Speaker: Mr. Kai Tanter (University of Melbourne)
Date: July 21 (Friday) 2017
Venue: Small meeting room in the basement, Faculty of Letters Main Building, Yoshida Campus, Kyoto University.
Title:Inferentialist Semantics for Atomics, Predicates, and Names
Inferentialism is a theory in the philosophy of language which claims that the meaning of expressions ought to be understood in terms of their inferential roles or relations, rather than truth and reference. It naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules applied within proofs, instead of more traditional model-theoretic semantics. Most work in proof theory has been focused on logical constants, with relatively little work on the semantics of atomic sentences and subatomic terms. Drawing on Robert Brandom’s idea of material inference and Greg Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a compositional proof-theoretic semantics for atomic sentences and their component names and predicates. Brandom’s notion of material inference applies to those inference which are good in virtue of their non-logical vocabulary. For example, from ‘Paula is a platypus’ to ‘Paula is a monotreme’. Applied to “parts” of sentences, Brandom’s claim is that predicates are governed by asymmetric and names by symmetric inferences rules. Based on Brandom’s ideas I set out general rule forms for atomic sentences, predicates, and names within the multiple conclusion sequent calculus. This system has several interesting features: (1) the rules for atomic sentences are determined by those for their component predicates names; (2) cut elimination for the system can be proved; (3) model theoretic extensions can be interpreted as idealisations derived from the more fundamental inference rules.