  The difficult question about these two moves, on which scholarship is divided, is how far the pendulum has now swung back towards conventionalism. There are reasons for being wary of exaggerating the swing. As regards the first argument, it is significant that Socrates nowhere in the dialogue admits any case in which the inappropriate elements in a name outnumber the appropriate ones (hence item 19 in the list of etymological principles, section 3 above). The test case, that of sklêrotês, is one where the score is even, so that convention has to be called in to break the deadlock. And as regards the argument about numbers, Socrates is explicit that convention needs to be invoked here, not to replace naturalism, but on the contrary to vindicate it: ‘[W]here do you think you’re going to get, to apply to numbers, a supply of names which resemble every single one of them, if you don’t allow the consent and agreement you spoke of to have some authority concerning correctness of names?’ (435b–c). And he does have a good point. There cannot be a simple set of direct and unmediated resemblances between numbers and their names, because there are infinitely many numbers, so that an infinite set of number-names made out of the finite stock of letters would be unable to place any limit on the length of those names. We therefore have to have agreed rules for composing their names out of smaller units: twenty-seven, two hundred and forty, etc. (English and ancient Greek are not very different in this regard.) And those rules will be where the element of convention creeps in. If so, the result is that the descriptive power of number-names is vindicated: thanks to this simple set of conventions we can name, by description, any one of the infinite series of natural numbers. This is very far from being an abandonment of naturalism.