Arithmetic, Logicism, and Frege’s Definitions

International Philosophical Quarterly 61 (1):5-25 (2021)
  Copy   BIBTEX

Abstract

This paper describes both an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions—and two interpretations that try to resolve that puzzle, what I call the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation primarily by criticizing the most careful and sophisticated defenses of the analysis interpretation, those given my Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s text either are inconsistent with the analysis interpretation or do not support it. I also defend the explicative interpretation from the recent charge that it cannot make sense of Frege’s logicism. While I do not provide the explicative interpretation’s full solution to the puzzle, I show that its main competitor is seriously problematic.

Similar books and articles

Frege on definitions.Sanford Shieh - 2008 - Philosophy Compass 3 (5):992-1012.
Formal Arithmetic Before Grundgesetze.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 497-537.
Neo-Logicism and Its Logic.Panu Raatikainen - 2020 - History and Philosophy of Logic 41 (1):82-95.
Logicism as Making Arithmetic Explicit.Vojtěch Kolman - 2015 - Erkenntnis 80 (3):487-503.
Ramified Frege Arithmetic.Richard G. Heck - 2011 - Journal of Philosophical Logic 40 (6):715-735.
The Basic Laws of Cardinal Number.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 1-30.
Logicism Reconsidered.Patricia A. Blanchette - 1990 - Dissertation, Stanford University
Ramified Frege Arithmetic.Richard G. Heck Jr - 2011 - Journal of Philosophical Logic 40 (6):715 - 735.
The ontological implications of neo-Fregeanism.María de Ponte - 2016 - Daimon: Revista Internacional de Filosofía 69:159-174.
Frege's Other Program.Aldo Antonelli & Robert May - 2005 - Notre Dame Journal of Formal Logic 46 (1):1-17.

Analytics

Added to PP
2021-02-05

Downloads
465 (#41,279)

6 months
157 (#21,170)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Timothy Perrine
Rutgers - New Brunswick

Citations of this work

No citations found.

Add more citations

References found in this work

Frege in Perspective.Joan Weiner - 2018 - Cornell University Press.
Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
Function and Concept.Gottlob Frege - 1960 - In D. H. Mellor & Alex Oliver (eds.), Properties. Oxford University Press. pp. 130-149.
Begriffsschrift.Gottlob Frege - 1967 - In Jean Van Heijenoort (ed.), From Frege to Gödel. Cambridge: Harvard University Press. pp. 1-83.
The Development of Logic.William Kneale & Martha Kneale - 1962 - Philosophy 40 (151):79-83.

View all 22 references / Add more references