User:Boris Tsirelson/Sandbox1: Difference between revisions
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If a contradiction exists in a given theory, this theory is called inconsistent. Otherwise, if no contradiction exist (rather than merely not found for now), the theory is called consistent. | If a contradiction exists in a given theory, this theory is called inconsistent. Otherwise, if no contradiction exist (rather than merely not found for now), the theory is called consistent. | ||
<blockquote>Superstitious dread and veneration by mathematicians in face of a contradiction (Wittgenstein)</blockquote> | |||
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Revision as of 12:39, 13 June 2010
Consistent or inconsistent
If a theory states that 2+2=5, it is a paradox but not yet a contradiction. By "paradox" people may mean
- a contradiction;
- an apparent contradiction;
- something counterintuitive;
- something surprising;
- something ironic;
etc. In contrast, a contradiction (in a mathematical theory) is, by definition, a pair of theorems (of the given theory) such that one is the negation of the other. Thus, two theorems
are still not a contradiction. Two theorems
are a contradiction.
If a contradiction exists in a given theory, this theory is called inconsistent. Otherwise, if no contradiction exist (rather than merely not found for now), the theory is called consistent.
Superstitious dread and veneration by mathematicians in face of a contradiction (Wittgenstein)