Talk:Consistency

message: The title of this entry should perhaps be not just "Consistency" but "Classical deductive consistency." See the remarks below regarding "classical consistency." As for "deductive consistency," this article pertains only to deductive logic, not logic broadly construed as a study of inference in general (including, e.g., statistical inference, or Peirce's and Hanson's abductive inference). --BurkeFT (talk) 21:08, 28 July 2013 (UTC)
replies: text: Yes, this applies only to classical logic. But most mathematicians and scientists assume classical logic unless one explicitly specifies another kind. Virtually all serious work on mathematics is done in classical logic. Classical logic is what is needed to deal with the real world. Other forms of logic are just games or fantasies. JRSpriggs 10:38, 31 October 2006 (UTC)
replies: text:  And when one specifies another kind, this definition doeesn't work.  All others being "Games or fantasies" is not a nice thing to say. I have to wonder if you are familiar with the others. But fortunately, there are others on wikipedia that don't agree with you that have put up pages on these other logics.  Too bad this page will have (without a statement to that effect) narrow information that doesn't apply to them. Nahaj 01:44, 1 November 2006 (UTC)
thread_title:  Alternate senses of Consistency 

message: I proposed here that Hilbert's second problem should be covered in its own article, separate from this one.  Please discuss it there. CMummert 14:36, 5 January 2007 (UTC)
thread_title:  What is this article about? 

message: This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 03:52, 10 November 2007 (UTC)
thread_title:  WikiProject class rating

message: The statement in item no. 2, "Since these theories are satisfactorily described by the model we obtain from the completeness theorem, such systems are complete" is incorrect. Usually, a theory is called complete if for any p, either p or \neg p can be proved from it. This indeed holds
for Presburger arithmetic, but it certainly does not hold for any theory that cannot talk about its own provability relation. Take Euclidean geometry without parallel axiom, for example: it is not complete.
--Tillmo (talk) 12:54, 18 January 2009 (UTC)
replies: text: That's far from the only problem with that section. It's a mess, really. I may rewrite it here in a few minutes. — Carl (CBM · talk) 01:44, 19 January 2009 (UTC)
replies: text: Thanks, much better now. However, you have deleted the classification into four or five different types of theories. Do you think that it cannot be corrected? --Tillmo (talk) 05:38, 23 January 2009 (UTC)
replies: text: The previous text had some strange claims - such as, any theory that cannot define its own provability predicate is complete. And it had the meaningless phrase "complete with respect to a model". Since I wasn't sure what the goal of the previous "classification" was, and since the text was so flawed, I thought deleting it and starting fresh was better. We can always continue to add additional correct material to the section in the future. Really, I'd like to double check a couple references to see how they handle this classification. — Carl (CBM · talk) 11:20, 23 January 2009 (UTC)
thread_title:  Incorrect statement about completeness 

message: I have read the talk page, and I don't understand why an article that was almost completely about consistency proofs was moved to here, and made to serve as a general article about consistency.  I think it does both the general concept of consistency, and the technical notion of consistency proof, a disservice. — Charles Stewart (talk) 13:13, 6 May 2009 (UTC)
thread_title:  Why was this moved? 

message: Why do we need the detailed paragraph about completeness in the lead? It seems to violate WP:LEAD, because the history of various completeness results/proofs is not the topic of this article. Tijfo098 (talk) 09:27, 8 November 2012 (UTC)
thread_title:  Coatrack, etc. 

message: I'm deleting the following for the same reason Travatore deleted it fromGödel's incompleteness theorems:
:However, on the other hand, Teodor Stepien and Lukasz Stepien delivered a talk at the Conference "2009 European Summer Meeting of Association for Symbolic Logic, Logic Colloquium'09" (July 31 - August 5, 2009, Sofia, Bulgaria). In this talk, entitled "On consistency of Peano's Arithmetic System", they presented a sketch of the proof of the consistency of Peano's Arithmetic System (of course, the full proof was constructed by Teodor Stepien and Lukasz Stepien before the Conference "Logic Colloquium 2009"). There in this proof are used only the axioms of first-order logic and the axioms of Peano's Arithmetic System. Thus, this proof is absolutely elementary. Hence, from the construction of this proof, it follows that Gödel's Second Incompleteness Theorem is invalid. http://ultra.ap.krakow.pl/~lstepien/ The asbtract of this talk was published in "The Bulletin of Symbolic Logic": T. J. Stepien and L. T. Stepien, Bull. Symb. Logic 16, 132 (2010).
This is just the professional equivalent of spamming. Bill Wvbailey (talk) 22:13, 23 November 2012 (UTC)
thread_title:  Stepien-family theorem 

message: Why does consonancy redirect here? Two alternative places it would be better redirected to are Consonance and dissonance and Literary consonance. --184.23.18.191 (talk) 17:38, 10 February 2016 (UTC)
thread_title:  Consonancy 

message: In the opening sentences (emphasis mine):
:The semantic definition states that a theory is consistent if and only if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true.
Surely that can't be right. All formulas would include negation pairs. Perhaps "all tautologies" was intended?
--phil (talk) 06:34, 28 February 2017 (UTC)
replies: text: A theory that includes negation pairs isn't consistent; in general a "theory" is just some set of formulas in a particular language. A consistent theory cannot contain all' the formulas in a language. — Carl (CBM · talk) 12:33, 28 February 2017 (UTC)
thread_title:  Semantic Definition