Wednesday 29 August 2007

Frustra fit per plura

Ocham of Beyond Necessity has spotted an occurrence in Auriol's Scriptum (1316) of the principle still known as Ockham's Razor:

Praeterea, non debet poni superfluum aut aliqua distinctio sine causa, quia frustra fit per plura quod potest fieri per pauciora.
(S I.8.21 §33)

Ocham writes: ‘it may be a Franciscan expression, and I think Scotus used it.’  Well, here is an instance from the Franciscan Ramon Llull's Liber reprobationis aliquorum errorum Averrois (1310?):

Quod Deus non agat immediate in istis inferioribus, sic probatur: Impossibile est, quod entia nobiliora frustrentur a suis operationibus.  Sed si Deus in istis ageret immediate, intelligentia et caelum frustrarentur in operationibus suis, quae sunt nobiliora entia.  Ergo impossibile est Deum agere in istis.
Quod autem intelligentia et caelum frustrarentur, patet; quia frustra fit per intelligentiam, caelum et etiam per Deum, quod posset fieri per Deum solum.  Si enim frustra fit per plura, quod potest per pauciora fieri et si sic non haberent operationes proprias, et per consequens non haberent naturas proprias; quod est impossibile.
’ (d. 2 pars 7)

Llull – who apparently met Scotus in 1297 – rejects this argument on the grounds that celestial motions would not be in vain if God acted immediately on terrestrial things.  So presumably he accepts the principle.  Did Averroes, too, or at least some Averroists?


Edward Ockham said...

Another thing I just spotted. Thorburn, in the paper you link to, writes

"Ueberweg cannot always be trusted, even when he does give a reference. On the previous page (461) of §104, he refers to the Scotist Petrus Aureolus (+ 1322 Archbishop of Aix): In SS. , ii., D.12, Q.1, for an assertion that: 'He (P.A.) enounced the principle subequently known as the Law of Parcimony: Non est Philosophicum, pluralitatem rerum ponere sine causa; frustra enim fit per plura, quod fieri potest per pauciora'. But there are no such clauses in the locus indicated; and the Index gives no clue to their presence anywhere else. It is indeed possible that he has written them somewhere; because the words had previously been used by his master Duns Scotus: a fact, with which Ueberweg does not seem to have been acquainted. Aureolus actually says (In SS., i., D.3, on p.164 of vol. I), referring to Aristotle's Physica (i.): 'In principiis debet tanta paucitas, quanta sufficit ad salvandum ea, quae sunt in natura necessaria'."

Interesting that Aureol does indeed say almost exactly what Ueberweg attributes to him, except in D8. We don't have the text of D12, unfortunately. Thorburn has not spotted this (not having the modern luxury of control-F), as is also clear from his comment that 'the Index gives no clue to their presence anywhere else' (i.e. he admits he is relying on the Index, and not the laborious method of reading through the text).

Brunellus said...

Well spotted. Poor Ueberweg. I wonder whether he scribbled down ‘VIII’ so untidily that he later read it as ‘XII’.

On the other hand, I.12 does concern a question of plurality, so perhaps he did read the principle into it after all. Cf. uno autem existente non necesse est duos esse (a. 2), spiratio significata deberet plurificari (a. 4).

The text of d. 12 is available in a preliminary critical edition at the Electronic Scriptum.

Brunellus said...

Whoops – I hadn't noticed that Ueberweg thought it was in Book II! In any case, I think I've identified the source of his error now.