The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik

History and Philosophy of Logic 17 (1):209-220 (1996)
As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell?s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed
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DOI 10.1080/01445349608837265
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PhilPapers Archive Richard Heck, The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik
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Gabriel Uzquiano (2015). Modality and Paradox. Philosophy Compass 10 (4):284-300.

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