Aim

The aim of this one-day workshop is to discuss and exchange new ideas and recent developments related to philosophical logics, broadly construed.

Date & Venue

• Date: February 28, 2017.
• Venue: Meeting room on the 1st floor of Rakuyu Kaikan, Kyoto University. (Building number 96 of this map)

Speakers

• Massimilliano Carrara (University of Padua)
• Ryosuke Igarashi (Kyoto University)
• Ryo Ito (University of St. Andrews & Kyoto University)
• Andreas Kapsner (LMU Munich)
• Chi-Yen Liu (Yang-Ming University & Kyoto University)
• Timo Weiss (University of Bonn)
• Maiko Yamamori (Kyoto University)
• Wei Zhu (Peking University)

Program

Session 1: Conditionals

09:30--11:00: Andreas Kapsner "Plausible World Semantics"

11:00--11:15: Coffee break

11:15--12:00: Ryo Ito "Bradley, the unity of the proposition and material implication"

12:00--12:45: Chi-Yen Liu "Conditional Probability, Conjunctive Probability, and defective truth table"

12:45--14:00 Lunch

Session 2: Modal and intuitionistic logics

14:00--14:45 Ryosuke Igarashi "The Law of Explosion and Intuitionistic Logic"

14:45--15:30 Wei Zhu "A contribution to ranking theory concerning belief revision"

15:30--15:45 Coffee break

Session 3: Paraconsistency and dialetheism

15:45--16:30 Timo Weiss "Some Notes on Inconsistent Arithmetic"

16:30--17:15 Maiko Yamamori "Paradoxes of Self-Reference and Contraction"

17:15--17:30 Coffee break

17:30--19:00 Massimilliano Carrara "Rejecting and Assuming (with a sketch of DLEAC, a Dialetheic Logic of Exclusive Assumptions and Conclusions)"

19:30-- Workshop dinner

Abstracts

Andreas Kapsner

Title: Plausible World Semantics

Abstract: In this workshop talk, I will try to combine some new and some older ideas I had concerning fictionality, paraconsistency and conditionals. I try to show in what ways telling a plausible story can lead to deeper insights about logic (my examples here will concern paraconsistent and constructive logics). I will then try develop one of the central ideas in my book “Logics and Falsifications”, namely that in some contexts assertibility correlates with verifiability, while in other contexts it correlates with unfalsifiability. I intend to apply this idea to subjunctive conditionals, where once again it will turn out that telling a plausible story is of vital importance. These considerations will lead to what I call "Plausible World Semantics", a variation on the Lewis/Stalnaker sphere semantics that also bears some similarity to Jaskowski's discussive logic.

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Ryo Ito

Title: Bradley, the unity of the proposition and material implication

Abstract: Material implication has often been criticised for its inclusion of seemingly unnatural inferences among valid ones. Russell, who (to my knowledge) coined the term, had some reasons to endorse it. In this talk I will introduce his response to Bradley's famous challenge to pluralism so that I can indicate another reason that has been unnoticed in the literature and looks purely metaphysical to the modern eye.

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Chi-Yen Liu

Title: Conditional Probability, Conjunctive Probability, and defective truth table

Abstract: In psychological studies of probability of indicative conditionals, three significant results emerge. First, most people believe that the probability of an indicative conditional is the corresponding conditional probability, or P(A→B)=P(B|A), which we call “conditional probability hypothesis”. Second, a few people believe that the probability of an indicative conditional is the probability of the conjunction of its antecedent and consequent, or P(A→B) = P(AB), which we call “conjunctive probability hypothesis”. Finally, most people have a defective truth table for indicative conditionals, with three truth values instead of two. But these three results cannot be all true. Most psychologists try to defend that P(B|A) is the probability of A→B, and they try to explain away why not a few people take conjunctive probability view about the probability of A→B. This paper argues for the opposite. I defend that conjunctive probability hypothesis is correct, and try to explain away why people take conditional probability view. I give two reasons to support this claim. First, conditional probability hypothesis cannot be correct because of triviality results. Triviality results have told us that P(B|A)≠P(A→B). Second, based on defective truth table, we can propose a 3-valued semantics for indicative conditionals which implies conjunctive probability, and we show that P(B|A) is the fair betting quotient of betting on A→B, provided that A→B is a simple indicative conditional. I conclude that though P(B|A) is not P(A→B), it guides us to evaluate a simple indicative conditional.

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Ryosuke Igarashi

Title: The Law of Explosion and Intuitionistic Logic

Abstract: In this paper, we will investigate natural understanding of the so-called Principle of Explosion (EFQ) and intuitionistic logic. Firstly, we argue that there is no intuitionistically well-explained validation to EFQ. Secondly, we show that intuitionistic logic is well-formulated with quasi-multiple-conclusion natural deduction, and that intuitionistic λ-calculus is better understood as one equipped with a catch/throw mechanism with computation abort.

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Wei Zhu

Title: A contribution to ranking theory concerning belief revision

Abstract: Belief revision theory has been a joint research field regarding human intelligence, which involves philosophy, logic, and computer science. Among various competing approaches apt at formalizing belief changes, AGM paradigm (so called after its three originators, Carlos Alchourrón, Peter Gärdenfors, and David Makinson (1985)), has been the most influential approach since 1985. In this paper, however I would like to introduce an alternative approach to belief revision theory, i.e. ranking theory, developed by Wolfgang Spohn (1983,1988) . In ranking theory roughly, beliefs are ranked with a natural number in order to distinguish their degrees. Therefore belief changes are expressed correspondingly as changes of belief ranks with respect to the impact of advents of new evidences. I would like to improve the mechanisms of ranking theory by stating several observations and build an improving plan.

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Timo Weiss

Title: Some Notes on Inconsistent Arithmetic

Abstract: Any attempt at a framework for mathematics arguably has to say something about arithmetic, as arithmetic is understood as an essential part of mathematics.

Unlike set theory, though, arithmetic does not seem to provide us with that many paradoxes by itself. However, Gödel's Incompleteness Theorems and Tarski's theorem on the undefinability of truth were proved for certain axiomatisations of arithmetic, using the expressive power of that arithmetic to code the meta-theory within the object theory.

These were serious limitative results for the classical framework of arithmetic. I wish to examine how an inconsistent framework for arithmetic is able to deal with these limitations by discussing Mortensen's (1995) and Priest's (1994,1997,2000) treatments of arithmetic and the connections with the logics involved. Interestingly, a finitist position also appears to be compatible with a paraconsistent (and non-Intuitionist) interpretation of arithmetic.

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Maiko Yamamori

Title: Paradoxes of Self-Reference and Contraction

Abstract: There are many paradoxes of self-reference, and many solutions have been proposed respectively. I think there is a general solution for them; contraction-freeness. This solution is, however, criticized again and again. In this talk, I will support to discard contraction.

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Massimilliano Carrara

Title: Rejecting and Assuming (with a sketch of DLEAC, a Dialetheic Logic of Exclusive Assumptions and Conclusions)

Abstract: If giving up the exclusivity of negation is the key to solving the semantic paradoxes, does not the exclusivity of denial land us back in paradox? I argue, first in an informal way, then formally, that intuitive norms for denial -- which dialetheists arguably accept -- give rise to paradox, provided one's language is rich enough to express deniability / rejectability. I consider some possible ways out, concerning both the formal language and the informal way of characterizing the paradox. In the appendix I propose a new logic -- a Dialetheic Logic with Exclusive Assumptions and Conclusions (DLEAC) -- including classical logic as a particular case. In DLEAC, exclusivity is expressed via the speech acts of assuming and concluding.

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Acknowledgment

Kyoto Philosophical Logic Workshop 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.