John Buridan's Sophismata

Buridan, Sophismata, pp. 965-997 (Week 13, 6 February)

  1. The seventh sophism, that every proposition is false, clearly cannot be true. But what is problematic about its being false because some proposition (e.g. that red things are colored) is true? In other words, why is it even a sophism?

  2. Precisely what is paradoxical about the eight sophism despite the fact that the pair of propositions is logically consistent? What is Buridan's solution?

    If Socrates utters only 'Plato says something false' and Plato only 'Socrates utters something false', then one can be true while the other is false. But which? Perhaps Socrates and Plato have precisely the same intentions and so on when they form the propositions (say each things the other said that God doesn't exist), so that if one is true/false, the other should be true/false. There appears to be nothing to break the symmetry. Buridan's answer is to say that both propositions are false. (This paradox has been called the "no-no" paradox by Roy Sorensen. It is similar to the so-called truth-teller paradox in that the truth-teller is also logically consistent; indeed it can be either true or false, yet there is nothing to break the symmetry.)

  3. In the fourteenth sophism, it is said "Plato does not know that [the disjunction] is true: for it would be necessary that he know one or the other member to be true, since for the truth of a disjunctive it is required that one of its disjuncts be true". Is this a good piece of reasoning?

    For conjunctions, yes; for disjunctions; no. One can certainly know the trivial logical truth that p or that not-p, without knowing which. Presumably for all p, we know that either p or not-p, yet we do not know every truth--we are not omniscient!

  4. The sixteenth sophism, "You will respond negatively", concerns a sort of disputational game, Obligations. (A classic account can be found in Walter Burley's "On the essentials of the art of logic.) An opponent and respondent play a game where the opponent tries to get the respondent to respond "badly", e.g. by accepting a known falsehood. What is Burley's solution to the sophism?

    He says that, given that the sophism concerns the respondent's response and thus involves self-reference, she should not accept the obligation since you know the proposition to be false (since it involves self-reference).

  5. Concerning the seventeenth sophism, "You will throw me in the water", Buridan says that it is either true or false but not determinately either. What do you make of this?

    The proposition is about the future, and if the future is not yet determined, perhaps does not yet even exist, how can the proposition be either true or false? Clearly it cannot be determinately so, but how can it be even indeterminately so? We know that the disjunction, "Either you will throw me in or you won't throw me in" is determinately true even though neither of its disjuncts are, but a lot more would need to be said concerning how the disjuncts have any truth value.