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FREGE MEETS BROUWER (OR HEYTING OR DUMMETT)

  • STEWART SHAPIRO and ØYSTEIN LINNEBO

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Corresponding author

*DEPARTMENT OF PHILOSOPHY THE OHIO STATE UNIVERSITY E-mail: shapiro.4@osu.edu
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF OSLO E-mail: oystein.linnebo@ifikk.uio.no

References

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Bell, J. (1999). Frege’s theorem in a constructive setting. Journal of Symbolic Logic, 64, 486488.
Bell, J. (2014). Intuitionistic Set Theory, Studies in Logic. London: College Publications.
Burgess, J. P. (2005). Fixing Frege. Princeton: Princeton University Press.
Cook, R. (2005). Intuitionism reconsidered. In Shapiro, S., editor. Oxford Handbook of the Philosophy of Mathematics and Logic. Oxford: Oxford University Press, pp. 387411.
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. 182.
Frege, G. (1884). Die Grundlagen der Arithmetik. Breslau: Koebner. Translated (1960) as The Foundations of Arithmetic (second edition), by Austin, J., New York: Harper.
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.
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.
Heck, R. (1997). Finitude and Hume’s principle. Journal of Philosophical Logic, 26, 589617.
Heck, R. (2011). Frege’s Theorem. Oxford: Oxford University Press.
Heck, R. (2011). Ramified Frege arithmetic. Journal of Philosophical Logic, 40, 715735.
Hilbert, D. (1899). Grundlagen der Geometrie. Leipzig: Teubner. Translated (1959) as Foundations of geometry, by Townsend, E., Salle, La, Illinois: Open Court.
Linnebo, Ø. (2004). Predicative fragments of Frege arithmetic. Bulletin of Symbolic Logic, 10, 153174.
Parsons, C. (2007). Mathematical Thought and its Objects. Cambridge: Cambridge University Press.
Shapiro, S. (1991). Foundations without Foundationalism: A Case for Second-Order Logic. Oxford: Oxford University Press.
Simpson, S. (2009). Subsystems of Second-Order Arithmetic. Cambridge: Cambridge University Press.
Tennant, N. (1987). Anti-Realism and Logic. Oxford: Oxford University Press.
Tennant, N. (2012). Cut for core logic. Review of Symbolic Logic, 5, 450479.
Visser, A. (2009). The predicative Frege hierarchy. Annals of Pure and Applied Logic, 160, 129153.
Walsh, S. (2012). Comparing Peano arithmetic, basic law V, and Hume’s principle. Annals of Pure and Applied Logic, 163, 16791709.
Wright, C. (1983). Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press.
Wright, C. (1992). Truth and Objectivity. Cambridge, Massachusetts: Harvard University Press.
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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