Talk:Hilbert's program

1920
Where did the 1920 date come from? My understanding of Hilbert's Program was that it was an umbrella term for all of the stated goals. Did Hilbert have a specific paper with those stated goals? I agree that these are the goals of the program, and it's not any OR to state them as such, but I'm just wondering how concrete the 1920 date is. His 1900 address certainly had a direct bearing to the program itself. Thanks! --M a s 20:59, 7 June 2006 (UTC)

Note to editors
The usage of the terminology, "Hilbert's program", rather than "Hilbert's Program" became established after the date of the post of 7 June 2006 above, and continues currently, as of the date of this post. &mdash; Newbyguesses - Talk 05:04, 12 June 2007 (UTC)


 * Grammatically, "Hilbert's program" means, "The program associated with Hilbert" whereas "Hilbert's Program" means, "That which is known by the name, Hilbert's Program." Crossaw (talk) 00:40, 4 March 2023 (UTC)

Hilbert's Response to Godel
This is not included, and I think it must. I will add it.Likebox 23:12, 12 October 2007 (UTC)

Ambiguous use of "completeness"
In the second item of the section "Hilbert's program after Gödel", the term "completeness" is used in two different meanings without notice, see "semantically complete" and "deductively complete" on the page Completeness. --Tillmo (talk) 13:20, 18 January 2009 (UTC)
 * Ten years later the problem hasn't been dealt with yet, so I've removed that sentence (which, actually, had anything to do there). 78.15.193.193 (talk) 15:34, 22 October 2019 (UTC)

Response to "Hilbert's Response to Godel"
The material after the bullet list beginning at "Hilbert wrote about Gödel's theorem" was added four years ago and seems to have gone mostly unquestioned since then, but I am very skeptical both about its value and its factual accuracy. At least one of the existing citations is spurious: the material ends claiming that "This process proves the consistency of Peano Arithmetic" with a citation to Gentzen 1936, but the argument sketched in the previous paragraphs has nothing to do with Gentzen's consistency proof. Also, I am not a historian, but I have never seen this particular interpretation of finitary methods attributed to Hilbert -- I do not know what paper the citation "(Hilbert 1931, p. 215)" is referring to (is it one of the two papers listed at the SEP article?). Without explanation from User:Likebox, my inclination would be to undo this entire revision. Noamz (talk) 16:09, 30 November 2011 (UTC)


 * I went ahead and deleted the passage. If somebody objects, please respond to these questions before restoring the material. Noamz (talk) 15:14, 3 December 2011 (UTC)

Typos in one sentence
The second paragraph ends with this sentence, "This refuted Hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore could not prove everything else." I think the "not" is a typo. Shouldn't it read, "... and therefore could prove everything else."? I'm not fixing it right now in case I am misinterpreting what the sentence is trying to say. Does anyone else see it the way I see it? Also, I think the comma should be removed, because the clause following the "and" is not independent. Crossaw (talk) 00:33, 4 March 2023 (UTC)