Paradox

QUINE’S QUESTION MARK 365To meet this corporate goal, Rescher imposes furtherrequirements on the structure of paradoxes. He says that eachmember of the paradox must be self-consistent. (2001, 8)That way, the rejection of any member of the set is enoughto restore consistency. Rescher defends this principle of selfconsistencywith the generalization that no contradiction isplausible.The plausibility of contradictions is made poignant byRescher’s own violation of the consistency requirement.Consider a barber who shaves all and only those who do notshave themselves. Does the barber shave himself? Rescherformulates the set with the following as its first element:“There is—or can be—a barber who answers the specificationsof the narrative.” (2001, 144) Rescher says that thismember of the set should be rejected: “there is not and cannotbe a barber who answers to the specified conditions.” Rescheris definitely correct; it is a theorem of logic that nothing cana bear a relation to all and only the things that do not bear itto themselves. (Thomson 1962, 104) But this means that theBarber paradox’s “aporetic cluster” contains a contradiction(not a mere joint inconsistency as Rescher requires).All of the direct answers to “Does the barber shavehimself?” are strict contradictions. Furthermore, they areindivisible contradictions. The contradiction cannot bedivided into self-consistent propositional components in theway “P and not P” can be segregated into a self-consistent Pand a self-consistent not P.Logical paradoxes are counterexamples to the principlethat logic alone never implies a solution to a paradox. Whena member of the paradox is a logical falsehood, logic doesdictate what must be rejected. Since the inference to a logicaltruth is premiseless, the conclusion cannot be avoided by