Paradox of entailment

The paradox of entailment is an apparent paradox derived from the observation that, in classical logic, inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all. This seems paradoxical, as it suggests that the following is a good argument:

Valid arguments

Validity is defined in classical logic as follows: An argument (consisting of premises and a conclusion) is valid if and only if there is no possible situation in which all the premises are true and the conclusion is false.

Related Topics:
Validity - Argument - Premise - Conclusion - If and only if

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Example:

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• If it is raining, water exists. (1st premise)
• It is raining. (2nd premise)

therefore

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• water exists (conclusion)

There is no possible situation in which the premises could be true while the conclusion was false. But note that if at least one of the premises is false, the conclusion can also be, while the argument is still valid. The point is that there is no counterexample: no case with true premises and a false conclusion.

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