Graham Priest Research Articles

Modal Formulas True at Some Point in Every Model

In a paper on the logical work of the Jains, Graham Priest considers a consequence relation, semantically characterized, which has a natural analogue in modal logic. Here we give a syntactic/axiomatic description of the modal formulas which are consequences of the empty set by this relation, which is to say: those formulas which are, for every model, true at some point in that model.

Άδύνατον and material exclusion1

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of ‘Law of Non-Contradiction’; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one.

Graham Priest. Towards non-being: the logic and metaphysics of intentionality. Oxford University Press, 2005, xi + 190 pp.

Graham Priest. Towards non-being: the logic and metaphysics of intentionality. Oxford University Press, 2005, xi + 190 pp.

Properties and Paradox in Graham Priest’s Towards Non‐Being

Graham Priest’s book is a treasure-trove, with many interesting things to discuss, but in these remarks, I want to address two main questions. The first concerns what properties and relations Priest’s non-existent objects should have simpliciter. The second is the question of whether Priest’s framework needs dialetheism—should the framework only be attractive to those who accept true contradictions? In these remarks I plan to grant, for the sake of discussion at least, that there are non-existent objects. I take it that the question of whether there really are things that don’t exist is one that is to be settled once we see how well the rival theories do—and so developing a theory of non-existent objects seems to me an important preliminary to the judgement of whether there are, after all, such things.

A CONSISTENT READING OF SYLVAN'S BOX

I argue that Graham Priest's story Sylvan's Box has an attractive consistent reading. Priest's hope that this story can be used as an example of a non‐trivial ‘essentially inconsistent’ story is thus threatened. I then make some observations about the role Sylvan's Box might play in a theory of unreliable narrators.

Dharmakīrti and Priest on an Inconsistent Theory of Change — A Comment to Mortensen

Dharmakīrti and Priest on an Inconsistent Theory of Change—A Comment to Mortensen Koji Tanaka Introduction In his article "Dharmakīrti and Priest on Change,"1 Chris Mortensen presents accounts of change (and motion) given by the Buddhist philosopher Dharmakīrti (along with his commentator Dharmottara) and the contemporary Western philosopher Graham Priest. He notices that the two accounts have striking similarities yet take opposing views on the issue of inconsistency. According to Mortensen, Dharmakīrti rejects and Priest accepts an inconsistent theory of change. Mortensen expresses sympathy for Dharmakīrti's position, though he argues that Dharmakīrti's position needs some qualifications. In this essay, I reexamine the accounts of change given by Dharmakīrti and Priest. In order to make explicit the philosophical nature of the essay, I will follow Mortensen's reading of Dharmakīrti and Priest as much as possible. Priest's arguments, as presented by Mortensen, are those in Priest's In Contradiction.2 With respect to Dharmakīrti, Mortensen for the most part follows Stcherbatsky's reconstruction of an argument given in Dharmakīrti's early work Nyāyabindu.3 Now, Stcherbatsky's reconstruction (of Dharmakīrti's philosophy in general) has been recognized as problematic in recent years.4 Yet to raise textual questions of this kind is to argue against Stcherbatsky and not Mortensen. Hence, I am not critical of Mortensen's reading of Dharmakīrti. Rather, the main aim of this essay is to examine Mortensen's own reconstruction of Stcherbatsky's reading of Dharmakīrti. I will argue that Mortensen's Dharmakīrti has no resources to argue against Priest once we understand the full extent of Priest's argument, contrary to what Mortensen claims. Priest on Change Graham Priest, in his In Contradiction, argues for an inconsistent account of change. He does this by arguing against the orthodox, consistent account of change. Priest calls such an account the cinematic view of change. This account states that an object occupies a different spatial location at each temporal point and that change is thought of as a series of pictures patched together where each picture represents the object at different spatiotemporal points. According to Mortensen, Priest offers two arguments against this consistent account of change.5 First, according to the cinematic [End Page 244] view of change, an object is represented as being in a state of rest at each spatiotemporal point. Hence, there is no time at which the object is changing. Therefore, change becomes impossible in the cinematic view. Priest's second argument is concerned with a "Laplacean universe" in which any instantaneous state in the future is determined by the state at any prior instant. Now, one cannot rule out a priori a Laplacean universe, and thus it is a possibility. However, the cinematic account of change makes a Laplacean universe a priori false. For the cinematic account makes it impossible that an instantaneous state determines any subsequent instantaneous state since each state is represented as a state of rest. Mortensen provides only two of Priest's arguments. In fact, Priest offers another argument that seems to be his main argument for his inconsistent account of change.6 In another place, Mortensen acknowledges this third argument and shows strong sympathy for it.7 Priest's third argument appeals to Zeno's arrow paradox. The cinematic account of change has it that an arrow doesn't advance at any given spa-tiotemporal instance. There is nothing that contributes to the movement of the arrow at any given instance. Yet, the arrow reaches its destiny in the end. "How can going somewhere be composed of an aggregate of going nowheres?"8 It is in response to the third argument against the cinematic account of change that Priest develops his inconsistent theory. He argues that change is possible because there are spatiotemporal points in which an object is changing. In such an instance, the object is said to be in a state of flux. Priest argues that a state of flux is contradictory by appealing to what he calls "Leibniz' Continuity Principle" (LCP). This principle essentially states that whatever the state holds up to a limit also holds at...

In Defense of Dharmakīrti -- A Response to Tanaka

In my 2004 article for this journal, I compared Dharmakirti’s consistent account of change with Graham Priest’s dialetheist (inconsistent) theory of motion.1 I contended that they take opposite positions on the law of noncontradiction (the thesis that no contradiction is true), and I argued that Dharmakirti’s theory was preferable, particularly in the light of modern physics. In his interesting comment, Koji Tanaka takes me to task for overestimating the resources Dharmakirti has for his theory. Correlatively, he argues that Dharmakirti cannot resist the full force of Priest’s arguments and thus ought to succumb to his dialetheist account. In this response, I argue that the additional arguments that Tanaka brings forward in Priest’s name are unsound, and that in consequence Dharmakirti’s position remains standing.

Negative truths and truthmaker principles

This paper argues that a consideration of the problem of providing truthmakers for negative truths undermines truthmaker theory. Truthmaker theorists are presented with an uncomfortable dilemma. Either they must take up the challenge of providing truthmakers for negative truths, or else they must explain why negative truths are exceptions to the principle that every truth must have a truthmaker. The first horn is unattractive since the prospects of providing truthmakers for negative truths do not look good neither absences, nor totality states of affairs, nor Graham Priest and J.C. Beall’s ‘polarities’ (Beall, 2000; Priest, 2000) are up to the job. The second horn, meanwhile, is problematic because restricting the truthmaker principle to atomic truths, or weakening it to the thesis that truth supervenes on being, undercuts truthmaker theory’s original motivation. The paper ends by arguing that truthmaker theory is, in any case, an under-motivated doctrine because the groundedness of truth can be explained without appeal to the truthmaker principle. This leaves us free to give the ommonsensical and deflationary explanation of negative truths that common-sense suggests.

Towards Non‐Being: The Logic and Metaphysics of Intentionality ‐ By Graham Priest

Towards Non‐Being: The Logic and Metaphysics of Intentionality ‐ By Graham Priest

Graham Priest and the Philosophy of the Paraconsistent

(ProQuest-CSA LLC: ... denotes non-USASCII text omitted.) The paraconsistent movement is typically concerned with systems of which not everything follows from a contradiction. Systems which everything does follow from a contradiction (referred to the literature as ECQ-ex contradictione quodlibet) are said to be or explosive. As Bueno (2002, 547) points out, a sufficient condition for a system of paraconsistent arithmetic's being trivial is the ability to establish it that 1 = O. While much of the work the area of paraconsistency has dealt with the practical applications of paraconsistent logics-the logics are, for example, very useful for processing information collected in the field, where not all of the data agree with one another-a large amount has dealt with the philosophical implications of paraconsistency. In this regard, it is fair to say that the work of Graham Priest is among the most important. In the present essay, I shall look at some of Priest's ideas, paying particular attention to those essays where he considers the limits of the world of experience. These essays are especially interesting, because they appear to undercut the theoretical viewpoint argued for some of his other writings. To provide a convenient point of reference, I offer the following (necessarily reductive) classification of Priest's work on the paraconsistent: (1) The mainly technical essays, where he is concerned with the minutiae of various paraconsistent systems;1 (2) The philosophical essays, where he is concerned to defend the idea that the world of human experience can embrace the paraconsistent; and (3) The philosophical essays, where he seems, on the contrary, to place the locus of paraconsistency beyond the world of experience. Given that the present essay is primarily concerned with metaphysics, I shall have little to say about work that falls under the first classification, but I shall have a great deal to say about work that falls under the second and the third. After presenting some background information, my procedure will be to summarize a selection of material classification (2), paying particular attention to the criticisms that can be made of it. I shall argue that these criticisms fact imply the necessity for the stance that Priest takes the essays of classification (3). Along the way and conclusion I shall present my own ideas as to the philosophical implications of the paraconsistent. Priest and Paraconsistency the World of Experience In Motivations for Paraconsistency: The Slippery Slope from Classical Logic to Dialetheism, Priest takes an historical perspective with regard to the paraconsistent movement. His main reason for doing this is to try to pinpoint the origins of the idea that all inconsistent systems must be explosive.2 Significantly, his finding is largely negative: he observes that the idea of explosion is to be found neither Aristotelian syllogistic nor Stoic logic. In fact, the earliest appearance of the principle that Priest can find is the work of the twelfth century French logician William of Soissons.3 Priest's emphasis on the comparative modernity of the principle, however, ought not to be interpreted as implying some invocation of the appeal-to-tradition fallacy; for his finding that explosion becomes entrenched only with the adoption of the classical logic promulgated by Boole, Frege, et al. points to a genuine theoretical paucity of evidence favor of the principle. Priest goes on to observe that while the paraconsistent movement had precursors roughly contemporary with Frege's work, it was only after the second world war that the movement achieved momentum. He also distinguishes three strands or levels the movement. The first is a simple dissatisfaction with explosion as a valid principle of inference (Priest 2000, 227); and researchers on this level can be seen largely to be attempting to redress the historical imbalance already mentioned. …

Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood

In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of "revenge Liar" arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's "useful four-valued logic", one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a "bi-and-a-half" lattice which determines seven-valued logics different from Priest's Logic of Paradox.

PRIEST AND THE BISHOP

Abstract: According to metaphysical realism, there may be features of reality which we cannot conceive. If this thesis of cognitive closure is inconsistent, then, pace dialetheism, metaphysical realism proves incoherent. Recently, Graham Priest has revived Berkeley's idealist argument meant to show that cognitive closure is inconsistent. If cogent, this argument poses a threat to metaphysical realism. I argue that while Priest's reconstruction of Berkeley's argument may be seen to be paradoxical on one interpretation of ‘conceive’, that interpretation is not the intended one. On the intended interpretation, the argument fails and hence leaves metaphysical realism unassailed.

Dialetheism, semantic pathology, and the open pair

Over the past 25 years, Graham Priest has ably presented and defended dialetheism, the view that certain sentences are properly characterized as true with true negations. Our goal here is neither to quibble with the tenability of true, assertable contradictions nor, really, with the arguments for dialetheism. Rather, we wish to address the dialetheist's treatment of cases of semantic pathology and to pose a worry for dialetheism that has not been adequately considered. The problem that we present seems to have broader bite, afflicting both consistent and inconsistent proposals for resolving semantic pathology. Thus, while our primary goal is to uncover some important connections between dialetheism, semantic pathology, and other, more general issues, the problem that we pose might be a worry for anyone who aims to resolve semantic pathology—consistently or not.

When seeing is not believing: A critique of priest's argument from perception

In this paper I critically examine an argument proposed by Graham Priest in support of the claim that the observable world is consistent. According to this argument we have good reason to think that the observable world is consistent, specifically we perceive it to be consistent. I critique this argument on two fronts. First, Priest appears to reason from the claim ‘we know what it is to have a contradictory perception’ to the claim ‘we know what it is to perceive a contradiction’. I argue that this inference fails to be valid. Secondly, I give reasons for thinking that if an observable state of affairs were to be contradictory, we would perceive it to be consistent. As such that the world we observe appears consistent does not constitute evidence that it is in fact consistent. That we see a consistent world is no reason to believe that the world is consistent. I conclude the paper with some reflections on the implications of this analysis for the plausibility of trivialism.

The Law of Non‐Contradiction: New Philosophical Essays Edited by Graham Priest, J.C. Beall and Bradley Armour‐Garb

<i>The Law of Non‐Contradiction: New Philosophical Essays</i> Edited by Graham Priest, J.C. Beall and Bradley Armour‐Garb

The law of non-contradiction: New philosophical essays, edited by Graham Priest, J.C. Beall, and Bradley Armour-Garb, Oxford University Press, Oxford, 2004, xii + 443 pp.

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Review of Logic: A Very Short Introduction, by Graham Priest

Review of Logic: A Very Short Introduction, by Graham Priest

Dharmakīrti and Priest on Change

Competing accounts of change and motion are given by the seventh-century Buddhist logician Dharmakirti and the contemporary analytical philosopher Graham Priest. They agree on much, but disagree on the issue of the Law of Non-Contradiction. This paper takes Dharmakirti's side, appealing to current space-time theory, while making some qualifications.

Paradox without satisfaction

According to Stephen Yablo, the above list generates a liar-like paradox without circularity (see Yablo 1985 and 1993). After all, in contrast with the usual liar paradox, no sentence in the Yablo list refers to itself, and as opposed to well-known liar cycles,1 no sentence refers to sentences above it in the list. However, similarly to the (usual or cyclic) liar, a contradiction is derivable from the list. But is Yablo’s paradox really non-circular? To this question, Graham Priest gave a surprising answer. In his view, despite initial appearances, the paradox is circular (Priest 1997). After all, if the formulation of the paradox doesn’t seem to involve circularity, the argument to contradiction definitely does. As Priest argued, Yablo’s paradox has ‘a fixed point ... of exactly the same self-referential kind as in the liar paradox’. As a result, ‘the circularity is ... manifest’ (Priest 1997: 238).2 In this paper, we challenge Priest’s answer – in a new way. To the best of our knowledge, everyone in the debate has conceded the adequacy of Priest’s reconstruction of the argument to contradiction. We point out a limitation that hasn’t been noted. Priest’s argument requires the existence of a satisfaction relation that plays the role of a fixed point in Yablo’s

Peripatetic Perversions

The idea that there is a coherent and morally relevant concept of sexual perversions has been increasingly called into question. In what follows, I will be concerned with two recent attacks on the notion of sexual perversion: those of Graham Priest and Igor Primoratz.2 Priest's paper is the deeper of the two. Primoratz goes methodically through various accounts of sexual perversion and finds difficulties in them. This is no small task, of course, but unlike Priest he does not attempt to provide any diagnosis of why any attempt to analyse the concept of sexual per version must fail. Priest argues that sexual perversion is an inapplicable concept: the presuppositions that would allow us to make sense of the notion have been rightly rejected. Without the theoretical backdrop of an moral teleology, we cannot provide a satisfactory account of sexual perversion, for only such a teleological world-view allows us to give some sense to the idea that a sexual practice might be morally wrong because it is unnatural. Priest surveys accounts of perversion that don't appeal to any idea of unnaturalness and rejects them?rightly I believe. But, Priest argues, Aristotle's own moral teleology is part and parcel of his wider views about purpose in nature. This natural teleology has been shown to be explanatorily superfluous. Though some sciences still talk of functions, this can be understood in terms of contributions to evolutionary survival. Though there is considerable disagreement about the details of the right account of function, all versions of this scientifically respectable teleology are morally neutral: it would not follow from the fact (if indeed it were a fact) that homosexual intercourse does nothing to propagate the agents' genetic.material to future generations that it is therefore morally wrong. Here too I think Priest is right. He also considers what he calls Aristotelian revivalism in Roger Scruton's account of sexual perver sion.3 I think Priest sells Aristotelianism short. I have no interest in