I posit the case that I utter this proposition "I am speaking falsely" and no other.
The sophism is proved, since in so speaking I speak either falsely or truly. If I speak truly, then it is true that I speak falsely. Thus the sophism is true. But if I speak falsely, then the case is as I say. Therefore, I speak truly, and therefore the sophism is true....
The opposite is argued, since if the sophism were true, it would also follow that it was false, and so it would be both true and false, which is impossible. The conseuqence is proved, since if the proposition is true, then it is true that I speak falsely, and so what I say is false. And yet it is posited that I say nothing other than that sophism. Therefore, it is false.
It will be noted that this is very similar to the insoluble (L) I briefly discussed in my last Liar, Liar post. As Buridan goes on to note, this sophism cannot be resolved without considering the reasons for which a proposition is said to be true or false. After discussing a large number of issues with regard to supposition and insolubilia, he comes back to this sophism with his answer:
I answer that the sophism is false, because from it and the proposition expressing the case, a false proposition follows. Yet since this proposition expressing the case is said to be true, and that false, what thus follows is that the sophism is both true and false at once. But a proposition is false, from which, together with its truth, a false proposition follows.
And the arguments for the opposite are answered, according to what was said earlier. For it is said that if it were false, it would follow that it is true. I deny that consequent. And you proved it because if it is false, then it signifies. I agree, with respect to the formal signification. But this is not sufficient because it reflects on itself. For because of this it is not true, for it is not as the consequent of it and of the case signifies. For that consequent is that A is true, positing that my proposition is properly named A. and it is not as this signifies: "A is true."
This is a bit dense, but I think we can provide a very simplified answer to the sophism along Buridan's lines. The key point of Buridan's answer is that (if we make A = the proposition "I am speaking falsely" when nothing else is spoken) if A is false, it does not follow that it is true. One way you can see this is to recognize that a contradictory proposition is the very paradigm of falsehood. Even contingent falsehoods can be regarded as those propositions that generate contradictions on the supposition of something true. So the fact that there is a contradiction in A is no more a problem than the fact that there is a contradiction in 1+1=3. It only looks like there is a problem, because we are misled by the self-reference into thinking that A (or L in the previous post) supports the inference that if it is false it is true. All it supports is the conclusion that A is false, because it implies something false or impossible.
[Burdian translation from John Buridan, Sophisms on Meaning and Truth, Theodore Kermit Scott, tr. Meredith Publishing, 1966.]
