Thursday, 17 September 2009

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).

Monday, 27 April 2009

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!

Saturday, 28 February 2009

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.