Talk:Soundness

From Wikipedia, the free encyclopedia

WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Stub Class High Priority  Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article.
This page is the product of a merge with Soundness theorem. 6 March 2008. Pontiff Greg Bard (talk) 20:36, 6 March 2008 (UTC)


Contents

[edit] Agent Strategy

I've removed the Strategy section, as it is out of place. The topic title states the page is about informal logic, not Software agents. Perhaps a link to a relevant intelligent agents page might be appropriate (if that is what the section was about that is, as there was no context). The section read "A strategy is sound for an agent if, and only if, it never dictates an illegal move for the agent." Ling, 82.71.98.21 20:49, 24 April 2006 (UTC)

[edit] Disputed

The content of this article is contradicted by an authority. See Talk:Logical_argument#RV_20040302.27s_edit for details. ---- Charles Stewart 13:03, 28 Oct 2004 (UTC)

[edit] Countered

This page can be viewed as a definition. It is consistent with other usage. IF the definition is qualified by other considerations, you are welcome to annotate the term with a parenthetical qualifier and insert references to other related terms which have a different set of conventions. Ancheta Wis 04:15, 28 Feb 2005 (UTC)

Still disputed, I'm afraid. You might have taken a closer look at my reasons for disputing this on Talk:logical argument. Look there for the renewed discussion. ---- Charles Stewart 12:14, 28 Feb 2005 (UTC)
I agree with Ancheta. The article is not disputed by any credible source I've ever come across -- it is simply standard usage of 'sound' as applied to (i)arguments and (ii)proof procedures (and sometimes (iii)systems as whole). Charles, if you can provide sources as evidence to the contrary, please do so. Otherwise the content is not disputed in any reasonable sense of that word.Nortexoid 02:22, 2 Mar 2005 (UTC)

The definition of 'sound argument' as (i) 'valid argument with true premises' as opposed to (ii) 'valid argument' is not universaly accepted, or if it is only recently. Definition (i) I note appear in the Oxford Dictionary of Philosophy. Definition; (ii) however appears in e.g. Mates, Elementary Logic, OUP:1972 p4: "An argument is said to be sound (correct, valid) if its conclusion follows from or is a consequnce of its premises; otherwise it is unsound".

Ancheta Wis says above "This page can be viewed as a definition. It is consistent with other usage.". For an encyclopaedia I would feel we should not be giving stipulative defintions, only reporting known definitions, and (for calrity) avoiding terms whise defeintions are not near enough universal. Why not avoid the term "sound" all together and write instead of "valid argument with true premises"; then we would be using a common language. --Philogo 23:11, 11 February 2007 (UTC)

[edit] other definitions

I have no problems with the current definition, but i think there's another common use of this term: the `soundness' of a system says that anything that can be derived in the system is indeed true (which is obviously desirable, but not always easy to prove :)). After looking at soundness, one usually looks at completeness, which considers whether or not all true statements can be derived in the system. It might be worth considering adding this definition to the page? (better worded than i just did, of course :)) -- Raboof

That definition is already included in the article: "A proof procedure (e.g. natural deduction) for a logic is sound if it proves only valid formulas (also tautologies)". Nortexoid 00:33, 27 Mar 2005 (UTC)
I agree, I simply seem to have overlooked that. It might be nice to add the following clarification there: `This is shown by proving that any statement that can be derived with the proof procedure, is indeed logically true. Formally: a system is sound when if "X1...Xn ⊢ Y", then also "X1...Xn ⊨ Y". Shall I add that? --Raboof 12:14, 13 Apr 2005 (UTC)

[edit] completeness

Spin-off discussion, can be discarded imho. --Raboof 12:14, 13 Apr 2005 (UTC)

But Kurt Gödel proved that systems that are stronger than first order logic or set theory are incomplete. That is another article. (So there is a bound on such systems.) Ancheta Wis 12:53, 26 Mar 2005 (UTC)
That is irrelevant. There are many sound but incomplete systems. Nortexoid 00:33, 27 Mar 2005 (UTC)

[edit] disambiguation

Another spin-off discussion. I agree with Nortexoid that as long as we don't have enough content to warrant 2 seperate pages, the 2 definitions can live happily together on this page. --Raboof 12:14, 13 Apr 2005 (UTC)

We're mixing up 2 meanings of the word `complete' here - see the Completeness page (under `proof theory' and `logic'). Raboof
That is a red flag which indicates the need to have separate articles PT-Completeness (proof theory) and L-Completeness (logic) as well as PT-Soundness (proof theory) etc. Otherwise we have linguistic confusion, in my opinion. Especially for a logic article, it is kind of fallacious to use the same tag for different items which have not been shown to be equivalent, in the same namespace. And it is not good enough to appeal to Authority A, who calls it soundness unless one is willing to preface the term with some phrase like (in the sense of Authority A, ... ). Otherwise, Soundness becomes a disambiguation page, like the Completeness page. Ancheta Wis 20:47, 26 Mar 2005 (UTC)
I don't think we need to do something so "drastic" (it's not really drastic, but it might be clearer to do what I suggest in the following). Simply provide both definitions of completeness on the completeness page. One notion is actually foramlizable within the system itself by the excluded middle (for any p, either p or not-p) while the other is a metalogical theorem bridging semantics (model theory) with syntax (proof theory). Nortexoid 00:33, 27 Mar 2005 (UTC)
I do not agree with having a disambiguation page because there are two definitions of the word. There should be more and with a lot of information for each article. There is not a whole lot of information to write for an encyclpedic entry on either definition of completeness or soundness. Nortexoid 00:33, 27 Mar 2005 (UTC)

[edit] Worthy of a separate article?

Couldn't we just merge this with validity and call it validity and soundness? It seems unnecessary to have a separate article. Richard001 (talk) 05:39, 26 January 2008 (UTC)

I would rather see this merged into Validity, and the article now called Soundness theorem moved here, with a hat note "For soundness of arguments in informal logic, see Validity. See also the section Argument (logic)#Valid arguments.  --Lambiam 18:36, 26 January 2008 (UTC)
I suppose, but how can you say which word is more important? If I can make an argument by analogy I might compare this situation with inductive arguments, where cogency and strength don't have their own articles, and probably shouldn't (strength doesn't exist at all). However, if we are to follow your suggested naming for this merge, the other one should be called 'strength (argument)' or something like that if we want to be consistent (do we?). In any case, I'll slap some merge templates up. Richard001 (talk) 07:31, 27 January 2008 (UTC)
oppose merge --Although, I am somewhat open to the proposal to merge both into one substantial article:Validity and soundness, as they are conceptually very related. I think there may be certain areas in which one or the other term is more appropriate. However, I think we should merge Soundness theorem and Soundness. Pontiff Greg Bard (talk) 04:16, 30 January 2008 (UTC)

[edit] Merge proposal:Soundness theorem

Is it really necessary for two articles on this. They are the same concept. I would think a lot of articles need to link to this. Pontiff Greg Bard (talk) 04:07, 30 January 2008 (UTC)

I agree, in my Basic Logic chapter it merges validity, soundness, truth, strenght, and cogency —Preceding unsigned comment added by 65.79.187.231 (talk) 18:57, 27 March 2008 (UTC)