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 | ||||||
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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 |
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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 |
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Date: | 23 June 2020 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/17367 |
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