Mediaeval Commentaries on the Sentences, vol. 2

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

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

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

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

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
Islamic Astronomy – R.G. Morrison
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 (October 2013): this is finally being published!]

Blackburn's Oxford Dictionary of Philosophy

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)

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

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

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

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.