  The solution Buridan finally settles on receives the somewhat tepid endorsement of being “closer to the truth” than the previous solution—a reflection, perhaps, of his awareness of the imperfectability of any formal system that tries to stick close to the facts of human language. Here, the idea that a proposition formally signifies itself to be true is replaced by the notion of implication from the doctrine of consequences. “Every proposition,” he says, “virtually implies another proposition in which the predicate ‘true’ is affirmed of the subject that supposits for [the original proposition]” (S 9.8, 7th sophism:  969).[32]  Unlike the old solution, in which the second proposition is signified by the first and hence part of its meaning, the new solution assumes only that the second proposition follows logically from the first, so that its meaning can be expounded separately. In this way, for the truth of any proposition P, it is required not only (1) that the subject and predicate terms of P stand for the same thing or  things,[33]  but also (2) that P implies another proposition, ‘P is true’, which must also be true. Otherwise, we would have a true antecedent and a false consequent, violating Buridan's fifth theorem regarding assertoric consequences, which states, “it is impossible for what is false to follow from what is true [impossibile est ex veris sequi falsum]” (TC I.8: 34, l. 97; Read (tr.) 2015: 77–78). Applying this to the 7th sophism, the constituent terms in the proposition uttered by Socrates—‘Every proposition’ and ‘false’—stand for the same things, since in the posited case, “all true propositions are annihilated and the false ones remain, and then Socrates propounds only this: ‘Every proposition is false’”. So the first condition is satisfied. But the implied proposition, ‘P is true’ (where P is the name of ‘Every proposition is false’), is false because its constituent terms, ‘Every proposition is false’ and ‘true’, do not stand for the same thing, since ex hypothesi, P stands for the antecedent proposition ‘Every proposition is false’, not for things that are true. But this gives us a true antecedent and a false consequent, and so the consequence does not hold. Therefore, the sophism is false.