Principle of Non-Contradiction

Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz’s mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhaṅgī, i.e. the theory of sevenfold predication. Before arguing for this formalist approach to philosophy, let us return to the reasons to be reluctant at it. For one thing, Balcerowicz (2008) made a clear-cut distinction between a constructivist and a reductionist method of interpretation. The former is defined by Balcerowicz (2008: 4), where the so-called “constructivist” method is not to be confused with the philosophy of mathematics and merely amounts to the exercise of formal reconstruction:

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.

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.

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.

Sass, like R. D. Laing before him, wants to make sense of schizophrenic discourse.  In 'Paradoxes of delusion – Wittgenstein, Schreber and the schizophrenic mind' he uses Wittgenstein’s later work, particularly the Blue Book, to this end.  Read criticises Sass for not taking Wittgenstein’s nonsensicalism seriously enough and suggests that some schizophrenic utterances cannot be understood at all.  I argue that Sass’s position is more consistent than Read’s, though it is probably true that Sass is the less thoroughgoing Wittgensteinian.  Read’s way of arguing his case exhibits all the difficulties that those who employ the notion of philosophical nonsense are apt to get themselves into.  The denigratory vocabulary he uses to characterise schizophrenic discourse – ‘confused’, ‘inchoate’, ‘incoherent’, ‘empty’, ‘without content’ – is itself confused and confusing, but, more importantly, his talk of ‘transitional remarks’ and his admission that he is himself ‘trafficking in nonsense’ suggest that he is falling into the very error of which he accuses Sass.

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.

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.

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”.

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.

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?

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.

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.

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

Jan Łukasiewicz’ work on Aristotle and the principle of non-contradiction, originally published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle.

Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it.

This introduction to examines the historical and philosophical background of Łukasiewicz’ work, its relation to Hegel 's metaphysical logic which gave rise to the debate about Die logische Frage (the question of logic), and Łukasiewicz’ attempt to develop a first Non-Aristotelian logic, a logic that does not require or endorse Aristotle's principle of non-contradiction.

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.

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).

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.

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.

Lo scopo del presente studio consiste nel riproporre il problema della determinazione in Aristotele, al fine di mostrare non soltanto come esso rimanga sottinteso e presupposto alla non-contraddizione, quanto piuttosto come ne segni il limite. Il perché della scelta di Aristotele, da questo punto di vista, credo sia chiaro: ché con questo, infatti, voglio mettere in questione il comune e quotidiano modo di guardare l’esperienza. 
Per far questo, ho diviso l’analisi in due momenti principali: un primo, in cui si mostra la presupposizione della determinazione al principio che rende possibile la scienza dell’ente in quanto tale; e un secondo, invece, nel quale – a partire dalla comprensione dell’articolazione dell’essere (o dell’accadere) dell’ente stesso così per come è inteso da Aristotele – si dimostra l’impossibilità di sostenere in modo acritico la non-contraddizione e la necessità di definire in altro modo (e in altro senso?) il rapporto fra l’atto e la potenza – e quindi la determinazione stessa.
Il progetto, così esposto, deve fare riferimento a due luoghi ben precisi degli scritti aristotelici: da una parte, il libro Γ (capp. 1-4), dall’altra il libro Θ della Metafisica; ai quali si accompagneranno sporadiche incursioni nella Fisica, nel De generatione et corruptione e, in conclusione, nel De Interpretazione.

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?

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?

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.

In this book, Timothy Snyder (Professor of History at Yale University) shows how the rhetoric of US President Donald J. Trump channels the propaganda of the infamous dictators of the twentieth century.  Snyder is an expert on twentieth-century totalitarianism and has written several scholarly books about that subject.

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?

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.

Gabriel Rodrigues da Silva e Pedro Geraldo Aparecido Novelli em “A contradição na lógica de Hegel”, discutem o significado e a função da contradição na lógica elaborada por Georg Wilhelm Friedrich Hegel. Para isso, utilizam tanto da bibliografia primária, isto é, a própria "Ciência da Lógica" de Hegel, considerada umas das principais obras do filósofo alemão, quanto da bibliografia secundária, isto é, obras de estudiosos e comentadores da filosofia hegeliana. O presente capítulo será dividido em três seções, as quais são: introdução, desenvolvimento e considerações finais. Na primeira delas, apresentam as questões iniciais que envolvem a concepção hegeliana de contradição. Já na seção seguinte, a partir da obra de Bordignon (2015), apresentam algumas interpretações sobre a função e o significado da contradição na lógica de Hegel. Na terceira e última seção, abordam a exposição da contradição de acordo com a "Ciência da Lógica", visualizando-a lado a lado com as interpretações referidas anteriormente.

Is there a notion of contradiction – let us call it, for dramatic effect, “absolute” – making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First, it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crip-pling expressive limitations and from revenge paradoxes – pending a rigorous non-triviality proof for a formal dialetheic theory including it.

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.

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?

Sass, like R. D. Laing before him, wants to make sense of schizophrenic discourse.  In 'Paradoxes of delusion – Wittgenstein, Schreber and the schizophrenic mind' he uses Wittgenstein’s later work, particularly the Blue Book, to this end.  Read criticises Sass for not taking Wittgenstein’s nonsensicalism seriously enough and suggests that some schizophrenic utterances cannot be understood at all.  I argue that Sass’s position is more consistent than Read’s, though it is probably true that Sass is the less thoroughgoing Wittgensteinian.  Read’s way of arguing his case exhibits all the difficulties that those who employ the notion of philosophical nonsense are apt to get themselves into.  The denigratory vocabulary he uses to characterise schizophrenic discourse – ‘confused’, ‘inchoate’, ‘incoherent’, ‘empty’, ‘without content’ – is itself confused and confusing, but, more importantly, his talk of ‘transitional remarks’ and his admission that he is himself ‘trafficking in nonsense’ suggest that he is falling into the very error of which he accuses Sass.

This paper is divided in two parts. In the first, I sketch the debate between Priest and Severino on the principle of non-contradiction (henceforth PNC) and its defence. I explain what the challenge to PNC amounts to, by distinguishing paraconsistency from dialetheism. Later I will dwell on Severino's broad conception of PNC integrating the laws of identity and of non-contradiction into a more basic law that can be dubbed the principle of ontic determinacy. A crucial point in the dispute is the conception of negation, that is, whether or not the PNC denier, while claiming a dialetheia, must avail herself of the exclusive negation, despite her intentions. If so, the charge is not so much of inconsistency but of holding a self-undermining position as any proposition affirming a dialetheia would be grounded on PNC itself. In the second part, I propose a mild interpretation of dialetheisms. By considering some reasons supporting it, I suggest that it is motivated by the view that reality is over-determinate, rather than indeterminate (as it would happen, according to Aristotle and Severino, if PNC turned out to be false), and by the fact that the conceptual, linguistic expression of this over-determination leads to contradictions. A dialetheia is, as it were, a two-footed creature whose being simultaneously both true and false is grounded upon two (or more) different facts. These are mutually conflicting and thus play the roles of, respectively, verifying and falsifying the very same proposition. The existence of these facts, however, must be an univo-cal datum also for a dialetheia. If so, dialetheism does not jeopardize the view that reality, at least at its most fundamental level, is absolutely determined-just as Aristotle and Severino claim.

We calculate the principle of non contradiction (p.d.n.c.) and subsequently we demonstrate it. We map his theory and shift the attention of all the logics to the p.d.n.c. Exactly, with this proof, we want to contain in a single rigor, within the p.d.n.c., all the classic and non classical logics, to conclude that all the logics are given by the p.d.n.c.

What is the meaning of the ‘and’ that joins two contradictory terms, in a true contradiction? Indicatively, there are three possible positions: dialetheism, non-adjunctivism, and a third option that I call conjunctivism. For dialetheists, the ‘and’ that joins ‘p’ and ‘not p’ is a normal ‘and’, truth-functionally defined by «‘p and q’ is true iff ‘p’ is true and ‘q’ is true». For non-adjunctivists, ‘p’ and ‘not p’ might be true, but in that case, their conjunction is untrue, so the Adjunction rule (the right-to-left side of the bi-conditional) fails. For conjunctivists, Simplification (left to right) fails: the conjunction is true, but each conjunct, separately taken, is untrue. I compare the three perspectives, then I focus on possible justifications, costs and benefits of conjunctivism.

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.

"Indice


Premessa

Avvertenza

Il problema
1. Per cominciare, alcuni esempi dal linguaggio ordinario, – 2. Perché uno studio sul principio di contraddizione – 3. Ipotesi di ricerca.

I. Incontraddizione
Il principio di contraddizione nella tradizione. Fonti, problemi, spiegazioni e implicazioni

1. La duplice via di Aristotele
1. La proposizione nel De interpretatione – 2. Le forme di opposizione fra proposizioni – 3. La portata esistenziale delle proposizioni e la negazione – 4. I principi di contraddizione e del terzo escluso come assiomi negli Analitici secondi – 5. Il principio di contraddizione come principio primo nella Metafisica, i: la formulazione ‘ontologica’ classica – 6. Il principio di contraddizione come principio primo nella Metafisica, ii: la formulazione ‘psicologica’.

2. La non-contraddittorietà come principio primo, legge del pensiero e condizione di pensabilità in Kant
1. La logica come scienza delle leggi naturali e formali del pensiero – 2. Non-contraddittorietà = possibilità = pensabilità – 3. Il principio di contraddizione nella Critica della ragion pura – 4. Critica del principio di contraddizione kantiano.

3. Priorità, formalità ed estensione del principio di contraddizione. Discussioni nell'ambito della tradizione logica ottocentesca
1. Primi passi verso un dibattito sul principio di contraddizione quale legge del pensiero – 2. William Hamilton – 3. John Stuart Mill – 4. Herbert Spencer – 5. Un dubbio e la posizione di Gerardus Heymans – 6. Il principio di contraddizione aristotelico e quello kantiano secondo Christoph Sigwart – 7. Critica delle interpretazioni psicologistiche del principio di contraddizione (Bolzano, Husserl, e i giovani Russell e Lukasiewicz) – 8. La logica formale non può prescindere dal riferimento al reale: la critica di Adolf Friedrich Trendelenburg – 9. Un'altra voce: Rudolf Hermann Lotze.

4. Dimostrabilità del principio di contraddizione? La natura del soggetto della proposizione
1. Sulla necessità di una giustificazione del principio di contraddizione – 2. La dimostrazione per via di confutazione di Aristotele – 3. La ‘dimostrazione diretta’ di Friedrich Ueberweg... – 4. ... e quella di Alexander Pfänder – 5. Le critiche del giovane Lukasiewicz contro la presunta priorità del principio di contraddizione – 6. La ‘dimostrazione’ di Lukasiewicz – 7. Il principio di contraddizione e la logica simbolica secondo Lukasiewicz – 8. Note conclusive sulla logica formale tradizionale.

II. In-contraddizione
Oggetti esistenti e oggetti non-esistenti

1. L'universo di Bolzano e l'in sé
1. Sulle “somme leggi del pensiero” – 2. L'anti-Kant: sulla logica e la forma logica – 3. L'in sé – 4. Le rappresentazioni senza oggetto.

2. Dalle rappresentazioni senza oggetto agli oggetti non-esistenti
1. La mediazione storica di Robert Zimmermann: breve storia redazionale della Philosophische Propaedeutik – 2. La Philosophische Propaedeutik e la Wissenschaftslehre a confronto, i: la concezione della logica e l'in sé – 3. La Philosophische Propaedeutik e la Wissenschaftslehre a confronto, ii: le rappresentazioni senza oggetto – 4. Rappresentazione, contenuto e oggetto in Kazimierz Twardowski – 5. Il capovolgimento delle rappresentazioni senza oggetto in Twardowski: rappresentazioni i cui oggetti non esistono.

3. Oggetti impossibili
1. La Gegenstandstheorie di Alexius Meinong: eine daseinsfreie Wissenschaft – 2. Oggetti impossibili e teoria dell'Außersein nella Gegenstandstheorie – 3. Russell versus Meinong: descrizioni ed esistenza.

III. In contraddizione
Verso logiche non-aristoteliche

1. Principio di contraddizione e sillogismo
1. An. post. A 11. 77a10-21: le interpretazioni di Jan Lukasiewicz e di Isaac Husik – 2. La finzione di Lukasiewicz e l'idea della logica non-aristotelica.

2. Mondi possibili con oggetti impossibili. La logica immaginaria di N.A. Vasil'ev
1. Cenni introduttivi – 2. Giudizi universali e giudizi particolari in Sigwart – 3. Sui giudizi particolari, il triangolo delle opposizioni e la legge del quarto escluso – 4. I contributi di Meinong e Husik e l'idea della “logica immaginaria (non-aristotelica)” – 5. Negazione e legge di contraddizione nella logica immaginaria – 6. Giudizi e sillogismi nella logica immaginaria - 7. Breve confronto con Lukasiewicz.

3. Individui, continuo e vaghezza in Peirce
1. Peirce, Vasil'év e la logica non-aristotelica – 2. Individui, contraddizione e terzo escluso – 3. Alcuni aspetti del continuo in Peirce – 4. I casi al bordo: Peirce versus Frege – 5. Vaghezza: oggetti indeterminati e predicati vaghi.

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Dialetheism is the view that some contradictions are true. One common motivation to the view concerns cases of contradictory concepts obtaining together. Allegedly, in these cases such concepts lead to a true contradiction. In this paper, we argue that this path is closed as a motivation for dialetheism. There are two basic difficulties to articulate the view: i) once contradictory or incompatible concepts are granted to obtain together, there is no longer any reason to claim that they were incompatible to begin with, and ii) it is not easy to go from such concepts to clear cases of negation-involving contradictions without already assuming the truth of dialetheism. Further difficulties discussed here concern the maintenance of the meaning of important concepts such as "contradiction" in a dialetheist setting. Those difficulties make the case for dialetheism hard to motivate via contradictory concepts.