The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi , by Graham Priest

Mind ◽  
2019 ◽  
Vol 129 (515) ◽  
pp. 965-974
Author(s):  
Jan Westerhoff
Keyword(s):  
Graham Priest

G. Priest and R. Routley. First historical introduction. A preliminary history of paraconsistent and dialethic approaches. Paraconsistent logic, Essays on the inconsistent, edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, pp. 3–75. - Ayda I. Arruda. Aspects of the historical development of paraconsistent logic. Paraconsistent logic, Essays on the inconsistent, edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, pp. 99–130. - G. Priest and R. Routley. Systems of paraconsistent logic. Paraconsistent logic, Essays on the inconsistent, edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, pp. 151–186. - G. Priest and R. Routley. Applications of paraconsistent logic. Paraconsistent logic, Essays on the inconsistent, edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, pp. 367–393. - G. Priest and R. Routley. The philosophical significance and inevitability of paraconsistency, Paraconsistent logic, Essays on the inconsistent, edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, pp. 483–539.

1991 ◽  
Vol 56 (4) ◽  
pp. 1503-1504
Author(s):  
F. G. Asenjo
Keyword(s):  
Historical Development ◽  
Paraconsistent Logic ◽  
Philosophical Significance ◽  
History Of ◽  
Graham Priest

scholarly journals Tree Trimming: Four Non-Branching Rules for Priest’s Introduction to Non-Classical Logic

2017 ◽  
Vol 12 (2) ◽  
Author(s):  
Marilynn Johnson
Keyword(s):  
Modal Logic ◽  
Classical Logic ◽  
Variable Domain ◽  
Free Logic ◽  
Intuitionist Logic ◽  
Branching Rule ◽  
Branching Rules ◽  
Graham Priest

In An Introduction to Non-Classical Logic: From If to Is Graham Priest (2008) presents branching rules in Free Logic, Variable Domain Modal Logic, and Intuitionist Logic. I propose a simpler, non-branching rule to replace Priest’s rule for universal instantiation in Free Logic, a second, slightly modified version of this rule to replace Priest’s rule for universal instantiation in Variable Domain Modal Logic, and third and fourth rules, further modifying the second rule, to replace Priest’s branching universal and particular instantiation rules in Intuitionist Logic. In each of these logics the proposed rule leads to tableaux with fewer branches. In Intuitionist logic, the proposed rules allow for the resolution of a particular problem Priest grapples with throughout the chapter. In this paper, I demonstrate that the proposed rules can greatly simplify tableaux and argue that they should be used in place of the rules given by Priest.

scholarly journals Power Matrices and Dunn--Belnap Semantics: Reflections on a Remark of Graham Priest

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Lloyd Humberstone
Keyword(s):  
Equational Logic ◽  
Consequence Relations ◽  
Consequence Relation ◽  
Power Matrix ◽  
Matrix Construction ◽  
The Given ◽  
The Universe ◽  
Power Algebras ◽  
Graham Priest ◽  
Natural Way

The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices (in the `logical matrix' sense) whose underlying algebras are power algebras (a.k.a. complex algebras, or `globals'), where the power algebra of a given algebra has as elements \textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis of those of the given matrix. The present discussion stresses the continuity of Priest's work on the question of which matrices determine consequence relations (for propositional logics) which remain unaffected on passage to the consequence relation determined by the power matrix of the given matrix with the corresponding (long-settled) question in equational logic as to which identities holding in an algebra continue to hold in its power algebra. Both questions are sensitive to a decision as to whether or not to include the empty set as an element of the power algebra, and our main focus will be on the contrast, when it is included, between the power matrix semantics (derived from the two-element Boolean matrix) and the four-valued Dunn--Belnap semantics for first-degree entailment a la Anderson and Belnap) in terms of sets of classical values (subsets of {T, F}, that is), in which the empty set figures in a somewhat different way, as Priest had remarked his 1984 study, `Hyper-contradictions', in which what we are calling the power matrix construction first appeared.

Rational belief and Dialetheism

2021 ◽  
Vol 18 (3) ◽  
pp. 309-335
Author(s):  
Paolo Bonardi
Keyword(s):  
Rational Belief ◽  
Mode Of Presentation ◽  
Novel Devices ◽  
Graham Priest

Abstract It is usually maintained that a subject with manifestly contradictory beliefs is irrational. How can we account, then, for the intuitive rationality of dialetheists, who believe that some manifest contradictions are true? My paper aims to answer this question. Its ultimate goal is to determine a characterization of (or rather a constraint for) rational belief approvable by both the theorists of Dialetheism and its opponents. In order to achieve this goal, a two-step strategy will be adopted. First, a characterization of rational belief applicable to non-dialetheist believers will be determined; this characterization will involve the semantic apparatus of Nathan Salmon’s Millian Russellianism but will get rid of the problematic and obscure notion of mode of presentation (guise in his own terminology), replacing it with a couple of novel devices, belief subsystems and cognitive coordination. Second, using ideas from Graham Priest, the leading proponent of Dialetheism, such a characterization will be modified, so as to devise a new one able to account for the intuitive rationality of both dialetheist and non-dialetheist believers.

Understanding as a Source of Justification

Mind ◽  
2020 ◽  
Vol 129 (514) ◽  
pp. 509-534
Author(s):  
Joachim Horvath
Keyword(s):  
Epistemic Justification ◽  
Second Order ◽  
The Law ◽  
Almost All ◽  
Graham Priest

Abstract The traditional epistemological approach towards judgments like BACHELORS ARE UNMARRIED or ALL KNOWLEDGE IS TRUE is that they are justified or known on the basis of understanding alone. In this paper, I develop an understanding-based account which takes understanding to be a sufficient source of epistemic justification for the relevant judgments. Understanding-based accounts face the problem of the rational revisability of almost all human judgments. Williamson has recently developed a reinforced version of this problem: the challenge from expert revisability. This is the problem that even the best candidate judgments for understanding-based justification can be rationally rejected by the relevant experts, who may not even have any disposition or inclination to accept these judgments. (Consider, for instance, Graham Priest, a leading logician who rejects the law of non-contradiction.) However, I argue that expert revisability is fully compatible with the proposed understanding-based epistemology, because expert revisability is true of sufficient sources of epistemic justification in general. A remaining metaphysical worry is that understanding might end up being ‘too thin’ to play the envisaged epistemological role. This worry can be countered with a novel metaphysics of understanding involving second-order dispositions.

scholarly journals Sets, lies, and analogy: a new methodological take

2020 ◽  
Author(s):  
Giulia Terzian
Keyword(s):  
The Other ◽  
Semantic Paradoxes ◽  
Starting Point ◽  
Uniform Solution ◽  
The One ◽  
Graham Priest

Abstract The starting point of this paper is a claim defended most famously by Graham Priest: that given certain observed similarities between the set-theoretic and the semantic paradoxes, we should be looking for a ‘uniform solution’ to the members of both families. Despite its indisputable surface attractiveness, I argue that this claim hinges on a problematic reasoning move. This is seen most clearly, I suggest, when the claim and its underlying assumptions are examined by the lights of a novel, quite general and, I contend, promising take on inter-theoretic analogy. The ensuing discussion is intended to serve as both a possible case study and a first step towards the broader aim of the paper: namely, to initiate a wider conversation on the methodology of paradox-solving on the one hand, and the use of inter-theoretic analogies on the other.

Graham Priest and the Philosophy of the Paraconsistent

2007 ◽  
Vol 51 (1) ◽  
pp. 91-103
Author(s):  
Daniel King ◽  
Keyword(s):  
Graham Priest
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