METAPHYSICS AND SCIENCE IN THE THIRTEENTH CENTURY: WILLIAM OF AUVERGNE, ROBERT GROSSETESTE AND ROGER BACON
Metaphysics and science in the thirteenth century: William of Auvergne, Robert Grosseteste and Roger BaconSteven MarroneBy the third decade of the thirteenth century there emerge the firstsigns of a new metaphysics. Alongside Neoplatonizing idealism wenow see attempts to lay greater emphasis on the ontological density ofthe created world and to structure reality without resorting to the termsof a relation to the divine ideal. The ensuing philosophical reassessmentwas more systematic, more technically precise and more self-consciousthan anything the medieval West had seen before. Given the catalysingrole played by logic, it was only natural that much of this programmewas carried out within the confines of an attempt to explain knowledge.For the early thirteenth century, metaphysics and epistemology wenthand in hand.The two figures who did the most to promote the new metaphysics,as well as a profoundly Aristotelianizing campaign to establish thecriteria for knowledge, were masters whose important work was donebetween 1220 and 1235 in the schools of theology at the newuniversities. Robert Grosseteste (d. 1253) was born in England probablybefore 1170, studied and taught the arts curriculum in provincialschools and perhaps at Paris and Oxford, and began to lecture ontheology at Oxford after 1214 but no later than 1225. His activity asa philosopher effectively ended with his appointment as bishop ofLincoln in 1235. William of Auvergne (d. 1249) was born in Francearound 1180, went to Paris to study, and began teaching there first inarts and then by the 1220s in theology. He was named bishop of Parisin 1228, although he continued to write about philosophical mattersfor some years thereafter.In Grosseteste’s earlier works there is, to be sure, no hint of the newattitude. His treatiseOn Truth (De veritate)offers an ontology stillfirmly grounded in the Neoplatonic world-view.Quoting Anselm, hedefines truth as a kind of ontological obligation: the correctness(rectitudo)of objective things ([9.3] 135:3–6). Such obligation is metinasmuch as things conform to God’s eternal word, or, more specifically,to an idea or reason(ratio, ratio aeterna)in God’s mind, eternallyrepresenting the object as it ought to be ([9.3] 137:1–2, 139:29–30).This idealized notion of truth is directly manifest in Grosseteste’snoetics. Drawing on an image commonplace in Latin Christiandiscourse since the time of Augustine, he explains that the intellect canattain the truth, its proper object, only in an intelligible light shiningfrom God himself ([9.3] 137:2–4). The image surely serves in part asshorthand for a more complicated epistemic argument. If objectivetruth is a quality arising out of the conformity between an object andits divine ideal, then the mind can seize the truth only when it perceives,and can compare, both thing(res)and idea(ratio)([9.3] 138:4–11). Itis clear, however, that Grosseteste also takes quite literally the existenceof a higher light in which truth must be known. He goes on to say thatjust as the eye can see a coloured body only when it is bathed in visiblelight, so the mind can know a thing in its truth only if the divine lightis shining on it ([9.3] 137:19–25).Yet when Grosseteste came to analysing Aristotle’s ideas about trueknowledge, a dramatically different vision took shape in his mind. IntheCommentary on the Posterior Analytics,his most mature accountof the relation between intellect and objective reality, dating probablyfrom the late 1220s, he speaks of truth as a simple thing in the world(illud quod est),with no mention of a comparison to God’s ideal ([9.6]99:17–18). The source of this view goes back toOn Truth,where forone uncharacteristic moment Grosseteste had recalled Augustine’sdefinition of truth as ‘what a thing is’(id, quod est),adding, in violationof traditional Boethian language, that this was the same as its being(esse)([9.3] 141:13–15). But what was merely an interesting aside inthe early work now takes centre stage. Grosseteste in the Aristotlecommentary is prepared to argue that the truth of a thing is exclusivelyits substantial presence in external reality. Another word for this is‘essence’, taken as a thing’s formal core shorn of all the accidents ofmaterial circumstance (puritas essentiae suae non cum admixtioneconditionum materialium([9.6] 406–7:82–4). So patent a breach ofNeoplatonizing principles appealed to William of Auvergne as well,for in his treatiseOn the Universe (De universo)from the early 1230she similarly defines the objective truth of a thing as its ‘substance, oressence, or being’. It is what is left to an object once all accidentals(circumvestitio accidentium)have been stripped away ([9.1] I:836aE;also I: 794bF).The new notion of truth opened the way for both thinkers to attackNeoplatonizing ontology and the conditions of knowledge it entailed.Referring to Plato and theTimaeus,William concedes inOn theUniversethat it is correct to posit an archetypal world of exemplaryideals(exemplaria)of which things in the perceived world are imitations(exempla),providing one locates the exemplary world in the mind ofGod. The problem with Plato is that he took the idea too far ([9.1] I:823aC, 823bC, 835aA). As should be clear from the definition of anobject’s truth as its being or substance, the truth of something in theworld and the truth of an idea in God’s mind are not the same ([9.1] I:837a (B-C)). Aristotle was right when he criticized Plato’s notion of thereference of simple terms. Words such as ‘earth’, ‘fire’, ‘water’ and ‘air’refer immediately to simple substances in the world and imply nocomparison or reference to the Creator ([9.1] I: 835aB). ANeoplatonizing theory of truth—like that we have seen in Grosseteste’sOn Truth—is both semantically and ontologically misleading.The Grosseteste of theCommentary on the Posterior Analyticsagreed. A long, often misinterpreted passage outlines five sorts of objectthat might serve as immediate referent for terms of universal predication([9.6] 139–41:99–145). The first are the eternal reasons(rationes)inGod, ‘what Plato called ideas or the archetypal world’; the second areexemplary forms impressed by God on the minds of angels; the thirdare the causal reasons(rationes causales)of earthly things residing inthe celestial spheres; the fourth, the inherent forms of real thingsthemselves, taken as signifying the whole substance; and the fifth,accidents read as signs of the substantial reality to which they adhere.Grosseteste comments that it was according to the fourth way thatAristotle explained the predication of kinds and types(genera et species),and it is clear from what he says throughout the work that he acceptsthis as the norm for human knowledge in the world.1Echoing William,he claims that Plato’s kinds and types—separate substances in anarchetypal world held to be properly predicated of subjects in this,their exemplified imitator—are monsters produced by an erring intellect(prodigia quae format error intellectus)([9.6] 224:142–8).For all their sympathy to Aristotle’s theory of reference, however, Williamand Grosseteste shared an ontology of essence quite unlike anythingAristotle had in mind. William rejects the authentically Aristotelian positionof Boethius whereby specific essences are individuated by the accidentsof their particular—or material—instantiation ([9.1] I: 802a (E-F)).Instead he maintains that individuals are both fully particular and fullyspecific—that is to say, general—in their essence, which was, for him, theirsubstance as well. Indeed, he insists that the numerical distinction ofindividuals of the same species can be reduced to what he calls an ‘essentialdifference’(differentia essentialis):the fact that the essence of this thing isnot precisely the essence of that ([9.1] I:858b–59a (G-A)). Recognizingthe awkwardness of his language, he hastens to add that the differencedoes not amount to a dissimilitude(dissimilitudo),which might sever theunity of the specific type, but should technically be referred to as a diversity(diversitas)among particulars ([9.1] I:802aG). Grosseteste, too, held tothe view that the essential nature of things was in and of itself individual([9.6] 213:221–4). Despite the philosophical ambiguity of such a position,it continued to be defended throughout the thirteenth century, nowheremore loyally than among Franciscans of the so-called Augustinian school,and provided the impetus for Scotus’ famous theory of the formaldistinction.A notion of essence as of itself fully individualized naturallycomplicated the explanation of universal predication, which by theterms of William’s and Grosseteste’s semantics entailed direct referenceto the very instantiated essences of which individuals were comprised.William never addressed the matter, but Grosseteste tried his hand at asolution that appears inspired by the terminist logic of his day.According to theCommentary on the Posterior Analytics,althoughuniversal predication cannot be reduced to an ontological configurationexactly the same as that of singularity, it must be founded on one thatis not entirely different ([9.6] 245:127–34). The notion of essence assimultaneously singular and general demanded as much. If, therefore,as Aristotle maintained, the universal is ‘one thing from and in many’([9.6] 161:329–35)—a single predicate drawn from the knowledge ofmany singulars and referring to them all—this is because the universaltaken in itself(universale secundum se)is neither one nor many(necunum nec multa)but somehow capable of being construed as both. InGrosseteste’s words, it ‘falls to’(accidit)the universal, most probablythrough the agency of the intellect, to be one thing while representingmany ([9.6] 244:110–14). Certainly Grosseteste had in mind here thelogician’s understanding of the supposition of terms, by which linguisticmarkers that in themselves could signify either the singular or generalaspect of an essence—words like ‘horse’ or ‘man’—took on eitheruniversal or particular reference according to the demands of thepropositions in which they were employed. Universals, in short, wereterms: words denoting essence used for the purposes of universalpredication (see [9.20] 185–7). The ambiguity of the term beforesupposition—of the ‘universal in itself’—simply mirrored the fact thatit signified an essence that was also in itself both singular and general.By now we have reached an ontology and a semantics almostanticipating the nominalism of the fourteenth century. There was,however, at least for William still room for Neoplatonizing views. Ashe explains inOn the Universe,while most words by which we describecreated things refer directly to substances in the world, there are somethat point more immediately to God and divine attributes. The reasonis that the objective truth for which such words stand lies more preciselyin God than in anything in the created world. When these words areused in discourse they consequently signify a divine object mostproperly—which is to say, univocally—and a created object only byequivocation, via an explicit or implied comparison(comparatio)toGod ([9.1] I:834a (F-G), 834b (G-H), 837b (A,B,D)). In short, for thesecases the Anselmian view of reality and human knowledge of it seenearlier in Grosseteste’sOn Truthapplies without qualification.What is most interesting about these special cases is the kind ofknowledge they entail. Although inOn the UniverseWilliam speaksof words implicating the ‘magnificence or excellence’ of God (like‘being’, ‘good’, ‘true’, ‘power’ and ‘powerful’) it is evident from whathe says in his nearly contemporaneous treatiseOn the Soul (De anima)that he also has in mind a class of terms like ‘whole’, ‘part’, ‘equal’ and‘odd’ out of which are constructed the fundamental propositions ofrational argument. The latter are, William notes, what ‘the philosophers’called ‘axioms’(dignitates)or ‘first impressions’(primae impressiones),what he refers to as the self-evident principles of science(principiascientiarum nota per semetipsa)([9.1] II suppl.: 209b). They constitutedAristotle’s common principles of demonstration, of which the mostbasic were the rules of non-contradiction and exclusive alternation.Relying on the Neoplatonizing interpretation of Avicenna, William addsthat Aristotle posited a separate agent intellect—a higher intelligencehovering above human souls—to impress on the mind the intelligibleforms(signa vel formae intelligibiles)by which such terms were known.He insists, instead, that it is God himself, the authentic archetypal world,who supplies the mind with these forms through his spiritualillumination ([9.1] II suppl.: 211a-b).Substantial concession to Neoplatonizing concerns, this theory ofprincipal cognition was, none the less, an anomaly, a flashback to aworld-view fast disappearing in William’s and Grosseteste’s thought.In all other respects, they worked singlemindedly to tie their theoriesof knowledge ever more tightly to an ontology of absolutes in theperceived world. Indeed they thought they could lay out a taxonomyof cognition true to the principles of evidence and argumentation foundin Aristotle, rivalling his ability to account for everything withoutrecourse to a Neoplatonizing ideal in a world above. Nowhere is thismore apparent than in their explanation of the greatest degree ofcertitude to which knowledge could lay claim. Here both scholasticsfully accepted Aristotle’s views. Grosseteste’sCommentary on thePosterior Analyticswas in fact a principal conduit by whichAristotelianizing epistemology was made available to the medievaluniversity world.The key wasscientiaor science, the Latinate equivalent of Aristotle’sepistēmē,which constituted knowledge that could be regarded asabsolutely certain. As Grosseteste makes plain in hisCommentary,scientific knowledge is demonstrated knowledge: knowledge of the truthof a proposition that has been proved by means of syllogistic argument.What renders the syllogism scientific—that is, properly demonstrative—is that the middle term picks out the immutable, or necessary, causemaking the subject—whether it be a simple nature or a complex stateof affairs—what it is ([9.6] 99–100:16–27, 406:76–9, 407:92–3). Ofcourse all this has to be approached from the essentialist perspective ofAristotle, by which the reality of things was immutably determinedaccording to fixed natures, but given this essentialism, one could easilybelieve that a clear understanding of the nature yielded the appropriatemiddle. From there it was simply a matter of logic to fashion a fullyreasonable(propter quid)—and absolutely certain—defence of astatement of the truth ([9.6] 189:23–30).Naturally, any such demonstration of the truth of a statement—thedemonstrated conclusion—depended on knowledge of the premissesfrom which the demonstrative syllogism was drawn, and if there werenot to be an infinite regress in arguments for truth, there had to existsome premisses whose truth was evident without any syllogism at all.These were Aristotle’s principles of science, whose truth was graspedimmediately bynous,a non-discursive habit of mind Latinized asintellectusand translatable as something like prepositional intuition.Following Aristotle to the letter, Grosseteste explains that it is by meansof the two modes of cognition,intellectusandscientia,that all absolutelycertain knowledge is attained, the former differing from the latter ininvolving no argument (no syllogism or middle term) and constitutingthe epistemic basis upon which the latter must reside ([9.6] 406–7:76–89 and 98–9, 281:89–91). It is, he says, the undemonstrated knowledgeof first principles(prima principia),themselves the indemonstrablefoundation for all demonstration ([9.6] 103:92–3, 278:3–7, 407:91;and 281:91–2, 407:93–5). William, too, accepts Aristotle’sepistemological scheme, referring to the classic exposition of it in thePosterior Analyticsand directing his readers to its exemplary applicationin thePhysics([9.1] II suppl.: 210a).In so far as the formal elaboration of this science-orientedepistemology entailed the application of the rules of prepositional andsyllogistic logic, it had little bearing on ontology, but there was at leastone aspect of an Aristotelianized theory of science that raised questionsabout being and reality. Scientific truths were supposed to be immutable.For Grosseteste, that meant that they had somehow to be perpetualand incorruptible ([9.6] 139:89–95).One way to take this was simply to recognize that demonstrationsconsisted of propositions employing universal terms. The immutabilityof science was thereby reduced to the incorruptibility of universals, aquality easily accounted for with Grosseteste’s essentially terministtheory of the universal in itself. As he says in theCommentary,universalsare corrupted not in themselves(ex non se ipsis)but only in so far asthe singular entities in which they are instantiated(deferentia)passaway ([9.6] 141:145–9). The instantiating entities might be the wordsstanding for universal terms in actual utterances or the existingreferential base of such terms at any given time, but either way theuniversal itself as a term available for supposition—a logical entity—escapes the existential restraints of its real base. And just in case thisanswer is deemed insufficient, Grosseteste proposes another, focusingmore on the real referents themselves. The perpetuity of universals canbe saved even in a world of constant change because for all valid generalterms, there is always somewhere at least one real individual to serveas referent and thus ontological anchor. After all, even though somethings die away in winter, there is always summer somewhere on earthwhere objects of the same type can flourish ([9.6] 141:149–54).2Yet the immutability of science might also be taken to mean that thepropositions themselves, and not just their conditions of truth, had tobe perpetual. This demand was commonly made in the Neoplatonizingtraditions from which both Grosseteste and William drew, and inOnTruthGrosseteste presented a most Neoplatonizing way of satisfyingit. Faithful to the tradition, he there takes perpetuity to mean eternity,as with the eternity of God. It is, he explains, possible to account forimmutable truth in a world where no human utterances areincorruptible or unchanging so long as one concedes that it is legitimateto fall back on the eternal utterance propositions are given in God’smind ([9.3] 139–41). But such an account would have sat uneasily inthe Aristotelianizing context of theCommentary on the PosteriorAnalytics,and in fact Grosseteste neither mentions it nor raises thequestion of the immutability of propositions in that work.We must turn to William’s writings for a theory to fill the gap. InOn the Universehe states quite plainly that people commit a grievouserror when they try to explain the eternal verity of statements whichare always true by pointing to an eternal ontological base in the FirstTruth, God himself ([9.1] I: 793aA). Instead, it is possible to accountfor such truths without having recourse to any supratemporalconditions at all. One need merely take advantage of scholasticinnovations in prepositional logic. Drawing on a familiar definition ofprepositional truth (derived from Avicenna) as the accommodation ofspeech and reality(adaequatio orationis et rerum),William insists thatthe truth implicated in a true statement is nothing more than a relation.As such, it does not imply a reality beyond that of the related extremes:an utterance and its complex referent ([9.1] I: 795a (B-D)).Here is where the new logic is relevant, for the precise words Williamuses for utterance and referent(enunciatioandenunciabile)reflect theincreasing agreement among logicians that a true statement refers to atruth-bearing entity, what we would call the proposition, separate fromany referential conditions in the real world.3Thus, as William makesclear, neither extreme of the relation of truth has more than a tenuousconnection to real existence. Utterances are as fleeting as words orthoughts, and propositions(enunciabilia)are merely the logicalrepresentations of reality as it is or might be. This being so, truth, arelation that places no additional ontological burden on the extremesit relates, need have no greater existential presence than normalutterances or propositions, even if it is held to be immutable. Somethingcan be said always to be true without there having to exist at everymoment an utterance expressing the truth or an actual referential base([9.1] I: 795b-96a (D-E)). Prepositional truth is, William concludes,‘rational or logical’(veritas rationales sive logica)and thereby formallyindependent of the question of actual existence ([9.1] I: 796aE). Inshort, the perpetuity of immutable truth was not so much an ontologicalas a logical condition, having little to do with the eternity of God.There remained one kind of scientific truth particularly perplexingto Grosseteste just because his own attenuated account of theimmutability of science seemed inadequate to explain it. He hadpredicated the perpetuity of universals partially upon his confidencethat there was always somewhere at least one real instance of everygeneral term, but this was not the case for some of the truths of whatwe would call natural science. There are not always lunar eclipses,although we feel justified in making universal statements about them.Or, to shift attention from the term to the proposition, we say it isuniversally true that heavy objects fall, even though any heavy objectcan be prevented from doing so. Such truths, Grosseteste notes in theCommentary,while not absolutely necessary, are regular enough—inscholastic parlance, their complex referents occur with sufficientfrequency(frequenter evenientia)—to satisfy the demands of science([9.6] 264:119–22). Still, how can they be called immutable? Grossetesteoffers two explanations, but the most relevant for us speculates thatAristotle intended to account for the perpetuity of such truths byinsisting that their demonstrations specify the conditions under whichthey would be true ([9.6] 144–5:200–19). Framed in conditional ratherthan categorical terms, such truths become just as immutable as thoseof the more necessary sciences, for whenever the conditions are met,they are indeed always true. Grosseteste appears here to be anticipatingthe notion ofex suppositionedemonstration first fully elaborated laterin the century by Albert the Great and by means of which even Galileostill defended the epistemic force of natural science.4Aristotle, however, had also talked about experience; it was, as hesaid at the beginning of theMetaphysics,along with memory one ofthe fundamental sources of scientific knowledge. The same term hadconsiderable resonance for Grosseteste and William, and not only inways Aristotle might have intended. Grosseteste’s ideas about experiencehave especially attracted the attention of historians of science ever sinceCrombie insisted that it was here we should look to find the medievalorigins of the modern experimental method ([9.18] 1 and 10–11). Yetbefore accepting Crombie’s judgement, we must remember that thewords employed by thirteenth-century scholastics to talk about whatcan be loosely translated as ‘experience’ were varied, including mostprominentlyexperientiaandexperimentum,and it is not easy toascertain the precise meaning of any of them. Historians must notassume too readily that their use has anything to do with ourunderstanding of experimental method.There is, in fact, only one occasion where Grosseteste talks aboutexperientiain a way suggestive of what we most often mean by‘experiment’. The passage, in theCommentary on the PosteriorAnalytics,begins by stating the intention of sketching out a methodfor establishing what Grosseteste calls ‘experimental universalprinciples’(principia universalia experimentalia)(see [9.6] 214–15:252–71). In other words, he will propose an empirical way to certify someof the principles—that is, syllogistic premisses—to be used for scientificdemonstration. From the context it is clear that the principles in questionwill all belong to natural science, constituting truths that can be heldneither with the absolute certitude of the principles of logic andmathematics nor with the still evident certitude of statements in naturalscience about the essential natures of things, for instance, the definitionsof man or animal. Experimental principles are fundamental propositionsfor which there is no immediate or, in Aristotle’s terms, purely analyticalway to determine their truth.According to Grosseteste, the first inkling of the shape of these truthscomes to the mind after repeated sensory exposure to a sequence ofevents in the external world. For example, one might witness the eatingof scammony followed by the passing of red bile often enough to suspecta relation of cause and effect. The intellect then goes on to form theproposition, ‘Scammony purges red bile’, but it is not yet able to claimwith scientific certitude that the proposition is true. For this, it mustturn to experiment(convertere [se] ad experientiam). In the exampleunder consideration, one must feed scammony to a subject after havingcarefully removed all other agents that might purge red bile and thenwatch what happens. If one does this many times and the result is thatthe subject invariably passes red bile, then one is justified in holdingthe proposition about scammony and bile to be universally true.It is impossible not to interpret all this as an account of experimentin the modern sense of the word, the controlled verification of ahypothesis or, in Grosseteste’s terms, of a candidate for inclusion amongthe principles of science. Although there is no evidence that anyone inthe thirteenth century considered the practical possibilities of aprogramme of experimentation set upon this theoretical foundation,or saw in any such programme the potential for a reformation of thesciences as was to be attempted in the seventeenth century, it is clearthat at least Grosseteste appreciated the philosophical principle thatclassical experimenters would later employ to dramatic effect.Yet this use of the idea of experiment constitutes an exception to therule. For the most part, when thirteenth-century scholastics spoke ofexperientiaorexperimentumthey had something quite different inmind. Often the reference was to what Hackett advises us to callpersonal experience, very like what Aristotle meant by his classicmention ofexperimentain theMetaphysics. This is surely what Williamis thinking of with his numerous appeals to experience, combined withteaching(doctrina et experientia)as a source for scientific knowledge([9.1] II suppl.: 212a, 214a; [9.2] 95:54–64). He even directs the readerto the passage in theMetaphysicsfor clarification ([9.1] II suppl.: 216b).The cognitive process intended involved a complicated induction fromsensation, bringing the intellect by means of Aristotle’s logic of divisionto knowledge of one of the typical principles of natural science, suchas those defining essential natures like ‘dog’ and ‘man’. Grossetestehas the same noetic procedure of discovery in mind when in hisCommentaryhe talks about the induction of universal principles(universalia composita)from sensible data ([9.6] 406:67–72). Inductiveexperience of this sort was perfectly natural and commonplace, as isindicated by William’s contrasting it to infused knowledge of the sortthat Solomon received from God ([9.1] II suppl. 214a).There was, however, yet another, dramatically non-Aristotelianizingnotion one might have of the place of ‘experience’ in science, and thistoo appears in both Grosseteste’s and William’s thought. It was Williamwho gave it the greatest attention. In the part ofOn the Universeinvestigating the powers and operations of demons, he refers withconsiderable fascination to the ‘experimenters’(experimentatores),whoin their writings describe the marvellous works they can do to theastonishment of the uninitiated ([9.1] I: 1059a–60a). He calls thesewritings ‘books of experiments’(libri experimentorum),and it is clearthat by this term he does not mean the controlled testing of hypothesesbut rather the miraculous feats associated with magic(opera magica).Among the numerous examples he cites are fashioning a candle out ofwax and serpent skin which, when lit, can make a room strewn withdried grass appear to be filled with writhing snakes, creating the illusionof water or a river where none really exists, and neutralizing the powersof enchanters or magicians by exposing them to certain snakes, or toquicksilver inserted just the right way into a reed tube. Such marvelsand occult operations(occultae operationes et mirabilia)are, he adds,what physicians and natural philosophers are accustomed to callempirica,a term drawn from the lexicon of the medical arts ([9.1] I:929bA).According to William the ignorant gaze upon such works andattribute them erroneously to devilish powers, an error in which theyare encouraged by the fact that some philosophers refer to the art bywhich the marvels are arranged as necromancy. The truth is, instead,that the ‘experiments’ of which he speaks, for all their miraculousappearance, can be traced back to the forces with which God hasimbued his creation(virtutes a Creators inditae). In this case the forcesare deeply submerged, hidden to all but those trained to see them, butthey are still fully natural, and their manipulation should be attributedto ‘natural magic’(magia naturalis)([9.1] I: 69bD).Here William is mining an intellectual tradition of great antiquityand readily available to him and his scholarly contemporaries throughtranslations from Hebrew, Arabic and Greek. In this tradition, thewords ‘experiment’ and ‘experience’ evoke the illusory and theunexpected. According to William, the surprise and wonder are dueto the fact that all the phenomena making up ‘experience’ in thissense arise from hidden forces(virtutes occultae)lying behind naturalpowers with which we are more familiar ([9.1] I: 1060a (E,H)).Grosseteste, too, was acquainted with the tradition and refersrespectfully to theexperimentatores,although he includes in this classthose who simply have seen odd things and faraway places, like thenorth pole, and written down their experiences for us to share ([9.3]68). He also counts among the experimenters scholars of optics who‘experiment’ with lenses, the power of which to make far-away thingsseem near is itself wonderful(admirandum, mirabile)and therebypart of the marvellous world with which all experiment of this sort istied ([9.3] 41, 73–4).What must be kept in mind is that despite the suspicion and fearwith which the writings of this tradition were often viewed, bothWilliam and Grosseteste believed that, if correctly received, they werenot only benign but also a welcome addition to human knowledge.William insists that natural magic, when not pursued with vain curiosityor used to do evil, is not harmful and does no offence to God ([9.1] I:663bD). It constitutes, in fact, a legitimate part of natural science ([9.1]I: 69bD, 648aG). Those that know it, and perform the operations orexperiments it reveals, are calledmagi,that is, doers of great things(magna agentes),and the association of them with evil, as well as thecharge thatmagusmeans ‘evil-doer’(male agens),is simply uninformed([9.1] I: 1058bH). Grosseteste, too, understands that many associatethe wordmaguswith sorcerers(malefici),quoting Isidore to that effect,but he recognizes that others maintain that the truemagiare wise men,like the learned divines of ancient Persia ([9.5] 23:17–34). Williameven holds great expectations for the application of natural magic,asserting that it is not beyond magic’s powers to produce things neverbefore encountered on earth, including completely new animals ([9.1]I: 7aE). All that is wanting to see such things happen even in his ownday is the right knowledge and an abundance of the proper tools andsupplies ([9.1] I: 1058bH).This was not to deny that there was evil magic, too, or that someexperimenters and their experiments were malign and caught up withdevils. William was familiar with what he thought were truly execrablemagical books, like theSworn Book of Honorius (Liber sacratus),andhe admits that even some potentially useful pieces of occult literaturemight mislead, just as theOn the God of Gods (De deo deorum)attributed to Hermes(Mercurius)—whom he calls an Egyptianmagician—had encouraged him in his youth to believe that with littleeffort he could raise himself to prophetic splendours ([9.1] I: 70aF,1056a-b (H-E), 1060bF; cf. 78aF). Then, too, there was astrology, ascience related to magic, which William said should be fought withsword and fire, at least in so far as it was taken to imply the necessityof all events ([9.1] 785aC, 785bB, 929bA). Grosseteste was likewisewary of astrology, although perhaps somewhat more ambivalent. Inhis earlyOn the Liberal Artshe praises astronomy, clearly signifyingjudicial astrology, as most useful for the understanding and applicationof natural science ([9.3] 5–6). Yet in theHexaëmeron,from the early1230s, he sets the science of astral motion—astronomy—against thescience of judging from the stars—astrology—condemning any attemptto use the latter to bind the will ([9.5] 41:24–33). Later in the samework he warns Christians to have nothing to do with astrologers, ormathematici,and calls for their works to be burned ([9.5] 170:4–7,172:3–5).Even farther from Aristotle was an aspect of Grosseteste’s sciencemore deeply and authentically mathematical than astronomy orastrology. Again Crombie’s picture of the thirteenth century must berecalled, for it was he who drew attention to Grosseteste as a medievalsource for the modern orientation of science towards mathematics([9.18] 60, 132–4). At a level not central to Crombie’s view,Grosseteste’s interest in mathematics takes us back to Aristotle.Grosseteste draws on the Aristotelian notion of the subordination ofsome sciences to others that explain more fully the subject ofinvestigation and occasionally even supply demonstrative principles.He shows how it is common for scientific disciplines that investigateonly the simple why and wherefore of a subject—in Aristotle’s terms,pointing out only the fact(quia)—to stand in such subordination toother disciplines that can actually supply demonstrative reasons—again, in Aristotelian language, laying out the reasoned fact(propterquid)([9.6] 194:126–36). It is the various mathematical sciences thattypically take this subordinating role, and Grosseteste mentionsamong other cases the science of radiant lines and figures (what wewould call optics) subordinated to geometry, the science of harmonysubordinated to arithmetic, and the science of navigation toastronomy.Of greater interest to Crombie was a more ambitious theory inspiredby Neoplatonic currents originating with Plotinus and taken to be thekeystone of what is often called Grosseteste’s ‘metaphysics of light’.5Since most of what is attributed to this ‘metaphysics’ is not metaphysicalat all, Lindberg wisely advises us to refer to it as a ‘philosophy of light’([9.19] 95). Of its four parts as Lindberg sketches them out, it is whathe calls a ‘cosmogony of light’ (that concerns us here. In his treatiseOn Light (De luce)Grosseteste argues that light is the first corporealform—corporeity, itself—by which matter, on its own absolutely simpleand dimensionless, takes on extension or, as we would say, dimension.Light manages this through its quite special power of instantaneousself-diffusion in all directions from the point of origin, by which meansas first form it literally carries all matter along with it ([9.3] 51:10–52:9). This is the way the universe was generated by God’s commandat the beginning of time, the reverberations of light from central pointout to the limits of a spherical extreme, and then back and forth againand again, rarefying and condensing matter until it took the form ofthe nine celestial spheres and the elemental regions of the sublunarworld ([9.3] 52:17–21, 54:11–56:18). A cosmogony of this sort wouldseem to give light, and the mathematically-formulated optics by whichit is understood, pride of place in our understanding of nature. That is,at least, what Crombie assumed.Yet though Grosseteste must have been sensitive to themethodological implications of his cosmogony, it is instead a differentelement in his thought, the part of his ‘philosophy of light’ Lindbergcalls the ‘physics of light’, upon which he based his principal argumentfor the relevance of mathematics to natural philosophy. Extrapolatingnot only from Neoplatonism but also from the tradition of Arabicoptics, Grosseteste fashioned a universal theory of natural causationreferred to as the doctrine of the multiplication of species ([9.19] 97–8). The Neoplatonic element is laid out inOn Lines, Angles and Figures(De lineis angulis et figuris). According to this treatise, all natural agentswork by multiplying or transmitting their power(virtus)in the form ofspecies(species)or likenesses(similitudines)sent out into thesurrounding medium, whether sensory or inert ([9.3] 60:16–29). Thesignificant thing about this multiplication is that it occurs in conformityto the rules of luminous radiation laid out in the science of optics. AsbothOn LinesandOn the Nature of Place (De natura locorum)makeclear, any agent’s species or likenesses are induced in all directions fromthe point of origin along straight lines which are bent, just like lightrays, as they pass through media of contrasting density ([9.3] 60:14–15, 66:1–3). It is, therefore, possible to describe all natural causationby means of the geometrical principles of lines, angles and figuresestablished in optics ([9.3] 65:27–9).Here Grosseteste turns again to the notion of subordination. Thegeometric explanation of all natural causation offered by optics—andGrosseteste uses the medieval name,perspectiva—is, because of itsformal precision, also the most fundamental. It gives the ‘reasoned’(propter quid)account of what the natural philosopher(physicus)otherwise knows only as fact ([9.3] 72:12–13, also 60:15–16). Indeedit is legitimate to say that one cannot truly know natural philosophywithout recourse to the laws of optical science ([9.3] 59:27–60:1).Because of the way nature works, the science of natural philosophy issubordinate to optics, and therefore mathematics, to which optics itselfis subordinated, must be the primary explanatory tool of the naturalscientist.Taken together, William and Grosseteste bequeathed a richmetaphysical and epistemological heritage to the rest of the thirteenthcentury. They were the first to weave the lines of Aristotelianism,Neoplatonism and Arabic and Jewish mathematics and magic into atexture alluring enough to engage the imagination of scholars in thenew schools. From their fertile beginnings can be traced much of thescientific and philosophical achievement of the thirteenth century. Butjust as their own sources were varied, so the lines of inspiration trailingout from them into the rest of the century took several different paths.In so far as they sought to bring Neoplatonic traditions, especially inepistemology and noetics, into line with the logical and linguisticexpectations of Aristotelianizing analysis, they laid the foundationsfor what is often called the Neo-Augustinianism of Bonaventure andhis successors from the 1250s on. Equally important, however, wasthe debt owed to them by the more authentically Aristotelian currentthat emerged in the late 1240s with Albert the Great and continuedwith his even greater pupil, Thomas Aquinas.Yet the figure who most literally reproduced the scientific ideal seenin William and Grosseteste—or perhaps who most dramaticallyamplified their idiosyncrasies—was Roger Bacon. Born in Englandaround 1210, Bacon studied and taught arts at Oxford up to the late1230s, moving on then to Paris where he lectured in the arts facultyuntil about 1247. Around 1257 he joined the Franciscan order, adecision which terminated his scholarly career for a decade until PopeClement IV gave it new life with his request for Bacon’s ideas on thereformation of learning. Perhaps in part because of this sign of papalfavour, Bacon fell into an increasingly bitter conflict with his superiors,culminating in the condemnation of his work by the minister generalof his order in 1278 and his probable incarceration. Apparently freeagain but still tormented by his fate, he died in 1292 or shortlythereafter.6Like Grosseteste, whose lectures he may have attended while atOxford, Bacon placed mathematics at the foundation of naturalscience—perhaps, indeed, of science altogether. He was even moreinsistent on this score than his illustrious forebear. InThe Character ofthe Natural Sciences (Communia naturalium)he criticizes Aristotlefor neglecting mathematics and excoriates renowned scholars of hisday, among whom is certainly intended Albert the Great, for theirignorance of the subject ([9.10] 2:5, 11), reserving his praise in theOpus maiusand theOpus tertiumfor Grosseteste and the nearlyidolized Peter Peregrinus of Maricourt, whom Bacon considered themathematicizing prophets of his century ([9.8] I: 108; [9.7] 34–5). ForBacon—just as, he thought, for Grosseteste and the ancient sages anddivines—only by means of mathematics, the ‘door and key’ to fullknowledge, could the other sciences be grasped with absolute certitude([9.8] I: 97, 98, 107).His defence of this assertion is partly delivered in Grosseteste’sAristotelianizing language of the subordination of sciences, wherebymathematics supplies the reasoned explanation(per causam)ofphenomena that the natural sciences can describe only as fact(pereffectum)([9.8] I: 169). Of greater weight for him, however, is thedescription of physical reality that Grosseteste had used to justify thesubordination at the epistemic level, the doctrine of causation by thetransmission of species or similitudes. Bacon enthusiastically embracesGrosseteste’s view, embellishing it with a theoretical exactitude thatmade Bacon’s version the model exposition of the matter for the nextcentury and a half ([9.8] I: 111; [9.7] 37; [9.9] 2). He goes so far as todevote a whole treatise to the process, referring to it with the precisename by which it has since been known:On the Multiplication ofSpecies. Just as Grosseteste had argued inOn LinesandOn the Natureof Place,so Bacon reasons that, because the species by which all naturalcausality is achieved are generated in straight lines in exact replicationof the phenomenon of luminous radiation, the science of optics offersthe only universal means of accounting for all natural effects ([9.10] II:24:21–9; [9.8] I: 112, II: 31; [9.9] 90–4). This not only makes optics(perspectiva)the most special and very first of the natural sciences(prima specialis scientia)but also explains why natural phenomenacannot be truly understood without the power of mathematics ([9.10]II: 5:25–31; [9.8] I: 110).Yet it is what Bacon made of Grosseteste’s and William’s commentson experience or experiment for which he is best known, leading manyto view him as the forerunner of his seventeenth-century namesake,Francis Bacon. To Roger’s way of seeing things there is in fact a discreteexperimental science,scientia experimentalis,which is the most certainof all and certifier for the others ([9.10] II: 9:1–6). Despite its ostensibleunity, this science is composed of three parts, each playing a differentrole—prerogatives or dignities as Bacon calls them—and for us tounderstand the whole we have to recognize that three constituents donot tend precisely to the same end ([9.10] II: 9:9–12; [9.8] II: 172;[9.7] 43–4).According to its first role, experimental science certifies by experiencethe demonstrated conclusions of the other sciences ([9.8] II: 172–3).Here Bacon has recourse to his conviction, surely evolved from weakernotions found in both William and Grosseteste, that while scientificdemonstration in the Aristotelian sense can make known the truth,only experience removes all doubt ([9.8] I: 105–6, II: 167; [9.7] 297).7One might know by reasoned argument that fire burns, but only theexperience of a scorched finger teaches one to avoid the flame. It istempting to see in this a version of the theory of verification byexperimentation, as many who praise Bacon have done. There is, afterall, the precedent of Grosseteste with his example of testing the powerof scammony to purge bile. But in fact Bacon, who is aware of the sortof verification Grosseteste described, takes it as having nothing to dowith the ‘experiment’ he has in mind. Natural sciences often do, asGrosseteste realized, establish their principles by experiment or fromexperience; they then anchor their conclusions to the principles inAristotelian fashion by demonstrative argument. Such methods, Baconadmits, have a legitimate place at the foundation of demonstrativescience. Yet he wants his experimental science to go beyond Aristotleand bring the mind to adhere to conclusions, in contrast to principles,with the assent only experience, not argument, can induce ([9.8] II:172–3; [9.7] 43). Experience in this case is not the controlled testing ofa hypothesized principle but rather the empirical confirmation of analready proved conclusion. Bacon’s first prerogative is thus a use ofexperience unlike anything Aristotle, or William and Grosseteste, hadconceived, pointing to the growing prestige of singular perception inthe noetics and epistemology of the late thirteenth and fourteenthcenturies.The second and third roles of experimental science are, if anything,even more un-Aristotelianizing, although not so novel. With them wereturn to the traditional notions ofexperimentaso well represented inWilliam’s thought. By its second prerogative, experimental sciencereveals truths about the subject-matter of the other sciences, whichnone of them can prove or dare to claim as true. The emphasis here ison practical accomplishments that are both marvellous and strange,as, for example, the construction of an astrolabe that would revolvedaily on its own natural power, or a knowledge of how to use medicinesdramatically to prolong human life ([9.8] II: 202–4). Experimentalscience’s third prerogative is more awesome still, making known thingsnot even dreamed of in the rest of scientific discourse. It penetrates allthe way to the secrets of nature and surpasses judicial astrology, withwhich it seems to compete, by making firmer predictions about thefuture and doing far more miraculous works(opera admiranda,mirabilia opera)([9.8] II: 215; [9.7] 44). It is primarily by thisprerogative that experimental science commands all other sciences astheir mistress(domina),and it is here that its practical value is realizedin the extreme ([9.8] II: 221; [9.7] 46).By now Bacon is clearly navigating in the waters of magical art, asis surely betrayed by his claim that the third prerogative explores theoccult(opera occulta)([9.10] II: 9:11–12). Times have changed,however, and Bacon is far more squeamish than William was aboutbeing associated with anything labelled ‘magic’. He not only refusesto call any aspect of experimental science ‘magical’ but also insiststhat one of his science’s functions is to lay open the falsehood of themagical arts(magicae artes)([9.10] II: 9:21–6). Yet more than justfear of censure separates Bacon from William of Auvergne. He is, likeWilliam, willing to accept an art like astrology that is traditionallyassociated with magic, so long as it does not postulate the absolutenecessity of all events or resort to the power of demons or fraud toimpress its audience. He even gives acceptable astrologers the name of‘true mathematicians’(veri mathematici)in contrast to the ‘falsemathematician’(falsi mathematici)who dabble in magic ([9.8] I: 240–2). But Bacon’s vision of experimental science, for all its debt totraditional magic, aspires to more than marvel. It presumes to drawthe power of knowledge, especially scientific knowledge, into acampaign to transform the world. Indeed, the impetus behind most ofBacon’s later work is his desire to lay the cognitive foundations forthe reformation of human life. Such practical ideals are not foreign tothe magic of William’s mental landscape, but as distilled in Bacon’sexperimental science they savour for the first time of the ambitionand energy of the seventeenth century.NOTES1 For an analysis of the passage and an argument for what constituted Grosseteste’sown view, see Marrone [9.20] 166–78.2 How this sort of perpetuity might suffice for a Christian like Grosseteste, whoheld the world to have a temporal beginning and end, is argued in Marrone[9.20] 234–9.3 See G.Nuchelmans,Theories of the Proposition,Amsterdam, North Holland,1973, esp. ch. 10.4 See W.A.Wallace, ‘Aristotle and Galileo: The uses of hypothesis(suppositio)inscientific reasoning’, in D.J.O’Meara (ed.)Studies in Aristotle,Washington, DC,Catholic University, 1981, pp. 47–77.5 See Baur [9.29] and [9.30] 77–92; and the origin of the term(Lichtmetaphysik)in C.Baeumker,Witelo, ein Philosoph und Naturforscher des XIII. Jahrhunderts,Münster, Aschendorff, 1908, pp. 257–422.6 For the dates of Bacon’s life, see Hackett [9.40], especially pp. 46–7.7 Marrone ([9.20] 36) points out William’s assertion of the mildly obscurativeeffect of demonstration, echoed (p. 223) by Grosseteste’s preference for principalcognition. A bias for particular experience appears inOn the Nature of Place([9.3] 66).BIBLIOGRAPHYOriginal Language EditionsWilliam of Auvergne9.1Opera omnia,2 vols, Paris and Orleans, Hotot, 1674; repr. in 2 vols, Frankfurton Main, Minerva, 1963.9.2 Switalksi, B. (ed.)De trinitate,Toronto, Pontifical Institute of Mediaeval Studies,1976.Robert Grosseteste9.3 Baur, L. (ed.)Die philosophischen Werke des Robert Grosseteste, Bischofs vonLincoln,Münster, Aschendorff, 1912.9.4 Dales, R.C. (ed.)Commentarius in VIII libros Physicorum Aristotelis,Boulder,Colo., University of Colorado Press, 1963.9.5 Dales, R.C. and Gieben, S. (eds)Hexaëmeron,London, British Academy, 1982.9.6 Rossi, P. 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