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paradoxes of material implication


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The truth function of material implication gives a proposition pq which is true except in the case in which p is true and q is false. It also corresponds fairly well to the conditional form ‘If p then q’. But whenever p is false, pq is true, and whenever q is true, pq is true. So ‘If Paddington Station is in France, London is in England’ is true (it has a true consequent) and ‘If the moon is made of cheese, it is made of ketchup’ is true (it has a false antecedent). The ‘paradox’ is not a genuine paradox, but puts some pressure on the identification of the conditional form as it is found in natural languages, with material implication.

Subjects: Philosophy.


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