10:30-12:00 大西琢郎 “Usefulness of deduction and Proof-Theoretic Semantics” [slides]
13:30-15:00 Shawn Standefer: “Truth and conditionals” [slides]
15:30-17:00 丸山善宏 “Categorical Harmony and Degrees of Paradoxity” [slides]
17:15-18:15 Greg Restall “Logical Constants and Focusing Disagreements” [slides]
(1)Speaker: Takuro Onishi
Title: Usefulness of deduction and Proof-Theoretic Semantics
Michael Dummett’s anti-realist theory of meaning is considered to provide a philosophical basis of proof-theoretic semantics, which is an inferentialis approach to logical validity. Unfortunately, in the debate of proof-theoretic semantics, due attention has not been paid to his fundamental consideration on the nature of deductive inference, in which he emphasizes its usefulness or fruitfulness as well as its validity. That is, deduction is a special kind of activity of extending our knowledge. Dummett represents it as involving a certain tension between validity and usefulness, and tries to reconcile it against the background of his own meaning theory. In this talk I present Dummett’s view on deduction, and compare it with G.Restall’s bilateralist explication of logical consequence which would justify classical logic.
(2)Speaker: Shawn Standefer
Title: Truth and conditionals
Some recent approaches to truth have adopted the strategy of enriching the underlying logic with a new conditional. I will provide some background on these approaches and distinguish different roles that such conditionals play in the theory. I will show how this distinction plays out in an extension of the revision theory of truth and use the distinction to offer a philosophical defense of that theory.
(3)Speaker: Yoshihiro Maruyama
Title: Categorical Harmony and Degrees of Paradoxity
Prior’s weird connective “tonk” compelled logicians to articulate the concept of a logical constant, eventually giving rise to developments of proof-theoretic semantics in the spirit of inferentialism, and to the notion of proof-theoretic harmony in particular, which works as a criterion to judge if a connective is a proper logical constant or not. Different concepts of harmony have been proposed and discussed by Belnap, Dummett, and many others.
Building upon Lawvere’s understanding of logic via category theory, I formulate a categorical concept of harmony relativised to primitive vocabulary, and compare it with other notions of harmony. The categorical conception of harmony leads us to a novel analysis of the nature of tonk: namely, the problem of tonk is the problem of equivocation in terms of adjoint functors. It finally turns out that there are different degrees of paradoxity of logical constants from a categorical perspective.
(4)Speaker: Greg Restall
Title: Logical Constants and Focusing Disagreements
For expressivists about logic (such as Robert Brandom and Jaroslav Peregrin), logical vocabulary gives us means to do more than we could without it. With concepts such as negation, conjunction, conditionality, and the quantifiers, we can express contents which would otherwise be out of reach to us. However, in another sense, logical vocabulary seems to be neutral with regard to content. It does not seem to add any new subject matter to our thoughts or conversations.
I will attempt to explain why a certain class of logical expressions (including the standard propositional connectives, first order quantifiers, and perhaps some modal operators) give us means to extend our expressive resources without adding new subject matter, by attending to the role special that logical vocabulary can play in articulating disagreements.