User:Boris Tsirelson/Sandbox1: Difference between revisions
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imported>Boris Tsirelson No edit summary |
imported>Boris Tsirelson |
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*something surprising; | *something surprising; | ||
*something ironic; | *something ironic; | ||
etc. | 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 | ||
: <math>2+2=4,</math> | |||
: <math>2+2=5</math> | |||
are still not a contradiction. Two theorems | |||
: <math>2+2=4,</math> | |||
: <math>2+2\ne4</math> | |||
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. | |||
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Revision as of 12:36, 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.