Talk:Contradiction

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Contents

[edit] Gödel Gone

I don't think that this belongs in the article:

"Misc You can't know that correct, formal reasoning will lead to consistent conclusions. This is implied in Gödel's second incompleteness theorem. This theorem says that in any system of reasoning that is powerful enough to define the numbers 1, 2, 3, ..., you cannot prove from that system that the same system will not lead to contradiction. Thus, even if you use formal rules that appear sound, it is impossible to actually prove, within that same system (or any system that is as strong - the result of Gentzen's theorem), that they will not lead to contradiction. Note that the system may still be consistent, but you may only rely on faith, intuition, and the empirical evidence stating that no such contradictions have yet been shown in such systems."

Predicate logic is not "powerful enough" to define the numbers 1, 2, 3... and therefore Godel doesn't apply to it. Furthermore the claim that "you may only rely on faith, intuition..." in logic is unsupported editorializing. The fact one cannot prove some logical system to be correct doesn't imply that one cannot know that the system is correct. Knowledge and proof are two different philosophical concepts.

To whoever added this: wikipedia is not your personal playground. There are rules against including your own original research, especially without a citation. Therefore I'm removing it. --207.252.227.7 20:53, 24 May 2005 (UTC)

[edit] German Gone

I'm removing the following German bit that was just added:

"A ist nicht A" darstellt einen einfachen Widerspruch. Obwohl man nicht ehrlich festhalten kann, dass ein Widerspruch wahr sei, kann man trotztdem den Widerspruch als etwas Schoenes ergreifen.

Unless the following Babelfish translation is altogether inaccurate, then this doesn't add anything new. And adding nothing new in another language doesn't help anyone.

"A is not A" represents a simple contradiction. Although one cannot hold honestly that a contradiction is true, one can seize defy-defying that the contradiction as something beautiful.

--Ryguasu 16:27 Apr 20, 2003 (UTC)

[edit] Helpful Suggestion

I take it doublethink would be difficult to place in the article. Though blackwhite might fit

[edit] article cleanup

this page seems to need cleanup by someone better versed in logic than I; it's full of little s(n)ide comments that detract from the page itself (and what's with all the bare question marks?). These seem like disagreements about the article that belong here on the talk page.

It’s still not very good, but are there specific issues left for which the current cleanup tag should remain? —xyzzyn 21:55, 12 June 2006 (UTC)
"In dialectics" appears to be way out of place. This article should discuss contradiction as an abstract (as in the logic section). It shouldn't get into specifics. Anyone could name any number of specific contradictions on any number of topics. Why is dialectics special? Well, it's not. Recommendation is that the "In dialectics" be removed without replacement. Fcsuper 00:46, 7 March 2007 (UTC)
Dialectics (especially the Marx-Engels version) has been of the most significant philosophical concepts of the last two centuries in terms of impact outside philosophy and contradiction is a central concept. It’s not very well explained in the article (and, really, deserves a separate article, should anybody have the time and knowledge to write one), but it should be mentioned. —xyzzyn 14:12, 7 March 2007 (UTC)

[edit] A paradox involving contradiction -- discarded?

Luckily, I have once glanced at this article and noticed that there was a proof to the famous `theorem', which claims that any statement can be derived from a contradiction. Since that, I was looking for this proof and could not find it. Thinking that the Contradiction article is a proper place for it, I have found the proof in the history. My research has shown that the paradox explanation is unique in the Internet. Nevertheless, the regarding section was replaced by a reference to some unintelligible Coherentism. Why was such unique material removed? I want it back. --Javalenok 22:15, 3 January 2007 (UTC)

BTW, contradiction implies false and "A false statement implies anything" and its logical equivalent, "Anything implies a true statement. --Javalenok 20:51, 13 January 2007 (UTC)

Um, what? That’s not much of a theorem. It’s usually trivial (and sometimes even the definition). Try any undergraduate textbook on logic. The diff you have provided only moves a bracket, so I have no idea to what exactly you are referring. —xyzzyn 21:52, 13 January 2007 (UTC)
Excuse me for the confusion. Now it refers exactly to the entertaining proof of "anything from contradiction", which was removed later. I want to know why the community does not want to see it? --Javalenok 16:27, 14 January 2007 (UTC)
Well, the example given there was quite loaded; that distracts and is therefore bad. What was described as a paradox isn’t (we really don’t need to go ‘Oh, that’s odd!’ at every fact that is not entirely intuitive). The proof consists of a look in the truth table for →. We currently assert as much in the article, but I can add it explicitely, if you wish. (The other proof is longer without adding anything interesting.) —xyzzyn 17:06, 14 January 2007 (UTC)
I strongly beleive that the fact that controvertial theories can ground anything, enforced by the logical proof, is worth mentioning. --Javalenok 17:29, 14 January 2007 (UTC)
That’s contradictory theories, and it’s already mentioned. I’ve added a reason. —xyzzyn 18:03, 14 January 2007 (UTC)
A (formal) proof is much better reason, IMO, than any expert's statement. Furthermore, the definition of contradictin in the sentence preceding your reason states that contradiction=false (iff). Therefore, your reason makes no sense. Why cannot wikipedia have the proof? --Javalenok 15:38, 15 January 2007 (UTC)
Formal proofs are good where something must be proven, but overkill for an encyclopaedia article that is not about formal proofs. By the way, why does my reason make no sense? (We can have the proof… if there’s a good place with enough context to put it.) —xyzzyn 16:10, 15 January 2007 (UTC)
Because the ones who know that 'false' implies anything also know that 'contradiction' implies anything. --Javalenok 16:29, 15 January 2007 (UTC)

[edit] Say what?

Why is this article tagged as {{contradiction}}? Or is that some kind of a joke? --Stratadrake 22:00, 8 January 2007 (UTC)

I guess so. [1] JackLumber. 22:14, 11 January 2007 (UTC)

[edit] Notation first?

I think the the section titled "Symbolic representation" should be the first body paragraph, rather than having two sections use the ⊥ symbol without explanation. - Callowschoolboy 17:03, 11 July 2007 (UTC)

[edit] Jargon

Can someone, ANYONE, clean this up? 63.215.29.113 23:56, 11 September 2007 (UTC)

[edit] WikiProject class rating

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