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Frege's theory of types

by   Bruno Bentzen, et al.

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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