Wednesday 5 December 2007

Paris University Statutes of 1366

The Parisian Statutes of 1366 show some interesting contraints on students of and lecturers on the Sentences:

Item quod scolares librum Sententiarum audientes noviter primis quatuor annis textum Sententiarum portent vel portari faciant ad scolas bachelarii, a quo Sententias audient, ut textum Sententiarum audiant diligenter.

Item quod legentes Sententias faciant honeste et sine verbis offensivis quibuscunque aut elatis sive scandalosis suas collationes et principia, omni injuria cessante servatoque sibi invicem congruo honore.

Item quod legentes Sententias non tractent questiones aut materias logicas vel philosophicas, nisi quantum textus Sententiarum requiret, aut solutiones argumentorum exigent, sed moveant et tractent questiones theologicas, speculativas vel morales, ad distinctiones pertinentes.

Item quod legentes Sententias legant textum ipsarum ordinate et exponant ad utilitatem auditorum.

Item quod nullus legens Sententias legat questionem suam aut suum principium per quaternum aut alias in scriptis. Non tamen propter hoc inhibemus, quin bachelarius possit portare ad cathedram aliquid ex quo possit, si necesse fuerit, sibi reducere ad memoriam aliquas difficultates questionem suam, aut argumenta seu auctoritates aut ad ipsam questionem aut aliquam expositionem pertinentes.

Item statuimus quod nullus magister aut bachelarius qui Sententias legerit, suam lecturam Sententiarum communicet tradendo stationariis directe vel indirecte, quousque sua lectura fuerit per cancellarium et magistrus predicte facultatis examinata.

(Chartularium Universitatis Parisiensis, vol. III, §1319, pp. 143f.)

Saturday 1 December 2007

Gregory of Rimini on the Eternity of the World

Gregory of Rimini's treatment of the paradoxes of infinity (S I.42-44.4) allowed him a swift response in S II.1.2.i to an Aristotelian argument that an endless world could not have had a beginning.

Here is the core of the Aristotelian argument:
Probatur minor, quia si detur oppositum, sequitur quod erit infinitum maius infinito. Nam tempus aeternum ex utraque parte super utrumque aeternum ex altera tantum addit reliquum tempus aeternum ex reliqua parte, ut super aeternum in praeterito tantum addit tempus aeternum in futuro tantum, et econverso. Cum igitur omne aeternum in futuro sit ens tempore infinito, sequitur quod fuit etiam ens infinito tempore praeterito.

And here is Gregory's response:
Ad secundam rationem principalem nego minorem, et dico quod probatio aeque militat contra Philosophum, qui posuit tempus aeternum in praeterito et in futuro, cum tamen aeternum in praeterito sit infinitum, et similiter aeternum in futuro, et aeternum ex utraque parte utrumque comprehendat. Quia tamen, secundum quod inferius dicam, possibile fuit tempus esse aeternum, quamvis de facto habuit initium, ac per hoc fuit possibile infinitum comprehendere in se plura infinita, dico quod hoc non est inconveniens, sicut in primo libro distinctione 44 declaratum est. Et pro nunc sufficiat exemplum de aliquo continuo, cuius utraque medietas continet infinitas partes proportionales alias ab his, quas reliqua continet.

The tu quoque here is a nice move.

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.

Thursday 12 July 2007

Time and Thought

This is just a collection of references to passages in Auriol about the relationship between time and thought. I'll update it as and when.

Scriptum I.3.14.ii.b (‘Quid sit memoria in Deo et in nobis’), §§45, 47.

Tuesday 10 July 2007

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.

Wednesday 6 June 2007

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.


I've started this blog as an experimental repository for notes on mediaeval philosophy, with no idea how useful, active, or long-lived it will prove to be. I've heard it said that academic blogging is inadvisable, either because people might steal your ideas, or because you might reveal traits that could put off potential employers. But I don't plan to use this blog as a therapeutic outlet, and I like to think of our corner of academia as a collaborative enterprise.