strict implication, paradox of

It follows from the definition of strict implication that a necessary proposition is strictly implied by any proposition, and that an impossible proposition strictly implies any proposition. If strict implication corresponds to ‘ q follows from p ’, then this means that a necessary proposition follows from anything at all, and anything at all follows from an impossible proposition. This is a problem if we wish to distinguish between valid and invalid arguments with necessary conclusions or impossible premises.

Philosophy dictionary. . 2011.

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