Talk by Ramazan Ayupov: “The Analysis of Analyticity in Hintikka’s Philosophy of Mathematics and Martin-Löf’s Type Theory”

On 17 June the 123rd session of the theoretical seminar "Formal Philosophy" took place.

Abstract

This talk addresses the question of whether an account of analyticity is possible that does not fall within the scope of the criticism advanced by W. V. Quine in “Two Dogmas of Empiricism.” The history of analyticity from Kant to the present can be understood as a history of changes in the criterion of analyticity itself. In Kant, analyticity is associated with the content of concepts and the relations internal to a judgment; in Frege, with justification; in Carnap, with linguistic rules; in Quine, with a critique of the unexplained notions of meaning, synonymy, and semantic rules; in Hintikka, with the plurality of forms of analysis; in Martin-Löf, with the form of judgment; and in Bentzen, with the computational semantics of intuitionistic type theory.

The central thesis of the talk is that the computational criterion of analyticity proposed by Bruno Bentzen within intuitionistic type theory can be regarded as a distinct sense of analyticity that supplements Hintikka’s typology. According to this criterion, a judgment is analytic when its correctness can be fully established through the evaluation of the expressions occurring in it, understood as their reduction to canonical forms. This account of analyticity does not rely on the unexplained notions of meaning, synonymy, or semantic rules targeted by Quine’s criticism and therefore allows the question of whether the analytic–synthetic distinction can be drawn to be posed in a different way.

Martin-Löf P. Analytic and Synthetic Judgements in Type Theory // Kant and Contemporary Epistemology / ed. by P. Parrini. The University of Western Ontario Series in Philosophy of Science. — Vol. 54.  — Dordrecht: Springer, 1994. — P. 87–100.

Bentzen B. Analyticity and Syntheticity in Type Theory Revisited // Review of Symbolic Logic. — 2024. — Vol. 17, no. 4. — P. 1119–1145.

Hintikka J. An Analysis of Analyticity // Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic. — Oxford: Clarendon Press, 1973. — P. 123–149.