Review of Symbolic Logic 2 (1):175-207 (2009)

Authors
Stewart Shapiro
Ohio State University
Abstract
At the beginning of Die Grundlagen der Arithmetik [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both programs are undermined at a crucial point, namely when self-evidence is supported by holistic and even pragmatic considerations.
Keywords self-evidence   mathematics   proofs   toread
Categories (categorize this paper)
DOI 10.1017/S175502030909011X
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: 65,703
Through your library

References found in this work BETA

Realism in Mathematics.Penelope Maddy - 1990 - Oxford, England and New York, NY, USA: Oxford University Prress.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press.

View all 30 references / Add more references

Citations of this work BETA

The Composition of Thoughts.Richard Heck & Robert May - 2011 - Noûs 45 (1):126-166.
The Ethics–Mathematics Analogy.Justin Clarke-Doane - 2020 - Philosophy Compass 15 (1).
Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
What is a Computer? A Survey.William J. Rapaport - 2018 - Minds and Machines 28 (3):385-426.

View all 15 citations / Add more citations

Similar books and articles

Frege's Notions of Self-Evidence.Robin Jeshion - 2001 - Mind 110 (440):937-976.
Self-Evidence.Carl Ginet - 2010 - Logos and Episteme 1 (2):325-352.
We Hold These Truths and the Pluralist Civilization.William Gould - 2011 - Catholic Social Science Review 16:95-104.
The Moral Truth.Mark Schroeder - forthcoming - In Michael Glanzberg (ed.), Oxford Handbook of Truth. Oxford University Press.
Fregean Hierarchies and Mathematical Explanation.Michael Detlefsen - 1988 - International Studies in the Philosophy of Science 3 (1):97 – 116.
Time, Actuality and Omniscience.Brian Leftow - 1990 - Religious Studies 26 (3):303 - 321.
Morality and God.Richard Swinburne - 2003 - Revue Internationale de Philosophie 57 (225):315 - 328.
Holding These Truths Today.Michael Novak - 2011 - Catholic Social Science Review 16:105-111.
The Paradox of Sufficient Reason.Samuel Levey - 2016 - Philosophical Review Recent Issues 125 (3):397-430.

Analytics

Added to PP index
2009-05-29

Total views
287 ( #34,346 of 2,462,538 )

Recent downloads (6 months)
4 ( #178,986 of 2,462,538 )

How can I increase my downloads?

Downloads

My notes