- material implication, paradoxes of
- The truth-function of material implication gives a proposition
*p*→*q*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,*p*→*q*is true, and whenever*q*is true,*p*→*q*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.

*Philosophy dictionary.
Academic.
2011.*

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