Hostname: page-component-f554764f5-fr72s Total loading time: 0 Render date: 2025-04-12T11:14:13.663Z Has data issue: false hasContentIssue false
  • English
  • Français

FREGE MEETS BROUWER (OR HEYTING OR DUMMETT)

Published online by Cambridge University Press:  13 February 2015

STEWART SHAPIRO  and
ØYSTEIN LINNEBO
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 3 , September 2015 , pp. 540 - 552
Copyright
Copyright © Association for Symbolic Logic 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

BIBLIOGRAPHY

Bell, J. (1999). Frege’s theorem in a constructive setting. Journal of Symbolic Logic, 64, 486–488.Google Scholar
Bell, J. (2014). Intuitionistic Set Theory, Studies in Logic. London: College Publications.Google Scholar
Burgess, J. P. (2005). Fixing Frege. Princeton: Princeton University Press.CrossRefGoogle Scholar
Cook, R. (2005). Intuitionism reconsidered. In Shapiro, S., editor. Oxford Handbook of the Philosophy of Mathematics and Logic. Oxford: Oxford University Press, pp. 387–411.Google Scholar
Frege, G. (1879). Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Louis Nebert. Translated (1967) as Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought. In Heijenoort, J. V., editor. From Frege to Gödel. Cambridge, Massachusetts: Harvard University Press, pp. 1–82.Google Scholar
Frege, G. (1884). Die Grundlagen der Arithmetik. Breslau: Koebner. Translated (1960) as The Foundations of Arithmetic (second edition), by Austin, J., New York: Harper.Google Scholar
Frege, G. (1893). Grundgesetze der Arithmetik 1. Olms: Hildescheim. Translated (2013) as Gottlob Frege: Basic Laws of Arithmetic, by Ebert, P. A. and Rossberg, M., Oxford: Oxford University Press.Google Scholar
Frege, G. (1903). Grundgesetze der Arithmetik 2. Olms: Hildescheim. Translated (2013) as Gottlob Frege: Basic Laws of Arithmetic, by Ebert, P. A. and Rossberg, M., Oxford: Oxford University Press.Google Scholar
Heck, R. (1997). Finitude and Hume’s principle. Journal of Philosophical Logic, 26, 589–617.CrossRefGoogle Scholar
Heck, R. (2011). Frege’s Theorem. Oxford: Oxford University Press.Google Scholar
Heck, R. (2011). Ramified Frege arithmetic. Journal of Philosophical Logic, 40, 715–735.CrossRefGoogle Scholar
Hilbert, D. (1899). Grundlagen der Geometrie. Leipzig: Teubner. Translated (1959) as Foundations of geometry, by Townsend, E., Salle, La, Illinois: Open Court.Google Scholar
Linnebo, Ø. (2004). Predicative fragments of Frege arithmetic. Bulletin of Symbolic Logic, 10, 153–174.Google Scholar
Parsons, C. (2007). Mathematical Thought and its Objects. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Shapiro, S. (1991). Foundations without Foundationalism: A Case for Second-Order Logic. Oxford: Oxford University Press.Google Scholar
Simpson, S. (2009). Subsystems of Second-Order Arithmetic. Cambridge: Cambridge University Press.Google Scholar
Tennant, N. (1987). Anti-Realism and Logic. Oxford: Oxford University Press.Google Scholar
Tennant, N. (2012). Cut for core logic. Review of Symbolic Logic, 5, 450–479.Google Scholar
Visser, A. (2009). The predicative Frege hierarchy. Annals of Pure and Applied Logic, 160, 129–153.CrossRefGoogle Scholar
Walsh, S. (2012). Comparing Peano arithmetic, basic law V, and Hume’s principle. Annals of Pure and Applied Logic, 163, 1679–1709.CrossRefGoogle Scholar
Wright, C. (1983). Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press.Google Scholar
Wright, C. (1992). Truth and Objectivity. Cambridge, Massachusetts: Harvard University Press.Google Scholar