The Consistency of predicative fragments of frege's grundgesetze der arithmetik
Titel:
The Consistency of predicative fragments of frege's grundgesetze der arithmetik
Auteur:
Heck, Richard G.
Verschenen in:
History and philosophy of logic
Paginering:
Jaargang 17 (1996) nr. 1-2 pagina's 209-220
Jaar:
1996
Inhoud:
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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