, 36), “being-outsideitself within being-within-itself” (“das Außersichsein in dem Insichsein”) (34, 35) “the simple sublating of the antithesis; it is not the sublatedness” (“das einfache Aufheben des Gegensatzes, nicht das Aufgehobensein”) (36, 37).

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6 Conclusions The limit and the contradictory structure it involves are not elements that are simply removed at the level of speculative discourse, which is the discourse of reason. This level of discourse is not simply placed beyond the discourse of the understanding as well as the dimension of the absolute is not simply a dimension placed beyond the dimension of the finite. The discourse of reason is rather that kind of discourse able to grasp the sublation of those determinations. This means that the discourse of reason is able to grasp the contradictory structure of the unrest of the something (Unruhe des Etwas) without dissolving it. What reason grasps is not the sublatedness, but the sublating of the finite, which is the basic dynamic of both the finite and infinity. From this point of view in the sentence “everything is inherently contradictory” contradiction is neither a mere evocative metaphor, nor a necessary moment through which we need to pass in order to get to the speculative level of discourse where contradiction itself is completely removed. In Hegel’s view, contradiction is a constitutive element of the discourse of reason. In a certain way, this thesis is crucial in contemporary paraconsistent logics too, and more precisely in dialetheism. Dialetheism is the philosophical thesis according to which there are true contradictions – in discourse and in reality. In Hegel’s logic and dialetheism contradiction is not thought of as something to be removed or to be eliminated, but rather as the logical structure able to express essential aspects of reality and thought. Contradiction is the structure through which everything is determined, because contradiction lies at the very basis of determinateness itself. As we have seen, contradiction is the constitutive logical dynamic of the limiting structure through which everything is determined, but also of the articulation of the finite that characterizes every determinate being. Priest is the most important advocate of the dialetheist thesis. His analysis of the articulation of the limit is extremely close to Hegel’s: I walk out of the room; for an instant, I am symmetrically poised, one foot in, one foot out, my centre of gravity lying on the vertical plane containing the centre of gravity of the door. Am I in or not in the room? By symmetry, I am neither in rather than not in, nor not in rather than in. The pure light of reason therefore countenances only two answers to the question: I am both in and not in, or neither in nor not in. [. . . ] If I am neither in nor not in, then I am not (in) and not (not in). By the law of double negation, I am both in and not in.⁵¹

51 Priest (1998), 415.

148 | Luca Illetterati The limit of the room is an example of an ontological contradiction. Its structure is characterized by the same kind of contradiction we meet in Hegel’s logic: when I am in the limit between the room and what is outside of it I am both in the room and not in the room. In this sense, we can wonder whether it is possible to develop a dialetheist explanation of Hegel’s notion of contradiction. The answer seems to be both negative and positive. It is possible to support a dialetheist reading of Hegel’s notion of contradiction insofar as Hegel, just like Priest, claims that some contradictions are true. Nevertheless, there are some crucial differences between Hegel’s and Priest’s approach to contradiction. Here I will focus only on the most important one, concerning the truth value ascribed to contradiction. Priest agues for the thesis of the truth of contradiction by claiming that these true contradictions are dialetheias: “A dialetheia is any true statement of the form: 𝛼 and it is not the case that 𝛼”.⁵² In order to show that some contradictions are true, Priest uses a three-truth-values (V, F, V and F) logical system. True contradictions are logical structures within which each contradictory element is both true and false. This strategy is not applicable to Hegel’s conception of contradiction at all. According to Hegel, contradiction is a principle of determination that cannot be said to be both true and false. Contradiction is simply and radically true because it is the speculative structure of logical-ontological determinations. In this sense, Hegel’s approach to contradiction seems to be even more revolutionary than Priest’s, to which it is not reducible, even if Priest’s account highlights some crucial aspects of it. For this very reason only the thought that does not stop and does not move back in front of contradiction is – in Hegel’s perspective – a thought that can conceive of the reality we experience in its more authentic and vital concreteness. This does not mean that the discourse of reason, insofar as it makes room for a determining and constitutive contradiction that has a true ontological value, is a contradictory discourse condemned to insignificance. A discourse which makes room for true contradictions that are meant to outline the logical dynamic lying at the basis of essential aspects of reality implies a kind of critique to the PNC, and more specifically to the semantic formulation of this principle. According to this formulation, as I have already pointed out, contradiction is necessarily false. Instead, according to Hegel, contradiction can be true insofar as it can be said to be the structure of determinateness itself. Within the linguistic context, true contradictions are expressed by syntactic contradiction, namely, a conjunction

52 Priest (1987), 4.

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of two propositions, one being the negation of the other. It is worth noting that Hegel’s way of conceiving this conjunction is different from the standard one, according to which if a conjunction is true, both the conjuncts are true too. According to Hegel, even if a contradiction is true, the two propositions expressing it – singularly considered – are not. Actually, each one expresses only one part of the whole contradictory structure in question, and therefore it is a necessary but not a sufficient condition for expressing what determinateness is. This is why each proposition is really true only in the conjunction that inherently unites it with the other contradictory proposition. Yet, this does not imply the contradictoriness of the discourse containing this kind of contradictions. Quite the contrary, the possibility to grasp and to make explicit these contradictions presupposes – on the linguistic level – an assumption of the PNC as guarantee of the coherence of any kind of discourse, even of that discourse that wants to express contradictions. In this sense, Hegel’s conception of contradiction can be said to be a non-contradictory conception of the truth of contradiction.⁵³

7 Appendix: A Marginal Digression In the first remark following the analysis of the determination of contradiction, Hegel refers to the relation between light and darkness. When I re-read these lines, the movie Der Himmel über Berlin by Wim Wenders came to my mind. In the remark in question Hegel talks about the opposition between the negative and the positive, and he mentions the example of light and darkness, as he frequently does in the logic. If the two determinations are assumed as fixed determinations, the one is simply the negative of the other, or, in other words, the one is the not-being of the other. In order to bring this fixed exclusion of the opposite terms into question Hegel writes: “it is a familiar fact that light is dimmed to grey by darkness”.⁵⁴ Under an intellectualistic perspective, opposite determinations are conceived as mutually exclusive. Instead, grey shows how they encounter and, in this very encounter, how they don’t get nullified. They rather give rise to a new determination, which involves both of them even in their being negated. Nevertheless, grey is not a real unity of opposite determinations. Grey – Hegel says – is a merely quantitative alteration. The encounter of darkness and light gives rise also to an alteration that Hegel defines as qualitative:

53 The thesis of the non-contradictory conception of contradiction has been developed by Chiereghin (1981), 257–270 and Chiereghin (2004). 54 Hegel (1969), 437. (Ger. orig.: Hegel (1968ff.), GW XI, 284).

150 | Luca Illetterati Besides this merely quantitative alteration it suffers also the qualitative change of being determined to colour by its relation to darkness.⁵⁵ Hegel’s reference in these lines is implicit but evident, namely, Goethe’s theory of colours. Hegel studied this theory, which plays an important role in his philosophy of nature. In the Theory of Colour Goethe claims that colour doesn’t arise from the dispersion of white light, as Newton thought. Colour has its origin in the encounter of light and darkness within a medium, which is the eye. In the point where light meets darkness something rises, and this something is neither light nor darkness, nor the simple mix of the two. This is what reminded me of Wim Wenders’ movie. In this movie the limit, meant as the locus within which the contact between light and darkness gives rise to colour, is the world of human beings, namely, the world concretely experienced by men and women. Men and women do not live in the pure light, or in the deepest darkness. Living in the pure light or in the deepest darkness is an experience that can be thought of only by an abstract thinking. Men and women do not live in that kind of grey mix of light and darkness either. In Wenders’ movie this grey mix dimension corresponds to the world of angels. The core issue of the movie is the story of an angel and of his meeting with the world of humans. The movie camera’s perspective corresponds to the eye of the angel, especially in the first part of the movie. The world of men and women flows as if it was something separated from this perspective. Reality appears to the angel’s eyes as something lacking concrete time, or, better said, as something immerged in a timeless and lifeless movement, i.e. a spatial movement lacking every kind of qualitative determination. Moreover, it could be said that the angel can see movement, but he cannot feel it. Looking at the screen through the angel’s eyes is watching (the) frames of a colourless world, a world in black and white, a world made of grey nuances. That is a world without pauses, a timeless world which flows as something strange and unfamiliar with respect to the eye watching it. The world is seen as coloured only when the framing represents human being’s perspective. Anyway, at a certain point even the angel’s eye gets to see colours. This happens just for a moment, when, for the first time, he looks at the body of a woman, a trapeze artist, who looks like a human angel. In this moment, the angel feels desire. According to Hegel, desire is an experience radically marked by contradiction. Through this very experience the angel lives a wholly human experience. Only this concrete experience of lack and laceration allows the angel to see colours. In the experience of desire the angel renounces its own nature and becomes a man. By renouncing himself in order to get into time, he renounces the aseptic timeless dimension within which he lived as an angel. By renouncing himself in order to get into history, he renounces an unstoried infinity characterizing his dimension. The angel decides to take on the weight of a body, which leaves traces on earth. He abandons the bird’s-eye view that allowed him to view everything from an external perspective. Now he looks at everything with a human’s eye. The angel chooses a mortal life. He decides to let himself go to the concrete experience of the world, that is an experience where time is time, body is body and desire is desire. Until the angel remained an angel he lived beyond any effort and struggle, beyond any pain and any

55 Hegel (1969), 437. (Ger. orig.: Hegel (1968ff.), GW XI, 284).

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distress. Nevertheless, this “being beyond” was what made it impossible for him to experience joy, which is to experience sharing and to experience love. He chooses that very experience made of contradictions, which is real life. Der Himmel über Berlin ends with a message, which is a wonderful image reminding of the beginning of the movie. In that image there is a hand that is writing. It is the angel’s hand after having become a man. He is writing these words:

Ich weiss jetzt, was kein Engel weiss. I now know what no angel knows. What is this something that is known now by the angel and that he did not know before? When the angel roams around and listens to the thought of humans, he already knows that the world of men and women is a world of struggle, of laceration, of suffering; but once he gets into it he then knows what this struggle and pain means. Only when he gets into this world he realizes that the world of humans is the world where what is other is really the other, namely a world where other people can be someone I meet and someone whose hand I can shake and feel each other’s warmth. The world of humans is a world where there are no indifferent choices, because choices are always real choices. The angel gets to know the world of life, the world of humans that is not a world in black and white but a world full of colours. Such coloured world cannot be felt and thought out of contradiction. Therefore, contradiction is not a sign of a malediction, of damnation and of a downfall. Contradiction is somehow the sign of life itself, of the world where touching means to touch, feeling means to feel, suffering means to suffer and love means to love. Hegel seems to say that men and women try everything to hide contradiction. They don’t realize that hiding contradiction is hiding the possibility of life itself, or at least the possibility of that coloured life which is the life that we concretely experience.

References Aristotle, Metaphysics, translated by W. D. Ross, Oxford, 1928. E. Berti (ed.), La contraddizione, Milan, 1977a. E. Berti, “La contraddizione in Aristotele, Kant, Hegel e Marx”, in: E. Berti (ed.), La contraddizione, Milan, 9–31, 1977b.

152 | Luca Illetterati E. Berti, “La critica di Hegel al principio di non contraddizione”, in Filosofia 31, 629–654, 1980. E. Berti, Logica aristotelica e dialettica, Bologna, 1983. E. Berti, Contraddizione e dialettica negli antichi e nei moderni, Palermo, 1987. F. Berto, Che cos’è la dialettica hegeliana. Un’interpretazione analitica del metodo, Padua, 2005. F. Berto, “Hegel’s Dialectic as a semantic Theory”, in: European Journal of Philosophy 15, 19– 39, 2007. R. Brandom, “Holism and Idealism in Hegel’s Phenomenology”, in: Tales of the Mighty Dead: Historical Essays on the Metaphysics of Intentionality, Cambridge, 178–209, 2002. F. Chiereghin, “Incontradditorietà e contraddizione in Hegel”, in: Atti del convegno di Padova (maggio 1980), Padua, 257–270, 1981. F. Chiereghin, L’eco della caverna. Ricerche di filosofia della logica e della mente, Padua, 2004. L. Colletti, “Contraddizione dialettica e non contraddizione”, in: Atti del convegno di Padova (maggio 1980), Padua, 7–62, 1981. K. de Boer, “Hegel’s Account of Contradiction in the Science of Logic Reconsidered”, in: Journal of the History of Philosophy 48, 345–373, 2010. J. N. Findlay, Hegel: A Re-examination, London, 1958. H. F. Fulda, “Unzulängliche Bemerkungen zur Dialektik”, in: R. Reede, J. Ritter (eds.), Hegel Bilanz, Frankfurt a. M., 231–262, 1973. F. Gregoire, Études Hégélienne, Les points capitaux du système, Louvain and Paris, 1958. G. W. F. Hegel, Gesammelte Werke. Ed. Rheinisch-Westfälische Akademie der Wissenschaften and Hegel-Archiv der Ruhr-Universität Bochum, Hamburg (quoted as GW, followed by the indication of the volume and page), 1968ff. G. W. F. Hegel, Science of Logic, transl. by A. V. Miller, London, 1969. N. Hartmann, “Hegel et le problème de la dialectique du réel”, in: Revue de Métaphysique et de Morale 38, 314–315, 1931. R.-P. Horstmann, “Schwierigkeiten und Voraussetzungen der dialektischen Philosophie Hegels”, in: R. P. Horstmann (ed.), Seminar: Dialektik in der Philosophie Hegels, Frankfurt a. M., 9–32, 1978. S. Houlgate, The Opening of Hegel’s Logic, West Lafayette, 2006. I. Kant, Kant’s Werke. Akademie-Textausgabe. Unaltered photocopy reprint of the text from the publication series of Kant’s complete works initiated by the Prussian Academy of Sciences, Berlin (quoted as KW, followed by the indication of the volume and page), 1968. D. Marconi, Contradiction and the Language of Hegel’s Dialectic. A Study of the Science of Logic, Pittsburgh, 1980. J. McTaggart, Studies in the Hegelian Dialectic, Ontario, 2000. A. Moretto, Hegel e la “matematica dell’infinito”, Trent, 1984. A. Moretto, Questioni di filosofia della matematica nella “Scienza della logica” di Hegel. “Die Lehre vom Sein” del 1831, Trent, 1988. A. Nuzzo, Hegel and the Analytic Tradition, London and New York, 2010. K. Popper, Conjectures and Refutation, London and New York, 2002. G. Priest, In Contradiction. A Study of the Transconsistent, The Hague, 1987. G. Priest, “What is so bad about contradiction?”, in: The Journal of Philosophy 95,410–426, 1998.

Klaus Vieweg

Zur Logik moralischer Urteile Das Kernanliegen der folgenden Überlegungen besteht darin, die Relevanz der Hegelschen Logik, speziell seines Verständnisses von Widerspruch und Antinomie, für die praktische Philosophie, hier für die Moralität als der zweiten Form im Stufengang der Hegelschen Rechtsphilosophie zu verdeutlichen.¹ Der Fortgang in drei Stufen – abstraktes Recht, Moralität, Sittlichkeit – bedeutet keinesfalls, dass die Sittlichkeit als dritte Stufe ,der Zeit nach etwas Späteres‘ darstellt als Recht und Moralität. Die Sittlichkeit wird sich vielmehr als Grundlage des Rechts und der Moralität erweisen (RPh § 81, A)², im systematischen Fortschreiten erfolgt die Legitimation des Anfangens.

1 Die Moralität oder die Freiheit des moralischen Subjekts Im Kapitel Moralität der Grundlinien der Philosophie des Rechts wartet Hegel mit einer subtilen Fortbestimmung der Begriffe Wollen und Handeln auf, mit der Prüfung, welches Wollen und Handeln einem freien Wesen angemessen und daher als ,gut‘ zu bewerten ist, mit einer Konzeption des moralischen Urteilens. Nachdem in der Personalität das Dasein der Freiheit im Bezug auf eine äußerliche Sache lag, geht es jetzt um den ,in sich reflektierten Willen‘, um die innere Willensbestimmtheit, worin der Wille notwendig auch als besonderer gedacht werden muss.³ Die Binnenperspektive des Subjekts, die Willensbestimmtheit des moralischen Akteurs kommt teils als die innerliche Zuschreibung, im Setzen der Bestimmungen als den seinigen, und teils als tätliche Äußerung, als Handlung zum Tragen: das Subjekt anerkennt nur das, lässt sich nur das zurechnen, was es

1 Ausführlich zur logischen Grundlegung von Hegels praktischer Philosophie: Vieweg (2012). Dieser Aufsatz ist eine gekürzte Passage aus dem Kapitel der Monographie über die Moralität. 2 RPh bezieht sich im Folgenden auf die Grundlinien der Philosophie des Rechts, Hegel (1969ff.), TW Bd. 7; RPh, A bezieht sich auf die eigenhändigen Zusätze Hegels zu den einzelnen Paragraphen, RPh, Z auf die Zusätze aus Nachschriften von Vorlesungen. 3 Die innovative Bedeutung sowie die logische und praktisch-philosophische Mittelposition der Moralitätslehre hebt schon Rosenkranz (1844), 331, hervor: „Der Begriff der Moralität, der früher in die übrigen Begriffe absorbirt war, ist selbständig als die Mitte zwischen dem abstracten Recht des Einzelnen und dem concreten Recht des Staates zum Wesen der ganzen Sphäre des objectiven Willens gemacht.“

154 | Klaus Vieweg in sich gewusst und gewollt hat (Enz § 503).⁴ Auch hier wäre Hegels Absicht an den Anfang zu rücken, dass praktische Philosophie eine logische Grundlegung benötigt, nur insofern ist sie angemessen als eine Handlungsphilosophie, als eine philosophische Handlungstheorie zu beschreiben. Auf die Problematik der Logizität des freien Willens und Handelns soll spezielles Hauptaugenmerk gelegt werden, wie in den anderen Passagen stellt sich diese Freilegung des logischen Koordinatensystem auch hier als eine entscheidende Aufgabe für die Interpretation der Grundlinien.⁵ Es handelt sich um eine theoretische Herausforderung, die bis heute trotz einiger wichtiger Beiträge als weitgehend unerledigt gilt.⁶ Der Aufweis dieser Grammatik muss beinhalten, inwiefern den Stufen des moralischen Willens und Handelns in besonderer Weise die logischen Formen des Urteils zugrunde liegen – die philosophische Theorie der Moralität hat ihre Tiefenstruktur in der Urteilslogik. Die in der Anmerkung zu RPh § 114 erwähnte logische Stützung des Weges der Moralität hilft beim Erschließen der Leistungen und Begrenzungen des moralischen Standpunkts, der Feststellung seines speziellen Rechts⁷, seiner Berechtigung, der Reichweite seiner Geltung: so werden unmittelbares Urteil, Reflexionsurteil und Begriffsurteil unterschieden. Auf dieser Dynamik der Urteilsformen ruht das Aufsteigen der Bestimmungen der Moralität in ihren drei Wegmarken.⁸

4 Enz bezieht sich im Folgenden auf die Enzyklopädie der philosophischen Wissenschaften, Hegel (1969ff.), TW Bd. 8 bis 10. 5 Henrich (1982), 428–450. 6 Wichtige Beiträge hierzu lieferten Schick (2002), Quante (1993) und James (im Erscheinen). Der Verf. dankt Herrn Daniel James für die Möglichkeit der Nutzung der Studie. Der Position von Pippin (2008), 169, dass mit dem Moralitäts-Kapitel keine unabhängige Diskussion von Hegels Theorie der Handlung vorliegt wäre zuzustimmen, die sittliche Dimension ist konstitutiv für die höchste Bestimmung des Handlungsbegriffs. 7 Die „Moralität hat auch ihre Rechte“. Hegel (2005), 103. 8 „Das Urteil ist die Diremption des Begriffs durch sich selbst; diese Einheit ist daher der Grund, von welchem aus es nach seiner wahrhaften Objektivität betrachtet wird. Es ist insofern die ursprüngliche Teilung des ursprünglich Einen“, das „ursprüngliche Teilen des Begriffs“. Hegel (1969ff.), TW 6, 304, 306.

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2 Die drei Stufen des Rechts des moralischen Willen (die drei Momente der Moralität) – § 114 a) Der Vorsatz und die Schuld Das abstrakte Recht der Handlung, ihr unmittelbares Dasein und ihr Inhalt als der Meinige unmittelbares Urteil

b) Die Absicht und das Wohl Das Besondere der Handlung als ihr innerer Inhalt, Reflexionsurteil b1) der Wert der Handlung für mich und wonach sie für mich gilt (Absicht) b2) der Inhalt der Handlung als mein besonderer Zweck meines partikularen Daseins (Wohl)

c) Das Gute und das Gewissen Der Inhalt der Handlung in seiner Allgemeinheit, als in die an und für sich seiende Objektivität erhoben – das Gute als absoluter Zweck des Willens, in der Sphäre der Reflexion mit dem Gegensatze der subjektiven Allgemeinheit, teils des Bösen, teils des Gewissens Begriffsurteil Die zugrunde gelegte Urteilslehre der Wissenschaft der Logik enthält keine bloße Aufzählung verschiedener Weisen des Urteilens, sondern die Fortbestimmung der Urteile als ,notwendig auseinander folgend, als ein Fortbestimmen des Begriffs, insofern kann das Urteil als der bestimmte Begriff angesehen werden‘.⁹ Die parallele, kombinierte Berücksichtigung der Logik des Urteils und der Logik des Zwecks ist deswegen erforderlich, da moralisches Handeln zureichend nur als logische Einheit von Subjektivität, der Urteilslogik, sowie der Objektivität, der Logik des Zwecks, erschlossen werden kann.

9 In Bezug auf das Verbrechen wurde dieses Verfahren schon praktiziert, daran kann direkt angeschlossen werden. Behandlung des Eigentums § 53: ,Urteil des Willens über die Sache‘ und Enz § 171.

156 | Klaus Vieweg Der spezifische Zusammenhang des Standpunkts der Moralität und der Urteilslogik geht aus der Charakteristik der moralischen Subjektivität hervor, die als ,urteilende, d. h. ursprünglich teilende Macht, die alles zerlegt und besondert‘, auftritt. Es geht um die Besonderung des Ich und die Unterscheidung der Willensformen. Zudem wäre wiederum auf Hegels Verständnis von ,Urteil‘ im Sinne der ursprünglichen Teilung zu erinnern: das Urteil wird zum Inbegriff der Trennung, des Widerspruchs und des Gegensatzes.¹⁰ Die gesamte Sphäre der Moralität stellt die Kollision, den Widerspruch der Besonderheit gegen die Allgemeinheit dar. Beim Ur-Teilen wird den Dingen, den ,Sachen‘ ein ihnen eigenes, besonderes Prädikat zugemessen, im Sinne des Zerlegens des ursprünglich Einen in ein in sich Unterschiedenes. Zugleich ist die Besonderheit des Wollens auf die Objektivität bzw. Allgemeinheit bezogen, es geht somit um das sich fortentwickelnde Verhältnis der Besonderheit zur Allgemeinheit (B zu A). Dies impliziert den Standpunkt der Moralität als Standpunkt des Verstandes, der Reflexion, der Relation, des Sollens, der Forderung, der Erscheinung des Willens. Wir bewegen uns im Terrain der Logik des Wesens und auf dem Standpunkt der Subjektivität und Objektivität, auf dem Standpunkt der moralischen Urteilskraft, der Differenz, der Endlichkeit und Erscheinung des Willens. Nachdem Hegel in seiner logischen Urteilslehre die grundsätzliche Form des Urteils bestimmt hat, würdigt er das Verdienst von Kant, eine logische Einteilung der Urteile nach dem Schema einer Kategorientafel vorgenommen zu haben. Trotz der Unzulänglichkeit dieses Schemas liegt diesem doch die Einsicht zugrunde, dass „es die allgemeinen Formen der logischen Idee selbst sind, wodurch die verschiedenen Arten der Urteile bestimmt werden“. Entsprechend der Hegelschen Logik sind „drei Hauptarten des Urteils zu unterscheiden, welche den Stufen des Seins, des Wesens und des Begriffs entsprechen“ (Enz § 171, Z). Hier kann eine Stufenfolge der ,praktischen Urteile‘ entfaltet werden, d. h. der Urteile, die sich auf Handlungen beziehen – Hegel Urteilstafel als System praktischer Urteile.¹¹ Für ein leichteres Nachvollziehen der folgenden Schritte erscheint eine solche an der Logik orientierte Übersicht über die praktischen Urteilsformen (inklusive entsprechender Beispiele) von Vorteil. § 114 fixiert die grundsätzliche Struktur des Rechts

10 Sans (2006), 219, verweist zu Recht auf Enz § 166: „Die etymologische Bedeutung des Urteils in unserer Sprache ist tiefer und drückt die Einheit des Begriffs als das Erste und dessen Unterscheidung als die ursprüngliche Teilung aus, was das Urteil in Wahrheit ist.“ Vgl. auch Sans (2004). 11 Vgl. dazu: Vieweg (2012), Kapitel zur Moralität. Vgl. dazu auch: Quante (2008). Hegels Konzept der Imputation bezeichnet Quante dort als „cognitivist ascriptivism“ (ebd., 226); aufschlussreich auch Quantes „Hegel’s map of our ascriptive practices“ (ebd., 224).

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des Moralischen, die „Bewegung des Urteils“ (WdL 6, 309),¹² die drei Stufen der Imputation durchläuft.

3 Das Gute und das Gewissen – Der gute Wille und das gute Handeln Der Gegenstand – das Handeln – wird in Relation auf den Begriff betrachtet, in Bezug auf seinen Begriff, nämlich der Freiheit als dem Begriffsinhalt des Handelns. Hierin wird der Transfer zu praktischen, normativen Urteilen vollzogen. Das Prädikat ,gut‘ drückt aus, dass „die Sache [das jeweilige Handeln] an ihrem allgemeinen Begriffe [Freiheit] als dem schlechthin vorausgesetzten Sollen gemessen und in Übereinstimmung mit demselben ist oder nicht“ (WdL 6, 344). Dieses ,Gemessen-Werden‘ bedeutet das Fällen eines normativen Urteils: Eine bestimmte einzelne Handlung wird geprüft und bewertet, ob sie als ,gut‘ gelten kann oder nicht, ob sie ihrem Begriff angemessen ist oder nicht. „Wenn wir sagen: »diese Handlung ist gut«, so ist dies ein Urteil des Begriffs [. . . ] das Prädikat [ist] gleichsam die Seele des Subjekts, durch welche dieses, als der Leib der Seele, durch und durch bestimmt ist“ (Enz § 172 Z). Die Kopula ,ist‘ und das für das Handeln wahrhafte Prädikat ,gut‘ enthalten die Bedeutung der Angemessenheit mit dem Begriff, die Form ,ist nicht gut‘ die der Unangemessenheit. Der Begriff der Handlung – frei zu sein – gewinnt jetzt eine zweite fundamentale Bestimmtheit: Freies Handeln muss nicht nur rechtens (gemäß dem formellen Recht), nicht nur eine Einheit von Intention und Aktion darstellen, sondern muss auch als gut bewertbar sein. Ein Spaziergang, das Gehen in eine Eisdiele, das Werfen eines Glases von einem Tisch, das Einschalten einer Kaffeemaschine oder das Backen einer Pizza sind nicht per se als Handeln zu klassifizieren.¹³ Die Handlung muss als ,der Beurteilung unterworfen‘ gedacht werden, der Beurteilung der eigenen und der Handlung anderer (RPh § 124 A). Auf die folgende Struktur des Begriffsurteil, der höchsten Form des Urteilens, soll im Blick auf Widerspruch und Antinomie besondere Aufmerksamkeit gerichtet sein: Die drei Stufen des Begriffsurteils bilden a) das assertorische Urteil, verbunden mit unmittelbarem Wissen und praktischem Dogmatismus; b) das problematische Urteil, welches zu Isosthenie, Antinomie, Urteilsenthaltung und prakti-

12 WdL bezieht sich im Folgenden auf die Wissenschaft der Logik, Hegel (1969ff.), TW Bd. 5 bis 6. Die Angaben verweisen auf Band und Seitenzahl. 13 In manchen analytischen Handlungstheorien werden häufig solche insuffizienten Beispiele für Handlung benutzt.

158 | Klaus Vieweg schem Skeptizismus führt und c) das apodiktisches Urteil, dessen Muster der kategorische Imperativ darstellt. Jeder Versicherung in einem assertorischen Urteil steht mit „eben dem Rechte die entgegengesetzte gegenüber“ (WdL 6, 347), was die Isosthenia und die Epoché, den Suspens des Urteilens nach sich zieht, dann liegt problematisches Urteil vor. Die Allgemeinheit der Handlung muss zusammen mit ihrer Beschaffenheit, ihrer besonderen Einzelheit, gedacht werden. Das Subjekt – Handlung – wird in die Allgemeinheit oder objektive Natur (das Sollen) und in die besondere Beschaffenheit des Daseins unterschieden und es ,enthält somit den Grund, ob es so ist, wie es sein soll‘. Die Teilung des Allgemeinen und Besonderen (welche das Urteil selbst ist) verweist hier auf ihre an sich bestehende Einheit in der Einzelheit, auf den Begriff.¹⁴ Die Beurteilung ,gut‘ verlangt die Berücksichtigung der Modalität des Handelns.¹⁵ Dies erfordert den Übergang zum apodiktischen Urteil, als dessen Modell Kants kategorischer Imperativ gilt.

4 Der kategorische Imperativ und das apodiktische Urteil Als logisches Fundament der Kantischen Moralitätsauffassung diagnostiziert Hegel das apodiktische Urteil, es fungiert zugleich als Übergangsform vom Verstand zur Vernunft, von der Reflexion zum begreifenden Denken. Kants kategorischer Imperativ kommt aus der Perspektive seiner Fundierung im Begriffsurteil und als Transformationsstufe zur logischen Form des Schließens in den Blick.¹⁶ Zuerst einige Anmerkungen zur betreffenden logischen Struktur E–B–A: Die eine einzelne (partikulare) Handlung – ,Handle so . . . ‘ – leitenden Gründe besonderen Handelns – ,Maximen deines Handelns‘ – sollen der Allgemeinheit gemäß sein, sollen als Prinzip einer allgemeinen Gesetzgebung gelten können. Die ,objektive Parti-

14 Hegel (1969ff.), TW 6, 348. „Die Sache selbst ist eben dies, daß ihr Begriff als die negative Einheit seiner selbst seine Allgemeinheit negiert und in die Äußerlichkeit der Einzelheit sich heraussetzt.“ Die Feststellung des Gut-Seins einer Handlung verlangt die Anstrengung des Begriffs, das Denken des Verhältnisses von Allgemeinheit, Besonderheit und Einzelheit, die Einschätzung Güte des Handelns entspringt keineswegs bloß aus Gefühlen oder Intuitionen. Ethiken, die ihr Fundament in Empfindungen, Gefühlen oder Intuitionen sehen, bewegen sich von vornherein auf brüchigem Eis und vertreten relativistische Positionen. 15 Hegel versteht Modalität allerdings nicht nur als Bestimmung der subjektiven Stellung des Denkens zu einem Sachverhalt wie Kant, sondern als interne Qualifikation des Verhältnisses von Einzelheit, Besonderheit und Allgemeinheit. Vgl. hierzu Schick (2002). 16 James (im Erscheinen), 51ff.

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kularität (E) an dem Subjekt gesetzt‘, seine Besonderheit als die ,Beschaffenheit seines Daseins‘ ist gut oder nicht gut. Die partikulare, unmittelbare Einzelheit (E) der Handlung (A) findet ihren sprachlichen Ausdruck im indexikalischen ,diese‘, die Besonderheit in der Rede vom ,So und so Beschaffensein‘, der Beschaffenheit des Daseins der Handlung.¹⁷ Die jetzt erreichte logische Binnenstruktur des Begriffs ,Handlung‘ lässt sich in einer Weise fassen, die ungeachtet der fortbestehenden Ur-Teilung schon die konkrete Identität des Begriffs ,Handeln‘ antizipiert: Handlungen sind eine, in der Freiheit ihre Bestimmung und ihren Zweck habende Gattung in einer einzelnen Wirklichkeit und von einer besonderen Beschaffenheit.¹⁸ Obschon sich der Begriff potentiell als Einheit seiner Momente und die Kopula, die Verbindung sich kraft ihrer ,Erfüllung‘ in die logische Form des Schlusses zu wandeln beginnt, verbleiben Besonderheit und Allgemeinheit und ihr Verhältnis unzulänglich bestimmt. Die Idee als des Guten, als Einheit des Begriffs des Willens und des besonderen Willens hat noch den Status einer Relation, noch nicht den gesetzter Identität. Das Gute hat somit die Struktur der Idee, aber von Begriff und Realität wird erst die Einheit gefordert, gesollt, die Einheit soll sein – das ,imperative‘ Paradigma. Das Prädikat ,gut‘ drückt aus, dass „die Sache an ihrem allgemeinen Begriffe als dem schlechthin vorausgesetzten Sollen gemessen und in Überstimmung mit demselben ist oder nicht“ (WdL 6, 334).¹⁹ Insofern die Idee des Guten noch abstrakt ist, besteht nur ein Sollen der Gemäßheit, der subjektive Wille soll dies sich zum Zwecke machen und vollbringen, zugleich kann das Gute nur mittels der subjektiven Willen in Wirklichkeit treten. Die Besonderheit steht in einem Sollensbezug, in einem Verhältnis zum Allgemeinen, sie ist ,noch nicht gesetzt‘ (RPh § 131, A). Das Recht der Einsicht in das Gute unterscheidet sich vom Recht der Einsicht in Bezug auf die Handlung als solche, thematisiert wird eine höhere Stufe der Einsicht, welche die Begrenzung der Moralität anzeigt und auf die Sittlichkeit vorgreifen muss: Das Respektieren des Rechtes der Objektivität impliziert die Anerkennung der Gesetze der wirklichen Welt, natürlich nur dann, wenn diese dem 17 ,Die Handlung so und so beschaffen ist gut‘. Hegel (1969ff.), TW 6, 349. 18 Das apodiktische Urteil gilt Hegel als ,wahrhaft objektiv‘, als ,die Wahrheit des Urteils überhaupt‘. „Subjekt und Prädikat entsprechen sich und haben denselben Inhalt, und dieser Inhalt ist selbst die gesetzte konkrete Allgemeinheit; er enthält nämlich die zwei Momente, das objektive Allgemeine oder die Gattung und das Vereinzelte. Es ist hier also das Allgemeine, welches es selbst ist und durch sein Gegenteil sich kontinuiert und als Einheit mit diesem erst Allgemeines ist“. Hegel (1969ff.), TW 6, 349. 19 Das apodiktische Urteil strengt „den Vergleich von Begriff und Sache auf der Grundlage der gewußten wirklichen Beschaffenheit an“. Schick (2002), 220.

160 | Klaus Vieweg Begriff der Freiheit genügen. Man darf von einem speziellen Recht, vom ,Recht des Subjekts‘ sprechen, die Handlung in der Bestimmung des Guten oder Bösen, des Gesetzlichen und Ungesetzlichen zu kennen‘ (RPh § 132). Hier haben wir es mit der ,dritten Zurechnungsfähigkeit‘ zu tun, mit dem Bezug zum Wissen des Guten: „nicht wie ich fühle – sondern weiß – Freiheit, Subjektivität im Wissen“ (RPh § 132, A). Hegels Grundlinien sprechen vom absoluten und unendlichen Recht des Wissens vom Guten – ein Recht des Wissens, was gut ist²⁰ – das Recht des Vernünftigen als des Objektiven und somit denkend Geprüften. Insofern kann das Gute als ,das Wesen des Willens in seiner Substantialität und Allgemeinheit‘ (RPh § 132) beschrieben werden. Daraus erwächst die Möglichkeit der Differenz zwischen dem Recht des subjektiven Willens (B) – der subjektiven Bildung – und diesem Allgemeinen (A); sie können in Widersprüche und Konflikte miteinander kommen. Es ist nur etwas gut, wenn es vom subjektiven Willen als berechtigt eingesehen wird, zugleich hat sich das Recht des Objektiven etabliert. Dieses Objektive darf aber nicht mit dem gerade Bestehenden und gerade Geltenden verwechselt werden.²¹ Wie das Ich als partikulare Besonderheit irren kann, so auch die bestehenden besonderen Gesetze und Regierungen (RPh § 132). Das Gute fungiert nur dann als Prüfstein für jegliches Handeln, insoweit es der Wille in seiner Wahrheit ist, insofern es sich im und durch das Denken legitimiert. § 133 der Grundlinien verhandelt das Verhältnis zwischen einer einzelnen Handlung (E) in ihrer Besonderheit (B) zum Guten als dem Allgemeinen (A), das Gute soll das Wesentliche des Handelns sein, dessen unbedingte Verpflichtung. Die Maxime als Legitimationsprinzip meines besonderen Handelns soll als objektives Prinzip, als ,allgemeines Gesetz‘ Geltung beanspruchen können. Die dem kategorischen Imperativ eingeschriebene Struktur der Beziehung von E–B–A entspricht der Verfasstheit des apodiktischen Urteils bei Hegel: ,Diese Handlung (unmittelbare Einzelheit – E), die so und so beschaffen ist (Besonderheit – B), ist gut (Allgemeinheit – A)‘ (Enz § 179). Der Charakter des Imperativs besteht darin, dass die Allgemeinheit dasjenige ist, was unbedingt sein soll. In der Beschaffenheit, in der Maxime der Handlung, die eine solche unbedingte Forderung erfüllen muss, hat das Urteil seinen Grund. Dieses Besondere, das ,So und so Verfasstsein‘ bildet das Kriterium dafür, ob diese Handlung ihrem Begriffe entspricht oder nicht. Den Kerngedanken sieht Hegel in der vom apodiktischen Urteil erreichten Identität von E, B und A fundiert. Es handelt sich um das alleinige (einzige und allen

20 Hegel (2005), 129. 21 Der höchste Maßstab ist die Idee des Staates, nicht das positive Recht, der Staat als die „Objektivität des Vernunftbegriffs“ (§ 132).

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gemeinsame) Gesetz, das sich jedes Subjekt frei und mit Vernunft selbst auferlegt und dem es aus Vernunft beipflichten kann. Es wird kaum überraschen, dass von Hegel die Gründung in der Vernunft besonders betont wird, die Fundierung in the autonomy of reason. Während die erste Zurechnung auf der Vorstellung, die zweite auf Reflexion und Verstand beruhte, fußt die ,dritte Imputation‘, die dritte Weise der Zurechnungsfähigkeit, auf der Kenntnis um das Gute: ,dass ich weiß, ob dieses Tun, diese Handlung gut oder böse ist‘. Diese dritte Form basiert somit ausdrücklich auf dem Denken, auf dem Begriffsurteil, das selbst den Übergang vom Verstand zur Vernunft anzeigt. Das apodiktische Urteil überwindet die Einseitigkeiten des assertorischen wie des problematischen Urteils, des dogmatischen Urteils der Art ,Diese Handlung ist gut‘ und ebenso die Beschränktheit der Urteilsenthaltung. Erst dem apodiktischen Urteil liegt der Begriff als Begriff zugrunde. Das assertorische Urteil hingegen beinhaltet die Setzung der allgemeinen Natur des Begriffs, dies aber in Gestalt der Willkür des Versicherns, in Form eines Subjektivismus des Postulierens und bloßen Behauptens. Das assertorische und das problematische Urteil fixieren dagegen die negative Seite des Begriffs und führen in das Dahingestelltseinlassen des Urteils. Insofern zwei Assertionen kontradiktorisch gegenüberstehen, tritt ein Verfahren ein, welches ,auf gelegentliche Veranlassung die eine oder die andere Maxime anwendet, je nachdem sie für gegebene Objekte für passend gehalten werden und nach der Wahrheit eben nicht gefragt wird‘ (WdL 6, 443). Der Begriff der Handlung bleibt so unterbestimmt und einseitig. Woran genau soll sich die Besonderheit orientieren? Was heißt ,allgemeines Gesetz‘? Laut Hegel bewegt sich dieses Allgemeine oder Vernünftige bei den Protagonisten der höchsten Stufe der Moralität der Form nach auf der Ebene des Begriffsurteils, somit auf der Höhe des Urteils des Begriffs, was eine positive und negative Konnotation hat. Eine konkrete Handlung kann erst jetzt eine wahrhafte Beurteilung erfahren, sie wird erst jetzt an ihrem Begriff gemessen: ,Das Schenken des Holzpferdes ist gut‘ – ,Das Fehlinformieren des Polizisten ist schlecht‘.²² Als Subjekt firmiert ein konkretes, unmittelbar Besonderes, das ,zum Prädikat die Reflexion des besonderen Daseins auf sein Allgemeines hat‘ (Enz § 178). Die Besonderheit, die konkrete einzelne Handlung – das Schenken des Holzpferdes, das Fehlinformieren des Polizisten – figuriert nur als Besonderung der Art und als negatives Prinzip der Gattung, d.i. die Besonderheit ist auch gleichgültig gegen das Allgemeine und kann der Allgemeinheit angemessen sein oder auch

22 Urteile wie „Diese Katze ist grau“ oder „Dieser Tisch ist groß“ sind selbstverständlich keine assertorischen Urteile.

162 | Klaus Vieweg nicht, B kann A gemäß sein oder eben nicht.²³ Am Subjekt (an diesem Schenken, an diesem Informieren) ist die Bestimmtheit noch nicht gesetzt, nicht die Beziehung von B zu A, welche somit erst nachträglich im Prädikat ausgedrückt werden muss. Kann das Schenken eines Holzpferdes als dem Prinzip des Allgemeinen gemäß, somit schlechthin als gut eingeschätzt sein? Die ,Bewährung‘ des gefällten Urteils hat nur den Status einer Versicherung, einer Assertion, einer Zusicherung, einer Meinung, einer Überzeugung, eines Glaubens (belief ) und befindet sich daher keineswegs im Modus des Wissens im Sinne des begreifenden Denkens. Dass etwas gut oder schlecht, richtig oder falsch ist, hat seinen Zusammenhang in einem äußeren Dritten.²⁴ Der kategorische Imperativ weist zwar die formale Struktur des apodiktischen Urteils, damit des höchsten Begriffsurteils auf, aber die Bestimmungsmomente E, B und A sind noch einseitig festgelegt, von vornherein wesentlich getrennt, nicht austauschbar und unterbestimmt. Da die Besonderheit vom Guten unterschieden ist und in den subjektiven Willen fällt, kann das Gute zunächst nicht als Besonderheit genommen werden, es trägt zunächst nur die Bestimmung der ,allgemeinen, abstrakten Wesentlichkeit‘: Die Pflicht soll Kant zufolge um der Pflicht willen getan werden. Die Handlung soll nicht aus besonderer Neigung, sondern eben lediglich gemäß dem allgemeinen Gesetze ohne alle Neigung erfolgen. Eine solche Allgemeinheit des Gesetzes soll für sich das Wahre, das Höchste, das objektive Prinzip sein. Die Besonderung, die Maxime, kommt hinzu, geht nicht aus der Allgemeinheit hervor, da es dieser Allgemeinheit ja an der immanenten Negativität gebricht. A und B sollen mit dem ,Hinzu-Kommen‘ bzw. mit dem ,Auch‘ verknüpft werden, was strenger logischer Stringenz entbehrt. Die subjektive Maxime soll dem universellen Gesetz gemäß sein. In Hegels Sicht leidet diese Hierarchie von abstrakter Allgemeinheit und Besonderheit und der damit einhergehende Dualismus an einem eklatanten logischen Defekt: Die anvisierte Identität von B und A wird nur formaliter erreicht, nur mittels eines unzulänglichen ,Hinzu-Kommens‘ des Besonderen, somit eines bloßen Herüberund Hinübergehens von A und B, von Unendlichkeit und Endlichkeit, von Unbestimmtheit und Bestimmtheit. Wie die Allgemeinheit als reine, abstrakt einseitig und unterbestimmt bleibt, so auch die Besonderheit. Die Maxime als Grundprinzip subjektiven Handelns, der Wille ,seiner subjektiven Beschaffenheit nach‘²⁵ erscheint im Vergleich zum

23 „Das Besondere soll dem Allgemeinen gemäß sein, aber das Erstere ist zugleich ein Anderes, also ist das Gute nur als Sollen gesetzt und der Gegensatz von dem Guten und Besonderen und der Pflicht ist nicht aufgehoben“. Hegel (1973ff.), 360. 24 Hegel (1969ff.), TW 6, 346. 25 Kant (1900ff.), AA IV, 413.

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,Reinen‘ als Herabgesetztes, jede Bestimmung erscheint als Beschränkung, als Schranke. Es geht um das Bestimmte und Endliche, das Negative, was Hegel zufolge schon dem Allgemeinen inhärent ist, die immanente Negativität. Die Besonderheit als ,die Beschaffenheit des Daseins des Handelns‘ bildet ein Moment des Begriffs des Handelns, das ,So und so-Beschaffen-Sein‘ bildet ein konstitutives Element des Handlungsbegriffs, so erweisen sich A und B in ihrem Unterschied als identisch. Die Besonderheit enthält die Dimensionen des Formalen und Inhaltlichen, die Mannigfalt des Besonderen. Kant reduziert jedoch das Substantielle der Handlung auf „die Form und das Princip, woraus sie selbst folgt“. Das Wesentliche-Gute der Handlung „besteht in der Gesinnung, der Erfolg mag sein, welcher er wolle“.²⁶ Damit wird der Besonderheit ein entscheidendes Bestimmungsmoment entzogen. Obschon die Definition der Maxime als Lebensregel, die besondere Beschaffenheit, in allen Dimensionen ins Visier nehmen müsste, bleiben Intersubjektivität und Kontextualität ausgeblendet. Dies verlangt nähere Bestimmung und markiert die Grenze der Moralität überhaupt, erst die Sittlichkeit gilt als die ,allgemeine Sphäre‘ des freien Handelns.²⁷

5 Der Synkretismus des Widerspruchs des moralischen Standpunkts – Antinomien des perennierenden Sollens In der Diagnose der abstrakten Allgemeinheit artikuliert sich Hegels Kritik am moralischen Standpunkt schlechthin, nicht bloß der Einwand gegen Kants praktische Philosophie.²⁸ Das perennierende Sollen kristallisiert sich auch als Achillesferse des Utilitarismus als einer Spielart des Konsequentialismus heraus, der letztlich auf der Ebene der Reflexion verharren und damit in die Sackgasse der unendlichen Approximation, der schlechten Unendlichkeit geraten muss. Sowohl Konsequentialismus als auch die Deontologie verfehlen den Begriff des Handelns, da sie die Gesamtheit der Dimensionen des Handelns nicht zureichend und angemessen berücksichtigen, da sie einzelne widerstreitenden Momente zum alleinig entscheidenden Kriterium für gutes Tun fixieren. „Der Grundsatz: bei den Handlungen die Konsequenzen verachten, und der andere: die Handlungen aus den Folgen zu beurteilen und sie zum Maßstab dessen, was recht und gut sei, zu ma-

26 Kant (1900ff.), AA IV, 416. 27 Hegel (1969ff.), TW 6, 325. 28 Vgl. dazu Wood (1997).

164 | Klaus Vieweg chen – ist beides gleich abstrakter Verstand“ (RPh § 118). Allerdings sieht Hegel in den Konzepten von Kant und Fichte den bislang höchsten Ausdruck des Gedankens moderner Moralität. Hegel zielt immer auf die Grundstruktur von Moralität als einer idealtypischen Form. Mit diesem Paradigma – mit dem Begriff der Moralität, nicht nur einer bestimmten geschichtlichen Ideenformation – haben wir das Wollen in der subjektiv-logischen Struktur des Begriffsurteils. Vor diesem Horizont sollen weitere Argumente vorgeführt werden, mit denen Hegel den Standpunkt der Moralität als einen vom Widerspruch geprägten Durchgangspunkt im Fortbestimmen des freien Wollens fasst, als ein notwendiges, aber nicht hinreichendes Definiens des Handlungsbegriffs.

6 Die Handlung als Einheit des inneren Zwecks und der Realisierung dieses Zwecks Glückswürdigkeit und Glückseligkeit, Recht und Wohl sind unabdingbare Konstituenzien für die Bewertung der Handlung; die notwendige Einheit kann als der umfassende Gute beschrieben werden. Allerdings hat Kant die Moralität der Glückswürdigkeit zugeordnet und so von der Glückseligkeit zunächst getrennt und braucht für die unverzichtbare Überwindung des Widerstreits und die Herstellung der Harmonie zwischen beiden das Postulat eines höchsten Gutes, welches eben das Übereinkommen von Glückswürdigkeit und Wohl garantiert, ein allergütigstes Wesen, von dem wir aber weiter nichts wissen können. So erscheint Hegel die Moralität bei Kant auf ein Forum Internum, auf die innere Prüfung, auf das Postulat und das Erhoffen von Glück und Wohl reduziert, entspringend aus der ursprünglichen Trennung, dem Widerspruch beider Momente. Bei der Antinomie von Freiheit und Notwendigkeit handelt sich um eine Antinomie, die wie jede Antinomie „auf dem formellen Denken [beruht], das die beiden Momente einer Idee getrennt, jedes für sich, damit der Idee nicht angemessen und in seiner Unwahrheit, festhält und behauptet“ (RPh § 57). Das Zusammenspiel von kategorischem Imperativ und Glückspostulat vermag Kant nur mithilfe der Konstruktion des all-gütigen Wesens zu sichern, die Gewährleistung des Glücks wird auf die Hoffnung einer künftigen Glückseligkeit reduziert. Hierzu benötigt Kant das Konstrukt der Unsterblichkeit der Seele und dieser Gedanke verbindet sich sodann mit der Annahme einer künftigen transzendenten Welt.²⁹ Für Hegel stellen sowohl Absicht und innerer Zweck, aber eben auch das Wohl und der Vollzug des Zwecks die unerlässlichen Komponenten moralischen Handelns dar. Nur

29 Vgl. Guyer (2000), 26.

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in dieser von vornherein zu denkenden Einheit von Beweggründen und Folgen haben wir eine vollständige moralische Handlung. Der Einspruch gegen Kant und dem Moralismus erfolgt so vom Standpunkt des Begriffs der Handlung. Das höchste, umfassende Gut gilt als rein, abstrakt und leer, wir vermögen es nicht weiter zu bestimmen, können nichts weiter erkennen. Es resultiert eine unheilige Allianz zwischen dem dogmatischen und dem skeptischen Moment. Die höchste praktische Vernunft als ,heiliger Gesetzgeber‘ erscheint so als Sein im Modus der Vorstellung, obschon gerade Kant stets klare Begriffe statt Bilder und Vorstellungen einfordert. Darin sieht Hegel nun einen eklatanten Verstoß gegen das ,Recht auf Wissen‘, hier genauer gegen das Recht auf Wissen des Guten.³⁰ Dieses Gute, dem ja auch Kant Allgemeinheit beimisst, kann nur im Denken und durch das Denken bestimmt werden. Wer behauptet, dass der Mensch aber nur Erscheinungen³¹ , nicht das Wahre – hier das höchste Gut – begreifen könne, ignoriert ein fundamentales Recht des moralischen Subjekts, das Recht vernünftiger Wesen auf Einsicht und Wissen.

7 Selbstbestimmung und Fremdbestimmung Das postulierte höchste Wesen als heiliger Gesetzgeber ,sorgt‘ für das Gelingen der Harmonie von Allgemeinem und Besonderem, denn „das moralische Bewußtsein kann nicht auf Glückseligkeit Verzicht tun und dies Moment aus seinem absoluten Zweck weglassen.“³² Es kommt ihm die Rolle eines Hervorbringers, eines Herrn und Beherrschers zu, was mit dem Charakter des assertorischen Urteils korrespondiert – das Subjekt in diesem Urteil ist dem Prädikat unterworfen, wird unter dieses subsumiert. Das einzelne moralische Subjekt steht diesem höheren Wesen als ein unvollständiges, unvollkommenes entgegen; die Zwecke dieses Subjekts sind ja durch das Sinnlich-Natürliche, die Begehrungen und Neigungen verunziert und kontaminiert. Das Wohl, die Bedürfnisse des menschlichen Körpers

30 Bei der kritischen Philosophie moniert Hegel, dass der Vernunft kein konstitutives, sondern nur ein regulatives Verhältnis zum Wissen erlaubt wird. Hegel (1969ff.), Glauben und Wissen oder Reflexionsphilosophie der Subjektivität in der Vollständigkeit ihrer Formen als Kantische, Jacobische und Fichtesche Philosophie, TW 2, 179. 31 Signifikant ist der Sprachwechsel hinsichtlich der Kopula vom ,Es ist‘ zum ,Es scheint‘. Die Kopula tritt hier also noch nicht als der vollständig bestimmte Begriff hervor. „Es ist darum die größte Inkonsequenz, einerseits zuzugeben, daß der Verstand nur Erscheinungen erkennt, und andererseits dies Erkennen als etwas Absolutes zu behaupten, indem man sagt, das Erkennen könne nicht weiter, dies sei die natürliche, absolute Schranke des menschlichen Wissens“ (Enz § 60). 32 Hegel (1969ff.), TW 3, 444.

166 | Klaus Vieweg und Geistes werden damit nicht zureichend beachtet und als ,Unreines‘ gegenüber dem Vortrefflich-Reinen herabgestuft. Das Postulat eines jenseitigen Herrn und Gesetzgebers – im Diesseits sei keine zureichende Glückseligkeit zu erlangen – steht aber dem selbst aufgestellten Prinzip der strikten Selbstgesetzgebung diametral entgegen. Denn gegenüber diesem ,Herrn‘ muss das endliche, moralische Subjekt die Epitheta ,unvollständig‘, ,unheilig‘, ,unvollkommen‘, ,den hohen Zweck verunzierend‘ und ,unwürdig‘ hinnehmen.³³ Das Perennierende am Sollen, das unaufhörliche Sehnen und Streben führt zum Hinausschieben, zur Vertröstung auf die schlechte Unendlichkeit, führt in die ewige Iteration des Gleichen, in die Langweiligkeit als absoluter Aufgabe, die stets eine solche bleibt und gegenwärtig nicht gelöst werden kann, die Antinomie bleibt unaufgelöst zurück. Der Weg geht in die logische Insuffizienz der unendlichen Progression. „Streben ist ein unvollendetes Tun oder an sich begrenztes Tun.“³⁴ Die Angemessenheit des Willens vermag Kant zufolge ,nur in einem ins Unendliche gehenden Progressus zu jener völligen Angemessenheit angetroffen werden‘.³⁵ Hegel zufolge pflegt dieser Gedanke der unendlichen Approximation, obwohl dieser ,nichts als der perennierend gesetzte Widerspruch selbst ist‘ (Enz § 60), für etwas Erhabenes, ja gar für eine Art Gottesdienst gehalten zu werden (WdL 5, 264). Hierin liegt der logische Kern der Hegelschen Kritik: Der Widerspruch wird nur einfach reproduziert, bleibt bestehen, seine Auflösung soll am St. Nimmerleinstag erfolgen, ad calendas graecas. Dieser Befund trifft (leider) heute noch immer zu. Ein solcher, heute sich mit verschiedenen Farben schmückender und sich als freies Denken auftretender Relativismus feiert ungeahnte und schier übermächtige Triumphe, obschon bereits einer seiner Väter, Friedrich Schlegel, den performativen Widerspruch feststellte und scharfsinnig darauf hinwies, dass der Satz ,Alles Wissen ist relativ‘ auch auf diesen Satz appliziert werden müsste. Heute scheint dies wahr, morgen etwas Anderes und übermorgen wieder etwas Anderes, so das relativistische Evangelium, das mit seiner Apotheose der Beliebigkeit dem Offenbarungseid der Philosophie leistet – banca rotta. Auf dem moralischen Standpunkt haben wir die Allgemeinheit im Status der Abstraktion, der inhaltslosen Identität, die Subsumtion von B unter A erscheint als nicht stringent, sondern zufällig. Zugleich sind die beiden entgegenstehenden Bedeutungen des Subjekts ihrer Wahrheit nach vereinigt, dies macht die Handlung als ,Eine‘ und zugleich als Eine ,je nachdem sie beschaffen ist‘ aus. Somit 33 Vgl. dazu den Abschnitt Der seiner selbst gewisse Geist. Die Moralität (besonders a. Die moralische Weltanschauung) in der Phänomenologie des Geistes, Hegel (1969ff.) TW 3. 34 Hegel (1969ff.), Vorlesungen über die Geschichte der Philosophie, TW 20, 407; Herv. K. V. 35 Kant (1900ff.), Kritik der praktischen Vernunft, AA V, 156.

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muss die nächste Form des Urteils die Art und Weise der Beschaffenheit einbeziehen. Zu dieser Beschaffenheit, dem So- und So-Sein gehört der Kontext der Handlung³⁶, die wesentlichen Umstände des Handelns, somit nicht nur formale, sondern inhaltliche Momente: ,Das Schenken des Holzpferdes als Spielzeug an die Tochter des Freundes ist gut‘ – ,Die athenische Schenkung eines Holzpferdes an die Trojaner war böse‘ – ,Das Fehlinformieren des Freundes (die Lüge) wegen meines finanziellen Vorteils war böse‘ – ,Das Fehlinfomieren seiner Freunde (die Not-Lüge) durch Jakob den Lügner war gut‘.³⁷ Die Grundstruktur dieser apodiktischen Urteile lautet: ,Diese Handlung unter bestimmten Umständen, in so und so beschaffenen Umständen vollzogen ist gut‘.³⁸ Darin wird die konkrete Allgemeinheit erreicht – das Allgemeine, welches es selbst ist und durch sein Gegenteil sich kontinuiert und als Einheit mit diesem erst Allgemeines wird. Das Resümee könnte lauten: Alle Handlungen sind eine Gattung in einer einzelnen Wirklichkeit von einer besonderen Beschaffenheit. Einer Handlung, die als frei beschrieben werden soll, inhäriert die logische Einheit von E, B und A. Diese Identität wird im bösen Tun verfehlt. Es gibt auch für Hegel kein vermeintliches Recht aus Menschenliebe zu lügen, das Kantische prinzipielle Lügenverbot bezüglich substantieller moralischer Tatbestände bleibt daher uneingeschränkt in Kraft. Nur bei der Bewertung der Handlung ,Fehlinformation‘ wird logisch stringent die Beschaffenheit einbezogen und damit ein neues Verständnis von Lügen konzipiert.³⁹ Jakob, der Lügner, war somit im strengen moralischen Sinne keinesfalls ein Lügner. In einem Mord- und Terrorregime – so die bereits behandelte Umkehrung aller Rechte – besitzt solch mit Fehlinformation agierender Widerstand Legitimität, eben als moralische Notwehr, ausschließlich als zweite, auf Unrecht und Unmoralität reagierende Handlung. An dieser Stelle kündigt sich schon das Überschreiten der Moralitätssphäre an. Das Urteil über eine Handlung, die zunächst nur eine moralische Bewertung erfährt, kann sich so durchaus umkehren. Formale Unehrlichkeit im Sinne von

36 Hegels Logik ist auch in diesem Sinne „eine Logik des Kontextprinzips avant la lettre [. . . ] Person bin ich nur in und durch meine sozialen Beziehungen zu anderen Personen in einer Personengemeinschaft“. Stekeler-Weithofer (2006), 42. 37 Vgl. Becker (1992). Die Hauptfigur, der Jude Jakob, erfindet im Warschauer Ghetto optimistische Nachrichten über den Kriegsverlauf und das Heranrücken der Roten Armee an Warschau und stärkt mit dieser Desinformation den Lebensmut der Gefangenen im Ghetto. 38 Bei Kant gilt der kategorische Imperativ als ein ,apodiktisch-praktisches Urteil‘, ohne dass Kant die logische Form eines solchen praktischen Urteils einer gründlichen Prüfung unterzieht. 39 Von Gewicht ist Hegels spezielles Verständnis von Wahrheit: ,Man soll die Wahrheit sagen‘, da gibt es aber ,viele Rücksichten‘. „Solche Wahrhaftigkeit ist dann eben eine solche, wo nichts dahinter ist. Wahrheit sagen in Rücksicht auf die endlichen Dinge, da ist größtenteils nicht darin. Jeder Augenblick tötet tausend Wahrheiten“. Hegel (2000), 82.

168 | Klaus Vieweg Not-Lügen, von moralischer Not-Wehr darf als gut eingeschätzt werden, nicht das Lügen schlechthin, denn letzteres erfüllt nicht die Bedingungen des Begriffs freier Handlung. Hierin sieht Hegel sowohl die Leistung als auch das Defizitäre des Formalismus, der intrinsischen Pflichten, der unbeschränkten Verbote, und zwar in dem Sinne, dass aus dieser deontologischer Perspektive die ethische Qualität dem Handlungstyp ungeachtet der Umstände und der sich ergebenden (möglicherweise desaströsen und unmenschlichen) Konsequenzen zukommen soll.⁴⁰ Die ,Gegenfüßler‘ der Glückseligkeitslehrer bezeichnete Jean Paul als „kategorische Imperatoren“, die eine ,formale Tugend‘ lehren. Sie opfern ,fremdes ebenso kalt wie eigenes Wohl auf‘, sie suchen ,andern wie sich nichts zu verschaffen als das einzige und höchste Gut‘, die ,formale Tugend‘.⁴¹ Kant hat Hegel zufolge in seinem Verständnis des Wollens als Zweck schon das konkrete Allgemeine im Auge, das objektive Urteil, worin der Zweck schon ,mehr als ein Urteil‘ darstellt, nämlich die logische Form des Schlusses, das Hinausweisen über die moralische hin zur sittlichen Perspektive, welche auf der Logik des Schlusses ruht. Aber die für Kant ebenso charakteristische ,Festhaltung des bloß moralischen Standpunktes‘, des Standorts des Urteilens, der nicht in den sittlichen Standort fortbestimmt wird, setzt den Gewinn, der mit den Rechten der Moralität erreicht wurde, wieder aufs Spiel.

8 Kurzes Resümee Der Übergang von der Moralität zur Sittlichkeit beinhaltet die Aufhebung des Widerspruchs des Moralischen, die Überwindung der Antinomie des perennierenden Sollens. In seiner Wissenschaft der Logik behandelt Hegel den logischen Defekt des unendlichen Progresses auch ,vornehmlich in seine Anwendung auf die Moralität‘ (WdL 5, 268). Der reine Wille und das moralische Gesetz einerseits und die Natur und die Sinnlichkeit andererseits werden schon als völlig ,selbständig und gleichgültig gegeneinander vorausgesetzt‘, der Gegensatz somit als Axiom postuliert und damit bereits ein Überschreiten des Widerspruchs ausgeschlossen. Der Widerspruch „wird im unendlichen Progreß nicht aufgelöst, sondern im Gegenteil als unaufgelöst und unauflösbar dargestellt und behauptet“ (WdL 5, 269). Es resultiert stets ,derselbe Widerspruch, mit welchem angefangen wurde‘ (WdL 5, 270). Der Progressus ad infinitum erweist sich als Widerspruch, der sich selbst zu Unrecht als Auflösung des Widersprechenden ausgibt (WdL 5, 166). Eine echte

40 Quante (1993), 131–133. 41 Jean Paul (1975), 813, 809.

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Überwindung der Antinomie scheitert, die Verlegung ins Jenseits und die vorgestellte Auflösung an einem jüngsten Tag bleibt eine Verlegenheitsantwort, ist nur Ausdruck für zuviel Zärtlichkeit gegenüber der Welt, die Widersprüche, die Kollisionen im moralischen Handeln sind letztlich entfernt, was das Verharren in unüberwundenen Widerspruch impliziert. Hegels Lösungsvorschlag wäre ein anderes Thema. Die Natur des spekulativen Gedankens sieht er darin, die Idealität beider Seiten des Widerstreitenden zu denken, d. h. sie von vornherein als Momente des Begriffs des moralischen Handelns zu verstehen, die entgegengesetzten Momente in ihrer sich bewegenden Einheit zu begreifen und den Übergang von der Moralität ins sittliche Handeln zu denken, zur Sittlichkeit, in welcher der Widerspruch des Moralischen nicht abstrakt verschwunden, sondern aufgehoben, bewahrt und überwunden wird.

Literatur J. Becker, Jakob, der Lügner, Frankfurt a. M, 1992. P. Guyer, “The Unity of Nature and Freedom: Kant’s Conception of the System of Philosophy”, in: S. Sedgwick (Hrsg.), The Reception of Kant’s Critical Philosophy, Cambridge 2000, 19– 53, 2000. G. W. F. Hegel, Werke in zwanzig Bänden. Theorie Werkausgabe. Auf der Grundlage der Werke von 1832–1845 neu edierte Ausgabe. Redaktion E. Moldenhauer und K. M. Michel. Frankfurt a. M. (im Text zitiert als TW mit Angabe des Bandes und der Seitenzahl), 1969ff. G. W. F. Hegel, „Philosophie des Rechts. Nach der Vorlesungsnachschrift K. G. v. Griesheims 1824/24“, in: Vorlesungen über Rechtsphilosophie 1818–1831, Bd. 3, hrsg. u. komm. v. Karl-H. Ilting, Stuttgart-Bad Cannstatt, 1973ff. G. W. F. Hegel, Vorlesungen über die Philosophie des Rechts. Berlin 1819/1820. Nachgeschrieben von J. R. Ringier, hrsg. v. E. Angehrn, M. Bondeli und H. N. Seelmann, Hamburg, 2000. G. W. F. Hegel, Die Philosophie des Rechts. Vorlesung von 1821/22, hrsg. v. H. Hoppe, Frankfurt a. M, 2005. D. Henrich, „Logische Form und reale Totalität. Über die Begriffsform von Hegels eigentlichem Staatsbegriff“, in: D. Henrich und R. P. Horstmann (Hrsg.), Hegels Philosophie des Rechts. Die Theorie der Rechtsformen und ihre Logik, Stuttgart, 428–450, 1982. D. James, Holismus und praktischer Vernunft. Hegels Moralitätskritik im Lichte seiner Urteilsund Schlusslehre, im Erscheinen. J. Paul, „Palingenesien“, in: Sämtliche Werke, Abt. I, Bd. 4, München, 1975. I. Kant, Kant’s gesammelte Schriften, hrsg. von der Königlich Preußischen (später Deutschen) Akademie der Wissenschaften, Berlin (im Text zitiert als AA, mit Angabe des Bandes und der Seitenzahl), 1900ff. R. Pippin, Hegel’s Practical Philosophy, Cambridge, MA, 2008. M. Quante, Hegels Begriff der Handlung, Stuttgart, 1993. M. Quante, “Hegel’s Planning Theory of Action”, in: A. Laitinen und C.-Sandis (Hrsg.), Hegel on Action, Houndmills, 212–231, 2008. K. Rosenkranz, Georg Wilhelm Friedrich Hegels Leben, Berlin, 1844.

170 | Klaus Vieweg G. Sans, Die Realisierung des Begriffs. Eine Untersuchung zu Hegels Schlusslehre, Berlin, 2004. G. Sans, „Hegels Schlusslehre als Theorie des Begriffs“, in: A. Arndt, C. Iber und G. Kruck (Hrsg.), Hegels Lehre vom Begriff, Urteil und Schluss, Berlin, 216–232, 2006. F. Schick, „Die Urteilslehre“, in: A. F. Koch und F. Schick (Hrsg.), G. W. F. Hegel. Wissenschaft der Logik, Berlin, 2002. P. Stekeler-Weithofer, „Warum ist der Begriff sowohl Urteil als auch Schluss?“, in: A. Arndt, C. Iber und G. Kruck (Hrsg.), Hegels Lehre vom Begriff, Urteil und Schluss, Berlin, 24–47, 2006. K. Vieweg, Das Denken der Freiheit. Hegels Grundlinien der Philosophie des Rechts, München, 2012. A. Wood, “Hegel’s Critique of Morality”, in: L. Siep (Hrsg.), G. W. F. Hegel. Grundlinien der Philosophie des Rechts,Berlin, 147–166, 1997.

| Part III: Actuality

Gianni Vattimo

Insuperable Contradictions Philosophy never tolerated contradictions. One may say that it was born exactly in order to eliminate them by the recourse to the ultra-mundane order of Plato’s ideas, or to the principle of non-contradiction in Aristotle’s logics and metaphysics, and so on. One may suggest that even the famous reversal expressed by Marx’s eleventh thesis on Feuerbach is basically directed against this traditional conciliatory essence of philosophy. That’s another reason for the “definitive” supremacy of Hegel; and, of course, the conservative appearance of his theory. When Berthold Brecht opposed a non-Aristotelian, or epic, theatre to the one described and prescribed by Aristotle’s Poetics, he was clearly re-vindicating the resistance of contradictions to the pretended force of the mediating reason. Given these presuppositions, it would be strongly self-contradictory (!) to propose the idea of insuperable contradictions for theoretical reasons. A theory, we assume in the ordinary language of philosophy, has to be non-contradictory, so it belongs to its very essence to be an overcoming of contradictions. The general character of philosophy since its birth in Greece is a sort of “pedagogical” vocation to offer a way of salvation to human beings. Very often, this offer is presented in the terms of the myth of the Platonic Republic, where the one who succeeds in seeing the true things outside the cavern calls on his fellow men to come and share his “vision”, with the constant temptation to oblige them for the sake of their happiness to follow him outside. My impression is that also the purpose of promoting a philosophical reflection upon contradiction follows this traditional path: there would be no point in discussing contradictions if it were not in order to create the conditions for a conciliation. (Remember Spinoza: neque flere neque ridere sed intelligere.)¹ Of course, as we can see from the reference to Spinoza, at the basis of the conciliation there is the view of the “objective” truth, independent from personal interests, which has to be “observed” both in terms of knowledge and in practical terms, which means that it imposes the respect of the given objective truth as the source of moral law. If one does not want to follow the traditional path of the metaphysical conciliation of contradictions, how would he/she explain the interest in a philosophical reflection on them? Is the pedagogical-metaphysical attitude the sole possible for philosophy? What I want to do in this paper is to propose a reflection on contradictions which does not assume that conciliation is the task of philosophy; but

1 Spinoza (1677): I, § IV, vol. 2, 434.

174 | Gianni Vattimo refusing this assumption implies several radical changes in the very notion of philosophy one tries to practice. First of all, the decision to propose a reflection on a topic like contradictions – as on any other topic chosen for a philosophical discussion – cannot be motivated by theoretical reasons. This would require that theory feels by itself the need to discuss – confirm, correct, renew etc. – its idea of contradictions. As if it were “contradictory” not to do that; as if philosophy needed to complete itself by clarifying this theme. I know that the editors of this book would not accept such a simplification of their decision. Very likely – and this is important especially from a “Hegelian” point of view – they would appeal to a sort of “actuality” of the theme in our present situation. It is exactly this implicit, presupposed actuality of the theme that I would like to challenge, in order to be able to better answer the questions proposed. Are we invited to discuss on contradictions because the current situation (a very general term, of course; analogous to the “general condition of world” which Hegel evokes in a point of his Vorlesungen über Ästhetik²) demands from philosophy a special cooperation in order to reduce conflicts, contradictions, etc.? This, I assume, would be more or less the explanation of the theme we are invited to discuss – an explanation which does not seem to need a strong analysis and attention: we all know that the problem of peace, both on international and on domestic level, is urgent. The fact is that the emphasis on the problem of conciliation has always been the favourite topic of philosophy, very often explicitly and many times at least implicitly. I do not remember a philosophy advocating for conflict, or for insuperable contradictions. Even Karl Marx’s eleventh thesis on Feuerbach as formulated within a perspective dominated by an eschatological hope in the final victory of the general class, the proletariat, entitled to make the revolution because of its capacity to catch the truth beyond the veil of ideology, i.e. without an interest disturbing the objective knowledge of the real meaning of history. What I mean is that, when we accept easily, and as obvious, that philosophy responds to the need for peace and reconciliation, we probably are already prepared for this by the fact that philosophy (love for Sophia, wisdom) has always thought of itself as a factor of pacification. My paper asks, very simply, if it is so obvious that today we need pacification, and therefore the task of philosophy has to be that of reflecting upon contradictions in order to overcome them in a realm of non-distorted truth.³ You may recognize at the root of this question the basic opposition between hermeneutics and the epistemological belief in the objectivity of

2 Hegel (1969ff.), TW 13, ch. 3 3 This is Fukuyama’s idea of the end of history: philosophy triumphs because and insofar as there aren’t conflicts. See Fukuyama (1992).

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scientific truth. In my view (not only mine, but also the view of classical authors of hermeneutics, starting with Heidegger), hermeneutics is not the discipline which studies the method of deciphering what appears prima facie non understandable, discovering its hidden meaning. Hermeneutics is basically the philosophy of the irreducible otherness of the other; which does not mean necessarily that it is a philosophy of conflict, but surely it is not a theory of the conciliation on the basis of the shared objectivity of (scientific) truth. Paradoxically, Marx’s eleventh thesis on Feuerbach is much closer to hermeneutics than to scientific objectivism. And more than that: Marxism cannot believe that changing the world involves overcoming interpretation in favour of objectivism if it does not want to turn into dogmatic Stalinism. Let me try to show that today’s world does not need more conciliation (also) through philosophy, or more catharsis through Aristotelian theatre, but rather the opposite. Take the rather generally acknowledged crisis of democracy; i.e. the loss of credibility of the representative institutions – something of the kind of the problems that were already well known to Winston Churchill, today intensified and magnified by the increasing possibilities of social control. In many of our “democracies” people don’t believe any longer in their capacity of influencing by their vote the policies of government. The participation in elections diminishes constantly; the public discussion is more and more limited to the gossip or to the complaint against politicians etc. Would anybody describe this situation as a multiplication of conflicts? Or is what we see simply a condition of progressive “neutralization” – to take the term from Carl Schmitt: or better of “lack of emergency” to use the expression of Heidegger? More recently, one uses to speak of “la pensée unique”; which, translated into political terms, means roughly “the Washington consensus”. The pensée unique is a strong enemy of hermeneutics, to which it reproaches its relativism. The more or less new “realism” of philosophers like John Searle (prized by George W. Bush some years ago) and that sort of mésalliance of the residues of phenomenology with the post-analytic empiricists seems to be substituting for the epistemological metaphysics of the past decades is, as a matter of fact (and sometimes independently from the intentions of the authors), the intellectual support of the neoliberalistic world, still centred in the imperial (military and economic) power of the US and the multinational capitalism. The Searle-Bush ideology wants to purify philosophy from the hermeneutic relativism, which appears as a threat to the official, scientific truth; its connections to the social and economic power don’t need to be proved, if one thinks of the public (military) and private money involved in the modern scientific enterprise. I don’t want to expand here on the analysis of the current condition of “lack of emergency”. In many senses, I could also refer to Fukuyama’s famous thesis

176 | Gianni Vattimo on the end of history; though I don’t share its ideological apologetic implications (democracy, liberal capitalism have triumphed, therefore no more history, i.e. no more conflict, neither of interpretations⁴ nor of weapons). Apparently, and not only apparently, nothing can happen. The sole emergencies seem to be those of “international terrorism” which has not the character of an enemy (in the Schmittian sense) but only of a criminal: NATO and even the UN are more and more involved in operations of international police; the so called public opinion seems to ask mainly for security, no matter how much it costs in terms of freedom, privacy, meaning of everyone’s life. Even the general humanitarian respect for “life”, which means, by the way, the mere biological survival, no matter in which conditions (see what happens with the euthanasia, prohibited even in case of pure vegetative status and of free decision of the individual etc.) seems to belong to this atmosphere of acceptance of a low-profile existence, very probably determined by the fear diffused by the media (fear of terrorists, fear of unemployment, fear of immigrants. . . ). In one word: the triumph, in practice and in theory, of the status quo. As I said, neither a reflection on contradiction(s) nor a theory advocating conflict corresponds to a theoretical need internal to philosophy. But even if one wants to explain theoretically the choice made by the editors of this book, one has to refer to “the general condition of the world”, whatever it means. To admit this elementary observation means already – be cautious – to accept a hermeneutical approach instead of the scientific objectivistic. But this does not mean to admit a realistic attitude, i.e. the idea that if you claim to correspond to a historical need of “the world” you have to “know” that need correctly, therefore its truth etc. What we call facts is what WE call facts: matter of experience more in a Hegelian sense than in empiricist terms. Do we have good reasonable, also philosophically motivated (obviously not “proved”) reasons to advocate for more conflict instead of a more intense pacification? The situation of “lack of emergency”, or neutralization, I described above may either be considered as a desirable “end of history” or as the extreme “Gefahr”, danger, of the forgetting of Being in favour of beings – the existent order taken as the sole possible “reality”. As Walter Benjamin wrote in his Theses on the Philosophy of History, there may well be people who prefer the existent order instead of any change: they are the “winners” in the game of history, for whom the actual world is the best possible one. Why should philosophy stay on the side of the others, the losers, and therefore advocate conflict in order to produce change? In other words: is philosophy intrinsically conservative or nec-

4 See Ricoeur (1969).

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essarily revolutionary? Again: from the point of view I am trying to propose, there cannot be any “logical” proof for one or the other alternative. One can only offer “historical” (even psychological) experiences; which are consciously related to a specific historical condition, the lack of emergency, and don’t claim to hold for ever. Of course, also the supporters of a metaphysical and logical order may be in favour of change – if the world is “out of joint”, it deserves to be put back in its joint.⁵ But always in the name of a given metaphysical structure, which is bound to eliminate conflicts (all wars are presented as the last one, in view of peace. . . ) and to re-establish to ti en einai, quodquid erat esse. . . With the already cited risk of Stalinism: revolution is over, now let’s go to work. . . I have the motivated impression that the philosophers engaged in a project on contradictions feel radically unsatisfied with a theory which does not propose, at least at the end, a conciliated ideal of rational life based in the acceptance of a metaphysical (stable, objective, etc.) truth. What can philosophy imagine instead of that? Even revolution – think of Marx – can only be inspired by the ideal of a final elimination of alienation, albeit remote and hard to reach. Hermeneutics accepts the risk of proposing a sort of open dialectics (I don’t know whether or not we are facing once more the Freudian duality between eros and thanatos.); which, considering itself nothing but a historically situated response to the call of the current situation (in theory and in political practice), does not have to offer a “complete” system, not even in terms of an ideal of “good life”: the sole good life (I think it’s a suggestion by McIntyre) is the one in which everybody is in the condition of deciding what good life means to her/him. Now, on the basis of what I argued for till now, insuperable contradictions are those which escape any logical conciliation; i.e. the claim by an “objective truth” to decide who is right and who is wrong. The simple introduction of interpretation into the picture “corrupts” everything. There is no “meta-language” capable of guaranteeing a radical translation, therefore one has to introduce the “principle of charity”; and there is no absolute neutral point of view independent of interests, and therefore one has to introduce the principle of negotiation or, when this does not work, the conflict. Even in order to regulate conflicts by a constitution one has very often to struggle, more or less violently, against the existing (dis)order. Insuperable contradictions may be described in the terms used by Richard Rorty in his (insuperable) book of Philosophy and the Mirror of Nature⁶: hermeneutic vs. epistemological. Should we really believe that a world in which every contra-

5 See Shakespeare (1996), act 1, scene 5, 186–190. 6 Rorty (1979).

178 | Gianni Vattimo diction is reducible to an epistemological “puzzle”⁷ would be better than ours? Should philosophy cooperate to that “end” (which would have the double sense of the term)? I don’t want to call hermeneutics an ontology of revolution, but it is in fact something of this kind. The reduction of every contradiction to an epistemological puzzle involves a Parmenidian ontology of eternal structures – even only in terms of stable laws of the becoming, where the sole possible changes concern the more or less complete knowledge of truth or the more or less complete development of a given plan. Metaphysics, in the sense criticized by Heidegger from the very beginning of his philosophical career in Being and Time, by its belief in truth as correspondence, involves the denial of any possible event, of course of any interpretation non purely functional to the correspondence intellectus et rei, and finally of historicity and freedom. I know very well that all this seem to be a way of charging too many faults on the shoulders of metaphysics, which at the very end seems to have helped strongly so many revolutions, starting with the French Aufklärung of the 18th century. If you cannot appeal to truth (natural law, natural human rights, etc.), how can you revolt against the tyrant? Well objected; but let’s not forget the dictum of the Gospel: truth will set you free. Relativists and pragmatists like Rorty (and myself, allow me to say) willingly agree with this sacred word. Only they take it very seriously: truth is (only) what sets you free. In order to accomplish this task, truth has to be historically effective. The idea of natural rights connected to the very nature of human beings has often been a useful device for revolutions (e.g. in order to combat the opposite belief in the divine right of the monarch), but in other situations it can become a way of reinforcing oppression: see what happens in the catholic morals where surely absurd authoritarian imperatives (the ban on condoms in times of Aids) are always justified in the name of the pretended natural law. To talk, as I dare to do, of an ontology of revolution in a time in which the dominating new realism of the Searle-Bush school tends to reduce ontology to the description of what objects “are”, proposing as phenomenology and ontology the everyday meaning of the words with a further apologetic addition, a “supplement d’ame” (in this case, a supplement of pretended reality), involves many risks. Not only of being considered a potential terrorist (relativism is social disorder) but also the risk of being expulsed from the category of philosophers. I can try to justify myself by recalling that the idea of Being as Event, Ereignis, proposed by Heidegger, which implies the consequences I tried to illustrate very shortly in this paper, is still (one of) the most reasonable alternative(s) philosophy has been

7 See Kuhn (1970).

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able to imagine to the metaphysical submission of theory and practice to the often violent authority of “what there is”. Insuperable contradiction is in many senses the very place where Being happens (sich ereignet, or: es, das Sein, gibt) and truth puts itself into work. The strong connection between truth, the event of being, and conflict, is a constant of the thought of the late Heidegger which a peaceful and irenic version of hermeneutics may have a bit left aside in its effort of “urbanization”. Let the philosophical meditation on contradiction, albeit inspired by the same purpose of promoting conciliation, serve (contradictorily) to remind us of the ontological necessity of conflict.

References W. Benjamin, “Theses on the Philosophy of History”, in: W. Benjamin, Illuminations, ed. by H. Arendt, London, 1999. F. Fukuyama, The End of History and the Last Man, New York, 1992. G. W. F. Hegel, Werke in zwanzig Bänden. Theorie Werkausgabe. New edition on the basis of the Works of 1832–1845. Ed. by E. Moldenhauer and K. M. Michel. Frankfurt a. M. (quoted as TW), 1969ff. M. Heidegger, Sein und Zeit, Tübingen, 1927. T. Kuhn, The Structure of Scientific Revolutions, 2nd edition, Chicago, 1970. P. Ricoeur, Le conflit des interprétations: essais d’herméneutique, Paris, 1969. R. Rorty, Philosophy and the Mirror of Nature, Princeton, 1979. W. Shakespeare, “Hamlet”, in: William Shakespeare. The Complete Work, Hertfordshire, 670– 713, 1996. B. De Spinoza, OperaPosthuma, Amsterdam, 1677.

Federico Vercellone

A Disenchanted Reenchantment Hermeneutics and Morphology

1 Hermeneutics and the Disenchantment of the World Hermeneutics pertains in essence to the epoch of the Weberian “disenchantment of the world”. An experience of opacity of the world is present in the development of the theory of interpretation from beginning to end. The awareness that things have lost their language and their power is an important motivation for its rise.¹ It is therefore legitimate to hypothesize that there is something similar going on in Gadamer’s approach. In Gadamer, in fact, as is well known, the consciousness of a fracture with fundamental traditions, which determines the ulterior necessity of a suture – of a recomposition – is notably present. From this demand, the urge arises in him to take back the modern hermeneutical tradition, and to put it into contact with Martin Heidegger’s thinking. It is also well known that Jürgen Habermas saw the way to build bridges in hermeneutics.² Through the recourse to traditions and to their founding force, hermeneutics explains in many ways the demand to restore what I would define as a “symbolic membership” in the world, where symbolic membership itself disappears. With “membership” here one means, above all, the idea of a remedy to the uprooting produced by modernity, a sort of compensation in the face of the excessive dominion of subjectivity in mature modernity. That domain, which resulted in the idea of a “purely self-sufficient humanism”,³ is an unconscious symptom of the political messianism of the nineteenth and twentieth centuries and of a technique which has for a long time denied all responsibility toward nature. As a response to this tendentially omnipotent domain of subjectivity, Gadamer returns to a compensatory ideal which is summed up in the idea of a “fusion of horizons”.⁴ As has been argued, the modern “disenchantment of the world”, as a consequence of a deployed subjectivity, which is produced in the

1 2 3 4

See on this point Taylor (2007), in particular chapter I. See Habermas (1971), 392–401. See Taylor (2007), 18. See Gadamer (1986), 311–312.

182 | Federico Vercellone technical domain of the world, necessitates in Gadamer’s eyes a recuperative meditation not just on traditions but also on common sense. As for Aristotle, a competent science is not sufficient in Gadamer’s eyes; a culture of the science in question must accompany it.⁵ In other words, no one can do anything without a sense of his work. It is upon this base, moreover, as is well known, that Gadamer reevaluates taste as a model of common sense, that depository of sense that is not immediately conceptual. This move is in contrast to aesthetic consciousness. We are talking about two dimensions that are completely antithetical even to Kantian aesthetics. We could say – borrowing perhaps too freely from Gadamer’s argument – that the creation of a sphere that is absolutely autonomous, destined for beauty, provided by the four moments of the “judgment of taste”, ends up coming into contrast with the ideal of taste as a depository of common sense.⁶ While aesthetic consciousness provides a substantial self-referential dimension, which alludes, to be clear, to the situation in which autonomous art is organized into its proper institutions (which are factories of a signification and of a valorization of the artistic product that is solely aesthetic), taste, as aesthetic “sensus communis”, alludes to an opposite signification. Taste roots art in tradition, demanding a universal judge that does not come, and cannot be given exclusively to the officers of art as an institution. Taste excludes the principle of an aesthetic function of art in favor of its rooting in the Lifeworld. It is thus important to ask if what can rightly be defined as the “democracy of taste”, the ideal of a communis opinio that guides the valuation of the artistic fact, can live with an autonomous system of art which opens into the institution – art here intended as a closed circuit which asserts itself. In this framework, for Gadamer, the model of play opens into a communality between subject and object, between myself and the world.⁷ In simple terms, hermeneutics proposes a return, as I said above, as an integration of sense and as a compensation toward a technological and instrumental rationality which suggests itself as the only possible model of reason. We have to do with an unambiguous, rigid model, which regulates the movement of the world in a disciplined and functional way, which necessitates, precisely for this reason, a supplementary logic, a grammar of sense which accompanies that of the concept.

5 Aristotle (2001), 639 a 1–5. 6 See Gadamer (1986), 48–61. 7 See Gadamer (1986), 107–126 and 491–494.

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Late-modern consciousness traverses its contradictions, searching for models of compensation. The expropriating domain of the concept, which creates reality under the auspices of a bad technique, insensible to cultural differences and of the capacity of nature to self-organize, makes new extramethodical forms of signification necessary. In other words, stretching the intentions of Gadamer, in contraposition to the expropriation of historical contexts and the places produced through the unambiguous path of uniform reason, which claims to equalize everything in its course, we can propose a recalibrating step. This is the idea of a new “rootedness”. In this way, Gadamer responds to a fundamental instance of German idealism, in particular Hegel, an instance contained in the idea of philosophy as Wissenschaft, as universal science. Philosophy, as an achievement of knowledge, as knowledge conscious of itself, represents, from this point of view, the sum of knowledge because it is the only one that cannot be separated from its own sense. Knowledge that does not know itself is not, from this point of view, real knowledge. It loses, among other things, a fundamental component of knowledge: the cognition of self that announces the responsibility of knowledge itself, which has its performance, for Gadamer, in the living text of the objective spirit reverberating in a story of sense, divided, sedimented, and codified in its passage through the many bends in the river of tradition.

2 Morphology and the Reenchantment of the World In many respects, in trying to give a solution to the contradictory movement of secularization considered above, the idea of morphology recaptures the idea of the hermeneutical system and its inspiration. But it does so with the awareness of a profound revision of cultural paradigms, a revision that follows the idea of the secular world and the secularized product of the rational “disenchantment of the world”, with its immediate, violent kickbacks and the profound modifications to its paradigms. At the most diverse levels there is a rediscovering of a sort of renewed necessity of juxtaposing universal reason with a model of reason that is more open to context, which we can define as “local reason”. The necessity of resuming the motivations of Horkheimer and Adorno’s Dialectic of the Enlightenment (varying the discourse and utilizing another reference point) is announced in this way. And it would perhaps be permissible in this framework to retranslate the polarity within which, in the eyes of the two authors, the fundamental contradiction of mature modernity is reflected. The dialectics of

184 | Federico Vercellone myth and enlightenment becomes in this frame the dialectics of rooting and uprooting. To come to the point, the following must be said. The uprooting of reason produces at the most diverse levels the necessity of new rootings that assume the aspect of myth, at least inasmuch as they are offered as absolute members, as new founding assets of the community and of existence. Do we want to say this in terms that make reference to the present day political panorama? As is all too well known, we are not so unrelated, for example, and in ways that are more and more worrisome, to fundamentalisms. And fundamentalisms, too, are derived at their core from the demand to renew their roots in the face of a too-abstract development that is uniform and equalizing. The necessity of escaping into this logic reverberates in the violent will of giving oneself back or returning oneself, as if speaking of a violated right, to the ubi consistam. This confirms, in the end, that this late-modern life suffers from its own uprooting. The “nonplaces” of late-modern existence, stations, airports, and so on, are precisely the places of transit, uninhabitable, alienating places that cause anxiety.⁸ We can confront the question from another perspective. We could say that inevitably secularization has found its limits in national and local culture, limits that were already revealed in the eyes of Gadamer, but in their positive significance, as motives of resistance against a sort of imperialism of conceptual reason that has been developed as a technical domain of the world. Nevertheless, on the one hand, the limits and the resistances of culture are revealed not just as limits or positive contradictions of a sort of imperialism of reason, but also as real and proper wells of a quantity of negative feedbacks. As we have said above, the necessity of rediscovering oneself produces newly rooted identities, as well new political-cultural structures of identity, which suggest nevertheless as absolute – as universal and inextensively valid and cogent – what should be relative to context instead (and that probably only from this last aspect can invoke the universal). That is: I refer to the fabric of customs, manners, beliefs, and common sense. All of this was, in a nutshell, already there in Gadamer, but now develops in terms of a conflictual and not complementary identity with respect to that of deployed reason. The integration of sense proposed by Gadamer is not in itself sufficient before the necessity of recovering identity or of producing it anew, even using the resources of tradition. This, it seems to me, is the real critical point of Gadamerian hermeneutics. The hermeneutical remedy is too weak in the face of a present evil. The integration of sense reveals itself as an ineffectual remedy when faced with the contradictory logic of secularization, when faced with the reactive

8 See Augé (1992).

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crisis of religious-cultural identity which aims to transform itself and suggest itself as a political power. For that matter, the radicality of identities, derived from the contradictory process of secularization, does not only cross cultures in declaratively violent frameworks, like those of the modern wars of religion, but also in places where, at least explicitly, totalitarianisms and fundamentalisms are not in question. After all, considering all the differences, in Italy too we see that a similar process takes place. In the end, Lega Nord and Slow Food provide a very different answer to the same need. The radical ethnic, religious, and gastronomic identities, in every case fictitious precisely because of their radicality, impose themselves like a kind of indispensable historical necessity, which proceeds with determination to meet violent or at least too apodictic outcomes. They impose an absolute identity that seems to negate one of the presuppositions of secularization, the resolving of identities in cultures that do not coincide necessarily with political boundaries or with ethnicities. But, in this picture, there is one remaining surprise. The same technology, in fact, now modifies those characteristics. From many points of view, technology seems increasingly less to lead to the disenchantment of the world, according to the model that is variably expressed by thinkers who are (no less) intellectually distant from one other, like Max Weber and Martin Heidegger. And it is increasingly configured instead as a form of enchantment,⁹ in the service of an art that attempts to produce new rootings. From the digital image, to the new possibilities discussed by the rendering of the image, to the work of artists like Olafur Eliasson, it is more and more evident that technology suggests itself, at least in some of its particularly significant moments, as a motivation for a new “re-enchantment of the world”, which is to say that it produces a new belonging. They seem, in other words, to open the possibility of a technology that is more inventive, more prudent toward place and nature, less devastating. One need think only of the meaning of an installation like Weather Project by Eliasson at the New Tate in London in 2004. We have here a sun, capable even of tanning, which illuminates and, as it were, “invents” a new environment that modifies our way of feeling, which intervenes, like a new energy, in the individual and collective sentiment, creating a new community which is lyrical and epical at the same time. All of this has coincided with an indubitable oscillation of the cultural paradigms that have brought to the center of attention the question of the image which, in the meantime, has become one of the dominant factors of cultural

9 See on these topics Gell (1992).

186 | Federico Vercellone communication. The image in this case does not suggest itself just as antithetical with respect to the concept, but also, and above all, as a form of conceptualization. And at this point, we must ask what image we are dealing with. It was Hans Belting who broached the question in the most perspicuous terms when he contrasted the image as representation, an outcome of the western perspective of vision, with the Arab world, which thinks of the image as from light and not from the gaze.¹⁰ According to Belting the eye that sees in perspective transforms the world into an image. The perspective gaze, we could say in this context, extremizing the thesis of Belting, becomes the principle of a nihilistic dissolution of the world, of its transformation into mere representation. That dissolution of the world into a multiplicity of points of view that vie with one another for the center of the perspective is what Nietzsche lucidly announced with the notion of the “will to power”. Heidegger took this up and developed it, proposing the idea of an Age of the World Picture.¹¹

3 Rooting Oneself in Images. . . The image reduced to a representation opens therefore into the logic of modern uprooting. But the image reduced to a representation is also an impoverished image, which has left behind it that invitation to rooting inherent in the mythical image.¹² I would like to explain this thesis, articulating it here in a series of points.¹³

a. In reality, the image opens a logic of membership that coincides with the historical, theoretical, and cultural demands upon which we have paused.¹⁴ In the image, the intuition that constitutes its prelude configures membership in places and contexts. The consciousness of images develops within a visible camp (and therefore, in a sense, “local”) in which it comes to clarify itself, moving from its initial motivation, i.e. the intuition, to expand itself into total articulation of vision. From this point of view, the logic of the image is next to hermeneutics, precisely to the extent that it articulates and gives development to a deposit of implicit sense.

10 11 12 13 14

See Belting (2008). See Heidegger (1977), 74–113. See Vercellone (2008), 7–29. See on these topics also Breidbach/Vercellone (2011). On the idea of a “postmodern rootedness” see Del Pozo Ortea (2011), 85–100.

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It responds nevertheless, in an ever more immediate way, to the necessity of a reintegration, for which hermeneutics sought to provide resources.

b. The image explains, then, a logic of membership inasmuch as it is stylistically characterized. And there should be no doubt that the style is, at least initially, the characterization of a place, the reason by which it explains its peculiarities, the sense of its traditions.

c. From this point of view, and in this framework, it also becomes possible to define the structure and subjectivity of the image. The category of the sublime will be useful again here. It will become useful when we want to propose a structuring of the universe of the image, a first instance of its peculiar semantic articulation. A first cell of what I would define as morphological. The image has a semantic articulation that is consecrated by a minimal expenditure of energy, an articulation attentive to the energetic economy of communication, which is a vehicle for complex content in the shortest time possible, that is, simultaneously. The economy of minimal force imposes itself in the framework of an increasing complexity and on the basis of the necessity to overcome it without betraying it, keeping faithful to the demand – incited in the logic of the image – of transferring a message semantically dense in a decisively quicker time than that allowed by the discursive/conceptual logic founded on the subject-predicate structure.

d. Once it is accepted that the image is a complex system such as this, one must ask how the images themselves constitute their syntax, how they articulate, that is, among themselves, following an alternative to the method furnished by discursive articulation. How can the connection between the images be produced? In what way can they put themselves into relationships with one another, furnishing some forms of organized sequence in a “logical” sense, broadly construed? I begin the discussion here, attempting to cast one glance onto the question.

e. To start, one might say that the condition for the connection of images is also that of their manifesting, that which allows their appearance. This is an occasion – in this regard – to resume a romantic teaching coming from Philipp Otto Runge. In order to appear, to assume the configuration they are entitled to, images need an obscure background that allows them to emerge. Inasmuch as Runge’s silhouettes testify, they individuate themselves – as they could never do in nature – precisely

188 | Federico Vercellone because of this background that throws their profile into relief. One could even say more, perhaps thinking of the influence on Runge exercised by Jakob Böhme. In the background one might read the provenance of the image, its emergence from the fabric of creation. Accepting this interpretation – at least inasmuch as it concerns Runge – one could say that nothing, as a background, is the condition of being for the emergence of the image.

f. A thesis of this sort could be developed apart from the romantic context of its first formulation. One could affirm – precisely by extrapolating this idea from its point of origin – that, in order to manifest itself in its morphological completion (and not reduce itself therefore in signs, as if they were points without extension), images are always turned outside of themselves, outside of their own perimeter and their own confines. The background is, precisely, their condition for being, as I said above in relation to Runge. In order to make their being emerge and, with it, also their complex identity – their meaning – images must stand out like this against that nothingness that is their origin. In order to divest the evil of nothingness of its power, but also to profit from it – the two opposing concepts go hand in hand here – images attempt to join themselves with other images without knowing beforehand the formula by which they will reach their objective. They are, therefore, always situated over the abyss. Images institute their peculiar syntax precisely in this way. It is an articulation that is not founded on the evidence of the copula but on its exorcism of nothingness. And nothingness is not just the condition of the appearance of the image tout court, but also – as I said above – of its appearance as an image.

g. We could also assert that, contrary to this discussion, the image is recognizable because – at least upon first glance – it proposes itself essentially in its singularity against a background that puts it at risk but renders it altogether intuitable. In this way, the image gives itself over to meaning through its intrinsic semantics, starting from its peculiar syntax. It is, as it were, constrained to watching through itself, outside of itself. On this basis, moreover – apart from its connection with the rest of the universe of images and with other semantic universes – its own minimal relationship can be stabilized: reference. It is the image of. . . This too confirms that precisely the constitutive transcendence of the image is the condition of its recognizability and therefore that which could define its ontological status.

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h. To summarize: Images are manifestations of something which, from them, emerges only inasmuch as they can appeal to the “background of nothing” that furnishes their sufficient stress. Thanks to this background, the ontological difference that defines them as images manifests itself, making it the case, in other words, that the image is an “image of. . . ” Now, if the making of an image in a system of signs depends on its standing out against nothing, we have ipso facto a connection to the structure of the sublime. The truth of an assertion of this kind becomes evident if we look at the situation from the opposite point of view: the signs that organize verbal discourse manifest, above all, their signifying quality, and not their “imaging”, insofar as they can be placed and seen in sequence. This is not true for the image that “powerfully” manifests its signification in solitude. It “searches” choral character, but does not hold it from the beginning. In other words, something comes to mean “in image” inasmuch as it transforms into infinite, into the 𝑛 that indicates the plurivocity of an indefinite principle of return, that glance onto nothingness that can make it nothing. In this way, the image becomes an image, and is semantically structured according to its particular articulation. Thus, it is from the beginning, as it were, “made” for montage installation and, on this foundation, as Georges Didi-Huberman reminded us recently, to execute a critical task.¹⁵ From this point of view, the image is inevitably the subject and object of its own structuring where, at most, the same distinction between the two planes almost has a meaning, again: almost nothing, because it cannot be seen from which point of view one can structure the gaze, from above or head on, to furnish the subjectobject structure with its peculiar development.

i. Style expresses, in this framework, a synthetic necessity connected to the logic of the image but also connected to the necessity, increasingly pressing, of explaining a complex logic, a highly articulated semantic content as quickly as possible. And the intuitive contemporaneity realized in the image and communicated by style is the quickest possible way of realizing itself from a communication of high semantic content.

j. In this perspective morphology is suggested as a continuation of hermeneutics within a theoretical framework profoundly altered with respect to context and motivation. The integration of sense is, as it were, natural in this scope, where

15 See Didi-Huberman (2010).

190 | Federico Vercellone intuition aids the knowledge that develops in the image, which will have further developments in the discursive arena.

k. We now have to address the logic of the image, which opens a radically new perspective with respect to the hermeneutical integration of sense proposed by Gadamer. This fundamentally depends on the fact that the image expresses a performative logic that is profoundly different from the discursive one articulated in the subject/predicate relationship, which is also the logic of the hermeneutical circle of question and response.

l. The image opens in fact into a holistic context in which we are therefore immersed. We do not have here the distance between subject and object typically established in a discursive realm. It is a holistic concept in which we are immersed and on which we depend as much as we influence it. It is a context – scientific or artistic, it doesn’t matter – characterized stylistically to which we obtain membership and, at the same time, exercise our influence.

m. In this way we must deal with a performative mode of thought that claims to have a precedence over action. Or better still: it reclaims the idea of “formativity”, which the Aesthetics of Pareyson proposed to us, the idea of “a doing which, as it does, invents the way in which it does.”¹⁶

n. One more aspect connected to the peculiarity of the significance of the image is that it “says” even in solitude. In contrast, no discursive component does so autonomously, or does so fully. Of course, it is not opportune to oppose image to concept in a drastic manner. In fact, it is placed at their mutual boundaries.

o. However, the image stabilizes its reference even by itself. It manifests its reference putting itself in relation to a proper background which makes it stand out as an image of. . . Upon this basis it combines with other images – and it does so precisely because of the opaque background, because of that nothing that surrounds it and that constitutes the condition of its signification. It is exactly

16 Pareyson (1988), 59.

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this background, the emptiness upon which the image stands out, which allows the image to establish contact with other images. The other images are possibilities of unedited relations, analogical-metaphorical relations that also belong to the discourse, but that the image holds with a decisively greater freedom. Here is the cognitive potential and the discovery of the image that is indissolubly joined to its stylistic priority. In fact, the more an image is stylistically characterized, the more it becomes recognized as its message by the community of its users/contemplators. And this is true for a work of art, a publication, or even a scientific image.

p. The image tends, therefore, at its heart, always to make itself into an icon. It tends to re-enchant by making recourse not to the romantic infinite but to technological devices. It is thus prone to artificially forcing time in the direction of eternity, rooting in a new space that is itself to be created, producing in this way new memberships.

References Aristotle, On the Parts of Animals, ed. by J. G. Lennox, Oxford, 2001. M. Augé, Non lieux. Introduction à une anthropologie de la surmodernité, Paris 1992, 1992. H. Belting, Florenz und Bagdad. Eine westöstliche Geschichte des Blicks, Munich, 2008. O. Breidbach and F. Vercellone, Anschauung Denken, Munich, 2011. M. Del Pozo Ortea, “‘Nocilla Dream’ y la literatura radicante: Un árbol en el desierto del la postmodernidad”, in: Lucerro. A journal of iberian and latin american studien 17/1, 85–100, 2011. G. Didi-Huberman, Remontages du temps subi. L’oeil de l’histoire, Paris, 2010. H.-G. Gadamer, “Warheit und Methode,. Grundzüge einer philosophischen Hermeneutik”, in: Gesammelte Werke, vol. 1, Tübingen, 1986. A. Gell, “The Technology of Enchantment and The Enchantment of Technology”, in: J. Coote and A. Shelton (eds.), Anthropology, Art and Aesthetics, Oxford, 1992. J. Habermas, “Urbanisierung der Heideggerschen Provinz”, in: J. Habermas (ed.), Philosophisch-politische Profile, Frankfurt a. M., 392–401, 1971. M. Heidegger, “Die Zeit des Weltbildes”, in: Gesamtausgabe, vol. 5: Holzwege, Frankfurt a. M., 74–113, 1977. L. Pareyson, Estetica: teoria della formatività, 4th edition, Milan, 1988. C. Taylor, A secular age, Cambridge, 2007. F. Vercellone, Oltre la bellezza, Bologna, 2008.

Wolfgang Welsch

Wie wir auf Konsistenz aus sind – und warum Eine Theorie der Konsistenz habe ich leider nicht anzubieten. Sondern nur einige Beobachtungen, die sich über Jahrzehnte eingestellt haben. Vielleicht lassen sich aus ihnen jedoch einige Bausteine zu einer Theorie der Konsistenz gewinnen. Eines vorab: Ich werde von Konsistenz und Kohärenz nicht wohlunterschieden sprechen. Üblicherweise sagt man, Konsistenz sei eine logische Bestimmung, die verlangt, dass ein Verbund von Aussagen keinen Widerspruch enthält (bzw. dass kein Widerspruch aus ihm ableitbar ist). Kohärenz verlange hingegen mehr, nämlich inhaltlichen Zusammenhang und idealerweise eine vollständige wechselseitige Stützung der Aussagen. So gesehen, wäre Konsistenz zwar eine notwendige, aber noch keine hinreichende Bedingung für Kohärenz. Ich bin mir nicht sicher. In den Fällen, auf die ich mich beziehen werde, scheint Konsistenz immer schon etwas von Kohärenz zu haben. Wie wenn die beiden durch eine Klammer verbunden wären, so dass, wenn man vom einen spricht, das andere unwillkürlich zugleich im Spiel ist. Vielleicht ist beides in Wahrheit nicht glasklar unterscheidbar. Ich sympathisiere mit Davidsons Idee, beides mehr oder minder gleichzusetzen: „coherence is nothing but consistency“.¹

1 Welche Erwartungen haben wir an Personen, wenn wir von ihnen (anscheinend nur) Konsistenz erwarten? Die folgende Frage bildet meinen Ausgangspunkt bzw. mein Ausgangsproblem: Warum verlangen wir von Personen, dass sie in ihren Aussagen konsistent seien? Warum ist das so? Ginge es nicht auch anders? Ich gehe also nicht von einer logischen, sondern von einer vergleichsweise existenziellen Fragestellung aus. Warum verlangen wir von Personen Konsistenz? Möglicherweise ist dies die tiefere Fragestellung als die logische. Vielleicht verlangen wir logische Konsistenz, weil wir personale Konsistenz wollen.

1 Davidson (1990), 134–138, hier 135.

194 | Wolfgang Welsch Jedenfalls ist unsere Konsistenzerwartung an Personen ein Faktum. Wir fordern Konsistenz im Alltag: „Du sagst mal so und mal anders. Was meinst Du eigentlich? Was willst Du wirklich? Willst Du im Urlaub ins Piemont fahren oder nach Bayern? Wein oder Bier? Entscheide Dich endlich!“ Und wir verlangen Konsistenz in der Philosophie: Heidegger beispielsweise verteidigte Sein und Zeit gegen den Vorwurf des Anthropozentrismus, indem er schrieb: „Welche Gefahren birgt denn ein ,anthropozentrischer Standpunkt‘ in sich, der gerade alle Bemühung einzig darauf legt, zu zeigen, dass das Wesen des Daseins, das da ,im Zentrum‘ steht, ekstatisch, d. h. ,exzentrisch‘ ist?“² Aber andererseits hat Heidegger den Anspruch der philosophischen Anthropologie, die grundlegende Philosophie zu sein, scharf kritisiert.³ Was soll nun gelten? Die Legitimierung der Zentralität der Anthropologie oder ihre Bestreitung? Beides geht doch nicht zusammen. Oder, wenn ich ein persönliches Beispiel anführen darf: Heute sagt man mir manchmal, man wisse gar nicht mehr, wo ich stehe. Früher hätte ich postmoderne Theorien vertreten, heute würde ich eine Art evolutionistischer Metaphysik verfolgen, die irgendwie an Whitehead erinnere. Was halte ich denn nun für richtig? Das eine oder das andere? Wofür will ich wirklich eintreten? Dass man zu unterschiedlichen Zeiten unterschiedliche Theorien entwickelt, sollte eigentlich kein Problem sein, jedenfalls so lange nicht, wie diese Theorien zu einander nicht in Widerspruch stehen. Und so verhält es sich hier. Die unterschiedlichen Theorien beziehen sich schlicht auf unterschiedliche Fragen und Sachfelder. Es stimmt, dass ich derzeit eine evolutionäre Ontologie verfolge, aber ich habe früher keine postmoderne Ontologie entwickelt – ein Konflikt ist also gar nicht möglich. Oder meine Äußerungen über die postmoderne Architektur einerseits und die Koevolution ontischer und logischer Strukturen andererseits berühren einander überhaupt nicht, können einander also ebenfalls nicht widerstreiten.

2 Heidegger (1967), 21–71, hier 58, Anm. 3 „Die Tendenz zur Anthropologie ist letztlich die Absicht darauf, überhaupt zu entscheiden, was wirklich ist und was nicht, was Wirklichkeit und Sein heißt; damit aber auch zu entscheiden, was Wahrheit besagt“. Heidegger (1997), 16. „Anthropologie ist heute denn auch längst nicht mehr nur der Titel für eine Disziplin, sondern das Wort bezeichnet eine Grundtendenz der heutigen Stellung des Menschen zu sich selbst und im Ganzen des Seienden. Gemäß dieser Grundstellung ist etwas nur erkannt und verstanden, wenn es eine anthropologische Erklärung gefunden hat. Anthropologie sucht nicht nur die Wahrheit über den Menschen, sondern beansprucht jetzt die Entscheidung darüber, was Wahrheit überhaupt bedeuten kann“. Heidegger (1965), 191.

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Aber obwohl somit von den Sachen (Theorien) her kein Anlass zur Rüge bestünde, moniert man die Unterschiedlichkeit.⁴ Jemand, der so unterschiedliche Theorien verfolgt, scheint irgendwie dubios zu sein. Er ist einem nicht geheuer. Was man möchte und erwartet, ist etwas anderes: dass jemand immer dasselbe vertritt oder ein und denselben Gedanken sukzessiv entwickelt, anreichert, verfeinert.⁵ Aber was ist der Grund, warum man dies verlangt oder erwartet? Der Theorienpluralismus – bei einer einzelnen Person – ist anscheinend nicht nur unpraktisch, sondern irritierend. Er ist störend. Man ist sich unsicher und fragt sich: Was meint dieser Mensch denn nun wirklich? Dabei geht es offenbar um mehr als logische Konsistenz. (Diese ist ja gewährleistet.) Wenn man fragt, was jener Mensch eigentlich meine, schwingt die Befürchtung mit, dass er uns möglicherweise täuschen könnte, dass er mit uns spielt, dass er uns an der Nase herum führt. Wir strengen uns an, seine Thesen zu verstehen, seine Theorie zu verfolgen. Der Proponent selber aber ist möglicherweise längst woanders. Vielleicht meint er seine Thesen gar nicht ernst, sondern plappert sie nur so daher. Vielleicht glaubt er selber nicht, dass sie wert seien, sich damit zu befassen, sich mit ihnen auseinander zu setzen – während wir uns gutgläubig große Mühe damit geben. Mit anderen Worten: Wir befürchten, dass dieser Kerl uns täuscht. Geht es also bei der Konsistenzforderung an Individuen eigentlich um die Erwartung sozialer Verlässlichkeit? Ist Konsistenz, tiefer als ein logisches, ein kommunikatives oder soziales Prinzip? Richard Rorty war dieser Auffassung.⁶ Aber ich zweifle – dazu später mehr.

4 In den vorgenannten Fällen (vom Bayern/Piemont-Beispiel an) handelt es sich natürlich nicht um Widersprüche im Sinn des Aristotelischen Nicht-Widerspruchs-Prinzips, denn man sagt ja nicht zu gleicher Zeit über dasselbe in derselben Hinsicht einander Widersprechendes. Die existenzielle Widerspruchs-Problematik geht über diese Forderung logischer Nichtwidersprüchlichkeit weit hinaus. Was logisch nicht widersprüchlich ist, kann existenziell gleichwohl als widersprüchlich gelten. Und diese Alltagswidersprüchlichkeit einer Person kann von anderen als unerträglich empfunden werden: So kann man nicht leben, diese Widersprüchlichkeit macht einen verrückt. 5 Eine derartige Erwartung erinnert mich allerdings an den Kunstmarkt: Künstler sollen dort eine eindeutige Identität haben, sie sollen auf Anhieb erkennbar sein und nicht einmal das das eine und ein andermal etwas anderes machen. Nicht nur corporate identity, auch individual identity ist ökonomisch bzw. marktstrategisch geboten. So auch in der Philosophie? 6 So jedenfalls hat Rorty im Jahr 2001 meine diesbezügliche Frage beantwortet.

196 | Wolfgang Welsch Im Moment will ich nur festhalten: Sofern das Bemerken von Inkonsistenz in den Verdacht übergeht, wir würden getäuscht, verlangen wir offenbar mehr als Konsistenz. Wir verlangen Wahrhaftigkeit. Wer inkonsistent ist, indem er inkohärente Thesen vertritt, scheint nicht wahrhaftig zu sein.⁷ Wahrhaftigkeit ist es, was wir eigentlich wollen, wenn wir Konsistenz einfordern.⁸

2 Innenperspektive Wechseln wir nun von der Außenperspektive, wo ein anderer sagt, jemand sei inkonsistent, zur Innenperspektive, wo eine Person ihre Inkonsistenz selber bemerkt und zu ihr Stellung nimmt. Ein Beispiel dafür sind die folgenden Zeilen aus Walt Whitmans Leaves of Grass: Do I contradict myself? Very well then . . . I contradict myself; I am large . . . I contain multitudes.⁹ Whitman bemerkt, dass er sich widerspricht. Und wie reagiert er darauf? Durch Akzeptation seiner Selbstwidersprüchlichkeit? Zunächst durchaus, indem er sagt: “Very well then . . . I contradict myself”. Aber dann gibt er eine Erklärung, die verständlich machen soll, dass diese Widersprüchlichkeit in Wahrheit doch eine Form von Kohärenz darstellt: „I am large . . . I contain multitudes“. Gemeint ist Folgendes: Wenn jemand eine Vielzahl von Positionen in sich vereint, dann ist es nur konsequent, dass mal diese, mal jene in den Vordergrund tritt – er sich in diesem Sinne also widerspricht. Es wäre geradezu inkonsequent, wenn bei einem solchen Menschen keine Widersprüche auftreten würden. Entweder besitzt eine Person wirkliche Pluralität, dann gehören zu ihr auch Widersprüche, oder sie gerät niemals in Widersprüche, dann war es mit ihrer vermeintlichen inneren Pluralität nichts. – Das also ist die Weise, wie Widersprüchlichkeit und

7 Wir unterstellen dabei nicht nur, dass der andere konsistent sein will, sondern auch, dass er es vollständig kann. 8 Vgl. hier den Beitrag von Enrico Berti und seinen Hinweis, dass Łukasiewicz der Auffassung war, dass Konsistenz eigentlich als praktischer und ethischer Wert zu begreifen sei. Vgl. Łukasiewicz (1951). 9 „Song of Myself,“ Whitman (1985), 85.

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Konsistenz hier zusammengebracht werden: Was auf der Ebene der Aussagen widersprüchlich ist, ist auf der Ebene der Person konsistent.¹⁰ Ich diskutiere ein weiteres Beispiel: Einer meiner Freunde träumt von einem Vortrag im Stil des Alters. Im Alter ist bekanntlich die Konzentrationsfähigkeit schwächer, man verliert öfters den Faden der Rede. Ein bewusster Altersvortrag würde diese Inkohärenz inszenieren. Man würde also wirklich inkohärent reden, Inkohärentes vortragen (ohne den Nichtzusammenhang zu klären oder auch nur Stellung dazu zu nehmen). Aber würde man nicht auch dabei noch einem Prinzip der Kohärenz folgen? Denn erstens: Dieser Redestil wäre kohärent zur Inkohärenz des Alters. Und zweitens: Man würde darauf achten, dass nicht doch Kohärenz (verborgenerweise) vorhanden wäre, weil das gegenüber der Intention (Inkohärenz!) inkohärent wäre. Es ist das (tiefere) Kohärenzgebot, das hier zu (manifester) Inkohärenz nötigt. Was diese Beispiele (Whitman, Altersvortrag) zeigen, ist, dass Konsistenz ein sehr starkes Gebot ist. Wo Inkonsistenz (einander widersprechende Aussagen) auftritt, sucht man zu zeigen, dass diese Widersprüchlichkeit doch nur eine vordergründige ist, dass auf einer höheren bzw. tieferen Ebene vielmehr doch Konsistenz besteht. Und wenn man inkonsistent reden will, achtet man darauf, dies konsequent bzw. konsistent zu tun – es darf kein Zusammenhang da sein, sonst wäre die Rede inkonsistent (weil ihre Inkonsistenz nicht konsistent durchgeführt wäre). Egal also, ob wir Konsistenz oder Inkonsistenz suchen: Wir fühlen uns in jeden Falle gedrängt, dies konsistent zu tun. Konsistenz ist das Metagebot. Und ein sehr starkes Gebot, ein sehr starker Imperativ.

3 Eine klassische Denkform: Aufhebung der Widersprüche einer niedrigeren Ebene auf einer höheren (höchsten) Ebene Die Figur, durch die Widersprüchlichkeit (Inkonsistenz) und Konsistenz zusammen gebracht werden, ist (in der Philosophie wie sonst) die einer Ebenenunterscheidung. Was auf einer unteren Ebene widersprüchlich ist, kann auf einer höheren Ebene konsistent sein. In Whitmans Beispiel war die untere Ebene die der Aussagen, die höhere Ebene die der Struktur der Person. Und im Fall der Alters-

10 Eine Stufe weitergedacht bedeutet dies: Wirklich plural ist derjenige, der nicht nur mehrfältig sein kann, sondern der gelegentlich auch einmal einfältig sein kann. Die Dauermehrfältigkeit wäre ihrerseits vergleichsweise einfältig. Dagegen stellt die Kombination von Mehrfältigkeit und Einfältigkeit die höhere und wahrhaftere Mehrfältigkeit dar.

198 | Wolfgang Welsch rede war die erste Ebene ebenfalls die inkohärenter Aussagen, die höhere Ebene aber die der strikten Konsistenz qua Inkohärenz. Das sind alles Beispiele einer klassischen Figur: Die Widersprüche einer niedrigeren Ebene erfahren auf einer höheren (höchsten) Ebene ihre Aufhebung. – Wir kennen alle die großen Beispiele dafür. Ich erwähne nur drei: Nikolaus Cusanus’ Lehre von der coincidentia oppositorum besagt: Unsere Welterfassung ist perspektivisch. Dabei stellen sich jedoch in den unterschiedlichen Perspektiven die gleichen Dinge unterschiedlich dar. Zum Beispiel weisen die Gegenstände in sinnlicher Perspektive Farben auf, in mathematischer hingegen nicht. Aber derlei Perspektivdifferenzen können nicht die letzte Wahrheit sein. Denn in Gott selbst muss alles eins sein, für Gott stellen sich die Dinge nicht derart perspektivisch dar. Also muss man über die Perspektivität und den mit ihr verbundenen Gegensatzcharakter auf Nicht-Kontrarietät hinausdenken. Auch wo uns die Erfassung dieser Nicht-Kontrarietät noch nicht gelingt, können wir doch sicher sein, dass sie besteht. Darauf bezieht sich Cusanus’ Formel von der „coincidentia oppositorum“. Was uns als Gegensatz erscheint, stimmt letztlich doch zusammen, fällt ineins. Der Zusammenfall der Gegensätze ist die eigentliche Wahrheit.¹¹ Diese Koinzidenz ist Gegenstand eines über die rationalen Gegensatzformen hinausgehenden, sie transzendierenden Wissens. Zu diesem gelangt man jedoch nicht gleichsam von oben (durch höhere Offenbarung, Gnade oder dergleichen), sondern von unten: durch Ausgang von den Gegensätzen, durch deren Höherentwicklung zur Zusammenstimmung, durch das Bewusstsein, dass eine solche Zusammenstimmung auch dort noch besteht, wo wir sie noch nicht zu explizieren vermögen. Die entsprechende Wissensform ist die docta ignorantia. Sie ist nicht mehr von der Begreifensart des Verstandes, sondern geht über dessen Eigenart, die auf begriffliche Bestimmtheit zielt und damit auf Abgrenzung und Gegensatzcharakter festgelegt ist, hinaus. Ein besonders bekanntes Beispiel für die Übersteigung der Gegensätze durch deren spekulative Aufhebung ist natürlich die Hegelsche Dialektik: Die Stufen des Bewusstsein bzw. des Geistes geraten in für sie unauflösbare Widersprüche, die sich erst auf der jeweils nächsthöheren Ebene aufheben, wo freilich, bevor nicht die Stufe des absoluten Wissens bzw. des vollkommenen Schlusses des Systems erreicht ist, erneut Widersprüche entstehen, die dann den Übergang zu einer weiteren Stufe ernötigen.

11 Eine konzise Darstellung der Lehre von der „coincidentia oppositorum“ bietet Kurt Flasch (1972), 215–255.

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Wichtig ist mir, dass sich die Figur der Transzendierung der Gegensätze in einer höheren Wahrheit auch in anderen Kulturkreisen finde, Wir treffen sie beispielsweise bei dem großen japanischen Philosophen D¯ogen (1200–1253) an. In einem seiner wichtigsten Texte –„Sansuikyo“ („Die Sutren der Berge und Flüsse“) – verfolgt D¯ogen einander widerstreitende Aussagen wie „das Wasser fließt“ und „das Wasser fließt nicht“ oder „die Berge fließen“ und „die Berge fließen nicht“.¹² Die Ebene, wo derlei Widersprüche auftreten und Bestand haben, ist die gewöhnliche Ebene der Perspektivität. Aber wohin führt ein tendenziell vollständiger Durchgang der Perspektiven und die Beachtung dessen, was dabei den gegensätzlichen Attributionen widerfährt? Er führt dazu, dass keines der Prädikate standhält. Man wird immer auf eine oder mehrere Perspektiven treffen, in denen, was der einen Perspektive zufolge ein essentielles Prädikat einer Sache ist, mit gleichem Recht gerade ausgeschlossen, negiert wird. Alle scheinbar essentiellen Prädikate einer Sache erweisen sich somit als bloß perspektivisch geltend und damit als gerade nicht essentielle Prädikate.¹³ D¯ogens Überlegungen zur Perspektivität münden daher in die Aufforderung: „Transzendiere die Unterscheidung von Gegensätzen!“¹⁴ Es geht für ihn darum, über die „Welt der Relativität“ hinauszugelangen.¹⁵ „Der ungeteilte Geist transzendiert alle Gegensätze.“¹⁶ „Ungeteilter Geist“ meint (im Unterschied zum „unterscheidenden Geist“) diejenige Geistform, die sich von der Haftung an die Welt der Relativität löst, die Welt trans-perspektivisch sieht und so „die ganze Realität“ erfasst.¹⁷ – Das ist offenbar der Sicht des Cusaners nicht unähnlich (nur dass D¯ogen diese Auffassung schon zweihundert Jahre früher entwickelt hat). Überhaupt – diese inter- oder transkulturelle Zwischenbemerkung sei hier gestattet – ist es nicht so, dass nur wir Abendländer konsistenzversessen oder widerspruchs-allergisch wären, sondern auch im asiatischen Bereich sind Widersprüche Widersprüche und sind zu vermeiden oder aufzuheben. Nur ist die Umgangsform mit den Widersprüchen vergleichsweise schonender oder sanfter als bei uns üblich. Selbstwidersprüchlichkeit ist also im Osten nicht weniger kontraindiziert als im Westen. Hierzulande sind wir es (insbesondere in der Philosophie) gewohnt,

12 Zenji D¯ogen (1983), 167–174. Vgl. meine ausführliche Interpretation in: Welsch (2011), 38–69. 13 Es gibt keine ausgezeichneten Perspektiven, keine ,Expertenperspektiven‘. Auch Fische sind nicht die verbindlichen Experten des Wassers. Unsere Perspektive auf das Wasser ist nicht weniger richtig (wertvoll) als die ihre – oder die von Möwen oder Steinen. 14 Zenji D¯ogen (1977), 32–39, hier 39. 15 Zenji D¯ogen (1977), 34. 16 Zenji D¯ogen (1977), 34. 17 Zenji D¯ogen (1977), 39.

200 | Wolfgang Welsch dass die sicherste (und vielleicht einzig zuverlässige) Widerlegungsart darin besteht, den Kontrahenten eines Selbstwiderspruchs zu überführen – ein solcher Nachweis ist für ihn argumentativ letal, daher kaprizieren wir uns so gerne auf diese Widerlegungsart. Aber auch im Osten gilt Selbstwidersprüchlichkeit als fehlerhaft. Der Unterschied ist nicht einer bezüglich der logischen Option, sondern nur hinsichtlich der kulturell üblichen Verfahrensweise, mit Selbstwidersprüchlichkeit umzugehen. Im Westen demonstrieren wir dem Gegner genüsslich seine Selbstwidersprüchlichkeit – und tun das zumal vor Publikum. Im Osten vermeidet man das. Man führt weder die Selbstwidersprüchlichkeit noch den Kontrahenten vor, sondern gibt dem anderen vergleichsweise sanft zu verstehen, warum er seine Position überdenken und vielleicht verändern sollte. Man vernichtet nicht, sondern schont. Das ist der kulturelle Unterschied im Umgang mit Selbstwidersprüchlichkeit. Aber die logische Basis – dass Selbstwidersprüchlichkeit fehlerhaft ist – ist gemeinsam.¹⁸

4 Konsistenzallergie Nun aber ist es an der Zeit, die Betrachtungsrichtung zu ändern. Bislang habe ich gezeigt, wie noch durch alle Widersprüche hindurch eine Konsistenzerwartung und -befolgung besteht. Konsistenz scheint das Höchste zu sein – in den Widersprüchen oder über den Widersprüchen. Jetzt aber soll die Opposition gegen Konsistenz das Thema sein. Man kann ja nicht übersehen, dass es auch so etwas wie eine Konsistenz- oder Kohärenz-Allergie gibt.

a System-Skepsis Der Widerstand gegen Konsistenz/Kohärenz bezieht sich zunächst nicht auf Personen, sondern auf Systeme, auf philosophische Systeme, auf Gedankensysteme. In noch relativ gemäßigter Form finden wir diesen antisystematischen Affekt bei Diderot, wenn er 1765 im Enzyklopädie-Artikel „Philosophie“ schreibt: Der systematische Geist wirkt dem Fortschritt der Wahrheit so sehr entgegen, weil diejenigen, die ein System von gewisser Wahrscheinlichkeit erfunden haben, nicht mehr eines Besseren belehrt werden können. Sie halten geflissentlich alle Dinge fest, die irgendwie zur Be-

18 Ein treffliches Beispiel für beide Aspekte bietet die Geschichte von Meister Zhuang und Meister Hui, die über eine Brücke schlendern und die Freude der Fische diskutieren. Zhuangzi (2003), 129f.

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stätigung ihres Systems dienen können, und beachten kaum alle jene Einwände, die gegen dieses erhoben werden, oder schieben sie durch irgendeine oberflächliche Unterscheidung beiseite. [. . . ] Sie sehen immer nur jenes Bild der Wahrheit an, das ihre auf Wahrscheinlichkeit beruhenden Ansichten mit sich bringen; sie halten dieses Bild unbeweglich vor ihren Augen fest, betrachten aber nie aus einem gewissen Abstand die Kehrseite ihrer Ansichten, die ihnen zeigen würde, wie verkehrt diese sind.¹⁹

Diderot meint also, dass Kohärenz gegen Wahrheit zeugt, dass sie durch Hilfskonstruktionen und Wegsehen erkauft ist – dass sie bloß Systemkitt ist und nicht Zeichen von Wahrheit.

b Nietzsche: Redlichkeit – als Grausamkeit In dramatischer Wendung finden wir das Motiv einer – gar auf Dauer gestellten – Infragestellung von Konsistenz bei Nietzsche, und zwar unter dem Stichwort „Redlichkeit“. „Nichts“, schreibt Nietzsche, „gilt mir heute kostbarer und seltner als Redlichkeit“ – diese Tugend der „freien Geister“.²⁰ Und wie lautet seine Maxime der Redlichkeit? Nie Etwas zurückhalten oder dir verschweigen, was gegen deinen Gedanken gedacht werden kann! Gelobe es dir! Es gehört zur ersten Redlichkeit des Denkens. Du musst jeden Tag auch deinen Feldzug gegen dich selber führen.²¹

Die Idee ist die gleiche wie bei Diderot: Es kann vollkommene Schlüssigkeit bestehen – und doch alles falsch sein. Daher gebietet Nietzsche einen (gar täglichen) Angriff auf Konsistenz bzw. Kohärenz – um der Wahrheit willen. Das dicht geknüpfte Netz eines schlüssigen Zusammenhangs ist eher verdächtig, es dient nicht der Wahrheit, sondern sich selbst. Wo die Maxime der Redlichkeit verfolgt wird, da gilt Wahrheit für höher als Kohärenz. Ich denke, dass Nietzsches Forderung für jeden heute Denkenden vorbildlich sein könnte: nicht in den Kokon irgendeines Systems – auch nicht des eigenen – sich einzuspinnen, sondern die eigene Auffassung erneut zu prüfen, an die Substanz, an die Eingeweide, ans Eingemachte zu gehen – und dann gegebenenfalls Erschütterungen und Erdbeben auszulösen, die schöne Konstruktion zu sprengen. Als Philosoph sollte man lieber selber an den Wänden des eigenen Denk-

19 Diderot (1961), 390–402, hier 402. 20 Nietzsche (1883–1884), 360 bzw. Nietzsche (1886), 162 [227]. 21 Nietzsche (1881), 244 [370].

202 | Wolfgang Welsch gebäudes rütteln, statt es krampfhaft vor Erschütterungen bewahren – bevor es ohnehin wie ein Kartenhaus zusammenfällt. Solche Redlichkeit scheint sehr schwer zu sein. Aber Nietzsche verlangt gar noch mehr. Er fordert Redlichkeit „in Bezug auf die Redlichkeit selber“.²² Die Redlichkeit darf sich nicht zu einer Haltung verfestigen, mit der alles ein für alle Mal als getan gilt. Noch die Redlichkeit ist dem Gebot unnachgiebiger Befragung auszusetzen. Als Nietzsche dies einmal tut, entdeckt er in der Redlichkeit einen Grund von Grausamkeit. Die Redlichkeit ist alles andere als eine unschuldige Tugend:²³ „Fast Alles, was wir ,höhere Cultur‘ nennen, beruht auf der Vergeistigung und Vertiefung der Grausamkeit – dies ist mein Satz [. . . ].“²⁴ Der Mensch wird heimlich durch seine Grausamkeit gelockt und vorwärts gedrängt, durch jene gefährlichen Schauder der gegen sich selbst gewendeten Grausamkeit. Zuletzt erwäge man, dass selbst der Erkennende, indem er seinen Geist zwingt, wider den Hang des Geistes und oft genug auch wider die Wünsche seines Herzens zu erkennen – nämlich Nein zu sagen, wo er bejahen, lieben, anbeten möchte –, als Künstler und Verklärer der Grausamkeit waltet; [. . . ] schon in jedem Erkennen-Wollen ist ein Tropfen Grausamkeit.²⁵

Kurzum: Redlichkeit ist durch Grausamkeit grundiert. Redlichkeit ist „gegen sich selbst gewendete Grausamkeit“.²⁶ An dieser Grausamkeitsdiagnose ist Einiges dran. Es ist tatsächlich so, dass wir Wissenschaftler, wir Philosophen, wir abendländische Rationalisten uns zu immer erneuter und noch gründlicherer Prüfung, zu wiederholtem Infragestellen und Durchdenken gedrängt fühlen. Wir halten es für nötig, Fehlersuche zu betreiben – noch im Gewohntesten, im scheinbar Sichersten. Wir glauben, alles für ausgemacht Geltende immer erneut einem Stresstest (wie man das heute nennt) unterziehen zu müssen. Das ist ein Imperativ unserer auf Logos, Begründung und Argument gestellten Kultur. Aber andererseits: Kann und will man das wirklich immer wieder erneut, immer weiter tun? Hat man nicht irgendwann genug? Reicht es einem nicht irgendwann? Will man es damit nicht endlich einmal genug sein lassen? Vielleicht mit fünfundsechzig, im Übergang zur Emeritierung? Um von nun an nur noch das Erarbeitete festzuhalten und zu sichern? Will man nicht irgendwann aus der endlo-

22 Nietzsche (1882–1884), 20. 23 Nietzsche sieht sie als „eine der jüngsten Tugenden“ an (Nietzsche (1881), 275 [456]) – den braven wie den unbeugsamen Menschen ist diese kommende Tugend noch fremd (Nietzsche (1882), 497 [159]). 24 Nietzsche (1886), 166 [229]. 25 Nietzsche (1886), 166f. [229]. 26 Nietzsche (1886), 166 [229].

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sen Erkenntnisbeunruhigung aussteigen (wie Skeptiker das schon viel früher tun) und im Kokon eines Systems seine Ruhe finden? Wie aber stünde diese Haltung zu Konsistenz bzw. Kohärenz? Ohne Zweifel wären die Letzteren darin anerkannt. Aber vielleicht nicht um der Wahrheit willen. Sondern weil unser Leben Halt und Zusammenhang braucht. Und der jetzt erreichte ist vielleicht nicht perfekt, nicht endgültig, sondern irgendwann erschütterbar – aber für die restliche Lebenszeit (für die Restlaufzeit) wird er halten, und das genügt.

c Die spezifisch moderne Situation Übersehen wir schließlich nicht, dass die moderne Zuwendung zu Kohärenz einen besonderen Hintergrund oder Grund hat. Kohärenz, das ist die typisch moderne Sicherungsmöglichkeit – seitdem wir modern wurden, also nicht mehr an Fundamente glauben. Dann ist die Sicherung durch komplexe Netze die einzig verbleibende Möglichkeit. Nietzsche hat das wunderbar beschrieben: Man darf [. . . ] den Menschen wohl bewundern als ein gewaltiges Baugenie, dem auf beweglichen Fundamenten und gleichsam auf fließendem Wasser das Aufthürmen eines unendlich complicirten Begriffsdomes gelingt; freilich, um auf solchen Fundamenten Halt zu finden, muss es ein Bau, wie aus Spinnefäden sein, so zart, um von der Welle mit fortgetragen, so fest, um nicht von dem Winde auseinander geblasen zu werden.²⁷

Und natürlich sind hier des Weiteren die Nietzsche-Erben zu nennen, zuerst Otto Neurath: Wie Schiffer sind wir, die ihr Schiff auf offener See umbauen müssen, ohne es jemals in einem Dock zerlegen und aus besten Bestandteilen neu errichten zu können.²⁸

Das Schiff der Wissenschaft hat keinen festen Anker, die Wissenschaft bietet keine absolute Sicherheit, sie ist selber den Schwankungen der hohen See ausgesetzt und vermag allenfalls von Zeit zu Zeit ein Leck zu reparieren und den drohenden Untergang zu verhindern.

27 Nietzsche (1896), 873–890, hier 882. 28 Neurath (1932/1933), 204–214, hier 206. – Dieser Satz Neuraths wurde dann auch zum Leitspruch von Willard Van Orman Quine (er bildet das Motto von Quine (1960), VII). Und selbst bei Karl Popper heißt es: „[. . . ] wir entdecken [. . . ], dass dort, wo wir auf festem und sicherem Boden zu stehen glaubten, in Wahrheit alles unsicher und im Schwanken begriffen ist“. Popper (1969), 103–123, hier 103.

204 | Wolfgang Welsch Ebenso Quine: Die Gesamtheit unseres sogenannten Wissens oder Glaubens [. . . ] ist ein von Menschen geflochtenes Netz, das nur an seinen Rändern mit der Erfahrung in Berührung steht. [. . . ] Jede beliebige Aussage kann als wahr aufrechterhalten werden, was da auch kommen mag, wenn wir nur anderweitig in dem System ausreichend drastische Anpassungen vornehmen. Selbst eine Aussage ganz nahe der Peripherie kann angesichts gegenläufiger Erfahrung als wahr aufrechterhalten werden, indem mit Halluzinationen argumentiert wird oder indem gewisse Aussagen jener Art berichtigt werden, die logische Gesetze genannt werden. Umgekehrt ist ebenso keine Aussage unrevidierbar. Die Revision selbst des logischen Gesetzes des ausgeschlossenen Dritten wurde vorgeschlagen, um damit eine Vereinfachung der Quantenmechanik zu erreichen; [. . . ]²⁹

Das Netz ist fragil. Gewiss muss es halten – aber nur dort, wo es wirklich darauf ankommt. Hingegen soll nicht alles absolut fest verspannt, gleichsam zementiert sein. Sondern das Netz muss – vgl. Nietzsche – zart sein, beweglich und von daher anpassungsfähig, veränderbar. Ich will noch ein literarisches Beispiel anfügen – Schriftsteller sind ja oft besonders sensibel für neue Zeitlagen. Italo Calvino schildert in Die unsichtbaren Städte eine „Spinnennetz-Stadt“ namens „Ottavia“:³⁰ Sie ist auf einem Netz errichtet, das zwischen zwei hohen Bergen gespannt ist. Alle Bauten dieser Stadt und der gesamte Verkehr sind an dieses Netz gebunden. „Unten ist Hunderte und Hunderte von Metern nichts: Ein paar Wolken ziehen dahin; noch weiter unten kann man den Boden der Schlucht erkennen“.³¹

Die Pointe von Calvinos Beschreibung liegt nun darin, dass in dieser Stadt – die doch konstruktiv von der evidentesten Unsicherheit ist – das Leben sicherer ist als in den anderen Städten: „Über dem Abgrund schwebend ist das Leben der Einwohner Ottavias weniger unsicher als in anderen Städten. Denn die Bewohner wissen, dass ihr Netz nur ein bestimmtes Gewicht zu tragen vermag.“³² Man kann die moderne Position vielleicht so zusammenfassen: Sie kombiniert Kohärenzsuche und Kohärenzallergie. Gewiss suchen und brauchen wir noch immer Kohärenz, aber kaum haben wir sie erreicht, da stellen wir sie auch schon wieder infrage, suchen sie aufzubrechen. Wir sind überzeugt, dass das gegenwärtige Netz nicht das endgültige ist bzw. sein kann. Also muss es umbau-

29 Quine (1979), 27–50, hier 47. 30 Calvino (1984), 85f. bzw. 81. 31 Calvino (1984), 85. 32 Calvino (1984), 86. – Natürlich ist für Calvino Venedig – die Stadt, die auf Pfählen ruht – das Urbild einer derartigen Stadt. „Jedes Mal, wenn ich dir eine Stadt beschreibe, sage ich etwas über Venedig“ (ebd., 100).

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fähig bleiben. Deshalb sind wir gegen das endgültige Festzurren – sind systemallergisch. Oder man könnte auch sagen: Wir sind gegen den systemfixierenden Typ von Konsistenz zugunsten eines flexibilitätsaffinen Typs von Konsistenz. Für belebende Widersprüche offen zu bleiben gilt uns als Gebot der Klugheit. * Blicken wir zurück: Die Konsistenz kann recht unterschiedliche und komplexe Formen annehmen. Es kann, bei vordergründiger Widersprüchlichkeit der Aussagen (und auch Handlungen) einer Person um die innere Konsistenz dieser Person gehen. Oder wir treffen, bei den Meisterdenkern, auf Konsistenz als die höhere dialektische Einheit gegenüber der Unterschiedlichkeit der Gegensätze (Heraklit, D¯ogen, Cusanus, Hegel). Oder wir streben, in der Moderne, nach Konsistenz und Kohärenz, indem wir haltgebende, aber zugleich flexibilitätsoffene Netze entwickeln. Ferner: Auch wo Einsprüche gegen Konsistenz auftreten, ist es doch nicht so, dass wir uns gänzlich von Konsistenz verabschieden würden. Schließlich: Hinter der Forderung nach Konsistenz kann immer wieder mal etwas anderes und mehr als die Forderung nach nur logischer Konsistenz stehen. Es kann um Verlässlichkeit, um Wahrhaftigkeit, um das Netz unserer wissenschaftlichen oder sozialen Überzeugungen etc. gehen. Zum Schluss will ich die Katze aus dem Sack lassen. Was steckt im Grunde, was steckt letztlich hinter unserer Forderung nach Konsistenz? Wenn Konsistenz nicht das Letzte ihrer selbst ist, wenn es in ihr um mehr als ein bloß logisches Prinzip geht; und wenn auch die bislang erwogenen Hintergrundsgrößen (Einheit der Person, soziale Verlässlichkeit, Kohärenz des Aussagennetzes etc.) nur vorläufige Statthalter sind, was ist es dann eigentlich, wovon her Konsistenz geboten ist?

5 Der tiefste Grund: ontologisch Letztlich und eigentlich, scheint mir, ist Konsistenz ein ontologisches Gebot. Konsistenz ist nämlich ein elementares Wirklichkeitsprinzip oder genauer: Wirklichkeitsbildungsprinzip. Diese meine Perspektive ist ungewohnt und überraschend – aber vielleicht mag man sie erwägen. Ich versuche sie hier in sehr abgekürzter Form plausibel zu machen.³³ In der Bildung des Universums fand sich von sehr frühen Stadien an eine bestimmte Tendenz: Seiendes tendiert zu Strukturbildung. Das Mittel dazu ist Selbstbezüglichkeit, Reflexivität. Sehr früh schon kam es zur Entstehung syste-

33 Vgl. dazu ausführlich Welsch (2012), 876 ff.

206 | Wolfgang Welsch martiger Entitäten. Das begann mit Kleinstsystemen: aus dem nach dem Big Bang entstandenen Plasma bildeten sich nach ca. 370.000 Jahren erste abgegrenzte Entitäten heraus, die Selbstbezüglichkeit aufwiesen – die Atome. Sie sind durch Systemcharakter und Selbstbezüglichkeit bestimmt, sofern ihre Glieder (Kern und Elektronenschale) strikt aufeinander bezogen sind und dieser wechselseitige Bezug für das Sein der Atome konstitutiv ist.³⁴ Selbstbezüglichkeit machte sich dann des Weiteren innerhalb von Großverbänden geltend, als sich winzig kleine Dichteunterschiede der Materie infolge der Gravitationskraft von selbst verstärkten und zur Bildung von Galaxien führten. Noch Subformen der Galaxien wiederholen das gleiche Schema: Sonnensysteme weisen eine sehr genaue und über Äonen stabilisierte und nachjustierte Abstimmung der Planeten untereinander und mit dem Zentralgestirn auf.³⁵ Auch etliche chemische Reaktionen führen zu temporär stabilen Formen von Selbstorganisation. Zum Beispiel weisen bei den Bénard-Zellen die prozessual (und erneut nach dem Schema der Selbstverstärkung kleinster Abweichungen) entstehenden Muster eine Fähigkeit zur Selbststabilisierung unter variierenden Energiebedingungen auf (auch wenn hier noch weitaus engere Grenzen gezogen sind als nachfolgend beim Lebendigen, das sich unter weit größeren Schwankungen seiner externen Bedingungen zu erhalten vermag). Beim Organischen entsteht dann erstmals wirkliche Individualität. Organismen sind Selbstbetreiber. Die Selbstbezüglichkeit ist beim Lebendigen gleichsam von der Systemebene ins Einzelseiende gerutscht – das nun in sich systemartig verfasst ist. Organismen sind durch ständige Kohärenzherstellung gekennzeichnet. Sie bewirken ihre innere Kohärenz (Homöostase, Metabolismus, Zellreproduktion) sowie ihre äußere Kohärenz (Passung im Verhältnis zur Umwelt, insbes. auf dem Weg sensu-motorischer Bezüge). Kohärenzherstellung ist die ratio essendi der Organismen. Insofern ist sie zunächst einmal ein biotisches Gebot – lange bevor sie ein logisches oder argumentatives Gebot ist. Aber Kohärenz ist eben nicht nur auf dem elementar-biotischen Niveau essentiell, sondern dann auch auf den höheren Niveaus des Lebendigseins, also beispielsweise im Bereich von Kognition, Selbstbewusstsein, Welterkenntnis. In der elementaren Erfahrung, dass man nicht gegen den Widerspruchssatz denken und leben kann, schwingt noch die Nötigung zu organismischer Kohärenz mit. Damit will ich jedoch nicht sagen: Weil Kohärenz ein organismisches Gebot ist, deshalb ist sie auch ein Denkgebot. Ich habe hier keinerlei Reduktionismus im Sinn. So

34 Atome sind im Anorganischen gewissermaßen die Vorläufer der Zellen im Organischen. Sie weisen Innenregulation und Außenabgrenzung auf. 35 Man könnte schon darin ein komplexeres Analogon zur Atomstruktur sehen.

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wenig Kohärenz deshalb ein organismisches Gebot ist, weil sie zuvor schon ein physikalisches Gebot war, so wenig ist sie ein mentales Gebot, weil sie zuvor bereits ein biotisches Gebot darstellte. Sondern ich sehe es so, dass Kohärenz ein seinsgenereller Zug ist – koextensiv mit der Tendenz zur Selbstorganisation, also dem allgemeinsten Treiber ontologischer Strukturbildung. Deshalb besteht die Nötigung zur Kohärenz im Physikalischen wie im Biotischen und dann auch Mentalen. Was nicht in einem elementaren Sinn stimmig wäre, könnte weder entstehen noch sich im Sein halten. Kohärenz ist somit das generellste ontologische Gebot – auf welcher Ebene auch immer. Wenn ich in das argumentative Kohärenzgebot (dem Philosophen sich so sehr und schier ausschließlich widmen) hineinhorche, dann vernehme ich als die tiefste Schwingung darin das generell-ontologische Gebot zur Kohärenz. Ich meine also: Wenn wir dem Nichtwiderspruchsprinzip folgen, so nicht bloß, weil wir Organismen sind, und nicht bloß, weil wir denkend sind, sondern weil wir Seiende sind, und weil Kohärenz das elementarste und generellste ontologische Prinzip ist. – In diesem Sinn dürfte Aristoteles dann doch recht gehabt haben, als er darauf insistierte, dass das Widerspruchsprinzip nicht einfach als logisches, sondern grundlegender als ontologisches Prinzip zu verstehen ist.³⁶

Literatur Aristoteles, Metaphysik, übers. von Thomas A. Szlezák, Berlin, 2003. I. Calvino, Die unsichtbaren Städte, München, 1984. D. Davidson, “Afterthoughts” [1987], in: Alan R. Malachowski (Hrsg.), Reading Rorty: Critical Responses to Philosophy and the Mirror of Nature (and Beyond), Oxford, 134–138, 1990. D. Diderot, Art. „Philosophie“ [1765], in: Philosophische Schriften, Bd. 1, Berlin, 390–402, 1961. K. Flasch, „Nikolaus von Kues: Die Idee der Koinzidenz“ [1972], in: J. Speck (Hrsg.), Grundprobleme der großen Philosophen: Philosophie des Altertums und des Mittelalters, Göttingen, 215–255, 1990. M. Heidegger, Kant und das Problem der Metaphysik [1929], Frankfurt a. M, 1965. M. Heidegger, „Vom Wesen des Grundes“ [1929], in: Wegmarken, Frankfurt a. M., 21–71, 1967. M. Heidegger, „Der Deutsche Idealismus (Fichte, Schelling, Hegel) und die philosophische Problemlage der Gegenwart“, Vorlesung Sommersemester 1929, in: Gesamtausgabe, Bd. 28, Frankfurt a. M, 1997. J. Łukasiewicz, Aristotle‘s syllogistic. From the standpoint of modern formal logic, Oxford, 1951. O. Neurath, „Protokollsätze“, in: Erkenntnis 3, (1932/1933), 204–214. F. Nietzsche, Sämtliche Werke. Kritische Studienausgabe in 15 Bänden, hrsg. von G. Colli und M. Montinari, Berlin und New York, 1999.

36 Aristoteles (2003), Metaph. IV 3, 1005 b 23–32. Vgl. dazu Welsch (1987), 237f.

208 | Wolfgang Welsch F. Nietzsche, „Morgenröthe“, in: Sämtliche Werke. Kritische Studienausgabe in 15 Bänden, hrsg. von G. Colli und M. Montinari, Bd. 3, Berlin und New York, 1881. F. Nietzsche, „Nachgelassene Fragmente“, in: Sämtliche Werke. Kritische Studienausgabe in 15 Bänden, hrsg. von G. Colli und M. Montinari, Bd. 10, Berlin und New York, 1882. F. Nietzsche, „Die fröhliche Wissenschaft“, in: Sämtliche Werke. Kritische Studienausgabe in 15 Bänden, hrsg. von G. Colli und M. Montinari, Bd. 3, Berlin und New York, 1882–1884. F. Nietzsche, „Also sprach Zarathustra“, in: Sämtliche Werke. Kritische Studienausgabe in 15 Bänden, hrsg. von G. Colli und M. Montinari, Bd. 4, Berlin und New York, 1883–1885. F. Nietzsche, „Jenseits von Gut und Böse“, in: Sämtliche Werke. Kritische Studienausgabe in 15 Bänden, hrsg. von G. Colli und M. Montinari, Bd. 5, Berlin und New York, 1886. F. Nietzsche, „Ueber Wahrheit und Lüge im aussermoralischen Sinne“ [entst. 1873, publ. 1896], in: Sämtliche Werke. Kritische Studienausgabe in 15 Bänden, hrsg. von G. Colli und M. Montinari, Bd. 1, Berlin und New York, 873–890, 1896. K. Popper, „Die Logik der Sozialwissenschaften“, in: T W. Adorno u. a. (Hrsg.), Der Positivismusstreit in der deutschen Soziologie, Neuwied und Berlin, 103–123, 1969. W. V. O. Quine, Word and Object, Cambridge 1960, 1960. W. V. O. Quine, „Zwei Dogmen des Empirismus“ [1951], in: Von einem logischen Standpunkt. Neun logisch-philosophische Essays, Frankfurt a. M., 27–50, 1979. W. Welsch, Aisthesis. Grundzüge und Perspektiven der Aristotelischen Sinneslehre, Stuttgart, 1987. W. Welsch, Immer nur der Mensch? Entwürfe zu einer anderen Anthropologie, Berlin, 2011. W. Welsch, Homo mundanus. Jenseits der anthropischen Denkform der Moderne, Weilerswist, 2012. W. Whitman, Leaves of Grass [1855], New York, 1985. D. Zenji D¯ogen, „Shinjingakudo“ („Lernen durch Körper und Geist“) [1243], in: Shob ¯ ogenz ¯ o¯ – Die Schatzkammer der Erkenntnis des wahren Dharma, Bd. 1, übers. v. M. Eckstein, Zürich, 32–39, 1977. D. Zenji D¯ogen, „Sansuikyo“ („Die Sutren der Berge und Flüsse“) [1240], in: Shob ¯ ogenz ¯ o¯ – Die Schatzkammer der Erkenntnis des wahren Dharma, Bd. 2, übers. v. J. Renner, Zürich, 167–174, 1983. Zhuangzi, Zhuangzi(Auswahl), Stuttgart, (2003).

List of Contributors Jc Beall is Professor at the Philosophy Department of the University of Connecticut, Director of the University of Connecticut Logic Group, and Professorial Fellow at the University of Aberdeen. He is author of several books on truth, logic, language, and metaphysics, among them: Logic The Basics, London: Routledge 2010, Spandrels of Truth, Oxford: Oxford University Press 2009, Logical Pluralism (with Greg Restall), Oxford: Oxford University Press 2006, Revenge of the Liar (ed.), Oxford: Oxford University Press 2008, Liars and Heaps: New Essays on Paradox (ed.), Oxford: Oxford University Press 2004, The Law of Non-Contradiction (ed., with G. Priest and B. Armour-Garb), Oxford: Oxford University Press 2004, Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic (with Bas van Fraassen), Oxford: Oxford University Press 2004. More information is available from Beall’s website: entailments.net.

Enrico Berti is professor emeritus of History of Philosophy at the Università di Padova. He is member of the Accademia Nazionale dei Lincei, Institut International de Philosophie, Istituto Veneto di Scienze, Lettere ed Arti, Société Européenne de Culture, Fédération Internationale des Sociétés de Philosophie, Accademia Galileiana di Scienze, Lettere ed Arti and the Società filosofica italiana (which he has directed from 1983 to 1986). His major works include: La contraddizione, Milan: Città Nuova 1977, Aristotele. Dalla dialettica alla filosofia prima, Milan: Bompiani 1977, Le vie della ragione, Bologna: Il Mulino 1987, Contraddizione e dialettica negli antichi e nei moderni, Palermo: L’Epos 1987, Le ragioni di Aristotele, Rome and Bari: Laterza 1989, Storia della filosofia (together with Franco Volpi), Rome and Bari: Laterza 1991, Aristotele nel Novecento, Rome and Bari: Laterza 1992, Introduzione alla metafisica, Turin: UTET 1993, Il pensiero politico di Aristotele, Rome and Bari: Laterza 1997, In principio era la meraviglia. Le grandi questioni della filosofia antica, Rome and Bari: Laterza 2007, Nuovi studi aristotelici, 4 volumes, Brescia: Morcelliana 2004–2010, Dialectique, physique et métaphysique, Louvain-la-neuve: Peeters 2008, Sumphilosophein, Roma-Bari: Laterza 2010, Invito alla filosofia, Brescia: La Scuola 2011, Aristotele, Brescia: La Scuola 2013.

Francesco Berto Francesco Berto is professor of metaphysics at the University of Amsterdam and research leader at the Northern Institute of Philosophy, University of Aberdeen. He has published various books and papers on metaphysics and the

210 | List of Contributors philosophy of logic, among them: L’esistenza non è logica. Dal quadrato rotondo ai mondi impossibili, Rome and Bari: Laterza 2010, There’s Something About Goedel. The Complete Guide to the Incompleteness Theorem, Oxford: Wiley-Blackwell 2009, How to Sell a Contradiction. The Logic and Metaphysics of Inconsistency, London: King’s College Publications 2007, Logica da Zero a Gödel, Rome and Bari: Laterza 2007, Teorie dell’Assurdo. I rivali del Principio di Non-Contraddizione, Milan: Carocci 2006.

Franca D’Agostini teaches Philosophy of Science at the University of Turin (Politecnico) and Logic and Epistemology of the Social Sciences at the University of Milan. She is author of books in Italian and English on Truth, Paradoxes, and the History of Contemporary Philosophy, among them: Analitici e continentali, Milan: Raffaello Cortina Editore 1997, Breve storia della filosofia nel Novecento, Turin: Einaudi 1999, Logica del nichilismo, Rome and Bari: Laterza 2000, Disavventure della verità, Turin: Einaudi 2002, Paradossi, Milan: Carocci 2009, The Last Fumes. Nihilism and the Nature of Philosophical Concepts, Aurora: Davies Group Publishers 2009, The Responsibility of the Philosopher (ed.), New York: Columbia University Press 2010, Introduzione alla verità, Turin: Bollati Boringhieri 2011, I mondi comunque possibili. Logica per la filosofia e il ragionamento comune, Turin: Bollati Boringhieri 2012.

Elena Ficara is junior professor at the University of Paderborn. Her works include: Die Ontologie in der Kritik der reinen Vernunft, Würzburg: Königshausen & Neumann 2006, Heidegger e il problema della metafisica, Rome: Casini 2010, Die Begründung der Philosophie im deutschen Idealismus (ed.), Würzburg: Königshausen & Neumann 2011, Philosophie und Skeptizismus. Kant, Fichte, Hegel (ed.), FichteStudien 39, 2012, “Dialectic and Dialetheism,” in: History and Philosophy of Logic 34, 2013, 35–52.

Luca Illetterati is professor of Theoretical Philosophy at the Università di Padova. He is author and editor of numerous books on Hegel, the concept of limit in German Classical Philosophy as well as on the philosophy of nature. Among them: Natura e ragione. Sullo sviluppo dell’idea di natura in Hegel, Trento: Verifiche 1995, Figure del limite. Esperienze e forme della finitezza, Trento: Verifiche 1996, Introduzione, traduzione e commento a: G. W. F. Hegel. Il meccanismo, il chimismo, l’organismo e il conoscere, Trento: Verifiche 1996, Filosofia come esperienza del limite. Problemi di introduzione, Padua: CUSL 2002, Tra tecnica e ragione. Prob-

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lemi di ontologia del vivente in Heidegger, Padova: Il Poligrafo 2002, La filosofia come esperienza del pensiero e scienza della libertà. Un approccio a Hegel, Padua: CLEUP 2009, Hegel (together with P. Giuspoli and G. Mendola), Milan: Carocci 2010.

Angelica Nuzzo is professor of Philosophy at the Graduate Center and Brooklyn College (City University of New York). She has received her PhD at the Scuola Normale Superiore di Pisa and her Habilitation at the Universität Heidelberg. She has been Alexander von Humboldt Fellow and is author of numerous books in English, German and Italian. Among others: History, Memory, Justice in Hegel, New York: Palgrave, 2012, Hegel and the Analytic Tradition, London and New York: Continuum 2009, Ideal Embodiment. Kant’s Theory of Sensibility, Bloomington: Indiana University Press 2008, Kant and the Unity of Reason, West Lafayette: Purdue University Press 2005, Logica e sistema. Sull’idea hegeliana di filosofia, Genoa: Pantograf 1996, Rappresentazione e concetto nella logica della Filosofia del diritto di Hegel, Naples: Guida 1990, System, Bielefeld: Transcript Verlag 2003.

Graham Priest is Distinguished Professor of Philosophy at the Graduate Center, City University of New York, and Boyce Gibson Professor Emeritus at the University of Melbourne. He is known for his work on non-classical logic, particularly in connection with dialetheism, on the history of philosophy, and on Buddhist philosophy. He has published articles in nearly every major philosophy and logic journal. His books include: In Contradiction: A Study of the Transconsistent, Dordrecht: Martinus Nijhoff 1987 (2nd edition: Oxford: Oxford University Press 2006), Beyond the Limits of Thought, Cambridge: Cambridge University Press 1995 (2nd edition: Oxford: Oxford University Press 2002), Logic: a Very Short Introduction, Oxford: Oxford University Press 2000, Towards Non-Being: the Semantics and Metaphysics of Intentionality, Oxford: Oxford University Press 2005, Doubt Truth to be a Liar, Oxford: Oxford University Press 2006. His new book, One, is about to appear with Oxford University Press.

Achille Varzi is Professor of Philosophy at Columbia University, New York. He is an editor of The Journal of Philosophy, a subject editor of the Stanford Encyclopedia of Philosophy, and an associate or advisory editor of The Monist, Studia Logica, Synthese, Dialectica, The Review of Symbolic Logic, and several other journals. He writes mainly on logic, metaphysics, and the philosophy of language. Among his books: Il mondo messo a fuoco [The world in focus], Rome: Laterza 2010;

212 | List of Contributors Insurmountable Simplicities (with Roberto Casati), New York: Columbia University Press 2006; Ontologia [Ontology], Rome: Laterza 2005; Parole, oggetti, eventi e altri argomenti di metafisica, Rome: Carocci 2001; Parts and Places (with Roberto Casati), Cambridge MA: MIT Press, 1999; An Essay in Universal Semantics, Dordrecht: Kluwer 1999; Holes and Other Superficialities (with Roberto Casati), Cambridge MA: MIT Press 1994.

Gianni Vattimo is professor of Theoretical Philosophy at the Università di Torino. He has been active in the Partito Radicale and the Democrats of the Left, and the party Italia dei Valori. Since 1999 he is a member of the European Parliament. He is author of numerous books (all translated into major languages), among them: Essere, storia e linguaggio in Heidegger, Turin: Filosofia 1963, Ipotesi su Nietzsche, Turin: Giappichelli 1967, Introduzione ad Heidegger, Rome and Bari: Laterza 1971, Il soggetto e la maschera, Milan: Bompiani 1974, Le avventure della differenza, Milan: Garzanti 1980, Al di là del soggetto, Milan: Feltrinelli 1981, Il pensiero debole (ed. together with P. A. Rovatti), Milan: Feltrinelli 1983, La fine della modernità, Milan: Garzanti 1985, Introduzione a Nietzsche, Rome and Bari: Laterza 1985, La società trasparente, Milan: Garzanti 1989, Etica dell’interpretazione, Turin: Rosenberg & Sellier 1989, Filosofia al presente, Milan: Garzanti 1990, Oltre l’interpretazione, Rome and Bari: Laterza 1994, Credere di credere, Milan: Garzanti 1996, The Future of Religion (together with R. Rorty, ed. by Santiago Zabala), New York: Columbia University Press 2005, Christianity, Truth, and Weak Faith (together with R. Girard, ed. by P. Antonello), New York: Columbia University Press 2009, Hermeneutic Communism (together with Santiago Zabala), New York: Columbia University Press 2011.

Federico Vercellone is professor of Aesthetics at the University of Turin. His works deal with the relationship between aesthetics and contemporary hermeneutics, the history of nihilism in European thought, and the tradition of German Romanticism. His most recent research focuses on the notion of morphology in order to provide a multidisciplinary approach to the concept of form, image, and phenomenon. His most recent publications include: Introduzione a Il nichilismo (1992; German translation, 1998); Nature del tempo. Novalis e la forma poetica del romanticismo tedesco (1998); Estetica dell’Ottocento (1999; Portuguese translation, 2000; Spanish translation, 2004); Morfologie del moderno. Saggi di ermeneutica dell’immagine (2006); Oltre la bellezza (2008, Castiglioncello prize 2009; Spanish translation, 2013); Pensare per immagini (2010, with Olaf Breidbach; new German

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edition, 2011; English edition, forthcoming); Le ragioni della forma (2011); Dopo la morte dell’arte (2013).

Klaus Vieweg is professor of German Classical Philosophy at the University of Jena. He has been Alexander von Humboldt scholar and visiting professor in several universities (Pisa, Seattle, Tuebingen, Kyoto, Vienna, Prague, Torino, Bochum, Naples, Siena, Medellin, Shanghai). His main interests include German Idealism, Hegel, ancient and modern Scepticism, practical and political philosophy. Among his publications are: Das Denken der Freiheit – Hegels ,Grundlinien der Philosophie des Rechts‘, Munich: Fink 2012; Philosophie des Remis – Der junge Hegel und das ,Gespenst des Skeptizismus‘, Munich: Fink 1999, Il pensiero della libertà – Hegel e lo scetticismo pirroniano, Pisa: ETS 2007, Skepsis und Freiheit – Hegel über den Skeptizismus zwischen Literatur und Philosophie, Munich: Fink 2007, Inventions of the Imagination, (ed. together with R. T. Gray et al.) Seattle: London 2011; Hegels Phänomenologie des Geistes (ed. together with W. Welsch) Frankfurt a. M.: Suhrkamp 2008; Die Aktualität der Romantik (ed. together with M. Forster) Berlin: LIT 2012; Shandean Humour in English and German Literature and Philosophy (ed. together with J. Vigus, K. Wheeler) Oxford: Legenda 2013; Genius loci. Ansichten großer Philosophen in Text und Bild, Darmstadt: WBG 2014.

Wolfgang Welsch is professor emeritus at Friedrich Schiller University Jena. He has been visiting professor in several universities, among them at Berlin’s Freie Universität, Humboldt Universität and Stanford University. He is author of several books about aesthetics, postmodernism, Hegel, and evolutionary philosophy. Among them: Aisthesis. Grundzüge und Perspektiven der Aristotelischen Sinneslehre, Stuttgart: Klett-Cotta 1987, Unsere postmoderne Moderne, Weinheim: VCH Acta humaniora 1987 (7th edition: Berlin: Akademie Verlag 2008), Ästhetisches Denken, Stuttgart: Reclam 1990 (6th edition: 2003), La terra e l’opera d’arte. Heidegger e il Crepusculo di Michelangelo, Ferrara: Gallio Editori 1991, Vernunft. Die zeitgenössische Vernunftkritik und das Konzept der transversalen Vernunft, Frankfurt a. M.: Suhrkamp 1995 (4th edition: 2007), Grenzgänge der Ästhetik, Stuttgart: Reclam 1996, Undoing Aesthetics, London: Sage 1997, Immer nur der Mensch? Entwürfe zu einer anderen Anthropologie, Berlin: Akademie 2011, Blickwechsel. Neue Wege der Ästhetik, Stuttgart: Reclam 2012, Mensch und Welt. Eine evolutionäre Perspektive der Philosophie, Munich: Beck 2012, Homo mundanus – Jenseits der anthropischen Denkform der Moderne, Weilerswist: Velbrück Wissenschaft 2012, Der Philosoph. Die Gedankenwelt des Aristoteles, Munich: Fink 2012.

Index of Names A Abel, G. v Alston, W. P. 32, 46, 47, 51, 52 Aristotle 1, 2, 6, 9, 31, 46, 51, 53, 59, 60, 63, 78, 80, 97–103, 105–108, 123, 137, 173, 182, 191, 207 Arló-Costa, H. 67, 78 Armour-Garb, B. 1, 2, 9, 13, 25, 26, 51, 52, 80, 107, 108 Arruda, A. I. 79 Asenjo, F. G. 59, 78 Assmann, J. 122, 124 Augé, M. 184, 191 B Batens, D. 19, 21, 23, 25, 80 Baum, M. 111, 116, 117, 124 Beall, JC 1–4, 9, 13, 28, 30, 37, 43, 48, 51, 52, 80, 100, 107, 108 Becker, J. 167, 169 Belnap, N. D. 65, 69, 78 Belting, H. 186, 191 Bencivenga, E. 53, 56, 78 Benjamin, W. 176, 179 Berti, E. 6, 97–99, 107, 132, 151, 152, 196 Berto, F. 2, 6, 9, 60, 78, 92, 99, 100, 106–108, 132, 135, 136, 143, 152 Bodei, R. 112, 124 Brandom, R. 71, 80, 132, 135, 152 Breidbach, O. 186, 191 Brown, B. 51, 81, 92 Bubner, R. 124 Burge, T. 33, 35, 45, 51 Butler, J. 1, 9 C Calvino, I. 204, 207 Carlson, D. G. 125 Cavini, W. 63, 78, 79 Cesa, C. 111, 117, 124 Chiereghin, F. 149, 152 Chihara, C. 16, 25 Christensen, D. 37, 51

Chuaqui, R. 79 Church, A. 38, 53, 79 Code, A. 98, 107 Cogburn, J. 51 Cohen, C. 63, 79 Cohen, S. M. 98, 107 Colletti, L. 152 Copi, I. 63, 79 Crubellier, M. 101, 107 D da Costa, N. 59, 67, 79, 99, 107 D’Agostini, F. v, 4, 5, 32–34, 46, 47, 52, 105, 107 Dancy, R. M. 6, 9, 98, 99, 107 Davidson, D. 193, 207 de Boer, K. 130, 152 Del Pozo Ortea, M. 186, 191 Deligiorgi, K. 125 DeVidi, D. 63, 79 Diderot, D. 200, 201, 207 Didi-Huberman, G. 189, 191 D¯ogen Zenji 199, 208 Dubikajtis, L. 67, 79 E Eklund, M. 28, 30 Eldridge-Smith, P. 3, 9, 28–30, 43, 45, 52 Eldridge-Smith, V. 3, 9, 30, 43, 45, 52 Evans, G. 58, 74, 79 F Fait, P. 101, 107 Faizi, H. v Ficara, E. 29, 32, 52 Field, H. 42, 52 Findlay, J. N. 131, 152 Fine, K. 58, 79 Flasch, K. 198, 207 Føllesdal, D. v Frege, G. 5, 55, 58, 79 Fukuyama, F. 174, 175, 179 Fulda, H. F. 136, 152 Furth, M. 98, 107

216 | Index of Names G Gadamer, H.-G. 8, 181–184, 190, 191 Gaio, S. 100, 107 Gell, A. 185, 191 Gobbo, E. 100, 107 Gödel, K. 53, 79 Goethe, J. W. 110, 124, 150 Gottlieb, P. 98, 100, 107 Gregoire, F. 132, 135, 152 Grim, P. 2, 9 Grünkorn, G. v Guyer, P. 164, 169 H Haack, S. 63, 79 Habermas, J. 181, 191 Harris, H. S. 124 Hartmann, N. 132, 152 Hegel, G. W. F. 1, 2, 6, 7, 9, 25, 32, 36, 51, 52, 97, 99, 103, 106, 107, 109–125, 127–133, 135–138, 140–154, 156–170, 173, 174, 176, 179, 183, 198, 205, 207 Heidegger, M. 8, 175, 178, 179, 181, 185, 186, 191, 194, 207 Henrich, D. 154, 169 Hintikka, J. 56, 79 Horstmann, R. P. 130, 152, 169 Houlgate, S. 125, 145, 152 Hyde, D. 58, 79 I Illetterati, L. 7 J James, D. 154, 158, 169 Jaśkowski, S. 57, 59, 65, 67, 69, 71, 79 Jean Paul 168, 169 K Kahn, C. H. 123, 124 Kant, I. 1, 2, 7, 9, 33, 47, 51–53, 79, 97, 109, 110, 113–119, 121, 124, 132, 133, 138–140, 145, 151, 152, 156, 158, 162–169, 182, 207 Kneale, M. 55, 79 Kneale, W. 79 Kneale, W. C. 55, 79

Kroon, F. 44, 49, 52 Kuhn, T. 178, 179 Künne, W. 46, 52 L Lambert, K. 54, 56, 79 Lehmann, S. 56 Leibniz, G. W. 60, 79, 97 Lennox, J. G. 191 Leonard, H. S. 56, 79 Levesque, H. 90, 92 Lewis, D. K. 65, 67, 69, 74, 79, 91, 92 Littmann, G. 100, 107 Łukasiewicz, J. 9, 59, 62, 63, 79, 97, 98, 105, 107, 196, 207 Luporini, C. 111, 124 Lynch, M. 52 M Maier, H. 97, 108, 111, 125 Malachowski, A. R. 207 Marconi, D. 135, 136, 152 Mares, E. 3, 9, 14, 16, 25, 48, 52, 81, 82, 87, 92, 100, 108 Matte Blanco, I. 98 McTaggart, J. 135, 152 Meheus, J. 13, 25 Meist, K. 111, 124, 200, 205 Mesch, W. 124 Meyer, R. 88, 93, 99, 108 Michel, K. M. 124, 169, 179 Mignucci, M. 98, 108 Miller, D. 23, 25, 107, 144, 152 Moldenhauer, E. 124, 169, 179 Moretto, A. 141, 152 N Neurath, O. 203, 207 Nietzsche, F. 43, 50, 186, 201–204, 207, 208 Nikolaus von Kues 207 Nuzzo, A. 7, 52, 111, 119, 120, 122, 125, 136, 152 P Pareyson, L. 190, 191 Pelletier, F. J. 58, 80 Pippin, R. 116, 125, 154, 169

Index of Names |

Popper, K. 25, 103, 104, 108, 130–132, 152, 203, 208 Poser, H. v Priest, G. 1–6, 9, 13–17, 24–26, 32, 33, 35, 37, 49, 51, 52, 59, 68, 71, 72, 78, 80, 82, 83, 86, 87, 93, 99, 100, 104–108, 147, 148, 152 Proudfoot, D. 65, 80, 91, 93 Putnam, H. 46, 49, 50, 52 Q Quante, M. 154, 156, 168, 169 Quine, W. V. O. 14, 25, 28, 30, 34, 52, 56, 80, 203, 204, 208 R Rantala, V. 86, 89, 93 Renner, J. 208 Rescher, N. 71, 80 Restall, G. 37, 51, 87, 93 Ricoeur, P. 176, 179 Roller, C. v Rorty, R. 177–179, 195, 207 Rosenkranz, K. 153, 169 Routley, R. 2, 9, 15, 26, 59, 68, 80, 88, 93, 99, 108 Russell, B. 5, 16, 18, 23, 26, 33, 53, 55, 56, 58, 72, 79, 80, 99 S Sainsbury, M. 34, 42, 52, 77, 80 Salmon, N. 58, 80 Sans, G. 156, 170, 208 Schick, F. 154, 158, 159, 170 Schlipp, P. A. 79 Schöps, D. v Severino, E. 98 Shakespeare, W. 177, 179 Shapiro, S. 100, 108 Simmons, K. 100, 107

217

Simon, E. v Soames, S. 14, 26 Solomon, G. 63, 79 Sorensen, R. 35, 36, 52 Speck, J. 207 Spinoza, B. 173, 179 Stekeler-Weithofer, P. 167, 170 Strawson, P. F. 71, 80 T Tahko, T. E. 108 Taylor, C. 181, 191 V van Woudenberg, R. 48, 52 Vander Laan, D. A. 87, 93 Varzi, A. C. 4, 5, 36, 52, 58, 67, 71, 74, 78, 80 Vasil’év, N. A. 59, 80 Vattimo, G. 8 Vercellone, F. 8, 186, 191 Vieweg, K. 153, 156, 170 Vorderobermeier, K. v W Weber, E. 13, 25, 181, 185 Wedin, M. V. 55, 62, 80, 100, 108 Welsch, W. 8, 9, 199, 205, 207, 208 Whitehead, A. N. 55, 80, 194 Whitman, W. 196, 197, 208 Williams, R. 58, 69, 80 Williamson, T. 52, 80 Wittgenstein, L. 35, 45, 52 Wood, A. 163, 170 Wouters, D. 13, 25 Z Zalta, E. 9, 87, 93, 107, 108 Zhuangzi 200, 208 Žižek, S. 1, 9

Subject Index A Antinomies 7, 34 f, 59, 124, 153, 157, 163 f, 166, 168 f Aufhebung 99, 112, 168, 197 ff B Belief 22, 33, 36 ff, 51, 59 f, 82, 88 ff, 97, 106, 114, 162, 174, 178 Bivalence 42, 58, 63, 68 f, 72 f, 76 f C Coherence 90, 149, 193, 196 ff, 200 f, 203 ff Concepts 13, 15, 17 ff, 21 ff, 48 ff, 67, 113, 132, 188 Conceptual Revision 17, 22 Conditional – relevant, 87 f Conflicting pieces of evidence 39 Conflicts 35, 38, 114, 132, 174 f, 177 – reliability 38 Consistency 89, 193 ff – allergy [Konsistenzallergie] 200 ff Contradictions – and determination 113, 118, 129 f, 134, 137 ff, 148 – and Hegel’s Sittlichkeit 115 ff – and Kant’s Moralität 115 ff, 153 ff – and limits 7, 24, 59, 114, 127 ff – and Verstandeslogik 110 ff – at the empirical world 3 f, 16 f, 27 ff, 33, 47 – by fiat 13 ff – conceiving 6, 82 – conceptual 3, 16, 24, 48, 51, 111, 114, 121, 136, 182, 184, 186 f – controlling 8, 173 ff – doxastic 36, 38, 46 f – effectiveness of 2 – evidence of 4 f, 31 ff, 49, 51, 59, 69 ff, 77 f, 106, 110 – genuine 4-5, 68 ff, 77 f – insuperable 173 ff – irreducible 3, 8 f, 34 f – justice of 6 f, 109 ff

– linguistic 3, 14, 16, 48 – morality of 7, 153 ff – necessary 8, 99, 133 ff – ontological implications of 4 f, 16 f, 31 ff, 131 ff – reality of 31 ff – representing 81 ff – true 2 ff, 31, 44, 99, 105 f, 130, 147 f Contravalence – and contradiction, 5, 59, 62 f, 64 ff D Democracy 175 f, 182 Dialetheia 2, 5, 13 ff, 43, 48, 69, 77 f, 106, 148 – de dicto/de re 5, 69, 77, – metaphysical 43 f – metaphysical/semantic 16 f, 48 f Dialetheism 1 ff, 13 ff, 31 f, 43, 45 ff, 59, 99 f, 103, 106, 148 – and alethic realism 45 ff – metaphysical/semantic 3 f, 15 ff, 48 ff Disagreement 1 E Ex contradictione quodlibet (ECQ) 61, 71, 81 Ex falso quodlibet (EFQ) 88, 130, 133 F Facts 3 ff, 17 f, 32 f, 39 ff, 69, 104, 110 f, 176 – de se/de re 32 – epistemic 39, 43 ff – kinds of 46 ff – liar-like facts 3, 42 ff – logical 42 f – modal 47 – negative 3, 17, 45 – semantic 43 ff – soft 43 ff Fiction 28 f, 36, 42 f, 48 f, 65 ff, 90 ff the Finite 142 ff – and the Infinite 145 f, 147 H Hermeneutics 174 ff, 181 ff

220 | Subject Index I Images 186 ff Inconsistency 19, 23, 71 L Laws of Logic 69, 87 f, 90, 113 f, 127, 129 f – and moral laws 115 ff – Contraposition 88 – De Morgan 22 – Double Negation 22, 147 – Excluded Middle 27, 58, 61, 63, 73, 76 – Identity 127 – Non-Contradiction 2, 5 f, 31, 53 ff, 97 ff, 113, 195, 207 Logic – and metaphysics 53 ff – and truth 53 f – and validity 53 f – classical 31, 49, 68, 71, 81, 83 – discursive 65, 67, 69 – epistemic 82, 88 – free 56, 57 f, 61 f, 71 – in the locked room 53 ff – non-classical 2, 35 – of fiction 69 – of representation 88 ff – paraconsistent 1, 5, 36, 59, 61, 71 f, 81, 99, 103, 147 – relevant 5, 81 f, 87, 90, 92 M Metaphysics 1 f, 17, 32, 39, 46 ff, 53 ff, 58 Moderne 203 ff Moralität 109 f, 114 ff, 117 f, 153 ff Morphology 181 ff N Negation 17, 20 ff, 33 f, 42, 47, 62, 68, 86, 131, 133, 138 f, 143, 145 – and determination 118 O Objects 4, 16 f, 24, 178, 198 – of experience 32 – spatial 140 – transcendental 47 – vague 74, 77

Ontological – neutrality 53 ff – overdeterminacy 5, 69 Ontology 17, 59, 63, 133 – and revolution 8, 178 f – postmodern 194

P Paradox – Fermi-Hart 39, 44 – in metaphysical perspective 40 ff – Liar 25, 28 f, 41 ff, 59, 99, 106 – of the Preface 37 f, 42 – Pinocchio 3 f, 27 ff, 43 ff – Rapunzel 3 f, 27 ff – Reliability 38 ff – Russell’s 16, 23, 99 – Semantic 4 – Set-theoretic 31, 35, 38 – Sorites 31, 34 f, 38 – True 34 ff, 45 – Veridical 34 ff – Zeno’s 38, 99

R Realism – alethic 4 f, 32, 45 ff – metaphysical 4, 47, 49 ff Reality 2 ff, 13, 18, 31 ff, 53, 91, 97, 103, 105 f, 110 ff, 123, 128 f, 131 ff, 147 ff, 159, 199, 176, 178, 183 Redlichkeit 201 ff Reductio ad absurdum 34 Refutation 6, 42, 97, 100 ff, 112

S Schranke 138 f, 144 ff, 163, 165 Selbstbestimmung – and Fremdbestimmung 165 ff Semantic predicates 14, 28 f Sorites see Paradox

Subject Index | 221

T Trivialism 5 f, 49 Truth 1 ff, 13 ff, 17 f, 24, 29, 32 ff, 37, 40, 43 ff, 53 ff, 67 ff, 81, 84 ff, 98, 102 ff, 106, 120 f, 128 ff, 148 f, 173 ff, 189 – at some world 4, 28, 85 f – concept of 4, 24, 49 ff – epistemic 40 f – in a story 4, 28, 43, 65 – realistic 40 – spandrels of 28 f Truth value gaps 21, 33, 40 f, 84 ff, 86 Truth value gluts 3, 33, 27 ff, 84 ff, 86

V Vagueness 17 ff, 58, 72. Validity 53 f, 60 ff, 65, 67, 75, 82, 87, 129 W Weltgericht 6 f, 119, 121 ff Weltgeschichte 6 f, 109, 119, 121 ff World – disenchantment of 8, 181 ff – empirical 3 f, 27 f – re-enchantment of 8, 185 Worlds – ersatz 67 – impossible 81 ff, 87 ff – non normal 6, 81 ff, 87 ff – possible 28, 44 f, 67, 69, 75, 84 ff, 87 ff, 99