Talk:Contradiction
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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)
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)
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.
