2nd Workshop

2nd Nagoya Meta-Philosophy Workshop

Date: 15:00 to 17:40pm, Nov 5, 2018

Venue: Liberal Arts and Sciences Main Building C40, 4th Floor

Program:

15:00 to 16:30pm

"Normic Support Reconsidered"

Rafal Urbaniak (University of Gdańsk)

Abstract: On many occasions, statistical evidence isn't considered sufficient for finding liability in legal cases. It seems that in such situations high probability isn't enough for a justified belief. This poses a difficulty for those who endorse some version of the Lockean thesis -- an epistemological view that identifies justification with the passing of a probability threshold given the evidence. Trying to solve this problem, Martin Smith offered an alternative approach, the normic support theory, which is built upon the notion of calling for an explanation. Evidence normically supports a hypothesis (given the evidence) just in case the falsity of the hypothesis would require more explanation than its truth. Smith argues that cases of statistical evidence being insufficient for finding liability are exactly those in which the evidence fails to normically support a given hypothesis.

The theory, we submit, doesn't reach the intended goal. Discussing the examples of the preface paradox and the Blue Bus problem, we argue that whether a fact calls for an explanation depends on what information an assessing agent has. We lay out the difficulties that arise from this, and a few other problems that various applications of the normic support theory run into.

16:40 to 17:40pm

"Phase Semantic Investigation into Proof-terms of Second-order Intuitionistic Propositional Logic"

Yuta Takahashi (Nagoya University and Japan Society for the Promotion of Science)

Abstract: Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form theorems. On the basis of these works, Okada and Takemura reformulated Girard's phase semantics so that it became phase semantics for proof-terms, i.e., terms of lambda calculus. They formulated phase semantics for proof-terms of Laird's dual affine/intuitionistic lambda-calculus and proved the normal-form theorem for Laird's calculus via a completeness theorem. Their semantics was obtained by an application of Tait's computability predicates method. In this talk, we first formulate phase semantics for proof-terms of second-order intuitionistic propositional logic by modifying Tait-Girard's saturated sets method. Next, we prove the completeness theorem with respect to this semantics, which implies a strong normalization theorem. This is joint work with Ryo Takemura.