Principle of Non-Contradiction

Contradictions constitute one fundamental aspect of human life. Humans are steeped in contradictory thoughts, feelings, and attitudes. In this debate, five anthropologists adopt an individual-centered and phenomenological perspective on contradictions. How can one live with them? How to describe them from an anthropological point of view? Should we rethink our dear notion of the " social agent " through that of contradiction? Once during my anthropology of gender class, one student explained to us her embarrassment when, being a convinced feminist, she realized that she was enthusiastically singing the sexist lyrics of a popular track. In the same vein, I often think about environmentalists who are, at the same time, frequent flyers or smokers. Take also anti-capitalist intellectuals who, through their editorial and

Speculative philosophers who seek to revive the classical opposition between empiricism and rationalism maintain a tormented relation to Gilles Deleuze. On the one hand, they are themselves the bastard children of a Deleuze reception which reassures us of his rationalistic credentials. Ever since Alain Badiou's The Clamor of Being (1997), the aim of this (mainly Anglo-American) tradition has been to establish an image of Deleuze as a bona fide (academic) philosopher who relieves us from decades of analytical and phenomenological relativism. This is the Deleuze of the great theoretical theses of immanence, the univocity of being, the externality of relations, the dice-throw, the syntheses of time, and so on. On the other hand, those very same speculative philosophers tend to reject the vitalist image of Deleuze that has dominated the earlier reception, which emphasized the empiricist, that is nonphilosophical and practical aspects of his work. It is these aspects which are now considered hippie and indiscernible from what Quentin Meillassoux has labelled the 'sceptico-fideist' position. On this account, the absolute and the nonhuman for Deleuze are a question of 'belief ' in the micropolitical event and not in the major powers of rational thought.

In the Parmenides, Plato delivered a series of devastating critiques that demonstrated how even our most basic semantic formulations of the perfect paradigms must be mired in a medley of contradictions. In the Sophist, Plato dissolved all such contradictions into relative differences and resolved all differences into proportions of identity-in-difference. Hegel may thus have found in the Divine Method of Plato's Philebus the the ancestor of his own dialectical solution to the Kantian antinomies, and interpolated this solution to re-interpret Plato's later dialogues as a positive dialectic: where the negative dialectic of the Parmenides dissolves all Ideas into a medley of contradictions, the Sophist suggests a resolution of these contradictions in and through self-moving spirits, and the Philebus proposes the Divine Method as a positive dialectic to fulfill Plato’s promise of philosophy.

The analogy of being was introduced by Aristotle, and later thematised by Thomas Aquinas, as a special mode of grammar in which one term may signify two or more meanings, but in which each of the signified meanings derives its primary meaning by participating in one common meaning. The analogy of being thus decisively presupposes this metaphysic of participation. But this very pillar of participation is also the principal source of the aporia of analogy. In the Science of Logic, Hegel outlined how the quantitative ratio and the syllogism of analogy may be successively sublated into the Idea in what I call a ‘speculative analogy’. When Erich Przywara later re-formulated the analogy of being at the apogee of phenomenology, he implicitly opposed Schelling’s rhythmically oscillating opposition of contraries to Hegel’s sublation of contradictions. This conflict over contradiction has produced two competing models of analogy: Hegel’s analogical dialectics in which contradictory differences are meant to be sublated into the ‘absolute middle’ of the Idea; and Przywara’s dialectical analogy in which contrary opposites are meant to participate in the mysterious ‘suspended middle’ of God. Przywara criticizes Hegel for evacuating the mystery into concepts, but Hegel might respond by criticizing Przywara for withholding these mysteries beyond the concept. This comparison illustrates how Hegel’s Science of Logic cannot adequately resolve all contrary opposites in a speculative analogy unless the middle terms the syllogisms are re-read against the letter of Hegel’s text as the absolute middle of Christ in the Trinity.

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true.

The present work is devoted to the exploration of some formal possibilities suggesting, since some years, the possibility to elaborate a new, whole geometry, relative to the concept of “opposition”. The latter concept is very important and vast (as for its possible applications), both for philosophy and science and it admits since more than two thousand years a standard logical theory, Aristotle’s “opposition theory”, whose culminating formal point is the so called “square of opposition”. In some sense, the whole present enterprise consists in discovering and ordering geometrically an infinite amount of “avatars” of this traditional square structure (also called “logical square” or “Aristotle’s square”). The results obtained here go even beyond the most optimistic previous expectations, for it turns out that such a geometry exists indeed and offers to science many new conceptual insights and formal tools. Its main algorithms are the notion of “logical bi-simplex of dimension m” (which allows “opposition” to become “n-opposition”) and, beyond it, the notions of “Aristotelian pq-semantics” and “Aristotelian pq-lattice” (which allow opposition to become p-valued and, more generally, much more fine-grained): the former is a game-theoretical device for generating “opposition kinds”, the latter gives the structure of the “opposition frameworks” containing and ordering the opposition kinds. With these formal means, the notion of opposition reaches a conceptual clarity never possible before. The naturalness of the theory seems to be maximal with respect to the object it deals with, making this geometry the new standard for dealing scientifically with opposition phenomena. One question, however, philosophical and epistemological, may seem embarrassing with it: this new, successful theory exhibits fundamental logical structures which are shown to be intrinsically geometrical: the theory, in fact, relies on notions like those of “simplex”, of “n-dimensional central symmetry” and the like. Now, despite some appearances (that is, the existence, from time to time, of logics using some minor spatial or geometrical features), this fact is rather revolutionary. It joins an ancient and still unresolved debate over the essence of mathematics and rationality, opposing, for instance, Plato’s foundation of philosophy and science through Euclidean geometry and Aristotle’s alternative foundation of philosophy and science through logic. The geometry of opposition shows, shockingly, that the logical square, the heart of Aristotle’s transcendental, anti-Platonic strategy is in fact a Platonic formal jungle, containing geometrical-logical hyper-polyhedra going into infinite. Moreover, this fact of discovering a lot of geometry inside the very heart of logic, is also linked to a contemporary, raging, important debate between the partisans of “logic-inspired philosophy” (for short, the analytic philosophers and the cognitive scientists) and those, mathematics-inspired, who begin to claim more and more that logic is intrinsically unable to formalise, alone, the concept of “concept” (the key ingredient of philosophy), which in fact requires rather geometry, for displaying its natural “conceptual spaces” (Gärdenfors). So, we put forward some philosophical reflections over the aforementioned debate and its deep relations with questions about the nature of concepts. As a general epistemological result, we claim that the geometrical theory of oppositions reveals, by contrast, the danger implicit in equating “formal structures” to “symbolic calculi” (i.e. non-geometrical logic), as does the paradigm of analytic philosophy. We propose instead to take newly in consideration, inspired by the geometry of logic, the alternative paradigm of “structuralism”, for in it the notion of “structure” is much more general (being not reduced to logic alone) and leaves room to formalisations systematically missed by the “pure partisans” of “pure logic”.

Plato’s contest for the early Academy was to answer Parmenides’ criticisms of the Theory of the Universal Forms through an interpretation of the dialectical exercises presented in the Parmenides (§I).  Plato’s Theory of the Universal Forms and the objections of the Parmenides may now be more precisely formulated in predicate logic using the notational convention developed by Edward Zalta (§II).  The two principal objections to Plato’s Theory of the Universal Forms are the Third Man Argument and the Greatest Difficulty Argument: the Third Man Argument can be answered by Constance Meinwald’s distinction of Self-Predication and Gail Fine’s distinction of Non-Identity (§III); and the Greatest Difficulty Argument implies the inconsistent set of Russell's Paradox, yet may be answered through the construction of a hierarchical set theoretical model that subsumes and restricts the semantic scope of each subordinate hypothesis (§IV).  The rejection of the external predication of the Third Man Argument and the two-world ontology of the Greatest Difficulty Argument suggests a monistic ontology of internal relations in the Concrete Universal form of all forms (§V).

The epistemic constellation that underlies the transformation of metaphysics in the 13th and 14th century is legitimized by the identification of the subject of first philosophy with the first object of the intellect. In this epistemic constellation, a new thought presents itself: the foundation of Aristotle’s unconditional starting point of thinking, i.e. the principle of non-contradiction, in the first known, transcendental concepts of the mind. The present article argues that, on the one hand, innovative attempts to found the principle of non-contradiction of the Franciscan Nicolaus Bonetus and the Carmelite John Baconthorpe demonstrate the stability of this epistemic constellation. It is true that, in their foundation of the principle of non-contradiction, Bonetus and Baconthorpe effect a dissociation of the subject of first philosophy and the first object of the intellect, which seems to challenge the very legitimizing strategy of the medieval transformation of metaphysics. But the very discourse that breaches the identification of the subject of metaphysics with the first object of the intellect, tacitly reproduces it by means of a division of first objects of the intellect. Its articulation of a first object of the intellect that surpasses the subject of first philosophy in generality, on the other hand, preludes tendencies in modern philosophy that, in presenting the thinkable as such as what grants access to reality, give full attention to the modes of being excluded from Aristotle’s Metaphysics.

As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? If so, what does it mean to forego such a bias in the interest of greater neutrality—and ought we to do so?

I originally entitled this paper ‘Why are there no uncontroversial examples of philosophical nonsense?’, but since this seemed apt to provoke rather superficial responses, I decided to re-title it.  In it I ponder the fact that, not only are there no uncontroversial examples of philosophical nonsense, there are no uncontroversial examples of what one might call ‘analogue philosophical nonsense’.  These would be non-philosophical cases of someone’s believing he means something when in reality he means nothing.  (Someone’s saying, ‘It’s 5 o’clock on the sun’ is sometimes offered as an example.)  I ask what conditions such cases would need to satisfy.  What would count as a compellingly clear case of an illusion of meaning?  Why has no one described one?

I suggest that, although the nonsensicalist challenge (obviously) matters, it has, at least in its Wittgensteinian form, been widely ignored.  On the other hand, those who still adhere to nonsensicalism (mainly Wittgensteinians) have been equally remiss in their failure to examine its presuppositions.

This paper starts from Tractatus, 6.53, and ask how one could show someone ‘that he had failed to give a meaning to certain signs in his propositions’.  Once one has fully mastered the ‘austere’ conception of nonsense – that nonsense has neither meaning, form, content, nor logic – the difficulties of the enterprise become evident.  It is not clear how one could be in a position to conclude much about an utterance without first finding a meaning in it.  Suggestions made by Guy Robinson, Edward Witherspoon and Hans-Johann Glock are considered but it is concluded that the last, best hope for nonsensicalism lies in a therapeutic approach.  I end with a plea for someone who is sympathetic to this aspect of Wittgenstein’s philosophy to make a serious attempt to work out the details.

A reconstruction of Aristotle's argument against the opponents of the principle of non-contradiction that relies on the semantic relations that are mentioned by Aristotle.

“Aristoteles über die Rechtfertigung des Satzes vom Widerspruch”, in: Zeitschrift für philosophische Forschung 47 (1993), 521-541

This book is an introduction in a double sense. It is intended to introduce beginners in philosophy to the idea of philosophical nonsense and the problems it raises. But it is also addressed to professional philosophers, most of whom seem virtually unaware of the issue.

Certain philosophers, here called ‘nonsensicalists’, believe that much philosophy (philosophical questions as well as assertions) is simply nonsense in the strict sense of being meaningless. They proceed as though it were an established fact that there is such a thing as philosophical nonsense and the notion were quite unproblematic. By contrast, many other philosophers proceed as though either they had never heard of it or it were quite obvious that there is no such thing.

There can be little doubt that what the nonsensicalists are saying is of great importance – if they are right. But there are at least eight questions that must be addressed before anyone is in a position to start hunting down philosophical nonsense and they have all been woefully neglected.

The idea of philosophical nonsense goes back to Thomas Hobbes at least and yet its history remains largely unresearched.

In view of the neglect of the problems raised by the notion of philosophical nonsense, even by professional philosophers, it is not unduly optimistic to suggest that it is a topic to which relative newcomers to the subject might make a contribution.

Ludwig Wittgenstein thought that good philosophy unties the knots in our thinking that bad philosophy has put there and must make movements as complicated as the knots it unties. Is the notion of philosophical nonsense an essential aid to this – as Wittgenstein himself thought – or just another knot?

Alan Darley has implored Radical Orthodoxy to become " more radically Thomistic " by recovering the law of non-contradiction that has lately been lost by Milbank, Pickstock, and Hoff in a " Cusanian tributary from the Neoplatonic river ". He contends that this prohibition on all contradictions can be explained through Aristotle's indirect demonstration against any possibility of denying it. But he fails to recognize how this very indirect demonstration already operates as a viciously circular formalized dialectic. Plato developed this dialectic into the self-determination of Intellect; Plotinus suspended it from the divine hypostases; and Proclus systematized it as the creative hypercontrariety that imparts every determination. Thomas Aquinas inherited Proclus' creative hypercontrariety from Pseudo-Dionysius of Areopagite, Aristotle's Principle of Non-Contradiction from Avicenna, and sublated all contrariety into the divine impartation of individuated acts of existence. This impartation of existence into entities may have produced an aporia of existence: if existence is multiple then it is contrary to the individuality of every entity; but if existence is unitary then it may conceal the creative contrariety of participation. The indiscriminate application of the Principle of Non-Contradiction threatens to break the bonds of being and dissolve the Thomistic metaphysics of participation into post-Ockhamist nihilism. The further radicalization of Thomism may thus require the aporia of existence to be resolved through a Neoplatonic dialectic.

The four strands are (a) the ‘austere’ conception of nonsense; (b) the view that a perfectly acceptable sentence of the language can be nonsense if it is uttered in unsuitable circumstances; (c) the view that rules of grammar are nonsense if construed as universal truths about the world; (d) the view that one cannot ‘mean a nonsense’.  (I think that this last has to be ascribed to Wittgenstein, though it is surprisingly difficult to find knock-down textual evidence for it.)  I argue that (c) is the odd man out and is not easily reconciled with the others.

Realist dialetheism is the view that there are contradictions in reality. One argument against this idea says that it is impossible because it has to make room for the possibility of a trivial reality, which is metaphysically impossible. Another argument against it says that the metaphysical structure of reality is such that it is impossible to have contradictions in it. I argue here that both arguments fail to establish the impossibility of realist dialetheism because they are based on a misconception about the notions of negation and contradiction which leads them, in the first case, to wrongly hold that dialetheism has to be compatible with trivialism, and, in the second case, to assume that the validity of the Aristotelian principle of non-contradiction prevents the existence of dialetheias.

I am planning a history of the notion of philosophical nonsense and naturally difficult historical and exegetical questions have come up.  Charles Pigden has argued that the notion goes back at least as far as Hobbes and that Locke, Berkeley, Hume, Kant (on some interpretations) and pragmatists such as William James, as well as numerous Twentieth-Century philosophers make use of it.  In this ‘paper’ I put forward for general discussion such questions as whether Hobbes was the first 'nonsensicalist', whether Kant was a 'nonsensicalist' at all, which philosophers if any have considered contradictions to be meaningless and whether Wittgenstein thought that his concept of criterion could legitimately be used verificationistically.  I shall continue to add further questions as they occur to me.

Thomas Nagel in ‘What is it like to be a bat?’ suggests that we don’t yet have much idea of how mental entities could be identical with physical ones (though he wisely stops short of accusing physicalists of not meaning ANYTHING WHATSOEVER by their identity-claims).  Colin McGinn goes further by suggesting that we may forever remain in this state of ignorance and incomprehension because of the inherent limitations of the human intellect.  I argue that the mere possibility that McGinn is right shows that it is over-hasty to conclude from philosophy’s failure to solve its problems that there must be something wrong with the problems themselves.  I also try to relate Nagel’s and McGinn’s view to David Stove’s response to philosophy’s apparent failure to make much progress.  He seems pessimistic about whether we will ever fully understand what is wrong with some philosophical claims.

There are passages in Wittgenstein where he compares his method to psychotherapy and one or two where he seems to suggest that the ‘patient’ has the last word on his ‘illness’ and ‘cure’.  This paper tries to take these seriously, especially in connexion with the idea that victims of philosophical confusion talk nonsense.

Philosophical accusations of talking nonsense made in a polemical spirit are bound to fail, since the only way one can effectively criticise another’s utterance is by attaching some meaning to it.  But if the other acknowledges the possibility that his puzzlement arises from his having been taken in by nonsense, then perhaps a co-operative investigation of this suggestion might be fruitful.  Indeed self-diagnosis ought in principle to be possible.  Ought it not to have happened at least once in the history of philosophy if philosophical nonsense has ever been exposed? 

But there are difficulties.  For example:
a) We must ask whether or not philosophical nonsense, when exposed as such, is supposed to lose all appearance of meaningfulness.  Either answer is problematic.
b) The acknowledged similarity of the methodology under investigation to that of psychoanalysis exposes it to many of the familiar objections to the methodology of psychoanalysis, especially those that draw attention to the misleading influence of suggestion by an authority-figure.
c) The proposal that relentless cross-questioning of a suspected nonsense-talker will eventually lead her to ‘dry up’ (if she really is talking nonsense) seems to involve a version of the so-called Socratic Fallacy.

I am planning a history of the concept of philosophical nonsense and naturally difficult historical and exegetical questions have come up.  Charles Pigden has argued that it goes back at least as far as Hobbes and that Locke, Berkeley, Hume, Kant (on some interpretations) and pragmatists such as William James, as well as numerous Twentieth-Century philosophers make use of it.  In this ‘paper’ I put forward for general discussion such questions as whether Hobbes was the first nonsensicalist, whether Kant was a nonsensicalist at all, which philosophers if any have considered contradictions to be meaningless and whether Wittgenstein thought that his concept of criterion could legitimately be used verificationistically.  I shall continue to add further questions as they occur to me.

Few would doubt that one often encounters the preposterous in philosophy.  Some would claim that preposterousness in philosophy is often a matter of literal nonsensicality, i.e. meaninglessness.  Is this plausible or is it itself an example of a preposterous philosophical claim?

This essay argues for the contingency of necessity, i.e. for the
contingency of reason. This essay is a rebuttal of Quentin Meillassoux’s argument for the necessity of contingency. While Meillassoux is a rationalist who presupposes the validity of the principle of non-contradiction as the condition of Hyper-Chaos, this essay contends that Hyper-Chaos is better explicated as a state both equal and unequal to itself at the same time. The principle of non-contradiction does not hold in Hyper-Chaos. Reason or the law of non-contradiction, therefore, can only be accrued to Hyper-Chaos as a consequent or belated necessity - a contingent necessity.

Published in 1908, C.S. Peirce's 'A Neglected Argument for the Reality of God' is one of his most difficult articles. Presenting a peculiar entanglement of scientific method and theology, it sketches a 'humble' argument for the reality—and not the existence—of God for Musers, that is, those who pursue the activity he calls 'Musement'. In Musement, Peirce claims, we can achieve a kind of perception of the intertwinement of the three universes of experience: of feeling, of brute fact, and of reason. He also somehow relates each universe to a distinct phase of inquiry, which is described by the use of induction, deduction, and abduction or retroduction. The way that he develops his claims allows him to outline God as an abductive vague hypothesis to explain how those three universes make up a single whole. The hypothesis being vague means that the principle of contradiction does not hold for it. In this presentation, we aim at throwing some light at these points, focusing on the concept of Musement and what is understood as the vagueness of the hypothesis.

Edward Witherspoon distinguishes Wittgenstein’s conception of nonsense from Rudolf Carnap’s.  The latter does not fully take into account the fact that, if something really is nonsense, it has no more meaning than ‘Ab sur ah’ and therefore cannot have any logical properties.  He finds the Carnapian conception even in professed Wittgensteinians such as Peter Hacker and Gordon Baker who think of themselves as rejecting it.  My question is where this leaves the notion of PHILOSOPHICAL nonsense.  Could anything that was utterly devoid of content play the crucial deceptive role that nonsensicalists, including Wittgensteinians, assign it?  Could it ever be detected if it did?

How do philosophical accusations of talking nonsense relate to the layperson’s notions of meaning and meaningfulness?  If one were to explain carefully what philosophical nonsense was supposed to be, would one be greeted with incredulity?  How do people react to being accused of talking nonsense themselves?  Is anything analogous to an illusion of meaning recognised in everyday life?  In dream-reports perhaps?  Or in the utterances of schizophrenics or those under the influence of drugs?  Or in certain jokes and hoaxes?  Are contradictions felt to be meaningless?  I argue that, though it is clear that experimental philosophy could shed some light on these questions, their subject matter creates special difficulties.  First, it is more difficult than usual to formulate questions and produce ‘vignettes’ that do not subtly encourage certain responses at the expense of others.  Second, the fact that philosophical nonsense is a metaphilosophical concept ensures that its investigation is going to be more indirect than would be that of knowledge or intention, for example.

Semantic paradoxes, like the Liar Paradox, are one of the best-known motivations for the dialetheists' claim that there are true contradictions. Liar-like arguments arise in natural language and dialetheists argue that the Liar sentence is true and false, i.e., it bears a glut as its truth-value. However, in a recent paper, JC Beall [4] argued that, by parallel reasoning, one should also be led from the resources of natural language to triviality by the use of validity paradoxes (Curry-style paradoxes involving a pre-theoretical notion of validity). Priest [11] answers Beall's challenge based on a typical move against Curry paradoxes: we avoid triviality by avoiding structural contraction, which is one of the steps in the derivation of triviality. We shall argue that this strategy poses some further difficulties for the dialetheist: i) it is hard for a dialetheist to motivate restriction of structural contraction; ii) structural contraction, if properly motivated, on the other hand, may lead one to avoid the Liar paradox too, and thus, the main motivation for the existence of gluts seems threatened; iii) the asymmetry in the treatment of paradoxes (take the Liar at face value, avoid the Curry) raises difficulties for the desideratum that pre-theoretical concepts should play a prominent role in motivating dialetheism.

How do philosophical accusations of talking nonsense relate to the layperson’s notions of meaning and meaningfulness?  If one were to explain carefully what philosophical nonsense was supposed to be, would one be greeted with incredulity?  How do people react to being accused to talking nonsense themselves?  Is anything analogous to an illusion of meaning recognised in everyday life?  In dream-reports perhaps?  Or in the utterances of schizophrenics or those under the influence of drugs?  Or in certain jokes and hoaxes?  Are contradictions felt to be meaningless?  I argue that, though it is clear that experimental philosophy could shed some light on these questions, their subject matter creates special difficulties.  First, it is more difficult than usual to formulate questions and produce ‘vignettes’ that do not subtly encourage certain responses at the expense of others.  Second, the fact that philosophical nonsense is a metaphilosophical concept ensures that its investigation is going to be more indirect than would be that of knowledge or intention, for example.

In both Metaphysics Γ 4 and 5 Aristotle argues that Protagoras is committed to the view that all contradictions are true. Yet Aristotle's arguments are not transparent, and later, in Γ 6, he provides Protagoras with a way to escape contradictions. In this paper I try to understand Aristotle's arguments. After examining a number of possible solutions, I conclude that the best way of explaining them is to (a) recognize that Aristotle is discussing a number of Protagorean opponents, and (b) import another of Protagoras' views, namely the claim that there are always two logoi opposed to one another.

I am planning a history of the notion of philosophical nonsense and naturally difficult historical and exegetical questions have come up.  Charles Pigden has argued that the notion goes back at least as far as Hobbes and that Locke, Berkeley, Hume, Kant (on some interpretations) and pragmatists such as William James, as well as numerous Twentieth-Century philosophers make use of it.  In this ‘paper’ I put forward for general discussion such questions as whether Hobbes was the first 'nonsensicalist', whether Kant was a 'nonsensicalist' at all, which philosophers if any have considered contradictions to be meaningless and whether Wittgenstein thought that his concept of criterion could legitimately be used verificationistically.  I shall continue to add further questions as they occur to me.

Liar-like paradoxes are typically arguments that, by using very intuitive resources of natural language, end up in contradiction. Consistent solutions to those paradoxes usually have difficulties either because they restrict the expressive power of the language, or else because they fall prey to extended versions of the paradox. Dialetheists, like Graham Priest, propose that we should take the Liar at face value and accept the contradictory conclusion as true. A logical treatment of such contradictions is also put forward, with the Logic of Paradox (LP), which should account for the manifestations of the Liar. In this paper we shall argue that such a formal approach, as advanced by Priest, is unsatisfactory. In order to make contradictions acceptable, Priest has to distinguish between two kinds of contradictions, internal and external, corresponding, respectively, to the conclusions of the simple and of the extended Liar. Given that, we argue that while the natural interpretation of LP was intended to account for true and false sentences, dealing with internal contradictions, it lacks the resources to tame external contradictions. Also, the negation sign of LP is unable to represent internal contradictions adequately, precisely because of its allowance of sentences that may be true and false. As a result, the formal account suffers from severe limitations, which make it unable to represent the contradiction obtained in the conclusion of each of the paradoxes.

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A final version of this paper is published in a special issue ("Logic: Consistency, Contradiction, and Consequence") of Principia 22(1), pp. 59 - 85, 2018.



https://periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2018v22n1p59

Here I bewail the slapdash and confusing way in which philosophers bandy about the word ‘incoherent’ (and ‘incoherence’ and ‘incoherently’).  To some it appears to mean: inconsistent; to others: pragmatically self-defeating; and to yet others: nonsensical, i.e. meaningless.  And often one is left guessing.

During the past few decades, Graham Priest has advocated for Dialetheism, the controversial position that some contradictions are true. Dialetheism entails that the Law of Non-Contradiction fails. In recent decades the philosophical community has begun to recognize the significant challenge posed by Priest's arguments. Priest has primarily appealed to paradoxes of self-reference, such as the Liar Paradox, to support his position. Following Priest's approach, I offer another argument for Dialetheism, which appeals to a self-referential paradox that has been more or less ignored in the philosophical literature on the subject: the paradox of the missing difference. When we reflect on the question 'what is a concept?' from the perspective of a classical model of conceptual analysis, we arrive at the paradox of the missing difference. Although contradictions may be improbable, when we reflect on the question 'how is the domain of concepts possible?' we are led to a startling principle: without dialetheia any theory concerning concept formation (from a classical perspective on concepts) would be impossible. Dialetheism is a necessary condition for the existence of a domain of concepts in general. As a result, Dialetheism may even be more central to philosophical reflection than even dialetheists themselves have recognized.

This paper goes naturally with my earlier paper 'The importance of Russell's Theory of Types for the emergence of twentieth-century nonsensicalism'.  In it I discuss the method Prior proposes in his paper ‘Entities’ for dealing with Russell’s Paradox without appealing to the concept of nonsense.

In this article, ,y purpose is  to introduce the reader to a seventeenth-century debate which originated in the Protestant University of Jena in Germany. The apparent intention of this debate was to present Jewish thought as an anti-Aristotelian tradition; its real purpose was to undermine the principle of the reception of the Dual Torah.

Il s'agit de montrer que la réinterprétation dialogique du Principe de non-contradiction chez Aristote (F. Wolff notamment) résiste bien à la pluralité de la formulation du PNC (sémantique, syntaxique, pragmatique) mais pas à l'examen de la sémantique de la négation.

The concept of contradiction plays an important role in philosophical discourse. Thus, it’s surprising that little effort has been exerted in evaluating the plausibility of the various prevalent non-equivalent definitions of ‘contradiction’ in the literature. This paper continues the project of evaluating available definitions by considering the explosion account of contradiction, an account which constitutes an apparent challenge to the plausibility of dialetheism by defining contradictions as (sets of) propositions that imply every proposition, thereby committing the dialetheist to the truth of every proposition. Two versions of the account are considered: ExS), which defines contradictions as explosive sets of propositions and ExP), which defines contradictions as explosive propositions. While ExS) is found to be inadequate for failing to facilitate important distinctions between sets of propositions and conceiving of contradictions as sets, ExP) is found to miscategorise certain logical falsehoods and non-logical falsehoods as contradictions, fail to respect the substance of the law of non-contradiction, and preclude the term ‘contradiction’ from entering the vocabulary of paraconsistent logics. The paper concludes that these criticisms give us good reason to believe that the explosion account, in both its forms, is an implausible definition of ‘contradiction’, and consequently isn’t a viable threat to the dialetheist’s thesis.

In his 1910 book On the principle of contradiction in Aristotle, Jan Łukasiewicz claims that syllogistic is independent of the principle of contradiction (PC). He also argues that Aristotle would have defended such a thesis in the Posterior Analytics. In this paper, we first show that Łukasiewicz's arguments for these two claims have to be rejected. Then, we show that the thesis of the independence of assertoric syllogistic vis-à-vis PC is nevertheless true. For that purpose, we first establish that there is no possibility to account for Aristotle's original views on syllogistic without using per impossibile deductions. At last, following an idea due to Smith 1983, we prove that there is a complete reconstruction of assertoric syllogistic using ecthesis instead of reductio ad absurdum. Contrary to what is claimed in Smith 1983, we show that Smith's system SE has to be improved for such a reconstruction. This results in an ecthetic system which is complete with respect to syllogistic arguments, not explosive and independent of PC.

I consider the dispute, not with a view to reaching a final verdict, but for the light it sheds on the notion of philosophical nonsense.  How does it look to a sceptic about philosophical nonsense?  It is generally agreed that the Tractatus is an unsatisfactory work, if the traditional reading of, for example, G. E. M. Anscombe or Peter Hacker is correct.  But is it any better on the ‘resolute’ reading of Cora Diamond or James Conant?  I maintain that it is more difficulty to handle the concept of nonsense than nonsensicalists of any stripe realise.  If the ‘ineffable truths’ and ‘important nonsense’ of traditional readings raise problems, so too do the contrast between meaningful frame and nonsensical core, Diamond’s idea that one can imaginatively identify with the nonsense-talker and the mysterious new entity, ‘transitional’ nonsense.  Meaning and communication, I suggest, keep reappearing precisely where they should not.