Why Axiomatize Arithmetic?

Sorites 16:54-61 (2005)
  Copy   BIBTEX

Abstract

This is a dialogue in the philosophy of mathematics that focuses on these issues: Are the Peano axioms for arithmetic epistemologically irrelevant? What is the source of our knowledge of these axioms? What is the epistemological relationship between arithmetical laws and the particularities of number?

Categories

Keywords

Reprint years

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,783

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Sub-Theory of Peano Arithmetic.Andrew Boucher - unknown
The development of arithmetic in Frege's Grundgesetze der Arithmetik.Richard Heck - 1993 - Journal of Symbolic Logic 58 (2):579-601.
Systems for a foundation of arithmetic.Andrew Boucher - manuscript
Equivalence of F with a sub-theory of peano arithmetic.Andrew Boucher - manuscript
“Strenge” arithmetics.Robert K. Meyer & Greg Restall - unknown
Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
The strength of nonstandard methods in arithmetic.C. Ward Henson, Matt Kaufmann & H. Jerome Keisler - 1984 - Journal of Symbolic Logic 49 (4):1039-1058.
Models without indiscernibles.Fred G. Abramson & Leo A. Harrington - 1978 - Journal of Symbolic Logic 43 (3):572-600.
The tractatus system of arithmetic.Pasquale Frascolla - 1997 - Synthese 112 (3):353-378.
Peano arithmetic may not be interpretable in the monadic theory of linear orders.Shmuel Lifsches & Saharon Shelah - 1997 - Journal of Symbolic Logic 62 (3):848-872.
Model-theoretic properties characterizing peano arithmetic.Richard Kaye - 1991 - Journal of Symbolic Logic 56 (3):949-963.
A model of peano arithmetic with no elementary end extension.George Mills - 1978 - Journal of Symbolic Logic 43 (3):563-567.
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Some remarks on initial segments in models of peano arithmetic.Henryk Kotlarski - 1984 - Journal of Symbolic Logic 49 (3):955-960.

Analytics

Added to PP
2011-01-19

Downloads
48 (#330,639)

6 months
1 (#1,467,486)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Charles Sayward
University of Nebraska, Lincoln

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references