Talk:Metamathematics

message: The term 'metamathematics' is obsolete?  Hmm...  Maybe I've been reading way too many old texts on math, but I've certainly come across it more often than this article seems to state.  Just because mathematical logic has more google hits means nothing in this circumstance.  Anyway, metamathematics does not have to be mathematical, does it?  But mathematical logic does.  I would think this means that mathematical logic is actually a subset of metamathematics.  Eric Herboso  02:00, 18 Feb 2005 (UTC)
replies: text: Yes, metamathematics does have to be mathematical.  It is (in my not-at-all-humble opinion) a subset of the intersection of mathematics and logic. 86.132.220.143 (talk) 20:25, 25 November 2017 (UTC)
thread_title: obsolete term?

message: Is using Googlefight in the way the article does really necessary and/or encyclopedic? --Aioth 15:21, 13 January 2006 (UTC)
thread_title:  Googlefight 

message: Shouldn't there be mention of Alan Turing as a key contributor to metamathematics? His work on decidability, which gave rise to the notion of the Turing machine, was prompted by the Hilbert programme -- The Entscheidungsproblem (the "decision problem"): Hilbert's tenth question of 1900.  —Preceding unsigned comment added by 81.151.101.2 (talk) 20:54, 10 March 2009 (UTC)
replies: text: Yes, the Entscheidungsproblem should be mentioned, as well as the problems from Hilbert's problems that had a foundational aspect. — Carl (CBM · talk) 21:58, 10 March 2009 (UTC)
thread_title:  Turing 

message: I trimmed the article some today. User:Bci2 expanded it some, and some of the new content was good, but much of it seemed to make the article hard to read (to my eye) or to diverge into ruminations about the difference between metamathematics, logic, mathematics, and metalogic. I do think that we can expand this article quite a bit, and I added a "milestones" section to start that. I also found a nice article on JStor about Tarski's use of the term metamathematics. 
The main difficulty I see with expanding this article is the disuse of the term "metamathematics" by many contemporary mathematical logicians. It may be hard to document more contemporary mathematical viewpoints, but we want to ensure that we don't write an article from the point of view of 1960 either. — Carl (CBM · talk) 21:54, 10 March 2009 (UTC)
thread_title:  Trimmed 

message: You also need a non-circular definition of metamathematics!
:The present definition is not circular: the study of mathematics itself using mathematical methods. Could you explain what circularity you see? — Carl (CBM · talk) 13:03, 12 March 2009 (UTC)
thread_title: Reply on your update

message: This is to propose adding the metatheory category to this article.<bR>
I just undid my last revision because it seemed that someone wasn't very happy about it.
Thanks for your attention.
Maurice Carbonaro (talk) 12:06, 10 November 2009 (UTC)
thread_title:  Proposal to add the metatheory category 

message: I'm proposing that Metalogic be merged into Metamathematics, although there is some justification for the reverse merge.  As far as I can tell, there's been no discussion since it was proposed in 2009, nor any distinction given between Metalogic and Metamathematics.  If we can't distinguish them, they should both be in the same article.  — Arthur Rubin  (talk) 14:01, 20 November 2012 (UTC)
replies: text: I see I proposed this before.  If both articles were to include the distinction (if any), I would withdraw the merge request, although both articles are basically stubs at this point.  Perhaps an article "Foundations of logic" which includes both?  — Arthur Rubin  (talk) 14:04, 20 November 2012 (UTC)

text: Please ignore the tags, to some extent.  After refreshing my memory of the previous discussions, I think Metalogic and Metamathematics should be merged somewhere.  They have a lot in common, but the name of the merged article would be the subject of heated debate, probably only of interest to those on the metalogic side.  — Arthur Rubin  (talk) 14:09, 20 November 2012 (UTC)

text: Perhaps they should both be merged into foundations of mathematics, and then split on a different basis if enough can be found to be worthy of a split.  Foundations of mathematics is a long article, but neither of these is much more than a stub.  — Arthur Rubin  (talk) 14:13, 20 November 2012 (UTC)
replies: text: Arthur, your statement is so full of falsehoods, presumptions, and wrong analysis, that it is hard to know where to begin, where to end, or if there is any hope that you will understand or respect the decisions of those who do. No. Neither the article, nor any courses taught are "about the book." Metalogic is the title of chapters of books, used in the titles of scholarly articles, and is a term well used in the literature. You need to face the fact that you are late to the party in that regard. It isn't up to me to prove that the terms are the same or different. If you are proposing to merge them, it's up to you to prove they are the same, as there are sources for the use of each, and you, yourself state explicitly that they are used in different contexts. You state your opinion that you see no "unifying theme" in the article metalogic. Being able to see the conceptual connections between things is a function of intelligence. I cannot help you there beyond the explicit and specific organization of the article metalogic itself. Furthermore, your claim that the previous discussion did not have a formal resolution is so disingenuous, as to call it question your integrity. There was a very clear consensus to oppose your proposal, by any reasonable standard. It wasn't "questionable" AT ALL. Greg Bard (talk) 06:02, 22 November 2012 (UTC)

text: Today, metalogic and metamathematics are largely synonymous with each other, and both have been substantially subsumed by mathematical logic in academia.
— Arthur Rubin  (talk) 15:45, 20 November 2012 (UTC)
thread_title:  Metalogic 

message: One should also note a statement in the (current) version of metalogic: 
:Today, metalogic and metamathematics are largely synonymous with each other, and both have been substantially subsumed by mathematical logic in academia.
— Arthur Rubin  (talk) 15:45, 20 November 2012 (UTC)
thread_title:  Discussion 

message: What contributions to metamathematics did Russell make?  I ask because /Principia Mathematica/ has no discussion of such metamathematical topics as redundancy of axioms, decidability, completeness.  Can anyone cite a work were Russell indicated an interest in any such matters? 86.132.220.143 (talk) 20:22, 25 November 2017 (UTC)
thread_title:  Russell? 

message: I hope it's not impolite to say so, but whoever wrote "Gödel's incompleteness theorem: proof that given any finite number of axioms for Peano arithmetic, there will be true statements about that arithmetic that cannot be proved from those axioms." doesn't know what they're talking about. There is an axiomatization of PA that unavoidably has infinitely many axioms - the first-order axiomatization.  And there is an axiomatization of PA that has finitely many axioms - the second-order axiomatization.  Both are incomplete.  But Gödel's incompleteness theorem isn't really about PA (2nd or 1st order), it is about a broad class of arithmetics.  Shall I delete the offending sentence? 86.132.220.143 (talk) 20:35, 25 November 2017 (UTC)
thread_title:  Error 

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thread_title:  External links modified (January 2018) 

message: I've read the German edition of this article and there is a reference to the philosopher and mathematican Paul Lorenzen and a work about Genzens' Hauptsatz. Would it be a good Idea to put this in the article, too? 2A02:908:424:9D60:0:0:0:4A03 (talk) 16:31, 25 August 2022 (UTC)
thread_title:  Gentzens' Cut-Theorem and Lorenzen?