Aim

The aim of this workshop is to discuss and exchange new ideas and recent developments related to philosophical logics, broadly construed, with a special emphasis on dialetheism and paraconsistent logics.

Date & Venue

• Date: June 19--20, 2017.
• Venue: Large conference room in the basement, Faculty of Letters Main Building, Yoshida Campus, Kyoto University. (No. 8 of this map)

Speakers

• Eduardo Barrio (University of Buenos Aires & CONICET)
• Yosuke Fukuda (Kyoto University)
• Ryosuke Igarashi (Kyoto University)
• Ryo Ito (University of St. Andrews & Kyoto University)
• Takuro Onishi (Kyoto University)
• Graham Priest (City University of New York)
• Damian Szmuc (University of Buenos Aires & CONICET)
• Wen-fang Wang (Yang-Ming University)
• Timo Weiss (University of Bonn)
• Shunsuke Yatabe (Kyoto University)

Program

June 19:

11:00--12:30 Eduardo Barrio "What is a Paraconsistent Logic?"

12:30--14:00 Lunch

14:00--15:00 Damian Szmuc "On all Weak Kleene generalizations of Classical Logic"

15:00--16:00 Takuro Onishi "Routley’s American plan revisited"

16:00--16:15 Coffee break

16:15--17:15 Yosuke Fukuda "On a computational interpretation of Rumfitt's bilateral natural deduction"

17:15--18:45 Shunsuke Yatabe "Deflationism, logical notion of truth and proof theoretic semantics"

19:00-- Dinner

June 20:

11:00--12:30 Wen-fang Wang "Three-Valued Semantic Pluralism: A Defense of A Three-Valued Solution to the Sorites Paradox"

12:30--14:00 Lunch

14:00--15:00 Ryosuke Igarashi "Kant's Transcendental Logic and Antinomies of Pure Reason"

15:00--16:00 Ryo Ito "Classes, Fusions and Russell's Theories of Classes (up to Principia Mathematica)"

16:00--16:15 Coffee break

16:15--17:15 Timo Weiss "Logic, Probability, Belief"

17:15--18:45 Graham Priest "Logical Theory-Choice: the Case of Vacuous Counterfactuals"

19:00-- Dinner

Abstracts

Eduardo Barrio

Title: What is a Paraconsistent Logic?

Abstract: Paraconsistent logics are logical systems that reject the classical conception, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate an invalidate both versions of Explosion, such as classical logic and Asenjo-Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egre, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively.

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Yosuke Fukuda

Title: On a computational interpretation of Rumfitt's bilateral natural deduction

Abstract: In Rumfitt(2000), he devised a bilateral natural deduction,which allows us to state not only assertions but also denials as primitive speech acts, to execute a defensive maneuver against the criticism of classical logic considered in the framework of Dummett(1991)'s Proof-Theoretic Semantics. However, Suzuki(2016) showed that Rumfitt's deductive system is not enough to dispel the criticism under Dummett's theory, and proposed "falsificationistic bilateralism'' to answer these problems. In this talk, I will discuss another possibility to justify Rumfitt's system in terms of computational logic, i.e., through the so-called Curry-Howard correspondence between logic and computation.

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Ryosuke Igarashi

Title: Kant's Transcendental Logic and Antinomies of Pure Reason

Abstract: This paper is intended as a formal analysis of Kant's transcendental logic and its relation to Leibniz-Wolfian logic. It is a widespread view that Kant criticized Leibniz-Wolfian school logic, and introduced his own logical system, i.e., transcendental logic. On the other hand, as Tiles (2004) pointed out, it may safely be stated that the subject matter of transcendental logic is to resolve the antinomies of pure reason. Hence, it is a promising approach to depict the characteristic of transcendental logic and its relation to Leibniz-Wolfian logic in terms of the resolution of the antinomies. In this paper, a formal semantics that can be applied to both Kantian and Leibniz-Wolfian logic will be proposed by expanding the results of Lenzen (2004) and Oyamada (2012). Then I will provide a formal analysis of the machinery of the antinomies and Kant's solution based on the semantics.

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Ryo Ito

Title: Classes, Fusions and Russell's Theories of Classes (up to Principia Mathematica)

Abstract: In the appendices of The Principles of Mathematics, Russell presents the very first version of theory of types. But even before the publication of the book he became unsatisfied with the theory and as a result he spent about 7 years preparing the promised second volume of the book, which eventually came out as Principia Mathematica. Some philosophers argue that he had to give up the original type-theory because he found it incompatible with a certain metaphysical doctrine which on their account he firmly endorsed. In this talk I will attempt to offer an alternative interpretation by looking into his attempts to either account for classes or dispense with them in The Principles of Mathematics and subsequent works including Principia Mathematica.

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Takuro Onishi

Title: Routley’s American plan revisited

Abstract: Routley (1984) examined how to extend the Belnap-Dunn style four-valued semantics (American plan) of relevant logic to cover full relevant logic incorporating implication. The obstacle to the extension is those principles like contraposition and reductio, which involve negation and implication and require a certain “cross-over” between truth and falsity. Routley’s main solution was to use “star-imitation”, a relation on the model structure that is similar to but weaker than Routley star. Then he showed that, as the logic is getting stronger, the relation become equated with Routley star that is a function, and that the four-valued semantics collapses into the standard two-valued relational semantics (Australian plan). In this talk, I will clarify more the relationship between the two plans by using twin star-imitation and examine how well the use of star-imitation is motivated.

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Graham Priest

Title: Logical Theory-Choice: the Case of Vacuous Counterfactuals

Abstract: There is currently a debate in logic concerning whether counterfactuals with necessarily false antecedents are vacuously true. I shall argue that they are not. More importantly, I will show how the relevant considerations fit into a general methodology concerning theory choice in logic.

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Damian Szmuc

Title: On all Weak Kleene generalizations of Classical Logic

Abstract: In a recent paper, Stefan Wintein studied all the inferential consequence relations induced by the (Belnap-Dunn four-valued extended) Strong Kleene scheme by requiring premises and conclusions to satisfy one of the generalizations of Classical Logic's standards for premises and conclusions. Namely, truth, exact truth (i.e. truth and non-falsity), falsity, and exact falsity (i.e. falsity and non-truth). In this paper, I focus on all the inferential consequence relations induced by the (Fitting four-valued generalization of the) Weak Kleene scheme by requiring premises and conclusions to satisfy one of the previously mentioned standards. The outcome of this analysis includes the famous three-valued systems Weak Kleene logic and Paraconsistent Weak Kleene logic, as well as some of their four-valued analogous, such as Harry Deutsch's logic S_fde and its dual. To conclude, I will highlight the importance of the analysis of the meta-inferential consequence relations of each logic, in order to show that in previous works some empty inferential consequence relations were perhaps unnecessarily discarded and assimilated.

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Wen-fang Wang

Title: Three-Valued Semantic Pluralism: A Defense of A Three-Valued Solution to the Sorites Paradox

Abstract: Disagreeing with most authors on vagueness, the author proposes a solution that he calls ‘three-valued semantic pluralism’ to the age-old sorites paradox. In essence, it is a three-valued semantics for a first-order vague language with identity with the additional suggestion that a vague language has more than one correct interpretation. Unlike the traditional three-valued approach to a vague language, three-valued semantic pluralism can accommodate the phenomenon of higher-order vagueness, and also the phenomenon of penumbral connection when equipped with ‘suitable conditionals.’ The author also shows that three-valued semantic pluralism is a natural consequence of a restricted form of the Tolerance Principle (T_R) and a few related ideas, and argues that (T_R) is well-motivated by considerations of how we learn, teach, and use vague predicates.

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Timo Weiss

Title: Logic, Probability, Belief

Abstract: Logic and Reasoning about Probabilities are somewhat related. The formal part of an inductive/probabilistic logic can be viewed as a "refinement" of non-probabilistic logic or propositions themselves can be ascribed probabilities (to be true/false/etc.). However, classical probability theory rather follows the Kolmogorovian approach to attribute probabilities to certain sets rather than to propositions.An important area of probability theory revolves around conditional probabilities and Bayes' Theorem. Considerations and results in this field have since been applied to epistemology and so-called belief revision theory.

I wish to shed some light on how some approaches to this topic from a non-classical paraconsistent logical point of view might be carried out.

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Shunsuke Yatabe

Title: Deflationism, logical notion of truth and proof theoretic semantics

Abstract: Treating the truth predicate as a logical connective whose use is capturable in formal inference rules is often regarded as a convenient way to represent deflationary view of truth. In this talk we take that idea seriously, and analyze the behaviour of truth from proof theoretic viewpoint.

One characteristic point of deflationism is to allow to represent infinite conjunctions, therefore we have to extend our language and our theory to allow such infinitely sentences. However, it is known that some careless extensions makes the theories omega-inconsistent (known as McGee’s paradox and Cable’s paradox). We show that, the extension is omega-consistent in case the Harmony of the introduction rule and the elimination rule of truth connective is suitably preserved in terms of coinduction and corecursion.

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Related events

• A talk by Wen-fang Wang, June 13, 18:15--19:45 at Kyoto University. [See here for the details.]
• Kyoto Workshop on Dialetheism and Paraconsistency II, June 27 at Kyoto University. [See here for the details]

Acknowledgment

Kyoto Philosophical Logic Workshop II is supported by Japan Society for the Promotion of Science (JSPS) through grant 16H03344.

Organizers

The workshop is organized by Yasuo Deguchi and Hitoshi Omori. For any inquiries, please write to Hitoshi at: hitoshiomori [at] gmail [dot] com.