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counterexample


Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


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L ogic, philosophical method A counterexample to a generalization is a case that is an instance of the kind to which the generalization applies but which does not have the property that the generalization asserts that things of that kind possess. For instance,“All swans are white” is a generalization. But if there is one swan that is not white, that non-white swan becomes a counterexample. A counterexample to an argument is a case in which all premises are true but the conclusion is false. The discovery of a counterexample to an argument indicates that the argument is not logically valid, or at least that its conclusion cannot be universally applied. Hence the absence of a counterexample becomes a mark of the validity of an argument. A valid inference is one that has no counterexample. Otherwise, it is invalid. “To find an interpretation which shows that an argument is logically invalid is the same thing as finding a counterexample to the argument.” Suppes, Introduction to Logic ... log in or subscribe to read full text

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