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 Bacon Steven Marrone By the third decade of the thirteenth century there emerge the first signs of a new metaphysics. Alongside Neoplatonizing idealism we now see attempts to lay greater emphasis on the ontological density of the created world and to structure reality without resorting to the terms of a relation to the divine ideal. The ensuing philosophical reassessment was more systematic, more technically precise and more self-conscious than anything the medieval West had seen before. Given the catalysing role played by logic, it was only natural that much of this programme was carried out within the confines of an attempt to explain knowledge. For the early thirteenth century, metaphysics and epistemology went hand in hand. The two figures who did the most to promote the new metaphysics, as well as a profoundly Aristotelianizing campaign to establish the criteria for knowledge, were masters whose important work was done between 1220 and 1235 in the schools of theology at the new universities. Robert Grosseteste (d. 1253) was born in England probably before 1170, studied and taught the arts curriculum in provincial schools and perhaps at Paris and Oxford, and began to lecture on theology at Oxford after 1214 but no later than 1225. His activity as a philosopher effectively ended with his appointment as bishop of Lincoln in 1235. William of Auvergne (d. 1249) was born in France around 1180, went to Paris to study, and began teaching there first in arts and then by the 1220s in theology. He was named bishop of Paris in 1228, although he continued to write about philosophical matters for some years thereafter. In Grosseteste’s earlier works there is, to be sure, no hint of the new attitude. His treatise On Truth (De veritate) offers an ontology still firmly grounded in the Neoplatonic world-view. Quoting Anselm, he defines truth as a kind of ontological obligation: the correctness (rectitudo) of objective things ([9.3] 135:3–6). Such obligation is met inasmuch as things conform to God’s eternal word, or, more specifically, to an idea or reason (ratio, ratio aeterna) in God’s mind, eternally representing 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’s noetics. Drawing on an image commonplace in Latin Christian discourse since the time of Augustine, he explains that the intellect can attain the truth, its proper object, only in an intelligible light shining from God himself ([9.3] 137:2–4). The image surely serves in part as shorthand for a more complicated epistemic argument. If objective truth is a quality arising out of the conformity between an object and its 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). It is clear, however, that Grosseteste also takes quite literally the existence of a higher light in which truth must be known. He goes on to say that just as the eye can see a coloured body only when it is bathed in visible light, so the mind can know a thing in its truth only if the divine light is shining on it ([9.3] 137:19–25). Yet when Grosseteste came to analysing Aristotle’s ideas about true knowledge, a dramatically different vision took shape in his mind. In the Commentary on the Posterior Analytics, his most mature account of the relation between intellect and objective reality, dating probably from 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 to On Truth, where for one uncharacteristic moment Grosseteste had recalled Augustine’s definition of truth as ‘what a thing is’ (id, quod est), adding, in violation of traditional Boethian language, that this was the same as its being (esse) ([9.3] 141:13–15). But what was merely an interesting aside in the early work now takes centre stage. Grosseteste in the Aristotle commentary is prepared to argue that the truth of a thing is exclusively its substantial presence in external reality. Another word for this is ‘essence’, taken as a thing’s formal core shorn of all the accidents of material circumstance (puritas essentiae suae non cum admixtione conditionum materialium ([9.6] 406–7:82–4). So patent a breach of Neoplatonizing principles appealed to William of Auvergne as well, for in his treatise On the Universe (De universo) from the early 1230s he similarly defines the objective truth of a thing as its ‘substance, or essence, 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 attack Neoplatonizing ontology and the conditions of knowledge it entailed. Referring to Plato and the Timaeus, William concedes in On the Universe that it is correct to posit an archetypal world of exemplary ideals (exemplaria) of which things in the perceived world are imitations (exempla), providing one locates the exemplary world in the mind of God. 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 an object’s truth as its being or substance, the truth of something in the world 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 the reference of simple terms. Words such as ‘earth’, ‘fire’, ‘water’ and ‘air’ refer immediately to simple substances in the world and imply no comparison or reference to the Creator ([9.1] I: 835aB). A Neoplatonizing theory of truth—like that we have seen in Grosseteste’s On Truth—is both semantically and ontologically misleading. The Grosseteste of the Commentary on the Posterior Analytics agreed. A long, often misinterpreted passage outlines five sorts of object that might serve as immediate referent for terms of universal predication ([9.6] 139–41:99–145). The first are the eternal reasons (rationes) in God, ‘what Plato called ideas or the archetypal world’; the second are exemplary forms impressed by God on the minds of angels; the third are the causal reasons (rationes causales) of earthly things residing in the celestial spheres; the fourth, the inherent forms of real things themselves, 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 that Aristotle explained the predication of kinds and types (genera et species), and it is clear from what he says throughout the work that he accepts this as the norm for human knowledge in the world.1 Echoing William, he claims that Plato’s kinds and types—separate substances in an archetypal 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, William and Grosseteste shared an ontology of essence quite unlike anything Aristotle had in mind. William rejects the authentically Aristotelian position of Boethius whereby specific essences are individuated by the accidents of their particular—or material—instantiation ([9.1] I: 802a (E-F)). Instead he maintains that individuals are both fully particular and fully specific—that is to say, general—in their essence, which was, for him, their substance as well. Indeed, he insists that the numerical distinction of individuals of the same species can be reduced to what he calls an ‘essential difference’ (differentia essentialis): the fact that the essence of this thing is not precisely the essence of that ([9.1] I:858b–59a (G-A)). Recognizing the awkwardness of his language, he hastens to add that the difference does not amount to a dissimilitude (dissimilitudo), which might sever the unity of the specific type, but should technically be referred to as a diversity (diversitas) among particulars ([9.1] I:802aG). Grosseteste, too, held to the 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, nowhere more loyally than among Franciscans of the so-called Augustinian school, and provided the impetus for Scotus’ famous theory of the formal distinction. A notion of essence as of itself fully individualized naturally complicated the explanation of universal predication, which by the terms of William’s and Grosseteste’s semantics entailed direct reference to the very instantiated essences of which individuals were comprised. William never addressed the matter, but Grosseteste tried his hand at a solution that appears inspired by the terminist logic of his day. According to the Commentary on the Posterior Analytics, although universal predication cannot be reduced to an ontological configuration exactly the same as that of singularity, it must be founded on one that is not entirely different ([9.6] 245:127–34). The notion of essence as simultaneously 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 of many singulars and referring to them all—this is because the universal taken in itself (universale secundum se) is neither one nor many (nec unum nec multa) but somehow capable of being construed as both. In Grosseteste’s words, it ‘falls to’ (accidit) the universal, most probably through the agency of the intellect, to be one thing while representing many ([9.6] 244:110–14). Certainly Grosseteste had in mind here the logician’s understanding of the supposition of terms, by which linguistic markers that in themselves could signify either the singular or general aspect of an essence—words like ‘horse’ or ‘man’—took on either universal or particular reference according to the demands of the propositions in which they were employed. Universals, in short, were terms: words denoting essence used for the purposes of universal predication (see [9.20] 185–7). The ambiguity of the term before supposition—of the ‘universal in itself’—simply mirrored the fact that it signified an essence that was also in itself both singular and general. By now we have reached an ontology and a semantics almost anticipating the nominalism of the fourteenth century. There was, however, at least for William still room for Neoplatonizing views. As he explains in On the Universe, while most words by which we describe created things refer directly to substances in the world, there are some that point more immediately to God and divine attributes. The reason is that the objective truth for which such words stand lies more precisely in God than in anything in the created world. When these words are used in discourse they consequently signify a divine object most properly—which is to say, univocally—and a created object only by equivocation, via an explicit or implied comparison (comparatio) to God ([9.1] I:834a (F-G), 834b (G-H), 837b (A,B,D)). In short, for these cases the Anselmian view of reality and human knowledge of it seen earlier in Grosseteste’s On Truth applies without qualification. What is most interesting about these special cases is the kind of knowledge they entail. Although in On the Universe William speaks of words implicating the ‘magnificence or excellence’ of God (like ‘being’, ‘good’, ‘true’, ‘power’ and ‘powerful’) it is evident from what he says in his nearly contemporaneous treatise On 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 of rational 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 (principia scientiarum nota per semetipsa) ([9.1] II suppl.: 209b). They constituted Aristotle’s common principles of demonstration, of which the most basic were the rules of non-contradiction and exclusive alternation. Relying on the Neoplatonizing interpretation of Avicenna, William adds that Aristotle posited a separate agent intellect—a higher intelligence hovering above human souls—to impress on the mind the intelligible forms (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 spiritual illumination ([9.1] II suppl.: 211a-b). Substantial concession to Neoplatonizing concerns, this theory of principal cognition was, none the less, an anomaly, a flashback to a world-view fast disappearing in William’s and Grosseteste’s thought. In all other respects, they worked singlemindedly to tie their theories of knowledge ever more tightly to an ontology of absolutes in the perceived world. Indeed they thought they could lay out a taxonomy of cognition true to the principles of evidence and argumentation found in Aristotle, rivalling his ability to account for everything without recourse to a Neoplatonizing ideal in a world above. Nowhere is this more apparent than in their explanation of the greatest degree of certitude to which knowledge could lay claim. Here both scholastics fully accepted Aristotle’s views. Grosseteste’s Commentary on the Posterior Analytics was in fact a principal conduit by which Aristotelianizing epistemology was made available to the medieval university world. The key was scientia or science, the Latinate equivalent of Aristotle’s epistēmē, which constituted knowledge that could be regarded as absolutely certain. As Grosseteste makes plain in his Commentary, scientific knowledge is demonstrated knowledge: knowledge of the truth of 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, cause making the subject—whether it be a simple nature or a complex state of affairs—what it is ([9.6] 99–100:16–27, 406:76–9, 407:92–3). Of course all this has to be approached from the essentialist perspective of Aristotle, by which the reality of things was immutably determined according to fixed natures, but given this essentialism, one could easily believe that a clear understanding of the nature yielded the appropriate middle. From there it was simply a matter of logic to fashion a fully reasonable (propter quid)—and absolutely certain—defence of a statement of the truth ([9.6] 189:23–30). Naturally, any such demonstration of the truth of a statement—the demonstrated conclusion—depended on knowledge of the premisses from which the demonstrative syllogism was drawn, and if there were not to be an infinite regress in arguments for truth, there had to exist some premisses whose truth was evident without any syllogism at all. These were Aristotle’s principles of science, whose truth was grasped immediately by nous, a non-discursive habit of mind Latinized as intellectus and translatable as something like prepositional intuition. Following Aristotle to the letter, Grosseteste explains that it is by means of the two modes of cognition, intellectus and scientia, that all absolutely certain knowledge is attained, the former differing from the latter in involving no argument (no syllogism or middle term) and constituting the 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 knowledge of first principles (prima principia), themselves the indemonstrable foundation for all demonstration ([9.6] 103:92–3, 278:3–7, 407:91; and 281:91–2, 407:93–5). William, too, accepts Aristotle’s epistemological scheme, referring to the classic exposition of it in the Posterior Analytics and directing his readers to its exemplary application in the Physics ([9.1] II suppl.: 210a). In so far as the formal elaboration of this science-oriented epistemology entailed the application of the rules of prepositional and syllogistic logic, it had little bearing on ontology, but there was at least one aspect of an Aristotelianized theory of science that raised questions about being and reality. Scientific truths were supposed to be immutable. For Grosseteste, that meant that they had somehow to be perpetual and incorruptible ([9.6] 139:89–95). One way to take this was simply to recognize that demonstrations consisted of propositions employing universal terms. The immutability of science was thereby reduced to the incorruptibility of universals, a quality easily accounted for with Grosseteste’s essentially terminist theory of the universal in itself. As he says in the Commentary, universals are corrupted not in themselves (ex non se ipsis) but only in so far as the singular entities in which they are instantiated (deferentia) pass away ([9.6] 141:145–9). The instantiating entities might be the words standing for universal terms in actual utterances or the existing referential base of such terms at any given time, but either way the universal itself as a term available for supposition—a logical entity— escapes the existential restraints of its real base. And just in case this answer is deemed insufficient, Grosseteste proposes another, focusing more on the real referents themselves. The perpetuity of universals can be saved even in a world of constant change because for all valid general terms, there is always somewhere at least one real individual to serve as referent and thus ontological anchor. After all, even though some things die away in winter, there is always summer somewhere on earth where objects of the same type can flourish ([9.6] 141:149–54).2 Yet the immutability of science might also be taken to mean that the propositions themselves, and not just their conditions of truth, had to be perpetual. This demand was commonly made in the Neoplatonizing traditions from which both Grosseteste and William drew, and in On Truth Grosseteste presented a most Neoplatonizing way of satisfying it. Faithful to the tradition, he there takes perpetuity to mean eternity, as with the eternity of God. It is, he explains, possible to account for immutable truth in a world where no human utterances are incorruptible or unchanging so long as one concedes that it is legitimate to fall back on the eternal utterance propositions are given in God’s mind ([9.3] 139–41). But such an account would have sat uneasily in the Aristotelianizing context of the Commentary on the Posterior Analytics, and in fact Grosseteste neither mentions it nor raises the question of the immutability of propositions in that work. We must turn to William’s writings for a theory to fill the gap. In On the Universe he states quite plainly that people commit a grievous error when they try to explain the eternal verity of statements which are always true by pointing to an eternal ontological base in the First Truth, God himself ([9.1] I: 793aA). Instead, it is possible to account for such truths without having recourse to any supratemporal conditions at all. One need merely take advantage of scholastic innovations in prepositional logic. Drawing on a familiar definition of prepositional truth (derived from Avicenna) as the accommodation of speech and reality (adaequatio orationis et rerum), William insists that the 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 William uses for utterance and referent (enunciatio and enunciabile) reflect the increasing agreement among logicians that a true statement refers to a truth-bearing entity, what we would call the proposition, separate from any referential conditions in the real world.3 Thus, as William makes clear, neither extreme of the relation of truth has more than a tenuous connection to real existence. Utterances are as fleeting as words or thoughts, and propositions (enunciabilia) are merely the logical representations of reality as it is or might be. This being so, truth, a relation that places no additional ontological burden on the extremes it relates, need have no greater existential presence than normal utterances or propositions, even if it is held to be immutable. Something can be said always to be true without there having to exist at every moment 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 formally independent of the question of actual existence ([9.1] I: 796aE). In short, the perpetuity of immutable truth was not so much an ontological as a logical condition, having little to do with the eternity of God. There remained one kind of scientific truth particularly perplexing to Grosseteste just because his own attenuated account of the immutability of science seemed inadequate to explain it. He had predicated the perpetuity of universals partially upon his confidence that there was always somewhere at least one real instance of every general term, but this was not the case for some of the truths of what we 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 is universally true that heavy objects fall, even though any heavy object can be prevented from doing so. Such truths, Grosseteste notes in the Commentary, while not absolutely necessary, are regular enough—in scholastic parlance, their complex referents occur with sufficient frequency (frequenter evenientia)—to satisfy the demands of science ([9.6] 264:119–22). Still, how can they be called immutable? Grosseteste offers two explanations, but the most relevant for us speculates that Aristotle intended to account for the perpetuity of such truths by insisting that their demonstrations specify the conditions under which they would be true ([9.6] 144–5:200–19). Framed in conditional rather than categorical terms, such truths become just as immutable as those of the more necessary sciences, for whenever the conditions are met, they are indeed always true. Grosseteste appears here to be anticipating the notion of ex suppositione demonstration first fully elaborated later in the century by Albert the Great and by means of which even Galileo still defended the epistemic force of natural science.4 Aristotle, however, had also talked about experience; it was, as he said at the beginning of the Metaphysics, along with memory one of the fundamental sources of scientific knowledge. The same term had considerable resonance for Grosseteste and William, and not only in ways Aristotle might have intended. Grosseteste’s ideas about experience have especially attracted the attention of historians of science ever since Crombie insisted that it was here we should look to find the medieval origins of the modern experimental method ([9.18] 1 and 10–11). Yet before accepting Crombie’s judgement, we must remember that the words employed by thirteenth-century scholastics to talk about what can be loosely translated as ‘experience’ were varied, including most prominently experientia and experimentum, and it is not easy to ascertain the precise meaning of any of them. Historians must not assume too readily that their use has anything to do with our understanding of experimental method. There is, in fact, only one occasion where Grosseteste talks about experientia in a way suggestive of what we most often mean by ‘experiment’. The passage, in the Commentary on the Posterior Analytics, begins by stating the intention of sketching out a method for establishing what Grosseteste calls ‘experimental universal principles’ (principia universalia experimentalia) (see [9.6] 214–15:252– 71). In other words, he will propose an empirical way to certify some of the principles—that is, syllogistic premisses—to be used for scientific demonstration. From the context it is clear that the principles in question will all belong to natural science, constituting truths that can be held neither with the absolute certitude of the principles of logic and mathematics nor with the still evident certitude of statements in natural science about the essential natures of things, for instance, the definitions of man or animal. Experimental principles are fundamental propositions for which there is no immediate or, in Aristotle’s terms, purely analytical way to determine their truth. According to Grosseteste, the first inkling of the shape of these truths comes to the mind after repeated sensory exposure to a sequence of events in the external world. For example, one might witness the eating of scammony followed by the passing of red bile often enough to suspect a relation of cause and effect. The intellect then goes on to form the proposition, ‘Scammony purges red bile’, but it is not yet able to claim with scientific certitude that the proposition is true. For this, it must turn to experiment (convertere [se] ad experientiam). In the example under consideration, one must feed scammony to a subject after having carefully removed all other agents that might purge red bile and then watch what happens. If one does this many times and the result is that the subject invariably passes red bile, then one is justified in holding the proposition about scammony and bile to be universally true. It is impossible not to interpret all this as an account of experiment in the modern sense of the word, the controlled verification of a hypothesis or, in Grosseteste’s terms, of a candidate for inclusion among the principles of science. Although there is no evidence that anyone in the thirteenth century considered the practical possibilities of a programme of experimentation set upon this theoretical foundation, or saw in any such programme the potential for a reformation of the sciences as was to be attempted in the seventeenth century, it is clear that at least Grosseteste appreciated the philosophical principle that classical experimenters would later employ to dramatic effect. Yet this use of the idea of experiment constitutes an exception to the rule. For the most part, when thirteenth-century scholastics spoke of experientia or experimentum they had something quite different in mind. Often the reference was to what Hackett advises us to call personal experience, very like what Aristotle meant by his classic mention of experimenta in the Metaphysics. This is surely what William is thinking of with his numerous appeals to experience, combined with teaching (doctrina et experientia) as a source for scientific knowledge ([9.1] II suppl.: 212a, 214a; [9.2] 95:54–64). He even directs the reader to the passage in the Metaphysics for clarification ([9.1] II suppl.: 216b). The cognitive process intended involved a complicated induction from sensation, bringing the intellect by means of Aristotle’s logic of division to knowledge of one of the typical principles of natural science, such as those defining essential natures like ‘dog’ and ‘man’. Grosseteste has the same noetic procedure of discovery in mind when in his Commentary he talks about the induction of universal principles (universalia composita) from sensible data ([9.6] 406:67–72). Inductive experience of this sort was perfectly natural and commonplace, as is indicated by William’s contrasting it to infused knowledge of the sort that Solomon received from God ([9.1] II suppl. 214a). There was, however, yet another, dramatically non-Aristotelianizing notion one might have of the place of ‘experience’ in science, and this too appears in both Grosseteste’s and William’s thought. It was William who gave it the greatest attention. In the part of On the Universe investigating the powers and operations of demons, he refers with considerable fascination to the ‘experimenters’ (experimentatores), who in their writings describe the marvellous works they can do to the astonishment of the uninitiated ([9.1] I: 1059a–60a). He calls these writings ‘books of experiments’ (libri experimentorum), and it is clear that by this term he does not mean the controlled testing of hypotheses but rather the miraculous feats associated with magic (opera magica). Among the numerous examples he cites are fashioning a candle out of wax and serpent skin which, when lit, can make a room strewn with dried grass appear to be filled with writhing snakes, creating the illusion of water or a river where none really exists, and neutralizing the powers of enchanters or magicians by exposing them to certain snakes, or to quicksilver inserted just the right way into a reed tube. Such marvels and occult operations (occultae operationes et mirabilia) are, he adds, what physicians and natural philosophers are accustomed to call empirica, a term drawn from the lexicon of the medical arts ([9.1] I: 929bA). According to William the ignorant gaze upon such works and attribute them erroneously to devilish powers, an error in which they are encouraged by the fact that some philosophers refer to the art by which the marvels are arranged as necromancy. The truth is, instead, that the ‘experiments’ of which he speaks, for all their miraculous appearance, can be traced back to the forces with which God has imbued his creation (virtutes a Creators inditae). In this case the forces are deeply submerged, hidden to all but those trained to see them, but they are still fully natural, and their manipulation should be attributed to ‘natural magic’ (magia naturalis) ([9.1] I: 69bD). Here William is mining an intellectual tradition of great antiquity and readily available to him and his scholarly contemporaries through translations from Hebrew, Arabic and Greek. In this tradition, the words ‘experiment’ and ‘experience’ evoke the illusory and the unexpected. According to William, the surprise and wonder are due to the fact that all the phenomena making up ‘experience’ in this sense arise from hidden forces (virtutes occultae) lying behind natural powers with which we are more familiar ([9.1] I: 1060a (E,H)). Grosseteste, too, was acquainted with the tradition and refers respectfully to the experimentatores, although he includes in this class those who simply have seen odd things and faraway places, like the north 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 things seem near is itself wonderful (admirandum, mirabile) and thereby part of the marvellous world with which all experiment of this sort is tied ([9.3] 41, 73–4). What must be kept in mind is that despite the suspicion and fear with which the writings of this tradition were often viewed, both William and Grosseteste believed that, if correctly received, they were not only benign but also a welcome addition to human knowledge. William insists that natural magic, when not pursued with vain curiosity or 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 or experiments it reveals, are called magi, that is, doers of great things (magna agentes), and the association of them with evil, as well as the charge that magus means ‘evil-doer’ (male agens), is simply uninformed ([9.1] I: 1058bH). Grosseteste, too, understands that many associate the word magus with sorcerers (malefici), quoting Isidore to that effect, but he recognizes that others maintain that the true magi are wise men, like the learned divines of ancient Persia ([9.5] 23:17–34). William even holds great expectations for the application of natural magic, asserting that it is not beyond magic’s powers to produce things never before encountered on earth, including completely new animals ([9.1] I: 7aE). All that is wanting to see such things happen even in his own day is the right knowledge and an abundance of the proper tools and supplies ([9.1] I: 1058bH). This was not to deny that there was evil magic, too, or that some experimenters and their experiments were malign and caught up with devils. William was familiar with what he thought were truly execrable magical books, like the Sworn Book of Honorius (Liber sacratus), and he admits that even some potentially useful pieces of occult literature might mislead, just as the On the God of Gods (De deo deorum) attributed to Hermes (Mercurius)—whom he calls an Egyptian magician—had encouraged him in his youth to believe that with little effort he could raise himself to prophetic splendours ([9.1] I: 70aF, 1056a-b (H-E), 1060bF; cf. 78aF). Then, too, there was astrology, a science related to magic, which William said should be fought with sword and fire, at least in so far as it was taken to imply the necessity of all events ([9.1] 785aC, 785bB, 929bA). Grosseteste was likewise wary of astrology, although perhaps somewhat more ambivalent. In his early On the Liberal Arts he praises astronomy, clearly signifying judicial astrology, as most useful for the understanding and application of natural science ([9.3] 5–6). Yet in the Hexaëmeron, from the early 1230s, he sets the science of astral motion—astronomy—against the science of judging from the stars—astrology—condemning any attempt to use the latter to bind the will ([9.5] 41:24–33). Later in the same work he warns Christians to have nothing to do with astrologers, or mathematici, 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 science more deeply and authentically mathematical than astronomy or astrology. Again Crombie’s picture of the thirteenth century must be recalled, for it was he who drew attention to Grosseteste as a medieval source 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 of some sciences to others that explain more fully the subject of investigation and occasionally even supply demonstrative principles. He shows how it is common for scientific disciplines that investigate only the simple why and wherefore of a subject—in Aristotle’s terms, pointing out only the fact (quia)—to stand in such subordination to other disciplines that can actually supply demonstrative reasons— again, in Aristotelian language, laying out the reasoned fact (propter quid) ([9.6] 194:126–36). It is the various mathematical sciences that typically take this subordinating role, and Grosseteste mentions among other cases the science of radiant lines and figures (what we would call optics) subordinated to geometry, the science of harmony subordinated to arithmetic, and the science of navigation to astronomy. Of greater interest to Crombie was a more ambitious theory inspired by Neoplatonic currents originating with Plotinus and taken to be the keystone of what is often called Grosseteste’s ‘metaphysics of light’.5 Since most of what is attributed to this ‘metaphysics’ is not metaphysical at 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 what he calls a ‘cosmogony of light’ (that concerns us here. In his treatise On Light (De luce) Grosseteste argues that light is the first corporeal form—corporeity, itself—by which matter, on its own absolutely simple and dimensionless, takes on extension or, as we would say, dimension. Light manages this through its quite special power of instantaneous self-diffusion in all directions from the point of origin, by which means as 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 command at the beginning of time, the reverberations of light from central point out to the limits of a spherical extreme, and then back and forth again and again, rarefying and condensing matter until it took the form of the nine celestial spheres and the elemental regions of the sublunar world ([9.3] 52:17–21, 54:11–56:18). A cosmogony of this sort would seem to give light, and the mathematically-formulated optics by which it 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 the methodological implications of his cosmogony, it is instead a different element in his thought, the part of his ‘philosophy of light’ Lindberg calls the ‘physics of light’, upon which he based his principal argument for the relevance of mathematics to natural philosophy. Extrapolating not only from Neoplatonism but also from the tradition of Arabic optics, Grosseteste fashioned a universal theory of natural causation referred to as the doctrine of the multiplication of species ([9.19] 97– 8). The Neoplatonic element is laid out in On Lines, Angles and Figures (De lineis angulis et figuris). According to this treatise, all natural agents work by multiplying or transmitting their power (virtus) in the form of species (species) or likenesses (similitudines) sent out into the surrounding medium, whether sensory or inert ([9.3] 60:16–29). The significant thing about this multiplication is that it occurs in conformity to the rules of luminous radiation laid out in the science of optics. As both On Lines and On the Nature of Place (De natura locorum) make clear, any agent’s species or likenesses are induced in all directions from the point of origin along straight lines which are bent, just like light rays, as they pass through media of contrasting density ([9.3] 60:14– 15, 66:1–3). It is, therefore, possible to describe all natural causation by means of the geometrical principles of lines, angles and figures established in optics ([9.3] 65:27–9). Here Grosseteste turns again to the notion of subordination. The geometric explanation of all natural causation offered by optics—and Grosseteste uses the medieval name, perspectiva—is, because of its formal 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). Indeed it is legitimate to say that one cannot truly know natural philosophy without recourse to the laws of optical science ([9.3] 59:27–60:1). Because of the way nature works, the science of natural philosophy is subordinate to optics, and therefore mathematics, to which optics itself is subordinated, must be the primary explanatory tool of the natural scientist. Taken together, William and Grosseteste bequeathed a rich metaphysical and epistemological heritage to the rest of the thirteenth century. They were the first to weave the lines of Aristotelianism, Neoplatonism and Arabic and Jewish mathematics and magic into a texture alluring enough to engage the imagination of scholars in the new schools. From their fertile beginnings can be traced much of the scientific and philosophical achievement of the thirteenth century. But just as their own sources were varied, so the lines of inspiration trailing out from them into the rest of the century took several different paths. In so far as they sought to bring Neoplatonic traditions, especially in epistemology and noetics, into line with the logical and linguistic expectations of Aristotelianizing analysis, they laid the foundations for what is often called the Neo-Augustinianism of Bonaventure and his successors from the 1250s on. Equally important, however, was the debt owed to them by the more authentically Aristotelian current that emerged in the late 1240s with Albert the Great and continued with his even greater pupil, Thomas Aquinas. Yet the figure who most literally reproduced the scientific ideal seen in William and Grosseteste—or perhaps who most dramatically amplified their idiosyncrasies—was Roger Bacon. Born in England around 1210, Bacon studied and taught arts at Oxford up to the late 1230s, moving on then to Paris where he lectured in the arts faculty until about 1247. Around 1257 he joined the Franciscan order, a decision which terminated his scholarly career for a decade until Pope Clement IV gave it new life with his request for Bacon’s ideas on the reformation of learning. Perhaps in part because of this sign of papal favour, Bacon fell into an increasingly bitter conflict with his superiors, culminating in the condemnation of his work by the minister general of his order in 1278 and his probable incarceration. Apparently free again but still tormented by his fate, he died in 1292 or shortly thereafter.6 Like Grosseteste, whose lectures he may have attended while at Oxford, Bacon placed mathematics at the foundation of natural science—perhaps, indeed, of science altogether. He was even more insistent on this score than his illustrious forebear. In The Character of the Natural Sciences (Communia naturalium) he criticizes Aristotle for neglecting mathematics and excoriates renowned scholars of his day, among whom is certainly intended Albert the Great, for their ignorance of the subject ([9.10] 2:5, 11), reserving his praise in the Opus maius and the Opus tertium for Grosseteste and the nearly idolized Peter Peregrinus of Maricourt, whom Bacon considered the mathematicizing prophets of his century ([9.8] I: 108; [9.7] 34–5). For Bacon—just as, he thought, for Grosseteste and the ancient sages and divines—only by means of mathematics, the ‘door and key’ to full knowledge, 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’s Aristotelianizing language of the subordination of sciences, whereby mathematics supplies the reasoned explanation (per causam) of phenomena that the natural sciences can describe only as fact (per effectum) ([9.8] I: 169). Of greater weight for him, however, is the description of physical reality that Grosseteste had used to justify the subordination at the epistemic level, the doctrine of causation by the transmission of species or similitudes. Bacon enthusiastically embraces Grosseteste’s view, embellishing it with a theoretical exactitude that made Bacon’s version the model exposition of the matter for the next century and a half ([9.8] I: 111; [9.7] 37; [9.9] 2). He goes so far as to devote a whole treatise to the process, referring to it with the precise name by which it has since been known: On the Multiplication of Species. Just as Grosseteste had argued in On Lines and On the Nature of Place, so Bacon reasons that, because the species by which all natural causality is achieved are generated in straight lines in exact replication of the phenomenon of luminous radiation, the science of optics offers the 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 phenomena cannot 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 comments on experience or experiment for which he is best known, leading many to view him as the forerunner of his seventeenth-century namesake, Francis Bacon. To Roger’s way of seeing things there is in fact a discrete experimental science, scientia experimentalis, which is the most certain of all and certifier for the others ([9.10] II: 9:1–6). Despite its ostensible unity, this science is composed of three parts, each playing a different role—prerogatives or dignities as Bacon calls them—and for us to understand the whole we have to recognize that three constituents do not 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 experience the demonstrated conclusions of the other sciences ([9.8] II: 172–3). Here Bacon has recourse to his conviction, surely evolved from weaker notions found in both William and Grosseteste, that while scientific demonstration in the Aristotelian sense can make known the truth, only experience removes all doubt ([9.8] I: 105–6, II: 167; [9.7] 297).7 One might know by reasoned argument that fire burns, but only the experience of a scorched finger teaches one to avoid the flame. It is tempting to see in this a version of the theory of verification by experimentation, as many who praise Bacon have done. There is, after all, the precedent of Grosseteste with his example of testing the power of scammony to purge bile. But in fact Bacon, who is aware of the sort of verification Grosseteste described, takes it as having nothing to do with the ‘experiment’ he has in mind. Natural sciences often do, as Grosseteste realized, establish their principles by experiment or from experience; they then anchor their conclusions to the principles in Aristotelian fashion by demonstrative argument. Such methods, Bacon admits, have a legitimate place at the foundation of demonstrative science. Yet he wants his experimental science to go beyond Aristotle and 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 of a hypothesized principle but rather the empirical confirmation of an already proved conclusion. Bacon’s first prerogative is thus a use of experience unlike anything Aristotle, or William and Grosseteste, had conceived, pointing to the growing prestige of singular perception in the noetics and epistemology of the late thirteenth and fourteenth centuries. The second and third roles of experimental science are, if anything, even more un-Aristotelianizing, although not so novel. With them we return to the traditional notions of experimenta so well represented in William’s thought. By its second prerogative, experimental science reveals truths about the subject-matter of the other sciences, which none of them can prove or dare to claim as true. The emphasis here is on practical accomplishments that are both marvellous and strange, as, for example, the construction of an astrolabe that would revolve daily on its own natural power, or a knowledge of how to use medicines dramatically to prolong human life ([9.8] II: 202–4). Experimental science’s third prerogative is more awesome still, making known things not even dreamed of in the rest of scientific discourse. It penetrates all the way to the secrets of nature and surpasses judicial astrology, with which it seems to compete, by making firmer predictions about the future and doing far more miraculous works (opera admiranda, mirabilia opera) ([9.8] II: 215; [9.7] 44). It is primarily by this prerogative that experimental science commands all other sciences as their mistress (domina), and it is here that its practical value is realized in the extreme ([9.8] II: 221; [9.7] 46). By now Bacon is clearly navigating in the waters of magical art, as is surely betrayed by his claim that the third prerogative explores the occult (opera occulta) ([9.10] II: 9:11–12). Times have changed, however, and Bacon is far more squeamish than William was about being associated with anything labelled ‘magic’. He not only refuses to call any aspect of experimental science ‘magical’ but also insists that one of his science’s functions is to lay open the falsehood of the magical arts (magicae artes) ([9.10] II: 9:21–6). Yet more than just fear of censure separates Bacon from William of Auvergne. He is, like William, willing to accept an art like astrology that is traditionally associated with magic, so long as it does not postulate the absolute necessity of all events or resort to the power of demons or fraud to impress its audience. He even gives acceptable astrologers the name of ‘true mathematicians’ (veri mathematici) in contrast to the ‘false mathematician’ (falsi mathematici) who dabble in magic ([9.8] I: 240– 2). But Bacon’s vision of experimental science, for all its debt to traditional magic, aspires to more than marvel. It presumes to draw the power of knowledge, especially scientific knowledge, into a campaign to transform the world. Indeed, the impetus behind most of Bacon’s later work is his desire to lay the cognitive foundations for the reformation of human life. Such practical ideals are not foreign to the magic of William’s mental landscape, but as distilled in Bacon’s experimental science they savour for the first time of the ambition and energy of the seventeenth century. NOTES 1 For an analysis of the passage and an argument for what constituted Grosseteste’s own view, see Marrone [9.20] 166–78. 2 How this sort of perpetuity might suffice for a Christian like Grosseteste, who held 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) in scientific 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 obscurative effect of demonstration, echoed (p. 223) by Grosseteste’s preference for principal cognition. A bias for particular experience appears in On the Nature of Place ([9.3] 66). BIBLIOGRAPHY Original Language Editions William of Auvergne 9.1 Opera omnia, 2 vols, Paris and Orleans, Hotot, 1674; repr. in 2 vols, Frankfurt on Main, Minerva, 1963. 9.2 Switalksi, B. (ed.) De trinitate, Toronto, Pontifical Institute of Mediaeval Studies, 1976. Robert Grosseteste 9.3 Baur, L. (ed.) Die philosophischen Werke des Robert Grosseteste, Bischofs von Lincoln, 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. (ed.) Commentarius in Posteriorum analyticorum libros, Florence, Olschki, 1981. Roger Bacon 9.7 Brewer, J.S. (ed.) Fr. Rogeri Bacon Opera quaedam hactenus inedita, London, Longman, 1859. 9.8 Bridges, J.H. (ed.) The ‘Opus Majus’ of Roger Bacon, 2 vols, Oxford, Clarendon Press, 1897; Suppl., London, Williams & Norgate, 1900. 9.9 Lindberg, D.C. (ed.) Roger Bacon’s Philosophy of Nature, Oxford, Clarendon Press, 1983. 9.10 Steele, R. (ed.) Opera hactenus inedita Rogeri Baconi, Fasc. 2–4: Communia naturalium, Oxford, Clarendon Press, 1905?–1913. English Translations 9.11 The Opus Majus of Roger Bacon, 2 vols, trans. R.B.Burke, Philadelphia, Pa., University of Pennsylvania Press, 1928. 9.12 Robert Grosseteste On Light, trans. C.R.Riedl, Milwaukee, Wis., Marquette, 1942. 9.13 A Source Book in Medieval Science, ed. E.Grant, Cambridge, Mass., Harvard University Press, 1974. Bibliographies 9.14 Alessio, F. ‘Un secolo di studi su Ruggero Bacone (1848–1957)’, Rivista critica di storia della filosofia 14 (1959): 81–102. 9.15 Gieben, S. ‘Bibliographia universa Roberti Grosseteste ab an. 1473 ad an. 1969’, Collectanea Franciscana 39 (1969): 362–418. 9.16 Hackett, J.M.G. and Maloney, T.S. ‘A Roger Bacon Bibliography (1957–1985)’, The New Scholasticism 61 (1987): 184–207. 9.17 Huber, M. ‘Bibliographie zu Roger Bacon’, Franziskanische Studien 65 (1983): 98–102. General Studies 9.18 Crombie, A.C. Robert Grosseteste and the Origins of Experimental Science 1100–1700, Oxford, Clarendon Press, 1953. 9.19 Lindberg, D.C. Theories of Vision from Al-Kindi to Kepler, Chicago, University of Chicago Press, 1976. 9.20 Marrone, S.P. William of Auvergne and Robert Grosseteste: New Ideas of Truth in the Early Thirteenth Century, Princeton, NJ, Princeton University Press, 1983. 9.21 Thorndike, L. A History of Magic and Experimental Science, vol. 2, New York, Macmillan, 1923. Studies on William of Auvergne 9.22 Baumgartner, M. Die Erkenntnislehre des Wilhelm von Auvergne, Münster, Aschendorff, 1893. 9.23 Jüssen, G. ‘Wilhelm von Auvergne und die Entwicklung der Philosophie im Übergang zur Hochscholastik’, in W.Kluxen (ed.) Thomas von Aquin im philosophischen Gespräch, Freiburg and Munich, Alber, 1975, pp. 185–203. 9.24 ——‘Wilhelm von Auvergne und die Transformation der scholastischen Philosophie im 13. Jahrhundert’, in J.P.Beckmann et al. (eds) Philosophie im Mittelalter, Hamburg, Meiner, 1987, pp. 141–64. 9.25 Masnovo, A. Da Guglielmo d’Auvergne a s. Tommaso d’Aquino, 3 vols, 2nd edn, Milan, Vita e Pensiero, 1945–6. 9.26 Moody, E.A. ‘William of Auvergne and his Treatise De anima’, in Studies in Medieval Philosophy, Science, and Logic, Berkeley, Calif., University of California Press, 1975, pp. 1–109. 9.27 Rohls, J. Wilhelm von Auvergne und der mittelalterliche Aristotelismus, Munich, Kaiser, 1980. 9.28 Teske, R.J. ‘William of Auvergne on the individuation of human souls’, Traditio 49 (1994): 77–93. Studies on Robert Grosseteste 9.29 Baur, L. ‘Das Licht in der Naturphilosophie des Robert Grosseteste’, Festgabe zum 70. Geburtstag Georg Freiherrn von Hertling, Freiburg im Breisgau, Herder, 1913, pp. 41–55. 9.30 ——Die Philosophie des Robert Grosseteste, Bischofs von Lincoln (gest. 1253), Münster, Aschendorff, 1917. 9.31 Callus, D.A. (ed.) Robert Grosseteste, Scholar and Bishop, Oxford, Clarendon Press, 1955. 9.32 Dales, R.C. ‘Robert Grosseteste’s scientific works’, Isis 52 (1961): 381–402. 9.33 Eastwood, B.S. ‘Medieval empiricism. The case of Grosseteste’s optics’, Speculum 43 (1968): 306–21. 9.34 ——‘Robert Grosseteste’s theory of the rainbow: a chapter in the history of non-experimental science’, Archives Internationales d’Histoire des Sciences 77 (1966): 313–32. 9.35 McEvoy, J. The Philosophy of Robert Grosseteste, Oxford, Clarendon Press, 1982. 9.36 Southern, R.W. Robert Grosseteste: The Growth of an English Mind in Medieval Europe, Oxford, Clarendon Press, 2nd ed., 1992. Studies on Roger Bacon 9.37 Easton, S.C. Roger Bacon and his Search for a Universal Science, New York, Columbia University Press, 1952. 9.38 Fisher, N.W. and Unguru, S. ‘Experimental science and mathematics in Roger Bacon’s thought’, Traditio 27 (1971): 353–78. 9.39 Hackett, J.M.G. ‘The attitude of Roger Bacon to the scientia of Albertus Magnus’, in J.A.Weisheipl (ed.) Albertus Magnus and the Sciences: Commemorative Essays 1980, Toronto, Pontifical Institute of Mediaeval Studies, 1980, pp. 53–72. 9.40 ——‘The meaning of experimental science (scientia experimentalis) in the philosophy of Roger Bacon’, Ph.D. dissertation, University of Toronto, 1983. 9.41 Lindberg, D.C. Studies in the History of Medieval Optics, London, Variorum, 1983. 9.42 Molland, A.G. ‘Roger Bacon as magician’, Traditio 30 (1974): 445–60. 9.43 Williams, S.J. ‘Roger Bacon and his edition of the pseudo-Aristotelian Secretum secretorum’, Speculum 69 (1994): 57–73.

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