Frege's Theorem in Plural Logic

Abstract

We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

The Contemporary Interest of an Old Doctrine.William Demopoulos - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:209 - 216.
Finitude and Hume's Principle.Richard G. Heck Jr - 1997 - Journal of Philosophical Logic 26 (6):589 - 617.
Plural Ancestral Logic as the Logic of Arithmetic.Oliver Tatton-Brown - 2024 - Review of Symbolic Logic 17 (2):305-342.
Finitude and Hume’s Principle.Richard G. Heck - 1997 - Journal of Philosophical Logic 26 (6):589-617.
The logic in logicism.Alexander Bird - 1997 - Dialogue 36 (2):341--60.
Neo-Logicism and Its Logic.Panu Raatikainen - 2020 - History and Philosophy of Logic 41 (1):82-95.
Is there a plural object?Byeong-Uk Yi - 2014 - In Aaron J. Cotnoir & Donald L. M. Baxter (eds.), Composition as Identity. Oxford: Oxford University Press USA.

Analytics

Added to PP
2021-07-07

Downloads
252 (#84,896)

6 months
83 (#71,215)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Simon Hewitt
University of Leeds

Citations of this work

Tuples all the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.

Add more citations

References found in this work

New work for a theory of universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
New Work For a Theory of Universals.David Lewis - 1997 - In David Hugh Mellor & Alex Oliver (eds.), Properties. New York: Oxford University Press.
Frege's conception of numbers as objects.Crispin Wright - 1983 - [Aberdeen]: Aberdeen University Press.
Frege meets dedekind: A neologicist treatment of real analysis.Stewart Shapiro - 2000 - Notre Dame Journal of Formal Logic 41 (4):335--364.

View all 8 references / Add more references