Truth and Consequence

Auriol has been leading me a merry dance this month. Besides the disjunction business, he says that verum non sequitur nisi ex vero, i.e. truth only follows from truth.

This principle has to be severely qualified before it can even begin to pass muster. The obvious types of counterexample (‘Grass is blue, therefore grass is coloured’, ‘I have hands and a rhinoceros, therefore I have hands’) can be dismissed if he's talking about formal consequences from one categorical proposition to another. But even then the principle falls foul of the mediaeval insistence on the existential import of universal affirmations, which licenses the inference ‘Every man is white, therefore some man is white.’

Has anyone else come across a similar principle elsewhere?

Burley on Indeterminate Positio

Walter Burley's Treatise on Obligations (1302) is also suggestive:

‘Positio, as the term is used here, is a prefix to something statable [indicating that the statable thing] should be held to be true. ... If it covers a composite statable, either it is a composite formed by means of a copulative conjunction – in which case it is called conjoined positio – or it is formed by means of a disjunctive proposition and is called indeterminate positio.’

Thus Kretzmann/Stump's Cambridge Translations I, p. 378.

Disjunction and Modality

As part of my attempt to explain Auriol's denial, I've been reading Ray Jennings's refreshingly irreverent book The Genealogy of Disjunction (1994). Jennings makes some interesting points about Latin and about the Stoics, but focuses on English 'or' and says little about our period. But he has suggested to me by email that Auriol might think of disjunctions as listing alternative possibilities, so that his denial might be prompted by the modal status of the disjuncts.

This suggestion is promising, because Auriol is adamant that the truth of ‹Antichrist will be› would entail its necessity, and so presumably the impossibility of ‹Antichrist will not be›. And given that the same reasoning should apply to propositions about the present and the past, this might be taken to corroborate my suspicion that Auriol thinks disjunctions are somehow indeterminate.

I'm now keener than ever to seek out any further remarks of Auriol's on disjunction. Watch this space.

Alone Among Contemporaries?

I mentioned before that Robert Caubraith's Quadrupertitum (1510) explicitly sanctions or-introduction. It turns out that so do Ockham's Summa Logicae II.33 (c. 1323) and Buridan's Tractatus de Consequentiis III.1.5 (c. 1335), not to mention Albert of Saxony's subsequent Perutilis Logica (1350s?). The licence is also implicit in William of Sherwood's Introductiones in Logicam I (c. 1245?) and Walter Burley's Tractatus Brevior 280,285 (c. 1320?) and Tractatus Longior II.3.i 548,551 (c. 1326?).

Does this mean that Auriol stands alone among his contemporaries?

Well, Giles of Rome (d. 1316) is thought to have followed Boethius (De Hypotheticis Syllogismis) in treating disjunction as exclusive, in which case he would have denied or-introduction as a rule of inference. But as I said before, the incompatibility of the two disjuncts in our particular case (‹Antichrist will be›, ‹Antichrist will not be›) renders such considerations inoperative. So this is unlikely to be relevant to Auriol's denial.

Disjunction in Mediaeval Logic

20th-century propositional logic allows ‘or-introduction’: the inference from P to (P v Q) for any Q. This rule is also explicitly stated in Robert Caubraith's Quadrupertitum (1510). But Peter Auriol's Scriptum (1316) denies the inference from ‹Antichrist will be› to ‹Antichrist will be or will not be›. The question is, why?

One answer might be that Auriol takes disjunction to be exclusive, so that (P v Q) is false if P and Q are both true. But although this would invalidate or-introduction as a rule of inference, it would not account for the Antichrist example, in which P and Q cannot both be true.

Another answer might be that Auriol takes ‹P or Q› to have an essential indeterminacy that renders it somehow incompatible with P – perhaps echoing Oswald Hanfling’s complaint in Philosophy and Ordinary Language (2000) that or-introduction falls foul of an ignorance condition: ‘Having been apprised of [P], I am no longer in a position to believe, or to know, that [either P or Q].’

My impression is that Auriol does somehow bind together disjunction and indeterminacy. I intend to investigate this connection.