Epimenides the Cretan

Extract

What I am offering here is a reconsideration, and in the end a solution, of the ancient paradox of the Epimenides. What has provoked this new assault on so old a stronghold is L. Jonathan Cohen's [2], in which it is rightly pointed out that the Epimenidean as contrasted with the Eubulidean version of the Liar paradox is the one that threatens logicians who attempt to formalise the use of indirect rather than direct discourse. Among these he includes myself, referring to the system sketched on pp. 130–131 of my [4], and suggesting that I ought to have shown how a person interpreting this system in the obvious way can avoid semantic antinomies. Here too he is right, and my main purpose now is not to criticise his paper, but to fill in this lacuna in my own work to which he has drawn attention. I do want, however, to make one small criticism at the start, namely that Cohen fails to notice what it is that is really paradoxical about the Epimenides, and in consequence fails to perceive the same paradoxical character in a proposition which he is himself quite happy to accept as a ‘logical truth.’

The point about the Epimenides, as was noted by Church in [1], is not that when we examine the truth value of a Cretan's assertion that nothing true is ever asserted by a Cretan we are led to contradictory conclusions, for we are not; the paradox is rather that such examination makes it seem possible to settle an empirical question on logical grounds. If we treat the Cretan's assertion as true, and so assume that nothing true is ever asserted by a Cretan, it follows immediately that the Cretan's assertion is false. If, however, we treat it as false, there is no way of deducing from this assumption that it is true. We can, therefore, consistently suppose it to be false, and this is all that we can consistently suppose. But to suppose it false (considering what the assertion actually is) is to suppose that something asserted by a Cretan is true; and this of course can only be some other assertion than the one mentioned. We thus reach the peculiar conclusion that if any Cretan does assert that nothing asserted by a Cretan is true, then this cannot possibly be the only assertion made by a Cretan — there must also be, beside this false Cretan assertion, some true one.