Finitism = PRA ? On a thesis of W. W. Tait

• Autorzy: Schirn M. , Niebergall K. -G.
• Języki publikacji: EN

Abstrakty

EN

In his paper `Finitism' (1981), W.W.~Tait maintained that the chief difficulty for everyone who wishes to understand Hilbert's conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive recursive. In our paper, we attempt to show that his thesis ``The finitist functions are precisely the primitive recursive functions'' is disputable and that another, likewise defended by him, is untenable. The second thesis is that the finitist theorems are precisely those $\Pi^0_1$-sentences that can be proved in (QF-IA).

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2005
• Tom: Nr 39
• Strony: 3--24
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Schirn M.

• Ludwig-Maximilians-Universitat Seminar fur Philosophie, Logik und Wissenschaftstheorie, Ludwigstr. 31, 80539 Munchen, Germany

autor

Niebergall K. -G.

• Ludwig-Maximilians-Universitat Seminar fur Philosophie, Logik und Wissenschaftstheorie, Ludwigstr. 31, 80539 Munchen, Germany

Bibliografia

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