Editing Hilbert's second problem (section)

==External links==
* [https://web.archive.org/web/20120205025851/http://www.mathematik.uni-bielefeld.de/~kersten/hilbert/rede.html Original text of Hilbert's talk, in German]
* [http://aleph0.clarku.edu/~djoyce/hilbert/toc.html English translation of Hilbert's 1900 address]

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:A definition of a "finitary formal system" is given by Goldstein (p. 144, footnote 7):
:: "...''finitary'' formal systems... formal systems with a finite or denumerable (or countable) alphabet of symbols, wffs [well-formed-formulas] of finite length, and rules of inference involving only finitely many premises. (Logicians also work with formal systems with uncountable alphabets, with infinitely long wffs, and with proofs having infinitely many premises."(p. 144, footnote 7)
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<!-- It is widely held that [[Gödel's second incompleteness theorem]] shows that there is no [[finitism|finitistic]] proof that PA is consistent (though Gödel himself disclaimed this inference [this needs a better reference-- but cf Dawson p.71ff "...Gödel too [like Hilbert] believed that no mathematical problems lay beyond the reach of human reason. Yet his results showed that the program that Hilbert had proposed to validate that belief -- his proof theory -- could not be carried through as Hilbert had envisioned" (p.71) See also p. 98ff for more discussion of 'finite procedure').  -->

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[[Category:Hilbert's problems|#02]]