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Frege's theory of types

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

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Abstract

There is a widespread assumption in type theory that the discipline begins with Russell's efforts to resolve paradoxes concerning the naive notion of a class. My aim in this paper is to argue that Frege's sharp distinction between terms denoting objects and terms denoting functions on the basis of their saturation anticipate a simple type theory, although Frege vacillates between regarding functions as closed terms of a function type and open terms formed under a hypothetical judgment. Frege fails to express his logical views consistently due to his logicist ambitions, which require him to endorse the view that value-ranges are objects.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Bentzen, Brunob.bentzen@hotmail.com0000-0002-5987-7806
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: 24 Jun 2020 16:12
Last Modified: 24 Jun 2020 16:12
Item ID: 17367
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: 23 June 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17367

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