I’m currently reading through Paloma Pérez-Ilzarbe and María Cerezo’s History of Logic and Semantics: Studies on the Aristotelian and Terminist Traditions, a collection of papers in honor of Angel d’Ors, and learning all sorts of interesting things. In Calvin Normore’s paper, “Ex Impossibili Quodlibet Sequitur (Angel d’Ors)”, he looks at Buridan’s criterion for a good consequence and how it relates to the titular Parvipontanean thesis. Lots of interesting things in there especially in relation to 13th-century discussions of the principle, which I am more familiar with than the 14th-century ones. But what caught my eye was something that reminded me of a paper I’ve got on “possible impossibilities” which has been in draft format around 85% done for the last…um…five years (Some day I will finish it. It’s a good paper!) — namely, four different degrees of necessity that Buridan distinguishes. The discussion occurs in the Treatise on Demonstrations, &sec; 8.6.3 in Klima’s translation, in the context of different types of per se propositions. Because per se propositions have to be necessary, and “there are diverse grades of necessity”, there are therefore also diverse grades of perseity:
The first grade of necessity occurs when it is not possible by any power to falsify the proposition while its signification remains the same, nor [is it possible] for things to be otherwise than it signifies.
Another grade occurs when it is impossible either to falsify it or for things to be otherwise by natural powers, although it is possible supernaturally or miraculously, as in “The heavens are moving”, “The heavens are spherical”, and “[Any] place is filled.”
The third grade occurs with the assumption of the constancy of the subject, as in “A lunar eclipse takes place because of the interposition of the earth between the sun and the moon”, “Socrates is a man”, and “Socrates is risible”. These are said to be necessary in this way because it is necessary for Socrates, whenever he is, to be a risible man, and it is necessary, whenever there is a lunar eclipse, that it take place because of the interposition of the earth between the sun and the moon.
There is yet a fourth mode, which involves restriction. For just as ‘possible’ is sometimes predicated broadly, in relation to the present, past, and future, and sometimes restrictively, in relation to the present or the future, in accordance with what is said at the end of On the Heavens — that no force or power can be brought to bear on the past, i.e., on that which is done, but only on that which is or will be (for we say that everything that has been necessarily has been, and cannot not have been) — the same goes for ‘necessary’ and ‘impossible’, which are also predicated either with restriction or broadly (p. 733).
I find this discussion fascinating. First, the distinction between natural and supernatural necessities is quite relevant in connection with positio impossibili and the way this genre of obligatio is used in connection with theological reasoning. Second, the third grade sounds an awful lot like contemporary “analytic truths”. Third, it’s not entirely clear to me what the difference between the first and the third grade is; can anyone suggest an example of something that is necessary according to the third grade but not the first? Fourth, with the discussion of the fourth grade, Buridan has almost everything he needs to run Diodorus’s Master Argument — the different ways to define ‘necessary’, the necessity of the past — all he needs now is to ask whether there is something possible which neither is nor will be true!