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.
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