G\"odel on Deduction

TL;DR

This paper explores Gödel's philosophical views on deduction within proof theory and investigates whether these views can extend to the logic of concepts, emphasizing deduction's central role in various logical frameworks.

Contribution

It provides a detailed commentary linking Gödel's philosophical ideas to proof theory and examines the potential extension of deduction's centrality to the logic of concepts.

Findings

Deduction is central in Gödel's views on predicate logic and set theory.

The paper discusses the possibility of extending deduction's importance to the logic of concepts.

It offers philosophical insights into the future role of deduction in logic.

Abstract

This is an examination, a commentary, of links between some philosophical views ascribed to G\"odel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from an infinitistic ideal perspective. It is inquired whether this centrality of deduction could also be kept in the intensional logic of concepts whose building G\"odel seems to have taken as the main task of logic for the future.