The second「論数哲」"Ron-Suu-Tetsu" (PhilLogMath) workshop

We will hold the 2nd 「論数哲」(PhilLogMath) workshop. Our aim is to provide opportunities of detailed discussions among philosophers, logicians and mathematicians. Everyone is welcome.

website url: http://researchmap.jp/jovzjd6b4-21098/#_21098

Date : March 14 (Wed) Place: Seiryo Kaikan (Nagata-cho, Tokyo) Room 4A and 4B (floor 4) http://metropolis.co.jp/listings/venues/type/stage-venue/seiryo-kaikan/ Time table 9:00-10:30 Takuro Onishi (Kyoto University) "BHK-interpretation and Bilateralism" 10:30-12:00 Katsuhiko Sano (JAIST) "An `Impossibility' Theorem in Radical Inquisitive Semantics" 13:30-15:00 Masahiko Sato (Kyoto University) "Bootstrapping Mathematics" 15:15-16:45 Richard Dietz (The University of Tokyo) "Comparative Concepts" 17:00-18:30 Conrad Asmus (JAIST) " Vagueness and Revision Sequences"

Any slot consists of 60 minutes talk and 30 minutes discussion basically. All talks are in English.

Abstracts: * Takuro Onishi "BHK-interpretation and Bilateralism" In this talk, H.Wansing's inferentialist semantics for Bi-intuitionist logic is examined.Bi-intuitionist Logic (a.k.a. Heyting-Brouwer logic) is an extension of Intuitionist Logic with a connective dual to implication. It is sort of an amalgamation of intuitionist and dual-intuitionist logic. Accordingly, BHK-like, inferentialist, or proof-theoretic semantics for the logic would be a bilateralist one appealing to not only "proof" but also"dual proof (disproof)" as primitive notions. In his "Proofs,disproofs and their duals" (2010),Wansing gives a correctness (soundness) proof of a display system for bi-intuitionist logic in terms of the bilateralist semantics. I point out that his proof involves controversial assumptions concerning the relation between proofs and dual proofs and present an alternative view on how they get together. (Although Wansing discuss a BHK-like interpretation for strong negation and its dual as well, I will concentrate on logics without them in this talk.)

*Katsuhiko Sano "An `Impossibility' Theorem in Radical Inquisitive Semantics" An aim of this talk is to show that it is impossible to provide a `natural' Kripke semantics with radical inquisitive semantics, recently proposed by Jeroen Groenendijk and Floris Roelofsen. Inquisitive semantics is a new formal framework for the semantics of both declarative and interrogative sentences. One of the main features of this semantics is that we assume there is no type distinction between the declarative and the interrogative, but we provide both classical and inquisitive meanings with each sentence. For example, the declarative sentence `Taro will drink tea or coffee.' proposes two alternatives `Taro will drink tea' and `Taro will drink coffee'. Inquisitive meaning captures such information of the alternatives. In conservative (non-radical) inquisitive semantics (Groenendijk and Roelofsen 2009), intuitionistic Kripke semantics captures how our group knowledge increases though a conversation, and also allows us to derive the inquisitive meaning of a sentence from the classical meaning. In the example above, we could give a reply `Taro won't drink tea or coffee' to the speaker. In conservative inquisitive semantics, however, we cannot cover such a negative reaction. Radical inquisitive semantics is an extension of conservative one such that we can provide with each sentence the positive and negative inquisitive meanings as well as the classical meaning. My contribution of this talk is to establish that *any* `natural' Kripke semantics fails to capture a link between the classical meaning and the negative inquisitive meaning.

*Masahiko Sato "Bootstrapping Mathematics" It is well-known that any formal mathematical system can be faithfully encoded within PRA (Primitive Recursive Arithmetic). It is also commonly accepted that any well-established part of mathematics can be presented as a formal system. Thus, it seems that we can bootstrap mathematics, within a computer, simply by implementing PRA in it. However, we will show that this view is too naiive both from computer science point of view and from foundational point of view. We also discuss an alternative approach to this problem by giving an overview of a proof assistant system we are developing.

*Richard Dietz "Comparative Concepts" Comparative concepts (such as ‘greener than’ or ‘higher than’)are fundamental to our grasp of associated categorical concepts (‘green’, ‘high’, respectively). Some comparative concepts seem natural, whereas other ones seem rather gerrymandered---e.g., compare ‘x is greener than y’ and ‘x and y are such that either (i) x and y are inspected before midday and x is greener than y, or (ii) x and y are inspected after midday and x is bluer than y’. What kind of cognitive structures under your ability to order objects? And why do we order objects the way we do,and not in other ways? The aim of this talk is to outline an account of comparative concepts within a conceptual spaces framework. The account bears for one on the account of naturalness for comparative concepts.For another, it bears on the theory of gradable concepts, i.e., the type of categorical concepts expressed by gradable terms in natural language.The approach is novel in that it carries some basic assumptions from Peter Gärdenfors' conceptual spaces account of categorical concepts over to comparative concepts (in his monograph ‘Conceptual Spaces’ [2000]).The offered approach is more general both (i) in that it supplies a framework for motivating various types of categorisation rules for gradable concepts, and (ii) in that it gives a model that subsumes ungraded categorisation as a limiting case.

*Conrad Asmus "Vagueness and Revision Sequences" Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.

*Workshop organizer (please replace [at] to @): Yuko Murakami Shunsuke Yatabe ( shunsuke.yatabe[at]aist.go.jp ) Takuro Onishi ( takuro.onishi[at]gmail.com )