Frege’s Theory of Types

Manuscrito 46 (4):2022-0063 (2023)
  Copy   BIBTEX

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.

Other Versions

No versions found

Similar books and articles

Sense, reference, and computation.Bruno Bentzen - 2020 - Perspectiva Filosófica 47 (2):179-203.
Stipulations Missing Axioms in Frege's Grundgesetze der Arithmetik.Gregory Landini - 2022 - History and Philosophy of Logic 43 (4):347-382.
Definition by Induction in Frege's Grundgesetze der Arithmetik.Richard Heck - 1995 - In William Demopoulos (ed.), Frege's philosophy of mathematics. Cambridge: Harvard University Press.
Types in logic and mathematics before 1940.Fairouz Kamareddine, Twan Laan & Rob Nederpelt - 2002 - Bulletin of Symbolic Logic 8 (2):185-245.
PM's Circumflex, Syntax and Philosophy of Types.Kevin C. Klement - 2011 - In Kenneth Blackwell, Nicholas Griffin & Bernard Linsky (eds.), Principia mathematica at 100. Hamilton, Ontario: Bertrand Russell Research Centre. pp. 218-246.

Analytics

Added to PP
2023-12-24

Downloads
315 (#79,629)

6 months
95 (#62,071)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Bruno Bentzen
Zhejiang University

Citations of this work

No citations found.

Add more citations

References found in this work

Uber Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25-50.
A formulation of the simple theory of types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (3):114-115.
Meaning and speech acts.R. M. Hare - 1970 - Philosophical Review 79 (1):3-24.

View all 21 references / Add more references