Paradox

210 A BRIEF HISTORY OF THE PARADOXBlack Death was caused by fleas,” I invite the inference thatI believe the Black Death was caused by fleas. This goes someway in explaining why it is difficult to assert “The BlackDeath was caused by fleas but I do not believe it.” Thesentence is consistent but I cannot consistently believe it. Thislimit to consistent belief is interesting because we tend toassume that any consistent proposition can be consistentlybelieved.BURIDAN ON THE INSOLUBLESBuridan’s sophisms can be traced to loopholes in obligationaldisputes. They are dialectical variants of pragmatic paradoxesand the liar paradox.Buridan’s first sophism in his chapter on the insolublesis “Every proposition is affirmative, so none is negative.” Isthe argument valid? Pro: the premise implies the conclusionbecause it is an instance of the valid argument from “All Fsare Gs, therefore, no Fs are non-Gs.” Con: a contingentproposition cannot imply a necessarily false conclusion. “Noproposition is negative” is false whenever it is uttered.Buridan’s solution is to insist that a proposition can bepossible even if it cannot be a true utterance. It is good enoughif the facts could be as the proposition says. For instance, “Nosentence on this page is nine words long” expresses a possibilitybecause there could be an absence of nine-word sentenceson this page. But the sentence cannot be both true andinscribed on this page because it is itself nine words long.Under this conception of possibility, the argument is valid.Buridan’s second sophism is “No proposition is negative,therefore some proposition is negative.” The argument seems