Bentzen, Bruno (2023) Frege's theory of types. Manuscrito. Rev. Int. Fil.,. ISSN 0100-6045

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Abstract

It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church’s simple theory of types. This claim roughly states that Frege presupposes a type of functions in the sense of simple type theory in the expository language of Grundgesetze. However, this view makes it hard to accommodate function names of two arguments and view functions as incomplete entities. I propose and defend an alternative interpretation of first-level function names in Grundgesetze into simple type-theoretic open terms rather than into closed terms of a function type. This interpretation offers a still unhistorical but more faithful type-theoretic approximation of Frege’s theory of levels and can be naturally extended to accommodate second-level functions. It is made possible by two key observations that Frege’s Roman markers behave essentially like open terms and that Frege lacks a clear criterion for distinguishing between Roman markers and function names.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Bentzen, Bruno b.bentzen@hotmail.com 0000-0002-5987-7806
Keywords:	Type theory; Frege; Grundgesetze; Martin-Löf type theory; Frege’s theory of function levels
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:	25 Dec 2023 18:27
Last Modified:	25 Dec 2023 18:27
Item ID:	22892
Journal or Publication Title:	Manuscrito. Rev. Int. Fil.,
Publisher:	Centro de logica, epistemologia e historia da ciencia-Unicamp
Official URL:	https://www.scielo.br/j/man/a/ptskGNwvqf5kh6KCRYsh...
DOI or Unique Handle:	10.1590/0100-6045.2023.v46n4.bb
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic
Date:	December 2023
ISSN:	0100-6045
URI:	https://philsci-archive.pitt.edu/id/eprint/22892

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• Frege's theory of types. (deposited 24 Jun 2020 16:12)
  • Frege's theory of types. (deposited 16 Nov 2020 14:57)
    • Frege's theory of types. (deposited 25 Dec 2023 18:27) [Currently Displayed]

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