Speculum Stultorum

You are Ricardus Anglicus and I claim my five pounds

2012-01-15T12:19:00.032Z

In 1897, a 26-year-old Prussian named Wilhelm Herkner received his doctorate in Medicine and Surgery from the Friedrich-Wilhelms-Universität in Berlin, where his inaugural dissertation was duly published under the title Kosmetik und Toxicologie nach Wilhelm von Saliceto (13. Jahrh.). This slim octavo of 32 pages has long been hard to find – I know of one copy in France, one in Switzerland, and a handful each in Germany and the US – but it's now available online.

Herkner's focus was ostensibly on the northern Italian surgeon William of Saliceto's Summa conservationis et curationis (c1280), and in particular on Books III and IV, which deal with cosmetics, dermatology, and toxicology. Half of the dissertation, however, is taken up with an interpolation that Julius Pagel had found between these books in MS Erfurt Amplon. F. 240 (c1300). Herkner quoted this in full, saying that its identification would have to await further research – a challenge that has gone unanswered for 114 years.

In 1922, meanwhile, a 28-year-old ex-Prussian named Hermann Beusing received his doctorate in Medicine, Surgery and Obstetrics from the University of Leipzig, where his inaugural dissertation was duly published under the title Leben und Werke des Richardus Anglicus, samt einem erstmaligen Abdruck seiner Schrift “Signa”. A more substantial booklet of 48 pages, this survives in over 20 copies (including at least two in the UK) but has yet to be digitized.

Beusing's dissertation provides almost exactly what the title suggests: a biobibliography of the elusive 12th-century physician Ricardus Anglicus, followed by an edition – based on MSS Erfurt Amplon. F. 288 (c1300) and Leipzig Univ. 1179 (1472), and lacking an apparatus criticus – of most of the Signa prognostica or De signis, the fifth and final part of his medical compendium Micrologus (?1180s).

Almost exactly, because it claims to provide an editio princeps, an honour that actually belongs (at least for the first three-quarters of Beusing's text) to Herkner's dissertation. Compare these incipits:

Finis medicine laudabilis ita dumtaxat existit cum auctor in singulis rationibus [?] quid futurum sit perpendat, quamvis omnis [!] curare non possit. (Beusing)
Finis medicinae ita dumtaxat laudabilis existit cum auctor in singulis valetudinibus quod futurum sit perpendit, quamvis curare omnes non possit. (Herkner)

And compare Herkner's ending with the relevant sentence in Beusing:

In alio autem ordine bonitatis et malicie vitae et mortis sunt signa, sed inter signa bonitatis primum. (Herkner)
In alio autem ordine bonitatis et malitie, inter signa bonitatis primum est signum tussis non laboriosa … (Beusing)

Beusing's text continues for 2½ more pages, ending on a promissory note about ‘critical days’ (a topic he considered too familiar to need printing). But that still leaves 8 pages that can now be checked against a printing from a third (and comparatively early) manuscript. This should be a godsend for anyone using this text; and all thanks to Google – for who would have thought to look for such a thing in Kosmetik und Toxicologie nach Wilhelm von Saliceto (13. Jahrh.)?

Traduttore traditore: a plea for intellectual history

2011-07-30T16:00:00.032+01:00

Working on a medieval Latin dictionary confronts me with material for which my training in intellectual history is little help – financial accounts, legal charters, historical chronicles, etc. Rest assured, though, that when I'm out of my depth I ask an expert. This post amounts to a plea for strangers to intellectual history to do the same.

The prestigious Oxford Medieval Texts series of critical editions with facing-page translations mostly steers clear of intellectual history, but occasional contact is inevitable. One such occasion is the appearance in Thomas Walsingham's Chronica majora of John Wyclif's Declarationes (1378), which contains the following sentence:

Sicut enim omne verum est necessarium [ex suppositione], sic omne falsum est impossibile ex suppositione, ut patet testimonio scripturae et sanctorum doctorum loquentium de necessitate futurorum.

This is more or less bread-and-butter stuff for anyone with the faintest acquaintance with scholastic philosophy:

For just as every truth is [hypothetically] necessary, so every falsehood is hypothetically impossible, as is clear from the testimony of scripture and of the holy doctors who speak of the necessity of the future.

But here's the OMT translation by Leslie Watkiss, praised by Antonia Gransden as ‘good’ and by Geoffrey Martin as of a ‘high standard’:

Just as all that is true is necessary, so all that is false is of its nature impossible, as is made clear by the testimony of Scripture and the learned saints when they speak of future sufferings.

Now, although scholastics are more interested in doctors than saints, ‘learned saints’ is a possible translation of ‘sanctorum doctorum’ (as if formed from the nonce-phrase ‘sancti docti’ rather than from the common phrase ‘sancti doctores’). But the other two mistakes are howlers that make a nonsense of what Wyclif was trying to say.

Impossibility ex suppositione – that is, hypothetical or conditional impossibility – was often called per accidens precisely because it is not intrinsic. It is not ‘of its nature’ impossible that Bush won the 2008 election; it is, however, impossible given the current facts.

And as for the surreal intrusion of ‘future sufferings’, one can only wonder how anyone could have missed the connection between the ‘necessitate’ here and the ‘necessarium’ in the first clause.

As it happens, these particular howlers (like so many others) could have been avoided by spending 5 minutes with Google. Generally, though, the best way of spotting such mistakes would be to have the translation read by someone who does have the relevant background – ideally, in this case, a Wyclif expert, but certainly someone with a serious interest in medieval intellectual history – but apparently neither the editors of this OMT volume nor the general editors of the series saw fit to take this elementary precaution. Thanks, guys.

Quis castigabit ipsum castigatorem?

2011-07-17T12:00:00.016+01:00

In his handbook chapter on ‘Mathematics in Fourteenth-Century Theology’ (2009), which introduces historians of mathematics to the surprising relevance of Sentences commentaries, Mark Thakkar focusses on a stand-off between the positions of Thomas Bradwardine and Gregory of Rimini on infinite multitudes. ‘Unfortunately,’ he writes, ‘[Bradwardine's] 'Sentences' commentary, which would have been written in around 1332, has not come down to us.’

Now, anyone familiar with the literature on Bradwardine will know that Jean-François Genest and Katherine Tachau claimed to have identified part of his Sentences commentary as long ago as 1990. Still, in some contexts Thakkar's remark might have been seen as an excusable simplification. What is embarrassing is the appearance in a collection that he himself cites of a chapter by Genest, ‘Les premiers écrits théologiques de Bradwardine: textes inédits et découvertes récentes’ (2002), that includes a 2½-page discussion of a question on infinity (c.1333) that is probably from Bradwardine's Sentences commentary and would have served his purposes admirably.

What he chooses to look at instead is De causa Dei, Bradwardine's ‘sprawling magnum opus’ of 1344. Readers may be interested to learn that, almost four hundred years after Henry Savile's lavish editio princeps (1618), the Austrian Science Fund has approved a project led by Edit Anna Lukács to study the manuscript tradition in Vienna (home to 11 of the 50-odd extant MSS) and to establish a ‘reception-specific’ critical edition. Hopefully this will pave the way for the full edition that John Marenbon recently highlighted as a desideratum for the British Academy's Auctores Britannici Medii Aevi series.

[Quisquiliae] Supplementare: a ghost story

2010-11-07T15:48:00.009Z

I've just started a job-related blog, Quisquiliae, whose remit will not always be separable from that of this blog. As and when there is an overlap, I'll add a cross-reference (with appropriate tags) here.

The first such import involves a quotation from Michael Scot's translation of Aristotle's De generatione animalium (a1220) in John Pecham's Quaestiones de anima (1270s). You can read the post here.

Peter Auriol and scholarly inertia

2010-02-11T11:18:00.035Z

The Cambridge History of Later Medieval Philosophy (1982) has only two substantial discussions of Peter Auriol (a page each on future contingents and on intentions), though there is also a footnote on his “esse apparens”. This fairly reflects the state of modern scholarship on Auriol when the CHLMP's chapters were written in the late 1970s.

But since the late 1980s, thanks to Katherine Tachau, historians of 14th-century philosophy have become increasingly aware that Auriol was just as important as his much more famous confrère William of Ockham, and the literature has proliferated accordingly. Readers might therefore expect him to feature rather more prominently in the brand-new Cambridge History of Medieval Philosophy (2010).

Alas, no. Not only is he now mentioned on fewer occasions, but the most substantial discussion of him in any of the chapters reads in its entirety as follows: “A fellow Franciscan, Peter Auriol, insisted that the infused virtue of charity plays a more important role in salvation. In his view, infused charity is not simply the consequence of divine acceptance but necessary by its very nature in order to make the soul acceptable to God” (ch. 36, “Virtue theory”, by Bonnie Kent).

In Robert Pasnau's introductory chapter, Martin Stone confidently predicts that “Within twenty years Henry, Giles, Durand, and Auriol will become a part of the canon” (p. 5). In your own time, folks.

Frustra fit per plura (V)

2010-02-01T23:52:00.003Z

Here's yet another of Auriol's statements of ontological parsimony:

‘Constat enim quod omnis natura refugit superfluitatem – quanto magis divina? Pluralitas quidem ponenda non est absque causa, quia frustra fit per plura quod fieri potest per pauciora.’ (S I.45.iii)

Mediaeval Commentaries on the Sentences, vol. 2

2010-01-26T10:57:00.015Z

I can't wait to get my hands on the second volume of Mediaeval Commentaries on the Sentences of Peter Lombard: Current Research, which so far seems to have only made it into the Warburg Institute library. In the meantime, as Brill are being coy about it, here's the chapter list (with authors omitted for clarity's sake):

— The Pseudo-Peter of Poitiers Gloss
— Stephen Langton
— The Glossa in IV libros Sententiarum by Alexander of Hales
— The Sentences Commentary of Hugh of St.-Cher
— Thomas Aquinas and his Lectura romana in primum Sententiarum Petri Lombardi
— Robert Kilwardby's Commentary on the Sentences of Peter Lombard
— William de la Mare
— Henry of Harclay and Aufredo Gonteri Brito
— On the Limits of the Genre: Roger Roseth as a Reader of the Sentences
— Richard Fitzralph's Lectura on the Sentences
— Peter of Candia's Commentary on the Sentences of Peter Lombard
— Martin Luther
— Conclusion: The Tradition of the Sentences

It seems some standardization of the titles wouldn't have gone amiss.

Fractio Aeris: A Cracking Tale of Two Villains

2009-09-17T02:49:00.075+01:00

In his excellent book Theology at Paris (2000), Chris Schabel reports Michael of Massa (fl. c.1330–37) as having suggested that God could form a declarative sentence about the future "by the cracking of the sky". This is a rather melodramatic translation; the Latin phrase ‘per aeris fractionem’ need only mean "by the cracking of air". But the history of this phrase is the history of a more serious mistranslation.

In De anima II.8, Aristotle says that sound is the result of the collision of solid objects with each other and with the air (or other medium), which "happens when the air remains after being struck and is not dispersed; wherefore it makes a sound if it is struck quickly and violently, for the movement of the striker must come sooner than (φθασαι) the dispersal of the air". He gives an analogy with a heap of sand: you must hit it quickly, or it will just part around your hand.

The first villain of the piece is James of Venice (fl. c.1125–50), who translated the last clause as "Oportet enim pertingere motum rapientis fracturam aeris" (for the movement of the violent snatcher must attain the breaking of the air), thus turning what the speed of the blow was meant to avoid into what it was meant to achieve.

Still, two commentaries from the mid-to-late 1240s gave generous glosses: "pertingere, id est antecedere" (ed. Bazan 1998); "pertingere, id est excedere, fracturam aeris, id est: oportet quod velocior sit motus percutientis quam possit esse [fracturam aeris] percussi" (ed. Gauthier 1985). Even better, in 1267 William of Moerbeke corrected ‘pertingere’ to ‘preoccupare’ (anticipate), and Aquinas presented an accurate account in his De anima commentary the following year: "oportet quod motus percutientis praeveniat divisionem aeris".

Enter the second villain of the piece: the influential florilegium Parvi flores or Auctoritates Aristotelis (c.1297–98), which paraphrases the De anima passage as saying that sound is caused by the collision of bodies aerem violenter frangentium (violently breaking the air).

In 1316, Auriol discusses Balaam's talking ass as a challenge to his claim that any form impressible on matter can be impressed on it by a natural agent (S I.42.1.iii.3). He points out that "similem sonum et fractionem aeris potest causare aliquod agens naturale" (a similar sound and breaking of the air can be caused by a natural agent); what is unnatural is just "motionem ipsius linguae brutalis ex qua sequitur fractio aeris et sonus in aere" (the motion of the beastly tongue itself from which there follows the breaking of the air and the sound in the air). This passage is surely sufficient to explain the Massa quotation.

My final exhibit is from the introduction to Jean de Meurs’ Musica speculativa secundum Boetium (1323): "Ad generationem soni tria necessario requiruntur, scilicet percutiens, percussum et medium percutiendi. Primum frangens aerem celeriter, secundum corpus sonabile naturaliter, tertium aer fractus violenter. … Est igitur sonus fractio aeris ab impulsu percutientis ad percussum."

This is a patchy story, but I think it will hold water. Anyone wishing to flesh it out should no doubt seek out (as I have not) Wittmann, Vox atque sonus: Studien zur Rezeption der Aristotelischen Schrift "De anima" und ihre Bedeutung für die Musiktheorie, 2 vols (1987).

Kaye on Auriol on the Semantics of Prophecy

2009-04-27T15:20:00.041+01:00

Sharon Kaye's article ‘Some Philosophical Reflections on the Coming of the Antichrist’ (2000) makes more depressing reading than its title might suggest. She erroneously ascribes to Auriol the thesis that what a prophet means in uttering a prophecy is contingent on what happens in the future – and the translation on which she bases this interpretation is the worst that I have ever seen in a learned journal.

Propositiones propheticae aliud significant ex institutione et ex natura propositionum, aliud vero dant intelligere ex intentione prophetae. … secundum autem intentionem prophetae, verae sunt, quia dant intelligere quod in divina notitia est quaedam veritas ineffabilis et quaedam determinatio illius materiae de qua formantur. (Auriol, Scriptum I.38.iii, 1166–71)

Roughly: ‘Prophetic statements signify one thing by convention and by the nature of statements, and give <us> to understand another by the intention of the prophet. … according to the intention of the prophet they are true, for they give <us> to understand that in the divine cognition there is a certain ineffable truth and a certain determination of the matter about which they are formed.’

Kaye's translation: ‘In one way, prophetic statements signify by convention and by the nature of the statement, but in another way, they express the intention of the prophet. … according to the intention of the prophet, they are true. For they express what is in the divine cognition, namely, a certain ineffable truth and a certain determination of the matter about which they are formed.’

This doubly misidentifies what is signified by prophetic utterances as (1) the prophet's intention and (2) something (or rather two things, one of which was supposed to be ineffable) in the divine cognition.

What is most striking here is how straightforward the Latin is. I can understand her immediately subsequent mistranslation of ‘quod a Deo praedicitur ut in pluribus evenit’ as ‘what is predicted by God happens in many ways’, because the correct translation (‘usually happens’) requires some knowledge of the subject-matter. But there is no such excuse for the flagrant errors identified above. O tempora!

Wimborne on the Logic of Flattery

2009-02-28T10:08:00.037Z

The mid-C13th satire De palpone by the Franciscan schoolmaster Walter of Wimborne includes this stanza (§64, spelling modified):

Palpo sententiae favet utrilibet,
gratus quibuslibet quia qualislibet;
contingens etenim est ad utrumlibet,
vel impossibile quod infert quidlibet.

The first couplet is straightforward enough:

The flatterer favours whichever opinion,
he pleases whoever 'cause he's a chameleon;

For the second couplet, George Rigg suggests in his 1978 edition: ‘“He is contingent on (depends on) either side, or on whatever impossible inference is made.” That is, the flatterer is like a conclusion in logic, dependent on the preceding premise, however impossible it may be. AB agree on quidlibet, but quilibet would be better.’

As I suspect anyone reading this will have noticed, this interpretation is faulty. The contingens line has nothing to do with dependence, but imputes to the flatterer an indeterminate attitude towards pairs of contradictory propositions. And the proposed emendation would break the allusion in the last line to the logical principle often termed ex falso quodlibet. If the text is correct, then, we may translate:

for he's the contingent towards either side,
or else the impossible all things implying.

Here I have construed Wimborne as metaphorically identifying the flatterer with things that have certain modal properties. If instead he were metaphorically ascribing these modal properties directly to the flatterer, we would expect impossibilis instead of impossibile, in which case (understanding quod as ‘because’) we could translate:

for he is contingent towards either side —
or rather impossible, all things implied.

I know nothing about mediaeval poetry, so for all I know this second suggestion may be metrically untenable. But the hybrid contingens ad impossibile construction that Rigg discerns here is very odd – and I flatter myself that both of my suggestions are more amusing.

Cambridge History of Science: The Middle Ages

2008-10-07T19:55:00.010+01:00

I have been salivating over the second volume of the Cambridge History of Science ever since it was first labelled ‘forthcoming’ – which is a very long time indeed. I'm afraid I have no news of its imminent arrival, but I can at least give a small sop to anyone who finds themselves in my position: a provisional chapter list, based on the bibliography to the 2008 second edition of David Lindberg's excellent introductory survey The Beginnings of Western Science.

Medieval Alchemy – W.R. Newman
Anatomy, Physiology, and Medical Theory – D. Jacquart
Astronomy and Astrology – J.D. North
Byzantine Science – A. Tihon
Change and Motion – W.R. Laird
Science and the Medieval Church – D.C. Lindberg
Cosmology – E. Grant
Cosmology, Astronomy, and Mathematics – B.S. Eastwood
Science in the Fifteenth Century – M.H. Shank
Geography – D. Woodward
Islamic Culture and the Natural Sciences – F.J. Ragep
Science in the Jewish Communities – Y.T. Langermann
Logic – E.J. Ashworth
Mathematics – A.G. Molland
Islamic Mathematics – J.L. Berggren
The Mathematical Sciences in Islam – E. Kheirandish
Early Medieval Medicine and Natural Science – V. Nutton
Medical Practice – K. Park
Medicine in Medieval Islam – E. Savage-Smith
Natural History – K. Reeds & T. Kinukawa
Natural Knowledge in the Early Middle Ages – S.C. McCluskey
The Organization of Knowledge: Disciplines and Practices – J. Cadden
The Science of Light and Colour: Seeing and Knowing – D.C. Lindberg & K. Tachau
The Social and Institutional Background of Medieval Latin Science – M.H. Shank
Technology – G. Ovitt
Translation and Transmission of Greek and Islamic Science to Latin Christendom – C.S.F. Burnett
The Twelfth-Century Renaissance – C.S.F. Burnett

Ah, well. It's nice to have something to look forward to.
[Update: the expected publication date is now August 2010. Thanks to Steve McCluskey for this information (see comments).]

Blackburn's Oxford Dictionary of Philosophy

2008-10-06T19:37:00.017+01:00

Simon Blackburn's endearingly idiosyncratic Oxford Dictionary of Philosophy first appeared in 1994 and received an expanded second edition in 2005. I've just bought the 2008 revision, and I'm pleased to report a substantial improvement in the coverage of mediaeval philosophers compared to the first edition: not only is Peter Lombard included, but the number of biographical entries for the 13th and 14th centuries has risen from 14 to 34. Specifically:

13th century. The first edition contained 7 entries: Aquinas, Albert the Great, Roger Bacon, Bonaventure, Ramon Lull, and Siger of Brabant. The second edition adds 11 names to this list: Alexander of Hales, Giles of Rome, Henry of Ghent, Peter John Olivi, Peter of Spain, Philip the Chancellor, Richard Rufus, William (of) Sherwood, William of Auvergne, William of Auxerre, and William of Moerbeke.

14th century. The first edition contained 7 entries: John Buridan, Dante, Duns Scotus, Gersonides, Marsilius of Padua, William of Ockham, and John Wyclif. The second edition adds 9 names to this list: Albert of Saxony, Thomas Bradwardine, Hasdai Crescas, Meister Eckhart, Gregory of Rimini, Richard Kilvington, Nicholas of Autrecourt, Paul of Venice, and Petrarch.

Now, any such selection is bound to disappoint, but the omission of Peter Auriol and Marsilius of Inghen is particularly surprising. One might also have expected to see an entry for Walter Burley, since he is mentioned in Kilvington's entry. Stranger still, a new entry on the Oxford Calculators fails to mention William Heytesbury and even Richard Swineshead, the Calculator par excellence.

Those interested in natural philosophy will miss Francis of Marchia and Nicole Oresme, but they will be more galled to read in the new entry on Aristotelianism that ‘the Schoolmen were more interested in defending the truth of Aristotle's dynamical and physical system, which they saw as substantially compatible with Christianity, than in promoting the empirical and scientific method that he championed, with the result that to the scientific revolution of the seventeenth and eighteenth centuries Aristotle was regarded as little but an obstacle: the author of fossilized and dogmatic scholastic nonsense.’

Still, I suppose such treatment beats a damnatio memoriae.

Frustra fit per plura (IV)

2008-09-03T10:23:00.007+01:00

My occasional posts on ‘Ockham's razor’ are knocked into a cocked hat by the more systematic research of the idiosyncratic Scotus scholar Antonie Vos, whose massive book The Philosophy of John Duns Scotus (2006) includes a section entitled ‘Methodological parsimony: the razor Scoti’ (§8.2). This should be the first port of call for anyone researching the history of the principle.

Here are the formulations quoted by Vos on pp. 304f.:

Numquam est ponenda pluralitas sine necessitate (QM I.4)
Pluralitas numquam ponenda est sine necessitate (IV.2)
Numquam ponenda sunt plura sine necessitate (VII.12)
Pluralitas non est ponenda sine necessitate (VII.12)
Nihil non manifestum ponendum est a philosophantibus sine necessitate (VII.18)
Non est ponenda pluralitas entium sine ratione (Lect. II.2)
Plura non sunt ponenda sine necessitate (II.14)
Sed haec positio ponere videtur pluralitatem sine necessitate (Ord. II.2)
Pluralitas specierum non videtur ponenda sine necessitate manifesta (III.34)

Vos points further to Lectura I.2.202 and Ordinatio IV.11.3 and IV.11.14, which I'm afraid I don't have to hand.

Auriol on the Nobility of Things

2008-08-04T11:47:00.007+01:00

In S I.2.[2/10].iv, discussing ‘whether God's existence is something per se known’ (utrum esse Dei sit aliquid per se notum), Auriol says that God's existence occurs to man naturally via an ‘imperceptible syllogism’ which involves defining God as the highest thing on the scale of nobility. Here, then, is how Auriol sees the world:

Omnes naturae sunt secundum nobilius et ignobilius ordinata. Hanc quidem propositionem assumimus ex sensu. Videmus namque in universo omnia sic disponi, videlicet quod melior est aqua quam terra, aer quam aqua, ignis quam aer, caelum quam ignis; et similiter ferrum quam plumbum, auricalcum quam ferrum, argentum quam auricalcum, aurum quam argentum; et similiter in animalibus et plantis.

‘All natures are ordered according to greater and lesser nobility. And this proposition we take from the senses. For we see universally that all things are thus disposed, namely that water is better than earth, air better than water, fire better than air, heaven better than fire; and likewise iron better than lead, brass better than iron, silver better than brass, gold better than silver; and likewise for animals and plants.’

Was this sort of intuitive hierarchy ever questioned?

Lawrence of Lindores on the Royal Road to Geometry

2008-07-28T12:59:00.014+01:00

In his questions on Aristotle's Physics, written in Paris at around the turn of the 15th century, the Scottish arts master Lawrence of Lindores asked whether one could arrive at knowledge of effects from knowledge of their causes (I.4, utrum ex cognitione causarum contingat devenire in cognitionem effectuum, ed. Dewender 2002).

One of the arguments under consideration involved the claim that, if knowledge of a cause was sufficient for knowledge of its effect,

sequeretur quod cognito aliquo statim cognoscerentur simul omnia possibilia cognosci ex illo. Consequens falsum, quia tunc sequeretur quod cognitis principiis geometriae statim cognoscerentur omnes conclusiones eius. Probatur, quia notitia principiorum geometriae est causa sufficiens ad habendum notitiam primae conclusionis, et notitiae principiorum una cum notitia primae conclusionis esset causa sufficiens ad habendum notitiam secundae conclusionis, et sic ulterius de tertia, quarta et quinta, et sic de aliis, ergo propositum.

‘it would follow that, once something was known, all that could be known from it would immediately be known at the same time. The consequent is false, because in that case it would follow that once the principles of geometry were known, all the conclusions of geometry would be known immediately. Proof: knowledge of the principles of geometry is a sufficient cause for having knowledge of the first conclusion, and knowledge of the principles together with knowledge of the first conclusion would be a sufficient cause for having knowledge of the second conclusion, and so on for the third, fourth and fifth, and so for the others, QED.’

Lindores was more down to earth in his response:

Et si dicatur "Ponatur quod Socrates habeat notitiam omnium principiorum geometriae et velit agere toto conatu suo ad disponendum illa principia in debito modo et figura ad inferendum omnes conclusiones geometriae, et non habeat impedimentum extrinsecum nec ex parte famis nec sitis aut frigoris vel quocumque alio extrinseco, tunc in isto casu, ex quo velit agere, sequitur quod statim cognosceret omnes conclusiones geometriae", respondetur admisso casu negando consequentiam. Et causa est ista, quia, quamvis Socrates non haberet impedimentum extrinsecum, tamen haberet intrinsecum, quia actualis consideratio circa illationem unius conclusionis impediret actualem considerationem circa illationem alterius conclusionis. Quo dato poneret magnum tempus ad inferendum duas conclusiones, ut pateret experientia, igitur et cetera.

‘And if someone says "Suppose Socrates had knowledge of all the principles of geometry, and wanted to put all of his effort into setting those principles in the mode and figure necessary for inferring all the conclusions of geometry, and had no extrinsic impediment from hunger, thirst, cold, or any other extrinsic thing – then in that case, from his wanting to do this, it follows that he would at once know all the conclusions of geometry", the response is to allow the case and deny the consequence. And the reason is as follows: although Socrates would not have an extrinsic impediment, he would still have an intrinsic one, because actual consideration concerning the deduction of one conclusion would impede actual consideration concerning the deduction of another. Given which, it would take a long time to infer two conclusions, as should be clear from experience; therefore etc.’

If only knowledge was closed under implication!

Editions of 14th-century Sentences commentaries

2008-07-24T13:02:00.004+01:00

I'm compiling a list of sizeable critical editions of 14th-century commentaries on Lombard's Sentences. In case it's of use to anyone else, here it is. At present the roll-call is: Scotus, Auriol, Marchia, Ockham, Chatton, Wodeham, Crathorn, Roseth, Langeley, Rimini, and Marsilius of Inghen.

'Contingit' and 'accidit' in Boethius and Moerbeke

2008-06-04T16:02:00.008+01:00

Albrecht Becker-Freyseng complained in his classic study Die Vorgeschichte des philosophischen Terminus 'contingens' (1938) that Boethius used 'contingit' as a dual-purpose translation of Aristotle's endechetai (it may be) and sumbainei (it happens) despite the availability of 'licet' for the former and 'accidit' for the latter.

Funnily enough, William of Moerbeke remedied this defect by rendering sumbainei as 'accidit' in his De interpretatione translation of 1268, but this version never gained currency – so much so that it still hadn't been printed by the time Becker-Freyseng was writing.

Becker-Freyseng would not, however, have been happy to see that Moerbeke followed the editio composita in using 'contingit' – rather than, say, 'accidit' – in his translation of Aristotle's phrase hopoteron/hopoter' etuchen (whichever/however it chances).

Loveland on Auriol on Foreknowledge of the Sunrise

2008-05-22T12:09:00.018+01:00

Jeff Loveland's article ‘Buffon, the Certainty of Sunrise, and the Probabilistic Reductio ad Absurdum’ (2001) contains a tantalizing reference to Auriol's take on foreknowledge of the sunrise in S I.30:

The authors Robert Holcot … and Peter de Rivo … – the latter perhaps influenced by Petrus Aureolus (Aureolus, 1312–20 [sic], pt. 1, p. 673) – were among those investigating the status of the assertion sol orietur cras – "the sun will rise tomorrow." (p. 468)

Alas, if you follow this up in the 1596 edition, you'll find no such thing. What's worse, the faulty reference doesn't look like a mere typo. Here's something you will find on that page:

Quarta demum propositio est, quod relationi repugnat in communi ex sua ratione, quod sit res in natura existens. Dicitur enim de ea, quod acquiritur, et oritur in fundamento sine sui mutatione, sola mutatione facta in termino. Illud ergo non est res, quod acquiritur in subiecto nullo agente ipsum attingente; sed manifestum est, quod albo existente in oriente, si fiat aliud album in occidente, similitudo intelligitur in esse [inesse] albo, quod praeteriit in oriente, absque hoc, quod aliquod agens ipsum attingat, praeterquam intellectus, qui ipsum comparat ad album aliud, quod de novo producitur in occidente. Non enim dealbans in occidente actionem suam protendit usque in oriens, et [ut] ibi similitudinem imprimit [imprimat], nec coelum, aut aliquid aliud potest impremere eam, nisi solus intellectus. Ergo poni non potest, quod aliqua talis res fuerit acquista, et per consequens relationi ex sui natura repugnat habere existentiam in natura. (p. 673, col. 2, A–C)
(The variants are from Henninger's transcription of MS Borghese 329 – which wrongly has 'ullo' for 'nullo' – in his Relations, p. 154, n. 13.)

The context is the ontological status of relations, which Auriol takes to be mental constructs. Here we find him defending his view with a thought experiment: if there is already a white thing in the east, and a white thing appears in the west, then the former acquires a similarity to the latter without any contact between the two. (You might say that the pre-existing white thing undergoes a 'Cambridge change'.)

Now, someone could conceivably misconstrue this passage as having something to do with the sunrise. But to do so he would have to read sola and solus as 'the sun' (rather than 'only') and oriens and occidens as 'rising' and 'setting' (rather than 'the east' and 'the west'); the former is indefensible, and the latter would make no sense in the context.

I hope this isn't the explanation – not just for academia's sake, but because I'd love to know what Auriol thinks about the necessity of the sunrise – but its ready availability would be a striking coincidence.

Bradwardine and Augustine, Pagans and Pelagians

2008-05-07T12:21:00.007+01:00

It is well known that Bradwardine's magnum opus De causa Dei was heavily influenced by Augustine's De civitate Dei, but scholars rarely if ever mention the obvious parallel between the two titles. From a quick survey, the best I can find is an incidental comment in Minnis and Johnson's introduction to The Cambridge History of Literary Criticism vol. 2 (2005): ‘the prosimetric elegance of Thomas Bradwardine's De causa Dei (written in proud imitation of Augustine's De civitate Dei)’.

The full title of Augustine's work is De civitate Dei contra Paganos. Bradwardine's work is usually cited as De causa Dei contra Pelagium, but sometimes as De causa Dei contra Pelagianos. If Bradwardine's title is a homage to Augustine, shouldn't that count in favour of the second version? Just a thought.

Rimini as Torturer of Infants (II)

2008-04-21T12:33:00.007+01:00

Oreste Delucca's biographical contribution to Gregorio da Rimini filosofo (2003) makes the origins of the nickname Tortor Infantium seem even murkier:

‘Quanto al casato di Gregorio, taluno lo dice appartenere alla famiglia Tortorini, o Tortorucci, o Tortorici; ma non si hanno prove documentarie al riguardo, per cui l'affermazione viene accolta con prudenza, ignorata o addirittura rigettata da molti storici.’ (p. 46)

‘As for Gregory's surname, some say he belongs to the Tortorini, Tortorucci, or Tortorici family; but there is no documentary evidence in this regard, because of which the statement is greeted with caution, ignored, or even rejected by many historians.’

Delucca cites Battaglini (1794), L. Tonini (1880), C. Tonini (1884), and Perini (1929) as being of the former persuasion; earlier we saw Trapp (1980) using yet another variant, 'Tortoricci'.

I'd like to follow up Delucca's references, but the Bodleian – which doesn't even stretch to Gregorio da Rimini filosofo – only has the Perini. The others are all at the Warburg (ENH 360, HNB 174, 175).

Leff on Future Contingents

2008-04-16T09:36:00.009+01:00

Gordon Leff's Gregory of Rimini: Tradition and Innovation in Fourteenth Century Thought (1961) might be expected to shed light on Rimini's nickname Tortor Infantium, but I'm afraid it doesn't.

I was pleased to read of Auriol's position as ‘somewhat anachronistically described by Michalski as 'three-value logic'’; Leff's wariness is echoed by Schabel in Theology at Paris, p. 3. But the following raised an eyebrow:

‘These two postulates [omniscience and bivalence] are the foundation of Gregory's view of the future; and they constitute an uncompromising repudiation of the two leading ideas among many of Gregory's confrères: that God cannot know future contingents necessarily, and that, as the future is itself undetermined, propositions about it are neutral.’ (p. 115)

Auriol is the only example Leff gives of the "many of Gregory's confrères" who think that propositions about future contingents are neither true nor false. Whether or not a Franciscan and an Augustinian can be said to be confrères, who are the others?

Henninger on Fiorentino on Rimini

2008-04-15T09:55:00.023+01:00

Francesco Fiorentino's book Gregorio da Rimini: Contingenza, futuro e scienza nel pensiero tardo-medievale (2004) is riddled with errors. For example, here is n. 16 on p. 9 of the introduction:

‘C. Normore, Peter Aureoli and his contemporaries on future contingents and the excluded middle, "Synthèse", 96 (1993), pp. 83-92. Nel 1999 C. Normore è ritornato sul tema secondo una prospettiva più ampia; cf. C. Normore, Contingenti futuri, in La logica nel Medioevo, The Cambridge History of Later Medieval Philosophy, a cura di N. Kretzmann, A. Kenny, J. Pinborg, Milano 1999.’

An attentive reader working on future contingents will immediately spot three mistakes in this one footnote. The first two are comparatively insignificant: the title of Normore's article begins with ‘Petrus’ and does not contain the definite article. The third is more worrying: the CHLMP was published in 1982, so Normore's 1993 article appeared after his CHLMP chapter, but Fiorentino (presumably using a 1999 translation) tells us that in the latter Normore ‘returned to the theme from a wider perspective’. The worrying thing is that the CHLMP has been the standard handbook of mediaeval philosophy since its appearance over 25 years ago.

Both author and publisher deserve a rap on the knuckles, so I was pleased to discover that Mark Henninger had already reviewed the book in Gregorianum. Pleased, that is, until I read the review.

Henninger is grateful for ‘certain logical principles he wisely provides in the introduction [actually Chapter 1]: the principle of bivalence, i.e., in whatever statement, either its affirmation or its negation is true; the law of contradictories, i.e., for every affirmative statement there exists its contradictory, and vice versa’. Unfortunately, both of these are more or less obvious howlers on Fiorentino's part.

If the meaning of ‘bivalence’ in a logical context is not clear enough from the etymology, even a standard dictionary will define it as the existence of only two truth-values, the corresponding principle being that every statement is either true or false. Worse, Fiorentino goes on (p. 24 n. 23) to cite Łukasiewicz's insistence on distinguishing between the principle of bivalence and the law of excluded middle. A reader following this up will be astonished, given Fiorentino's formulation, to read on p. 82 of Łukasiewicz, Aristotle's Syllogistic: ‘…the so-called principle of bivalence, which states that every proposition is either true or false, i.e. that it has one and only one of two possible truth-values: truth and falsity. This principle must not be mixed up with the law of the excluded middle, according to which of two contradictory propositions one must be true.’

As for the law of contradictories, Fiorentino refers only to Aristotle, De int. 9, 18a28-31. The reader following this up will find a discussion of the truth or falsity of an affirmation and its corresponding negation – not the mere assertion that there is a corresponding negation. And I think the reader checking in Rimini and Auriol will find that the law of contradictories is that if one part of a contradictory pair is false then the other part is true (Rimini), or vice versa (Auriol).

Henninger's verdict is that ‘Fiorentino provides a well-researched, thorough and balanced investigation of the teaching of Gregory of Rimini … In the introduction, Fiorentino sets the context with a helpful historiography of the problem of future contingents and divine foreknowledge as treated mostly by researchers in the last century, as well as a survey of the literature on Gregory of Rimini. … This is a fine work by a fine scholar.’

Sadly, then, Fiorentino's book still awaits a properly critical review.

Rimini as Torturer of Infants

2008-04-11T16:28:00.007+01:00

Historians of philosophy like to point out that Gregory of Rimini's views on baptism and salvation earned him the nickname Tortor Infantium, but they are remarkably coy about supporting this with references. The nickname was supposedly derived from Rimini's family name, Tortoricci (Trapp, "Notes on the Tübingen Edition of Gregory of Rimini II", 1980). But when did it first appear in print?

A preliminary search puts an upper bound on the date: 1709, when Leibniz wrote in his Essais de Théodicée (§92): ‘Grégoire de Rimini, général des Augustins, avec peu d'autres, a suivi saint Augustin contre l'opinion reçue des écoles de son temps, et pour cela était appelé le bourreau des enfants, tortor infantum.’

But surely it can't be hard to find something that antedates Leibniz.

Frustra fit per plura (III)

2008-04-11T12:06:00.008+01:00

Here's another of Auriol's statements of ontological parsimony:

‘multitudo ponenda non est nisi ratio evidens necessaria illud probet aliter per pauciora salvari non posse. Deus enim et natura nihil faciunt frustra’ (S II.14.1.ii)

(Mark Henninger, Relations: Medieval Theories (1989), p. 156 n. 25.)

Refugium Miserorum

2008-03-06T16:47:00.005Z

I like Auriol's dismissal of the theory that the generation of substantial forms requires the intervention of higher powers:

‘Hoc est refugium miserorum in philosophia, sicut Deus est refugium miserorum in theologia.’ (S IV.1.1.iii)

‘This is the refuge of the wretched in philosophy, just as God is the refuge of the wretched in theology.’

(Anneliese Maier, Zwei Grundprobleme, 3e (1968), p. 182 n. 29.)

Brunellus versus the Brownshirts

2008-02-25T18:03:00.007Z

Here's an extraordinary story from Gadamer's time in Leipzig:

‘You must understand that during that period one denunciation would come after another, and in my opinion it was pure idiocy – it didn't pay to take it soo seriously. But one time a real denunciation did come along. A student wrote about my seminar to her girlfriend who was not there that semester: "I was with Gadamer today. Can you believe he actually said, 'All asses are brown'?" Now, the girl to whom the letter was written was from a family with Nazi parents. She left the letter lying around, the parents saw it, read it, and I was reported to the rector. So I was asked to go to the rector, who was no Nazi sympathizer (no more than I was) but ... he said to me, "So, my dear colleague, how did you come to speak out against the Brown-shirts by saying, 'All asses are brown'? What did you mean by that?" "You don't understand," I replied, "I was merely explaining the first premise of an Aristotelian syllogism with the famous medieval example, 'All asses are brown; Brunellus is an ass; therefore, Brunellus is brown.' For medieval philosophers, all asses are brown, and Brunellus is the name of an ass that they often used." So the rector wrote into the record, "Professor Gadamer was merely explaining the first premise of a syllogism using a medieval example." The rector and I were of similar minds, and there were very few Nazis in Leipzig anyway.’

(A Century of Philosophy: Hans-Georg Gadamer in Conversation with Riccardo Dottori, trans. Coltman & Koepke (2003), p. 104.)

Frustra fit per plura (II)

2008-02-11T13:50:00.001Z

An update to an older post: I have found in Auriol the exact phrase attributed to him by Ueberweg. It occurs in S I.9.1.i, where he asks quomodo se habet generare seu dicere ad ipsam intellectionem. As his third and final negative thesis, he argues quod dicere non sit formam specularem et realem producere, quam intellectus aspiciat:

‘non est philosophicum pluraritatem rerum ponere sine causa, frustra enim fit per plura, quod potest fieri per pauciora. Sed nulla necessitas ducit ad ponendum talem rem ... Ergo si talis forma ponatur, erit absque omni causa et ratione; et per consequens vanum est ponere eam, et superfluum in natura.’
(ed. Friedman 2003; the 1596 edition, p. 319, has 'inducit')

Moreover, I may have found the source of Ueberweg's mistaken citation: Barthélemy Hauréau, De la philosophie scolastique, II (1850). In chapter 27, ‘Disciples et Adversaires de Duns-Scot’, pp. 404–410, Hauréau discusses Auriol. He quotes on p. 406 from Auriol's remarks on prime matter in S II.12.1.i and II.12.1.ii, and then he moves on to discuss Auriol's negative thesis about real specular forms – but unfortunately his subsequent footnotes simply say ‘Ibid.’ And there, on p. 408, is the very phrase quoted by Ueberweg.

Paris University Statutes of 1366

2007-12-05T14:11:00.004Z

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.)

Gregory of Rimini on the Eternity of the World

2007-12-01T11:42:00.000Z

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.

Frustra fit per plura

2007-08-29T09:31:00.001+01:00

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?

Truth and Consequence

2007-08-26T18:13:00.000+01:00

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

2007-08-02T13:01:00.000+01:00

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.

Time and Thought

2007-07-12T10:42:00.001+01:00

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.

Disjunction and Modality

2007-07-10T17:21:00.000+01:00

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?

2007-07-10T14:31:00.000+01:00

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

2007-06-06T15:57:00.000+01:00

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

2007-06-06T11:53:00.000+01:00

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.

Incipit

2007-06-06T11:11:00.001+01:00

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.