Near the end of Sophisms on Meaning and Truth Jean Buridan presents a group of epistemic paradoxes that bear a close relation to modern formulations of the Hangman Paradox. 1 What is interesting about them is that they seem to teach a lesson not immediately evident in the latter-day puzzle. My purpose here is to analyze and amplify these paradoxes, articulate the lesson, and criticize Buridan's solution.
In Sophism 13 of Chapter VIII Buridan supposes that the following proposition is written on the walt:
Socrates knows the proposition written on the wall to be doubted by him. 2 Socrates reads it, thinks it through and is unsure (doubts) whether or not it is true. Further, he knows that he doubts it. Buridan asks whether or not the proposition is true.
Buridan gives two arguments for its truth, and one against. (A) By hypothesis, Socrates doubts the proposition and knows he does. But this is what the proposition says. So it is true. The second positive argument is (B) that anyone who uttered another token of the same sentence would be regarded as speaking the truth. But (to amplify Buridan's brief remarks) such a token has exactly the same component references and extensions as the token on the wall. So the two have the same truth value. Against the truth of the proposition, Buridan argues (C) that if it were true, Socrates would per impossible know and doubt the same proposition. For by hypothesis, he doubts it. Yet if we only assume that he knows that he knows that he doubts the proposition on the wall, we can derive that he knows it. (For the sentence in italics itself represents the proposition on the wall.)
Buridan attempts to resolve his puzzle by attacking argument (C) and counting the proposition true. He begins by distinguishing between primary knowledge and remote knowledge. Primary knowledge is roughly assent to a