ellauri096.html on line 188: The logical myth that “You cannot prove a universal negative” is itself a universal negative. So it implies its own unprovability. This implication of unprovability is correct but only because the principle is false. For instance, exhaustive inspection proves the universal negative ‘No adverbs appear in this sentence’. A reductio ad absurdum proves the universal negative ‘There is no largest prime number’.
ellauri096.html on line 199: Several commentators on the surprise test paradox object that interpreting surprise as unprovability changes the topic. Instead of posing the surprise test paradox, it poses a variation of the liar paradox. Other concepts can be blended with the liar. For instance, mixing in alethic notions generates the possible liar: Is ‘This statement is possibly false’ true? (Post 1970) (If it is false, then it is false that it is possibly false. What cannot possibly be false is necessarily true. But if it is necessarily true, then it cannot be possibly false.) Since the semantic concept of validity involves the notion of possibility, one can also derive validity liars such as Pseudo-Scotus’ paradox: ‘Squares are squares, therefore, this argument is invalid’ (Read 1979). Suppose Pseudo-Scotus’ argument is valid. Since the premise is necessarily true, the conclusion would be necessarily true. But the conclusion contradicts the supposition that argument is valid. Therefore, by reductio, the argument is necessarily invalid. Wait! The argument can be invalid only if it is possible for the premise to be true and the conclusion to be false. But we have already proved that the conclusion of ‘Squares are squares, therefore, this argument is invalid’ is necessarily true. There is no consistent judgment of the argument’s validity. A similar predicament follows from ‘The test is on Friday but this prediction cannot be soundly deduced from this announcement’.
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