ellauri096.html on line 142: If you know that your beliefs are jointly inconsistent, then you should reject R. M. Sainsbury’s definition of a paradox as “an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises” (1995, 1). Take the negation of any of your beliefs as a conclusion and your remaining beliefs as the premises. You should judge this jumble argument as valid, and as having premises that you accept, and yet as having a conclusion you reject (Sorensen 2003b, 104–110). If the conclusion of this argument counts as a paradox, then the negation of any of your beliefs counts as a paradox.
ellauri096.html on line 151: If paradoxes were always sets of propositions or arguments or conclusions, then they would always be meaningful. But some paradoxes are semantically flawed (Sorensen 2003b, 352) and some have answers that are backed by a pseudo-argument employing a defective “lemma” that lacks a truth-value. Kurt Grelling’s paradox, for instance, opens with a distinction between autological and heterological words. An autological word describes itself, e.g., ‘polysyllabic’ is polysllabic, ‘English’ is English, ‘noun’ is a noun, etc. A heterological word does not describe itself, e.g., ‘monosyllabic’ is not monosyllabic, ‘Chinese’ is not Chinese, ‘verb’ is not a verb, etc. Now for the riddle: Is ‘heterological’ heterological or autological? If ‘heterological’ is heterological, then since it describes itself, it is autological. But if ‘heterological’ is autological, then since it is a word that does not describe itself, it is heterological. The common solution to this puzzle is that ‘heterological’, as defined by Grelling, is not a genuine predicate (Thomson 1962). In other words, “Is ‘heterological’ heterological?” is without meaning. There can be no predicate that applies to all and only those predicates it does not apply to for the same reason that there can be no barber who shaves all and only those people who do not shave themselves.
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’.
ellauri096.html on line 247: There is no problem with third person counterparts of (M). Anyone else can say about Moore, with no paradox, ‘G. E. Moore went to the pictures last Tuesday but he does not believe it’. (M) can also be embedded unparadoxically in conditionals: ‘If I went to the pictures last Tuesday but I do not believe it, then I am suffering from a worrisome lapse of memory ’. The past tense is fine: ‘I went to the picture shows last Tuesday but I did not believe it’. The future tense, ‘I went to the picture shows last Tuesday but I will not believe it’, is a bit more of a stretch (Bovens 1995). We tend to picture our future selves as better informed. Later selves are, as it were, experts to whom earlier selves should defer. When an earlier self foresees that his later self believes p
ellauri172.html on line 254: Later writers satirised this view in terms of an ass which, confronted by both food and water, must necessarily die of both hunger and thirst while pondering a decision. Some proponents of hard determinism have granted the unpleasantness of the scenario (not for the donkey, it will end up eating both), but have denied that it illustrates a true paradox, since one does not contradict oneself in suggesting that a man might die between two equally plausible routes of action. For example, in his Ethics, Benedict de Spinoza suggests that a person who dies because he can't decide is an ass, or worse.
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