reason was given by Thomas Aquinas and, more clearly, by Leibniz: we have not shown that our definition of divine perfection is more than verbal, or as Leibniz puts it, nominal. Consider the definition: 'necessarily-existing round-square'. To deny its existence is contradictory, for we should be saying that the necessarily true is yet false. However, to assert its existence is also contradictory, for we should be saying that what is round is in the same respect not round. The way out of the maze is to reject the proposed definition as an ill-formed expression, incapable of either truth or falsity. Anselm presents us with this question, Is his definition of God capable of describing anything thinkable? And since, as we have seen, the definition is ambiguous, meaning either 'none greater except itself', or 'none greater simpliciter', our question becomes a double one. That Anselm's own meaning, the one last mentioned in the previous sentence, is paradoxical we have pointed out. A paradoxical concept cannot furnish the basis of a cogent argument for the truth of that concept. Whether the alternative construction of the definition can evade the paradoxes, without falling into others of its own, is a question which lies outside the present essay. That it does not face the same paradoxes we have seen.
Modern logic has made a point of the distinction between 'predicates', which individual cases may 'instantiate' or 'embody', and the individual cases themselves. The latter 'exist' only in a tautological sense. To be an individual is to exist in the only sense in which an individual can exist. A predicate, in contrast, may have a sort of thinkable reality,