Bentzen, Bruno (2020) Frege's theory of types. [Preprint]

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Abstract

Frege never explicitly advocated a doctrine of types like Russell, but a naive type theory can be found in his concept-script in his 1893 Grundgesetze der Arithmetik. Frege did not endorse a semantic account of typing, unlike most type theorists who use different types for booleans, natural numbers, products, etc. His concept-script is confined to a syntactic approach where object terms are identified with closed terms but the behavior of function terms alternates between that of closed terms of a function type and open terms. My aim in this paper is to rehabilitate Frege as a key figure in the history of type theory with an exegetical account of the developments anticipated in his concept-script from the perspective of modern type theory.

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Item Type:	Preprint
Creators:	Creators Email ORCID Bentzen, Bruno b.bentzen@hotmail.com 0000-0002-5987-7806
Keywords:	Frege, Type theory, Value-ranges, Lambda Calculus
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic
Depositing User:	Dr. Bruno Bentzen
Date Deposited:	16 Nov 2020 14:57
Last Modified:	16 Nov 2020 14:57
Item ID:	18405
Official URL:	https://sites.google.com/site/bbentzena/publicatio...
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic
Date:	14 November 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/18405

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    • Frege's theory of types. (deposited 25 Dec 2023 18:27)

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