Notre Dame Journal of Formal Logic

On a Consistent Subsystem of Frege's Grundgesetze

John P. Burgess


Parsons has given a (nonconstructive) proof that the first-order fragment of the system of Frege's Grundgesetze is consistent. Here a constructive proof of the same result is presented.

Article information

Notre Dame J. Formal Logic, Volume 39, Number 2 (1998), 274-278.

First available in Project Euclid: 7 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B10: Classical first-order logic
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 03F25: Relative consistency and interpretations


Burgess, John P. On a Consistent Subsystem of Frege's Grundgesetze. Notre Dame J. Formal Logic 39 (1998), no. 2, 274--278. doi:10.1305/ndjfl/1039293068.

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  • [1] Boolos, G., ``Whence the contradiction?,'' Aristotelian Society Supplementary, vol. 67 (1993), pp. 213--33.
  • [2] Demopoulos, W., editor, Frege's Philosophy of Mathematics, Harvard University Press, Cambridge, 1995.
  • [3] Heck, R., ``Grundgesetze der Arithmetik I \S \S 29--32,'' Notre Dame Journal of Formal Logic, vol. 38 (1997), pp. 437--74.
  • [4] Parsons, T., ``On the consistency of the first-order portion of Frege's logical system,'' Notre Dame Journal of Formal Logic, vol. 28 (1987), pp. 161--88.