Philosophia Mathematica 5 (2):97-115 (1997)

Authors
Colin McLarty
Case Western Reserve University
Abstract
often insisted existence in mathematics means logical consistency, and formal logic is the sole guarantor of rigor. The paper joins this to his view of intuition and his own mathematics. It looks at predicativity and the infinite, Poincaré's early endorsement of the axiom of choice, and Cantor's set theory versus Zermelo's axioms. Poincaré discussed constructivism sympathetically only once, a few months before his death, and conspicuously avoided committing himself. We end with Poincaré on Couturat, Russell, and Hilbert.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/5.2.97
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: 63,319
Through your library

References found in this work BETA

Russell's Mathematical Logic.Kurt Gödel - 1944 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Northwestern University Press. pp. 119--141.
Poincaré Against the Logicians.Michael Detlefsen - 1992 - Synthese 90 (3):349 - 378.
On Some Difficulties in the Theory of Transfinite Numbers and Order Types.Harold Chapman Brown - 1906 - Journal of Philosophy, Psychology and Scientific Methods 3 (14):388-390.

View all 13 references / Add more references

Citations of this work BETA

Zermelo and Set Theory.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.

Add more citations

Similar books and articles

Poincare on Mathematics, Intuition and the Foundations of Science.Janet Folina - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:217 - 226.
Space, Number and Structure: A Tale of Two Debates.Stewart Shapiro - 1996 - Philosophia Mathematica 4 (2):148-173.
Poincaré's Conception of the Objectivity of Mathematics.Janet Folina - 1994 - Philosophia Mathematica 2 (3):202-227.
Hilberts Logik. Von der Axiomatik zur Beweistheorie.Volker Peckhaus - 1995 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 3 (1):65-86.

Analytics

Added to PP index
2009-01-28

Total views
79 ( #135,812 of 2,448,688 )

Recent downloads (6 months)
1 ( #445,641 of 2,448,688 )

How can I increase my downloads?

Downloads

My notes