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| | ==In Science and Logic== | | ==In Science and Logic== |
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| − | For example, the well-proven theory that cigarettes cause [[lung cancer]] has the '''counterexample''' of the (rare) individual who might smoke his entire life and not develop lung cancer. The counterexample does not disprove the theory.
| + | A '''counterexample''' cannot disprove correlation or causation. An example of flawed [[liberal logic]] is the use of a counterexample to argue that a theory is false, as in "I don't go to church and I'm not a bad person, and therefore church is not needed." |
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| − | A '''counterexample''' cannot disprove correlation or causation. An example of flawed [[liberal logic]] is the use of a counterexample to argue that a theory is false, as in "I don't go to church and I'm not a bad person, and therefore church is not needed."
| + | Another example is the well-proven theory that cigarettes cause [[lung cancer]]. An '''counterexample''' of the (rare) individual who might smoke his entire life and not develop lung cancer. The counterexample does not disprove the theory. |
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| − | A theory of universality, such as the claim that ''all'' species [[theory of evolution|evolved]], can be disproved by just one '''counterexample''', such as a species (like the [[whale]]) that lacks a plausible evolutionary path. | + | A theory of universality, such as the claim that ''all'' species [[theory of evolution|evolved]], can be disproved by just one '''counterexample''', such as a species (like the [[whale]]) that lacks a plausible evolutionary path. See [[Counterexamples to Evolution]], [[Counterexamples to Relativity]]. |
| − | [[category:logic]] | + | [[Category:Logic]] |
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| | ==In Mathematics== | | ==In Mathematics== |
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| − | The word counter-example originated in mathematics. It means an example that contradicts a general statement; therefore, the single example proves the statement false. Consider the statement | + | The word counterexample originated in mathematics. It means an example that contradicts a general statement; therefore, the single example proves the statement false. Consider the statement |
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| | + | "Every number ending in the digit 7 is prime." 7, 17, 37, 47, 57, and 67 are all prime, but 27 is not, so 27 is a counterexample. |
| | + | ==See also== |
| | + | *65 [[Counterexamples to an Old Earth]] |
| | + | *54 [[Counterexamples to Evolution]] |
| | + | *52 [[Counterexamples to Relativity]] |
| | + | *5 [[Counterexamples to an Ice Age]] |
| | + | *3 [[Counterexamples to String Theory]] |
| | + | *Numerous [[Counterexamples to Global Warming]] (article not organized the same way) |
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| − | "Every number ending in the digit 7 is prime." 7, 17, 37, 47, 57, and 67 are all prime, but 27 is not, so 27 is a counterexample.[[Category:Mathematics]]
| + | {{Counterexamples}} |
| | + | [[Category:Mathematics]] |