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.

A Suggestive Passage in Auriol

In Scriptum I.2.9, Auriol denies that the concept of being is univocal, saying instead that it is wholly ‘confused’ (lacking distinction). He reports the opinion of some others (including, apparently, Scotus):

‘quod conceptus entis includit conceptum substantiae et accidentium disiunctive, et sumus certi de aliquo quod est ens, quia vel substantia vel accidens disiunctive; ignoramus tamen quid sit determinate, sicut audito quod canis est in macello, statim sum certus quod est ibi piscis vel latrabilis canis, non sum autem certus determinate de uno vel de alio. Secundum hoc ergo conceditur quod est alius conceptus entis a conceptibus propriis, sicut disiunctum est aliud a determinato.’ (D.1, §116)

‘that the concept of being includes the concept of substance and of accidents disjunctively, and we are sure of something that it is a being, because <we are sure that it is> either a substance or an accident disjunctively; but we do not know which it is determinately – just as, on hearing that there is a dog in the butcher's, I am immediately sure that there is a dogfish or a barking dog there, but I am not sure determinately about one or about the other. Accordingly, therefore, it is conceded that the concept of being is different from proper concepts in the same way that disjunct is different from determinate.’

Now, this is not Auriol's own opinion. He denies the analogy with the lexical ambiguity in ‘canis’, and he argues that such a disjunct concept could not account for ‹God is a being›. But he does not bat an eyelid at the claim (however taken) that disiunctum is different from determinatum.

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.