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.

'Contingit' and 'accidit' in Boethius and Moerbeke

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

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

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)

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

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

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

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)

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

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

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 too 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)

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.