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 146: The preface paradox pressures Kyburg to extend his tolerance of joint inconsistency to the acceptance of contradictions (Sorensen 2001, 156–158). Consider a logic student who is required to pick one hundred truths from a mixed list of tautologies and contradictions. Although the modest student believes each of his answers, A1,A2,…,A100
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 275: The points made so far suggest a solution to the surprise test paradox (Sorensen 1988, 328–343). As Binkley (1968) asserts, the test would be a surprise even if the teacher waited until the last day. Yet it can still be true that the teacher’s announcement is informative. At the beginning of the week, the students are justified in believing the teacher’s announcement that there will be a surprise test. This announcement is equivalent to:
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