Frege's theory of types

30 Jun 2020  ·  Bruno Bentzen ·

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. read more

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