Aim
The aim of this workshop is to discuss and exchange new ideas and recent developments related to dialetheism and paraconsistent logics.
Date & Venue
Speakers
Program
13:00--14:30: Wen-fang Wang "Why Must A Dialetheist also Be a Gap Theorist"
14:30--14:40: Break
14:40--16:10: Eduardo Barrio "A recovery operator for non-transitive approaches."
Abstracts
Eduardo Barrio
Title: A recovery operator for non-transitive approaches
Abstract: In some recent papers, Cobreros, Egré, Ripley and van Rooij have defended the idea that abandoning transitivity may lead to a solution to semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a non-transitive theory of truth, where the structural property of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut that involve semantic notions. In this paper we intend to meet the challenge of answering how to regain the safe instances of Cut, within the language of the theory, with the help of a unary recovery operator. Taking into account some concerns related to revenge paradoxes, in this talk, I am going to prove that the triviality of the theory resulting from this addition depends on the way self-reference is expressed. If it is expressed through identities, then the resulting theory is indeed trivial, but if it is expressed employing the conditional of the underlying logic, then the resulting theory is non-trivial. I'll consider the latter route, draw its connection with the so-called Goodship Project, and provide a sound and complete calculus for it.
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Wen-fang Wang
Title: Why Must A Dialetheist also Be a Gap Theorist
Abstract: Dialetheism is the view that there are true contradictions. Classical dialetheism holds further the view that the law of excluded middle is indeed a logical law. Most famous dialetheists, such as G. Priest and Jc. Beall, are classical dialetheists; they take classical dialetheism to be the only plausible solution to the semantic paradoxes. The main contention of the paper is, however, that their views should be rejected. Based on inspecting Priest’s and Beall’s dialetheist theories from a special perspective, this paper contends that classical dialetheism has no natural and plausible way to assign truth values to various truth-ineliminable sentences, i.e., sentences whose truth-conditions essentially involve the property of being true. Several examples of such truth-ineliminable sentences are given in the paper, and two classical dialetheist strategies for assigning them truth values are inspected. This paper argues that none of these strategies is successful.
Related events
Acknowledgment
Kyoto Workshop on Dialetheism and Paraconsistency 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.