Talk:Entscheidungsproblem

message: I deleted the rambling that was here.  Wikipedia is not a place to publish new ideas. CMummert · talk 14:31, 12 January 2007 (UTC)
thread_title:  Talk page cleaned up 

message: I've changed the importance of this page from "low" to "mid".  Actually, I think it rates a "high", but philosophers who are not mathematicians may think differently.  The subject of the page is the impossibility of deciding every question that can be posed. Rick Norwood 19:39, 7 September 2007 (UTC)
replies: text: I'm neither mathematican nor a philospher and I think it could be mid-to-high, at least from a (mathematics) foundational and historical perspective. In particular it has application to the philosophy of mind (that's the secret reason for my interest). Some writers fault the philosphers for not understanding the issues at gut-deep level but nevertheless concocting dubious pronouncements and arguments (e.g. not understanding quantum mechanics re philosophy of mind; also all the examples in Torkel Franzen 2005 Godel's Theorem: An Incomplete Guide to this Use and Abuse, A K Peters, Ltd. Wellesley MA). Another reason is: all three proofs of the 1930's that were so significant -- Church 1936, Turing 1936-7, Kleene 1943 -- all revolve the unsolvable "decision problem", and they all use similar techniques to arrive at their proofs (conversion of proofs to numbers, their subsequent enumeration (listing) and Cantor's diagonal argument).  Godel 1931 (his theorem VI, the so-called first incompleteness theorem) is also a proof of undecidability and follows a similar tack. Is any of this of use to philosphers constructing arguments? I dunno, but I would hope so. wvbaileyWvbailey 21:52, 7 September 2007 (UTC)
thread_title:  Importance 

message: I am very disappointed that there is no mention, either in the article or this talk page, of Alfred Tarski's theorems (in 1936) that truth is undefinable (see Indefinability_theory_of_truth). Hccrle (talk) 01:24, 1 October 2009 (UTC)
replies: text: After reading this I consulted Grattan-Guiness (2000) The Search for Mathematical Roots 1970-1940 pp. 551-553. I see some interesting stuff, but nothing about his contributions to the Engscheidungsproblem, nor about "truth is undefinable". In fact, Tarski's truth is definable by going outside the formal system (theory) into the metasystem (metatheory); Grattan-Lewis in fact gives Tarski credit for the names "metalanguage" and "metatheory). To make the point, Grattan-Guiness gives the example directly from Tarski: '"it is snowing" is a true sentence if and only if it is snowing'" (Tarski 1936a, 156)(cf Grattain-Guinness 200:552). Bill Wvbailey (talk) 18:42, 1 October 2009 (UTC)
thread_title:  Lack of mention of Tarski's theorems 

message: What has the reference to Whitehead and Russell at the end of the article got to do with the subject matter? 213.122.67.212 (talk) 12:52, 6 November 2010 (UTC)
thread_title:  Reference to Whitehead and Russell 

message: This section states: "Turing reduced the halting problem for Turing machines to the Entscheidungsproblem."
I don't think this is accurate. Turing & Church showed that deciding provability of arithmetic statements could be used to decide the Halting Problem, which really means that the Entscheidungsproblem was reduced to the halting problem and not the other way around?  — Preceding unsigned comment added by Froskoy (talk • contribs) 08:28, 5 February 2013 (UTC)
thread_title:  Negative solution 

message: IF there was an Algorithm to decide whether a Statement of FOL was universally valid, THEN there would be Algorithm to solve the Halting Problem. An "Algorithm" is identified with a Turing Machine. The Halting Problem cannot be solved (in general) by a Turing Machine. From the Contraposition, we deduce that there is no Algorithm to decide whether a Statement of FOL is universally valid. So the "Entscheidungsproblem" is reduced to the "Halteproblem"!
In Turing's paper, the text is: "Corresponding  to  each  computing  machine it  we construct  a  formula Un (it)  and  we show that,  if  there  is  a  general  method  for  determining whether  Un  (.11)  is  provable,  then  there  is  a  general  method  for  determining  whether  it   ever  prints  0"
The associated link in the Wikipedia text also refers to the page on "Reduction" as used in Complexity Theory, which is absolutely not what this is about at all.
Note that instead of referring to FOL, Turing refers to "functional calculus K in Hilbert and Ackermann's "Grundzüge der Theoretischen Logik (Berlin, 1931), chapter  3", which is about (many-sorted) first-order logic of relations (without equality) ... one should take a look at what functional calculus K actually is.
So, I'm changing the text in the page!  There is a T101 in your kitchen (talk) 23:56, 17 November 2016 (UTC)
thread_title:  Yes, this should be other way around. 

message: I have fixed the incorrect date on Turing's 1936 paper. The footnote at the end of Bob Soare's 1996 paper "Computability and Recursion": [www.people.cs.uchicago.edu/~soare/History/compute.pdf] has a good explanation of the correct dates. The reprint of Turing's paper in the collection edited by Martin Davis, (which was referenced before) only says that the reprint is from ser. 2, vol. 42 (1936-7), pp. 230-265, so I don't think the previous explanation of the date is justified from that book. As far as I can tell, the dating is incorrect in MathSciNet, (explaning many people incorrectly referencing the paper from 1937), but it is correct in Zentralblatt.  — Preceding unsigned comment added by 131.215.108.224 (talk) 21:32, 1 May 2013 (UTC)
thread_title:  Date of Turing's paper 

message: That language reference is not set. Any sane reason for that?--Crackwitz (talk) 14:40, 6 October 2013 (UTC)
replies: text: I believe it is because the German word Entscheidungsproblem literally means Decision problem, and the German Wikipedians decided to link to that English-language article instead of this one. Please see my proposal at the  Decision problem talk page for merging this page's text into that article. — Objectivesea (talk) 01:27, 12 November 2014 (UTC)
thread_title:  de:Entscheidungsproblem 

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thread_title:  External links modified 

message: The page preview shows this image: https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Flag_of_Israel.svg/640px-Flag_of_Israel.svg.png which is not part of the article. This seems to be some sort of vandalism, but I found no obvious way to fix it. Similar issue is discussed in this reddit thread: https://www.reddit.com/r/NoStupidQuestions/comments/127b5oj/why_is_the_preview_image_for_american_cuisine_on/ 2001:14BA:23EF:1A00:2811:49BF:3BC9:B97E (talk) 12:40, 15 September 2023 (UTC)
replies: text: The vandalism has been reverted. Please be patient until the cache expires. Nardog (talk) 18:50, 15 September 2023 (UTC)
thread_title:  Page preview image