Talk:Proof theory

message: I think we should merge proof theory and proof (math) because to me they seem the same thing, but I am not sure enough to do that. Any though? -- Taku 00:26 2 Jun 2003 (UTC)
: Hmm, careful. While I have no clue about the subject, it seems like Proof theory is a sort of meta- discussion about proofs. I'd leave it. Evercat 00:28 2 Jun 2003 (UTC)
I mean the definition of them can vary; mathematical proof is a formal proof in math while proof theory is the study of proof. I mean I guess I am not sure after all. I will leave this for more knowledgable people. -- Taku 05:01 2 Jun 2003 (UTC)
: They are different fields, one is an area of study in logic (including mathematical logic), the other is a tool used by mathematicians.  There's much less overlap between the two fields than one might think. ---- Charles Stewart 09:12, 16 Aug 2004 (UTC)
thread_title:  Taku's merge suggestion 

message: I've deleted the following section:
:More informally , the term proof theory is also used (in logic classes, for example) to refer to a concrete calculus. For example, one may state that there is no proof theory for second-order logic, meaning that there is no syntactical calculus for this logic that simultaneously (1) is sound, and (2) is complete, and (3) is decidable (admits a proof-checking algorithm). First-order logic and many logics "below" admit a proof theory.
because, while it documents a standard usage, it is perfectly comprehensible formally. ---- Charles Stewart 18:34, 25 Aug 2004 (UTC)
thread_title: Informal use?

message: IF logic, as far as I know, admits of a proof-theoretic characterization using e.g. a natural deduction calculus. In fact, in several articles he gives modified definitions for quantifier intelim rules. However, it does not admit of a complete characterization, or if it does, then not a finitely axiomatizable one.
Since IF logic is equivalent to the Sigma-1-1 fragment, all properties of the latter carry over to the former. Nortexoid 20:44, 5 May 2006 (UTC)
thread_title:  IF logic and proof theory 

message: Where is proof theory described as one of the four pillars of foundations of mathematics?  [qn by User:CBM ]
:Barwise (1978),  Handbook of Mathematical Logic, North-Holland.   It is described as such in the introduction justifying the organisation of the book; the other pillars are set theory, model theory, and recursion theory. A lot of logicians like this way of carving up the field; I think the omission of algebraic logic is hard to excuse. — Charles Stewart (talk) 18:53, 3 May 2009 (UTC)
thread_title:  Looking for citation 

message: The later summary sections get shorter and shorter.  The history section could use an inline citation to a published history of the field.  A section describing current work in the area would round out the coverage, which is currently mostly historical. CMummert 14:19, 25 October 2006 (UTC)
thread_title:  Math rating B+ 

message: I've proposed that logic system be merged into this article (proof theory) or one of its subarticles.  To the extent that there's something there in logic-system, it's an abstraction or example (depending on the precise structure) of a formal proof system.  — Arthur Rubin |  (talk) 19:53, 16 November 2006 (UTC)
replies: text: Withdrawing merge request.  A better target has been found.  — Arthur Rubin |  (talk) 15:43, 17 November 2006 (UTC)
thread_title:  Proposed merge 

message: There is no citation on between Proof (which has a mathametical basis) and truth (more a level of personal or widespread acceptance).   Article needs a little help here.  --71.245.164.83 (talk) 03:00, 7 October 2010 (UTC)
thread_title:  Proof vs. Truth 

message: On the different kinds of proof systems (Hilbert/ND/Sequents), it says "Indeed it is unusual to find a logic that resists being represented in one of these calculi." Wrong. There are many logics that cannot be represented in these kind of calculi,  —Preceding unsigned comment added by 94.173.19.247 (talk) 20:45, 14 May 2011 (UTC)
thread_title:  Wrong 

message: Substituted at 03:27, 30 April 2016 (UTC)
thread_title: Assessment comment

message: I don't see very many in-line citations at all. Should it be flagged with a page issue?
104.1.153.62 (talk) 05:30, 20 October 2018 (UTC)
thread_title:  Where are the in-line citations?