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?

Sunday 26 August 2007

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?

Thursday 2 August 2007

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.