Notre Dame Journal of Formal Logic 41 (3):271-315 (2000)

Authors
Jamie Tappenden
University of Michigan, Ann Arbor
Abstract
It is widely believed that some puzzling and provocative remarks that Frege makes in his late writings indicate he rejected independence arguments in geometry, particularly arguments for the independence of the parallels axiom. I show that this is mistaken: Frege distinguished two approaches to independence arguments and his puzzling remarks apply only to one of them. Not only did Frege not reject independence arguments across the board, but also he had an interesting positive proposal about the logical structure of correct independence arguments, deriving from the geometrical principle of duality and the associated idea of substitution invariance. The discussion also serves as a useful focal point for independently interesting details of Frege's mathematical environment. This feeds into a currently active scholarly debate because Frege's supposed attitude to independence arguments has been taken to support a widely accepted thesis (proposed by Ricketts among others) concerning Frege's attitude toward metatheory in general. I show that this thesis gains no support from Frege's puzzling remarks about independence arguments
Keywords geometry   independence   logic   invariance   Frege   Hilbert   duality   axiom of parallels
Categories (categorize this paper)
DOI 10.1305/ndjfl/1038336845
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 51,591
Through your library

References found in this work BETA

What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Logic and Truth in Frege.Thomas Ricketts & James Levine - 1996 - Aristotelian Society Supplementary Volume 70 (1):121 - 175.
Metatheory and Mathematical Practice in Frege.Jamie Tappenden - 1997 - Philosophical Topics 25 (2):213-264.
Frege and Hilbert on Consistency.Patricia A. Blanchette - 1996 - Journal of Philosophy 93 (7):317-336.
Compound Thoughts.Gottlob Frege - 1963 - Mind 72 (285):1-17.

View all 15 references / Add more references

Citations of this work BETA

Why Is a Valid Inference a Good Inference?Sinan Dogramaci - 2017 - Philosophy and Phenomenological Research 94 (1):61-96.
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.
Frege on Consistency and Conceptual Analysis.Patricia A. Blanchette - 2007 - Philosophia Mathematica 15 (3):321-346.
Frege’s Philosophy of Geometry.Matthias Schirn - 2019 - Synthese 196 (3):929-971.

View all 10 citations / Add more citations

Similar books and articles

Causal Independence in EPR Arguments.Jeremy Butterfield - 1990 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:213 - 225.
Frege's New Science.G. Aldo Antonelli & Robert C. May - 2000 - Notre Dame Journal of Formal Logic 41 (3):242-270.
Frege on Indirect Proof.Ivan Welty - 2011 - History and Philosophy of Logic 32 (3):283-290.
Frege's Theory of Incomplete Entities.Michael David Resnik - 1965 - Philosophy of Science 32 (3/4):329-341.
Frege on Consistency and Conceptual Analysis.Patricia A. Blanchette - 2007 - Philosophia Mathematica 15 (3):321-346.
To Represent as So.Charles Travis - 2008 - In David K. Levy & Edoardo Zamuner (eds.), Wittgenstein’s Enduring Arguments. Routledge.
A Repair of Frege’s Theory of Thoughts.Mark Textor - 2009 - Synthese 167 (1):105 - 123.

Analytics

Added to PP index
2009-01-28

Total views
111 ( #81,720 of 2,331,160 )

Recent downloads (6 months)
6 ( #121,927 of 2,331,160 )

How can I increase my downloads?

Downloads

My notes