Dietrich of Freiberg on the Succession of Forms in the Intensification of Qualities

DIETRICH OF FREIBERG ON THE SUCCESSION OF FORMS IN THE INTENSIFICATION OF QUALITIES

Brian Francis CONOLLY

Abstract

Dietrich of Freiberg defends the succession of forms theory in the intensification of qualities, first by arguing that unlike substances, qualities do not have the interiority that would permit any variation while remaining numerically the same. He argues further that because degrees of intensity are properties of a quality, and because properties are both relative and privative, they cannot be the terminus of a motion; rather only a new quality can. The most important philosophical objection to the succession of forms with respect to the intensification of qualities is that it seems to entail a passage through an actual infinity of degrees of intensity. Dietrich responds to this objection by arguing that intensification is not a continuous motion. Instead, he argues, intensification proceeds through a series of very small, but finite, qualitative leaps, resulting in a motion that is discrete, stepwise and discontinuous.

The intensification of qualities — as when, for example, the hotness that characterizes water in a kettle on a stove becomes hotter, or as the yellow of the goldfinch becomes brighter as spring moves into summer — gives rise to a number of problems that were discussed at great length and in detail in the late thirteenth and early fourteenth centuries. A particularly fruitful discussion concerned whether an intensified quality remains numerically the same through the course of intensification. The theory that maintains that it does not has become known as the “succession of forms” since it characterizes intensification as a process in which the more intense quality completely replaces the less intense. The underlying subject, e.g., the water or the goldfinch, is thus characterized by a succession of numerically distinct qualities. The theory maintains that each new increase

Recherches de Théologie et Philosophie médiévales 81(1), 1-35. doi: 10.2143/RTPM.81.1.3030621 © 2014 by Recherches de Théologie et Philosophie médiévales. All rights reserved. 2 B.F. CONOLLY or decrease in the intensity of a quality, such as heat or color, requires that a new and numerically distinct quality with the new degree of intensity completely replace the previous quality characterized by the prior degree of intensity. Thus, for example, as the water in a kettle on a stove increases in heat, the quality hotness1 of intensity d1 at time t1 is completely replaced by the new quality, hotness2 of intensity d2 at time t2. The successive qualities are numerically distinct from each other inasmuch as their respective degrees of intensity are distinct; hence, as the quality of hotness intensifies as the water in the kettle remains on the hot stove, the numerical identity of the intensifying quality of hotness is not preserved. A variety of theories were developed in opposition to the succession of forms, all of which maintain, on the contrary, that the remitted quality (with respect to the process of intensification) is not replaced, but in some manner remains, for instance, either insofar as it is itself varied or insofar as it is added to, but in any case in such a way that numerical identity between the remitted and intensified quality is preserved.1 The philosophical discussion of the problem can be traced to Aris- totle’s Categories, where Aristotle raises the question of whether qualities receive more and less. The late medieval discussion of the problem sometimes, however, takes on a distinctly theological character, especially inasmuch as it involves questions concerning the increase in the

1 See J.-L. SOLÈRE, “Tension et intention. Esquisse de l’histoire d’une notion,” in: L. COULOUBARITSIS – A. MAZZÙ (eds.), Questions sur l’intentionnalité, Brussels 2007, pp. 59-124. In this valuable historical overview of the problem from the ancient through the medieval and early modern periods, Solère distinguishes amongst the late medievals three proposed solutions to the problem: (1) succession, (2) addition, and (3) participation or latitude of forms. In the participation model, the quality itself in effect remains invariant throughout the process of intensification or remission; the degree of intensity is determined by the relation between quality and underlying subject. The addition solution comprises at least two variants, namely, the nutrition model and the perfection model (to be discussed below). These two are distinguished from each inasmuch as the former is more quantitative, the latter more qualitative. That is, in the latter, addition is made not part by part, but in such a way that the intensified quality is related to the remitted quality as more perfect to less perfect. See also ID., “Les variations qualitatives dans les théories post-thomistes,” in: Revue Thomiste 112 (2012), pp. 157-204; and E. JUNG, “Intension and Remission of Forms,” in: H. LAGERLUND (ed.), Encyclopedia of Medieval Philosophy. Philosophy Between 500 and 1500, Dordrecht 2011, Vol. 1, pp. 551-555. DIETRICH OF FREIBERG ON INTENSIFICATION 3 theological virtue of charity in the human soul.2 As is typical for late medieval philosophy, such theological concerns inform the philosophical discussion, especially inasmuch as the theological concern over the increase in charity gives rise to, and provides considerable support for the theory that qualitative intensification takes place through the addition of more of the quality in question, so that intensification becomes understood, in its simplest version, in terms of accumulation, sometimes considered in a manner analogous to nutrition, wherein something extrinsically advening is appropriated by the form already in place, whereby it becomes more intense.3 Such a theory of intensification would apply not only to charity or other virtues, but also to the affective qualities, e.g., color, heat, etc. This nutrition model of qualitative intensification is, in some thinkers, amended to what might be called the perfection model, perhaps in response to various objections to the former. In this latter version of the theory the more intense quality in some manner is received by and thus perfects the less intense quality, in a manner analogous to certain theories of generation, in which the prior and inferior form, e.g., the sensitive soul, receives (without being altogether replaced) and is thus perfected by the posterior and superior form, viz., the rational soul. In either case, that is, whether the nutrition model or the perfection model, two features are shared in common: (i) intensification occurs through the addition of some extrinsically advening form and (ii) the advening form and the prior form already in place are united in such a manner as to preserve numerical identity. This

2 This can be gleaned simply from the number of quodlibet questions in which it is asked whether charity is increased by the addition of something. See P. GLORIEUX, La Lit- térature Quodlibétique (2 vols.), Paris 1925 and 1935. See also S. PIRON’s database : (search caritas). 3 See, for instance, JACOBUS DE THERINIS (JACQUES THÉRINES), Quodlibet II, q. 14, “Utrum caritas augmentata sit eadem numero que prius?,” ed. P. GLORIEUX, Paris 1958, pp. 292-294. In addition, Hervaeus Natalis, who argues at some length against the succession theory, is somewhat unclear with respect to the theory he himself subscribes. See HERVAEUS NATALIS, Quodlibet II, q. 13, “Utrum in qualibet alteratione infinitae formae differentes sint sive si remissum et intensum realiter differunt?,” Venice 1513 (reprint, Ridgewood, N.J. 1966), 58vB-61rB. Hervaeus expressly characterizes the addition theory of intensification in terms of the nutrition model, but as he develops his arguments against the succession theory appears to modify it to something much more resembling the perfection theory, and ultimately characterizes the difference between intensified and remitted quality as that between more and less perfect. 4 B.F. CONOLLY latter can be made clear by analogous examples: thus, Socrates remains Socrates regardless of how much bread he eats; alternately, Socrates remains Socrates as he progresses from being a boy to being a man.4 It must be emphasized that the result of the addition of the extrinsically advening form is, on these theories, not a mere conglomeration, a heap, or a pile. Rather the extrinsically advening form is in some manner appropriated by the prior form, again either in a manner analogous to nutrition, or in a manner analogous to perfection. Numerical identity is thus preserved in the sense that what was there previously, namely, the less intense or imperfect form, in some real manner remains upon intensification. It does not depart upon the arrival of the intensifying addition.5 The discussion to follow will focus upon the unusual contribution to this debate made by Dietrich of Freiberg.6 Although Dietrich was by no means the only proponent of the succession of forms theory of intensification and remission,7 his discussion of the problem and

4 See, for example, JEAN QUIDORT, Quodlibet I, q. 8, “Utrum aliquid positivum possit produci a non ente? ,” ed. A. J. HEIMAN, in: J.R. O’DONNELL (ed.), Nine Medieval Thinkers, Toronto 1955, pp. 284-286. 5 Although this characterization of the addition theory draws upon Dietrich of Frei- berg’s characterization of the same (discussed below), Thomas de Bailly similarly characterizes the theory in terms of the addition of an extrinsically advening form. See THOMAS DE BAILLY, Quodlibet III, q. 15, “Cum caritas intenditur, utrum gradus minus intensus corrumpatur essentialiter?,” ed. P. GLORIEUX, Paris 1950, pp. 208-217. 6 On Dietrich of Freiberg’s life and work, see K. FLASCH, Dietrich von Freiberg: Phi- losophie, Theologie, Naturforschung um 1300, Frankfurt 2007. Dietrich of Freiberg is best known for his careful analysis of the optics of the rainbow (perhaps the most noteworthy achievement of late medieval empirical science), and increasingly, for his distinctive theory of intellect, which draws heavily upon Proclus. In addition, however, Dietrich’s works display a remarkable competence and distinctive independence and originality in Aristo- telian metaphysics and natural philosophy, with a decidedly Averroist bent, as the number and quality of his treatises on such subjects attest. In this respect, see, for instance, A. MAURER, “The De Quiditatibus Entium of Dietrich of Freiberg and its Criticism of Thomistic Metaphysics,” in: Medieval Studies 18 (1956), pp. 173-203, (revised, updated and reprinted in: A. MAURER, Being and Knowing. Studies in Thomas Aquinas and Later Medieval Philosophers, Toronto 1990, pp. 177-199). 7 Walter Burley is perhaps the most famous proponent of the succession theory, although (i) he was active a decade or two later than Dietrich and (ii) aspects of his theory differ considerably from Dietrich’s. For an informed discussion of Burley’s theory, see E. SYLLA, “Infinite Indivisibles and Continuity in Fourteenth-Century Theories of Alter- ation,” in: N. KRETZMANN (ed.), Infinity and Continuity in Ancient and Medieval Thought, Ithaca 1982, pp. 231-257. Proponents of the theory much closer to Dietrich’s time and DIETRICH OF FREIBERG ON INTENSIFICATION 5 defense of the succession of forms theory is worthy of attention for at least two reasons. First, his arguments focus upon the nature of the relation between the quality and the degree of intensity that characterizes it. In particular, he calls directly into question whether intensification can be understood in terms of addition, and indeed argues quite expressly that, on the contrary, intensification must be understood as an intrinsic qualitative increase; it can involve nothing extrinsically advening. Dietrich thus addresses, argues against, and undermines one of the fundamental assumptions of those opponents of the succession theory who understand intensification in terms of addition. His approach to the problem thus differs considerably from that of others among the late medieval philosophers who defend the succession of forms, such as Godfrey of Fontaines and Thomas de Bailly, whose arguments tend to concentrate on the physics of motion.8 While it must be granted that Dietrich’s approach to the place include certainly Thomas de Bailly, and very probably Godfrey of Fontaines (cf. J.-L. SOLÈRE, “Édition de la Question ordinaire n° 18, « de intensione virtutum », de Godefroid de Fontaines,” in: J. MEIRINHOS – O. WEIJERS (eds.), Florilegium Medievale. Études offertes à Jacqueline Hamesse, Turnhout 2009, pp. 83-107). For other known proponents of the doctrine, see S. DUMONT, “Godfrey of Fontaines and the Succession Theory of Forms at Paris in the Early Fourteenth Century,” in S. BROWN – T. DEWENDER – T. KOBUSCH (eds.), Philosophical Debates at Paris in the Early Fourteenth Century, Leiden 2009, pp. 39-125. It is worth noting that there is some evidence suggesting that Godfrey was familiar with Dietrich’s work. See M.-R. PAGNONI-STURLESE, “Per una datazione del De Origine di Teodorico di Freiberg,” in Annali della Scuola Normale Superiore di Pisa 33, no. 11 (1981), pp. 431–45. FLASCH, Dietrich von Freiberg, pp. 162-165, however, subscribes to a more cautious view of the evidence put forward by Pagnoni-Sturlese. 8 The argument that seems to have generated the most interest focuses upon the incompossibility of the termini of motion, if numerical identity of the remitted and intensified quality is assumed. See, for example, THOMAS DE BAILLY Quodlibet III, q. 15, “Cum caritas intenditur, utrum gradus minus intensus corrumpatur essentialiter?,” ed. P. GLORIEUX, Paris 1950, pp. 208-217, especially p. 209, 15-28: “Motus cum termi- netur ad formam, oportet quod diversi motus terminentur ad diversas formas, sicut diversi secundum speciem ad diversas formas secundum speciem, et diversi motus solo numero ad diversas formas solo numero. Modo constat quod motus quo heri aliquid factum est album et motus quo hodie de isto albo fit magis album, sunt motus solo numero differentes; ergo et forme ad quas sunt, scilecet minus album ad quod terminabatur primus motus et magis album ad quod terminabatur secundus motus, sunt forme differentes solo numero. Cum ergo duo accidentia realia solo numero differentia non possunt simul esse in eodem subiecto, patet quod adveniente magis albo per secundum motum corrumpitur minus albus quod introductum fuit per primum motum; et eodem modo est de magis et minus in caritate et in quacumque alia forma recipiente magis et minus.” Cf. S. DUMONT, “Godfrey of Fontaines,” p. 54, who provides a concise account of this line of argument: “It argues for the strict enforcement of the requirement in Physics V that any real change 6 B.F. CONOLLY problem does not seem to have achieved the same kind of resonance or generated as much response as these latter arguments, it must be seen that Dietrich’s discussion nevertheless increases the philosophical scope of the problem precisely because of his clearer articulation of the underlying metaphysics.9 A second and perhaps even more interesting reason for why Dietrich’s discussion of this problem is worthy of our attention is his response to one of the most common and effective philosophical arguments against the succession of forms theory. This objection argues that inasmuch as intensification takes place over some period of time, and inasmuch as it is assumed that intensification is a continuous motion, such that degrees of intensity correspond to the con- tinuously successive nows of time, it appears to follow that according to the succession of forms theory, any intensification would require, absurdly, the passage through an actual infinity. The prevailing response to this objection (such as can be gleaned directly from Thomas de Bailly, but also indirectly from the extended discussion of the problem by Hervaeus Natalis) was to discover some manner in which to preserve the continuity of intensification without being sad- dled with the absurdity of passage through an actual infinity, e.g., by arguing, for example, that it is a passage through merely a potential infinity. Dietrich, by contrast, responds to this objection by abandon- ing continuity, and arguing, on the contrary, that intensification and remission are discontinuous motions. His arguments will again be seen to address the fundamental assumptions behind the otherwise must be between opposites. Since the change from a lesser to greater degree of a form is real, the degrees must be opposed. They cannot therefore exist together, and so must be numerically distinct.” 9 For further consideration of the attempt to situate Dietrich’s discussion of the problem within the context of his contemporaries, see K. FLASCH, Dietrich von Freiberg, Frank- furt 2007, pp. 431-438. Flasch (p. 438) characterizes Dietrich as remaining within the lines laid out by ALBERTUS MAGNUS, Liber de sex principiis, tr. 1, c. 3, ed. A. BORGNET, Paris 1890, p. 310, and by Godfrey of Fontaines (see note above), both of whom appear to have defended the succession of forms with respect to the intensification of qualities. This appears to be correct at least in regard to the position defended. Albertus Magnus’ discussion, however, while very suggestive concerning the question of antecedents of and influence upon Dietrich, is too brief and without sufficient argument to allow for detailed comparative analysis with Dietrich’s discussion. Furthermore, it will become clear in the discussion to follow that Dietrich’s arguments depart considerably from those associated with Godfrey, and depend upon other doctrines that are distinctively his own. DIETRICH OF FREIBERG ON INTENSIFICATION 7 unsupported premise that intensification is a continuous motion. The result is a most unusual and distinctive theory of change among medieval philosophers: intensification (and remission) must be understood as a discrete and finite succession of numerically distinct qualities differing by degree of intensity. In the discussion to follow I shall first examine in some detail Dietrich’s arguments concerning the problem of intensification and remission of qualities, as they are found in his opusculum De magis et minus.10 Special attention will be given to two of the four arguments therein inasmuch as these address expressly the fundamental assumption of his opponents, namely, that intensification of quality is achieved through the addition in some manner of an extrinsically advening form.11 In one of these arguments, Dietrich will argue from the assumption that intensification, on the contrary, must be understood as a qualitative increase intrinsic to the form, and argue that a quality, in contrast to substance, does not have the requisite interiority of essence in order to persist or endure as numerically the same through any alteration. The second of Dietrich’s arguments will establish that more and less are in any case properties of qualities, in the strict Porphyrian sense, and therefore pertain to the essence of the quality. Hence, he will argue, any change in a property, and in particular, with respect to more and less, must reflect a change in the essence itself, which is to say, there cannot be such change without a numerically distinct quality being the result. In the second part of the discussion, I shall consider Dietrich’s response to the “actual infinity” objection to the succession of forms theory. I shall do so by providing a detailed examination of Dietrich’s

10 DIETRICH OF FREIBERG, De magis et minus, ed. R. IMBACH in Opera Omnia III, Hamburg 1982. 11 For very brief, but clear and concise summaries of all of Dietrich’s arguments concerning the numerical distinctness of intensified and remitted qualities, see W.A. W ALLACE, The Scientific Methodology of Theodoric of Freiberg, Fribourg 1959, p. 103, n. 1. In addition, K. FLASCH, Dietrich von Freiberg, especially pp. 427-431, provides a detailed discussion of the first of Dietrich’s arguments for the numerical distinctness of intensified and remitted qualities. Throughout his discussion, Flasch emphasizes Dietrich’s departure from orthodox Aristotelianism insofar as Dietrich allows for the intensification of substances; hence his interest only in the first of Dietrich’s argument concerning the intensification of qualities, insofar as that argument develops from both the comparison of the intensification of substances and of qualities, and from a consideration of the important differences between substance and accidents in general. 8 B.F. CONOLLY analysis of time and motion whereby he arrives at the startling conclusion that intensification is a discontinuous motion that proceeds not through an infinite number of infinitesimal degrees but through a finite series of determinate degrees of intensity. Some evaluation of the cogency of Dietrich’s arguments will be offered here throughout, as well as some attempt to situate his con- tributions to the discussion precisely within the timeframe of the discussion, namely, the late thirteenth century into the first decade of the fourteenth century. The discussion will conclude with several questions and a prospectus for further investigation.

1. ‘More and less’ and Aristotle’s Categories Dietrich’s treatise De magis et minus reads more as a partial commentary on Aristotle’s Categories than as a work that derives from a dis- puted question — such as appears to be the case with respect to his treatise De corpore Christi mortuo.12 Indeed, along with De natura contrariorum,13 which in many respects complements De magis et minus, Dietrich brings together some of the most fundamental problems in Aristotle’s Categories, namely, how the various categories are distinguished from each other. Aristotle distinguishes the various categories from each other insofar as they are, or are not, receptive of or characterizable by several different attributes, such as has a contrary, or is receptive of contraries, or is receptive of more and less, etc.14 In this way Aristotle is able to draw detailed distinctions among at least the

12 DIETRICH OF FREIBERG, De corpore Christi mortuo, ed. M. R. PAGNONI–STURLESE, Opera Omnia II, Hamburg 1980. 13 DIETRICH OF FREIBERG, De natura contrariorum, ed. R. IMBACH, Opera Omnia II, Hamburg 1982. 14 Contrariety and more and less are the two most important of the attributes that Aristotle considers in distinguishing the categories from each other. He does consider other attributes as distinguishing characteristics, for example, whether substances have correlatives, or whether quantities are dispositional, in the sense of having parts arranged in relation to each other, but only (i) whether the category admits of more and less, (ii) whether a representative of the category possesses a contrary, and (iii) whether the category is receptive of contraries, is asked of all four of the categories he investigates in detail (substance, quantity, quality, and relation). These three attributes (two of which involve contrariety) thus fundamentally distinguish the first four categories from each other. Diet- rich’s two treatises therefore must be seen as complementary works on one of most important aspects of Aristotle’s opusculum. DIETRICH OF FREIBERG ON INTENSIFICATION 9 first four categories (leaving the distinction among the remaining categories, along these lines, as an exercise for his readers). As is well known to students of the Categories, substance is distinguished from qualities, among other reasons, because substance does not admit more and less, whereas at least some qualities do. Thus, one man is not more a man than another, but one white, e.g., that of snow, is more white than another, e.g., that of milk.15 In his treatise, Dietrich is thus concerned to determine and explain why, precisely, there is this difference between substance and qualities. While he does treat therein a problem that was gaining currency in Paris certainly by the 1280’s, namely, whether numerical identity is preserved in the intensification and remission of qualities, he does not respond explicitly to any arguments for the position contrary to his own; indeed he scarcely acknowledges any awareness of such arguments apart from asserting that intensification of qualities does not come about through addition. So again, the treatise appears not to have been written in response to any controversy — even if it does weigh in on an important controversy. It instead seems to be written as a commentary on the Categories. That he should weigh in on this important controversy concerning the numerical identity of intensified qualities is a matter of course, inasmuch as Aristotle himself raises it. To the extent that there is a problem that Dietrich is responding to in the treatise, it is largely one of his own making. This is because, despite the fact that Aristotle clearly maintains that substances are neither receptive of nor characterizable by more and less, and are (for this and other reasons) thus clearly distinguished from qualities, Dietrich has a theory of substantial generation and corruption which suggests that substances can indeed be characterized by more and less. This is because one substance, at a certain stage in the process of generation, can be more or less perfect than another at a different stage in the process of generation, when perfect is understood to signify the completion and

15 The problems discussed in De natura contrariorum are somewhat more complex, inasmuch as Dietrich therein needs to explain not only why qualities have contraries and substances do not (whereby they are thus distinguished) but also how it is that contrariety behaves differently, as it were, when it comes to dividing a genus. Thus contrariety in the genus of substance amounts to possession and privation; whereas in the genus of quality, contrariety amounts to two extremes between which there is a range, as is the case of colors, which are a range between the extremes black and white. 10 B.F. CONOLLY fulfillment of the course of generation, e.g., the adult human being. Thus, the adolescent may be said to be more a man than the infant, simply because the adolescent is further along, and thus closer to the completion, fulfillment, and perfection, of the course of generation that culminates in the fully adult man or woman.16 The main problem, for Dietrich, then, is to show that despite his theory of substantial generation, substances and qualities can still be distinguished from each other with respect to the question of more and less, in a manner consistent with Aristotle’s position and arguments. Dietrich does so by focusing on the question of whether numerical identity is preserved in change involving intensification and remission. To this end, he asserts (i) that it is preserved with respect to substances; (ii) that it is not preserved with respect to qualities (at least with respect to some qualities); and (iii) that more and less are properly attributable to a form only when numerical identity is not preserved. Hence the distinction between substance and qualities on this score is preserved, in accordance with Aristotle’s doctrine. Dietrich does offer arguments, of course, on both points, namely, that numerical identity is preserved in change characterized by more and less with respect to substance, and that it is not preserved with respect to qualities. In the present discussion, we are of course primarily interested in the latter. These arguments, however, depend to a large extent upon the differences between substance and accidents in general, as well as the complete ontological dependence of accident upon substance. It will therefore be unavoidable to touch upon his arguments for the former at least incidentally. Dietrich’s focus upon the differences between substance and accidents in general is what is perhaps most distinctive about his treatment of the problem of the numerical identity of intensifying and remitting forms. Other, presumably later treatments of the problem, while not disregarding the ontological relation between substance and accident, tend to highlight problems pertaining to the termini of motion in intensification and remission, thus, with greater interest in

16 As will be discussed below, despite such differences describable in terms of more and less, there is an invariant and invariable essential identity, so that the substance in question is invariably — neither more nor less — a human being at any one stage in comparison with any other. DIETRICH OF FREIBERG ON INTENSIFICATION 11 the physics of the problem than in the metaphysics. In any case, Dietrich’s arguments are certainly interesting, if not completely com- pelling, and therefore worth examining in some detail.

2. Intrinsic qualitative increase It will be helpful to consider first precisely how Dietrich understands intensification and remission, especially inasmuch as his understanding of these two types of change in effect constitutes an argument for his position. Dietrich makes clear, and repeats several times in his De magis et minus that “intensification is only a certain invigoration interior to the essence which is said to be intensified, the contrary of which is remission, which pertains also to the interior of the essence which we say is remitted.”17 It is easy to imagine a lamp, the increase or decrease in brightness of which is caused by turning a dimmer switch one way or another, instead of adding or removing any number of light bulbs as a means of illustrating an intrinsic qualitative increase or decrease in brightness. Dietrich emphasizes the intrinsicality of this increase or decrease in vigorousness, especially when arguing that substance remains numerically the same when intensifying or remitting. In particular, he reminds us that the very meaning of the terms ‘intensification’ and ‘remission’ therefore do not allow for these kinds of change to be accounted for in terms of the addition or subtraction of anything extrinsic or extraneous to the form undergoing intensification or remission: And the words ‘intensification’ and ‘remission’ express this through themselves, which, in their proper sense, do not signify the acquisition or loss of any form in the thing which is being intensified or remitted. Rather, from the force of their signification they designate only a certain interior qualitative increase or decrease […].18

17 DIETRICH OF FREIBERG, De magis et minus, p. 53, 69-71: “[…] intensio autem non est nisi quaedam vigoratio intranea essentiae eius, quae dicitur intendi, cuius contrarium est remissio pertinens etiam ad intraneum essentiae, quam dicimus remitti […].” 18 DIETRICH OF FREIBERG, De magis et minus, p. 62, 100-104: “Et hoc sonant per se ipsa verba intensionis et remissionis, quae secundum proprietatem suae significationis non important adeptionem vel abiectionem alicuius formae in re, quae intenditur et remittitur, sed solum ex vi suae significationis designant quoddam intraneum qualitativum incremen- tum vel decrementum […].” 12 B.F. CONOLLY

In other words, the very meaning of the terms ‘intensification’ and ‘remission’ indicates only an intrinsic qualitative increase or decrease.

3. Interiority and intensification Even if we were to accept Dietrich’s reasonable notion that intensification and remission pertain strictly to an intrinsic qualitative increase or decrease, it does not immediately follow that numerical identity is not preserved when a quality undergoes intensification and remission. To this end, Dietrich proceeds by showing, first, that given this notion of intensification, numerical identity is preserved when a substance undergoes such change. Then, taking the intensification of substances as his model, Dietrich argues that there is a significant and relevant difference between substances and qualities such that given this understanding of intensification and remission, substances undergoing such change maintain numerical identity, while qualities do not. The explanation of this difference, then, is Dietrich’s first argument for why numerical identity is not preserved in qualities undergoing intensification. The crucial difference between substance and accidents, with respect to intensification and remission, Dietrich points out, is that it is possible, with respect to substances, to distinguish intentionally three rationes of increasing abstraction, any of which, however, implies the whole essence of the thing; whereas no such distinctions can be made with respect to qualities. In particular, it is possible to distinguish, within substance, the intentions or rationes of essence, substance, and individual as such (that is, essence, substance, and individual are intentionally distinct in regard to substance). ‘Essence’ refers to the substance only insofar as it is dependent upon its own principles; it thus abstracts from substantial modes of potency and act, which is to say (as will be explained below), it abstracts from substance insofar as it is at some stage in the course of its generation. ‘Substance’ as such refers to the substance with respect to these substantial modes of potency and act, that is, again, with respect to the stages in the course of generation. ‘Substance’ as such, however, abstracts from the individuating conditions of a substance, which for Dietrich is having parts posterior to the whole, by which he means, having limbs and organs, etc. Finally, individual as such refers to the substance with respect to these individuating conditions, that is, DIETRICH OF FREIBERG ON INTENSIFICATION 13 again, as having parts posterior to the whole. These are three intentionally distinct ways of considering the same substance, and therefore, any of them implies the whole of the essence. Thus, the whole essence of the young Socrates (e.g., as he appears in Plato’s Parme- nides) is implied whether I regard him as this young man with his snub-nose, or as this young man who has a few years to go before he reaches his maturity as a man, or as this rational animal.19 Even though each of these intentions implies the whole of the essence, it can thus be seen that with these three intentionally distinct rationes there are increasing levels of abstraction. ‘Substance’ as such abstracts from the individuating conditions; ‘essence’ as such abstracts from the individuating conditions as well as from those substantial modes of being, potency and act, characteristic of the consideration of the substance in terms of substance as such. It is important to note here that not only is essence the most abstract of these intentions but is also to be characterized as innermost and ownmost, or to use Dietrich’s term, intimus. These intentional distinctions allow Dietrich to give an account of the intensification of substance in which numerical identity is preserved. It is possible to give such an account inasmuch as intensification can be understood as a variation pertaining to one such intention or ratio while the others remain invariant. Because these are intentional distinctions, we should not be misled into thinking that Dietrich is conceiving of intensification in terms of the standard analysis of alteration, in which there is a variation at the level of form while an underlying subject remains invariant, as when an oak leaf alters from green to red in the autumn. Rather, these intentional distinctions draw attention to the notion that while the substance is certainly invariant in one respect, namely, with respect to its dependence upon its own principles, it is in another respect inherently dynamical. It changes, grows, and

19 The distinction between a substance considered with respect to its own principles (for example, form and matter) and considered with respect to its individuating conditions, whether these be accidents, or as Dietrich claims here, possessing parts posterior to the whole, is perhaps not so unusual in late medieval philosophy. What does appear to be somewhat unusual — but also crucially important for Dietrich’s discussion — is the third, or middle ratio that Dietrich introduces here, namely, the substance considered with respect to the substantial modes of potency and act. This ratio introduces a dynamical aspect to the consideration of substance that is absent from the other two rationes. 14 B.F. CONOLLY develops over time yet in accordance with its own principles. This inherent dynamism of the substance is brought to the fore when we consider the substance with respect to those substantial modes of potency and act, which, for Dietrich in the present context are to be understood as signifying, respectively, the various stages in the process of generation prior to the completion and fulfillment of that process (e.g., the stages of infancy, childhood, and adolescence), and the cul- mination and perfection of that process (e.g., the adult man or woman). Even though the changes that take place are cognitively manifest through accidents (the adult Socrates is taller, broader, and heavier than the adolescent Socrates), the difference between the adolescent and adult Socrates is not merely accidental. Rather, this difference is aptly characterized in terms of potency and act, which Dietrich has identified as substantial modes of being: the boy Socrates is still in potency in relation to the man that he will become. This, again, is not an accidental difference, such as there would be between pale Socrates and dark Socrates; rather it is a difference in terms of substantial modes. There is a substantial potency in the boy Socrates (namely, in relation to the adult man that he will become) that is not in Socrates the adult, fully developed man. The fully developed adult Socrates is not in potency to any further substantial development. His generation and development is complete. Hence, if we allow Dietrich to consider such substantial development as intensification, as clearly he does,20 then it becomes evident that in such intensification numerical identity is preserved. For the boy Socrates is essentially, and therefore numerically the same as the adolescent Socrates as well as the adult Socrates. If we were to abstract from the differences among these stages of substantial development, there is only the one essence, one and the same Socrates. Despite such changes, essence, in the innermost and ownmost interiority and intimacy of the substance, remains invariantly the same. Now it has been necessary to go on at some length concerning these intentional distinctions within substance because Dietrich’s first argument for why numerical identity is not preserved in intensifying qualities is on the grounds that such distinctions, whereby numerical

20 And expressly so in several places in De magis et minus. See, for instance, § 9, p. 54, 4-5. DIETRICH OF FREIBERG ON INTENSIFICATION 15 identity of the intensifying form is made possible, cannot be made with respect to accidents in general, qualities in particular. If we posit anything to be changed in such a manner, namely from less white to more white or from less hot to more hot, and so concerning similar things intensified and remitted, such qualities, I say, differ according to intensification and remission or according to more and less, they differ by essence not only in diverse individuals, of which one is more intensely white or hot than another, but also in the same individual that undergoes change from such a remitted quality to a more intense one; such a quality, I say, that differs in the same individual according to intensification and remission, differs by essence. Now the reason for this is to be drawn primarily from those things that were said earlier concerning the difference between substance and accidents with respect to what is proper to and the manner of their essences, namely, that there is not to be found in accidents so great an intimacy of their essence that it could be changed or varied according to any of its essential intentions without it being changed in its essence as such and its act of existing. For there is no intention of its essence other than the act of existing.21 A thorough discussion of the reason why such distinctions cannot be made with respect to accidents would require a significant digression into Dietrich’s theory of the relation between essence and esse, and his critique of Thomistic metaphysics, as discussed in his De esse et essentia and in his De quiditatibus entium. Therein he defends the notion that the essence and quiddity of an accident just is its substance.22 For the sake of brevity, however, it would be better to treat

21 DIETRICH OF FREIBERG, De magis et minus, §§ 23-24, p. 63, 35-50: “Si nos ponamus aliquam rem sic transmutari, scilicet de minus albo in magis album vel de minus calido in magis calidum et sic de similibus intensis et remissis huiusmodi, inquam, qua- litates differunt secundum intensionem et remissionem sive secundum magis et minus, differunt per essentiam non solum in diversis individuis, quorum unum est intensius album vel calidum quam aliud, verum etiam in eodem individuo transmutato de remissa tali qualitate ad magis intensam, huiusmodi, inquam, qualitas in eodem invididuo diffe- rens secundum intensionem et remissionem differt per essentiam. Huius autem rationem trahendum primo ex his, quae praemissa sunt de differentia substantiae et accidentium quoad proprietatem et modum essentiarum suarum, quia videlicet non est in accidentibus reperire tantam essentiae suae intimitatem, ut secundum aliquam intentionum suarum essentialium possit mutari seu variari, nisi mutetur etiam per essentiam suam inquantum huiusmodi et actum existendi, quia non est alia intentio essentiae suae ab actu existendi.” 22 See A. MAURER, “The De Quiditatibus Entium of Dietrich of Freiberg” for a particularly clear account of this doctrine; see also K. FLASCH, “Introduction,” in: DIETRICH DE FREIBERG, Œuvres choisies. Tome I: Substance, quidités et accidents. Traités des accidents. Traité des quidités des étants. Textes latins traduits et annotés par C. KÖNIG-PRALONG avec la collaboration de R. IMBACH, Paris 2008, pp. 26-39. 16 B.F. CONOLLY these reasons in a more summary manner, as Dietrich himself does in his De magis et minus. Following Dietrich, then, let us return to the fundamental distinction between substance and accident: Now the ratio of substance consists in having its essence or quiddity according to itself and absolutely, not in relation to any extrinsic essence from which it would receive a mode by which it would be quiddified or which would be its quiddity or essence, but exists in itself and through itself absolutely from its own proper principles, as elsewhere was discussed at length concerning substance and accidents. An accident, however, is a certain mode or disposition of a substance, and this is its quiddity and proper essence, namely, that it is a disposition of a substance. Hence the Philosopher says in Metaphysics VII that accidents are beings because they are of a being, namely, of a true being, which is substance.23 Whereas substance has its being and essence in itself and from its own proper principles, accidents, by contrast, have their being, and thus their essence and quiddity, from their substance; and hence, from something extrinsic to the accident itself. In other words, in sharp contrast to substances, “their entire essence is only in relation to something outside them, that is, to the substance of which they are a disposition; and this is their essence.”24 Because of the complete ontological dependence of accidents upon substance, their essence is something extrinsic and exterior to them. This then is in sharp contrast to the essence of substance, which is seen as what is not only intrinsic to the substance itself, insofar as it is dependent only upon its own proper principles, but also what is innermost, ownmost, and most intimate. It follows therefore that it is not possible to distinguish within the accident itself the intention of its act of existing from its essence, in the manner in which it is possible with respect to substances, which distinction allowed for a variation of the substance with respect to one such intention while remaining invariant with

23 DIETRICH OF FREIBERG, De magis et minus, § 10, pp. 54, 35 – 55, 43: “Consistit autem ratio substantiae in habendo essentiam seu quiditatem suam secundum se et absolute, non respectu alicuius extrinsecae essentiae, ex qua recipiat aliquem modum, quo quidificetur vel qui sit eius quiditas vel essentia, sed constat in se et secundum se absolute ex propriis principiis suis, sicut alibi latius tractatum est de substantia et accidentibus. Accidens autem est quidam modus seu dispositio substantiae, et hoc est eius quiditas vel essentia, ut videlicet sit dispositio substantiae. Unde Philosophus dicit in l. VII Primae Philosophiae, quod accidentia sunt entia, quia sunt entis, entis scilicet veri, quod est substantia.” 24 DIETRICH OF FREIBERG, De magis et minus, § 22, p. 62, 6-7. DIETRICH OF FREIBERG ON INTENSIFICATION 17 respect to another. That is, this distinction makes possible an intensification of the substance with respect to its substantial modes of being (potency and act) while remaining essentially and therefore numerically the same. In other words, a quality undergoing intensification does not and cannot remain numerically the same. Qualities that differ by more and less therefore differ numerically. Now the reason for this is to be drawn primarily from those things that were said earlier concerning the difference between substance and accidents with respect to what is proper to them and the mode of their essence, namely, that there is not to be found in accidents such an intimacy of their essence that it could be changed or varied according to any of its essential intentions without it also being changed by its essence as such and its act of existing. For there is no intention of its essence other than the act of existing. For the act of existing is in an accident according to the ordering to the same principles from which it has its essence. And for the same reason there is also not to be found in the accidents themselves any essential intention more intimate than those that were said, which are one intention according to the ratio of the intentions, and not only according to this, that they are something by essence.25 In other words, since there are no such intentional distinctions within an accident — in fundamental contrast to substances — it is not possible for there to be a change within an accident without the very essence of the accident also changing, that is, into a numerically distinct essence. Thus the conditions of the possibility of the numerical identity of an intensified quality have been proscribed by the fundamental metaphysical distinction between substance and accident.26

25 DIETRICH OF FREIBERG, De magis et minus, § 24, p. 63, 45-55: “Huius autem rationem trahendum primo ex his, quae praemissa sunt de differentia substantiae et accidentium quoad proprietatem et modum essentiarum suarum, quia videlicet non est in accidentibus reperire tantam essentiae suae intimitatem, ut secundum aliquam intentionum suarum essentialium possit mutari seu variari, nisi mutetur etiam per essentiam suam inquantum huiusmodi et actum existendi, quia non est alia intentio essentiae suae ab actu existendi. Actus enim existendi inest accidenti secundum ordinem ad eadem principia, ex quibus habet essentiam suam. Et secundum eandem rationem nec in ipsis accidentibus est invenire aliquam intentionem essentialem intimiorem istis, quae dictae sunt, quae sunt una intentio et secundum rationem intentionum, non solum secundum id, quod sunt aliquid per essentiam.” 26 Dietrich offers a second, closely related argument, which again turns upon the notion that an accident is merely a disposition of a substance and nothing more. It is a brief argument, which, in comparison, to the first and rather more elaborate argument, reaches the same conclusion by means of a shortcut. If we focus just on this notion of accident, then any difference in the manner in which a substance is disposed is a numerical difference in the manner in which the substance is disposed. If we can discern the 18 B.F. CONOLLY

It is an unusual argument, to be sure. Indeed, at the current state of research, there appears to be no similar argument from any other philosophers from this period, namely, in which the development of a substance through its various stages in the course of generation is taken as the model of intensification wherein numerical identity is preserved.27 Dietrich’s argument thus amounts to showing the deficiencies of qualitative intensification with respect to this model, which deficiencies result in the failure to preserve numerical identity. That Dietrich takes substantial development as the model of intensification stems no doubt at least in part from his notion that intensification must be intrinsic, and cannot be accumulative in any way. But if Dietrich is able to distinguish intensification both from accumulation and from alteration (which he in effect also does when he insists that intensification is an intrinsic qualitative increase), it is not clear that he adequately distinguishes it from generation — or at least it is not clear whether or how the examples he uses of intensification of a substance pertain to some kind of change other than generation, or that generation is a species of change (peculiar to substances) of which intensification is the genus.28 There must also be some question as to whether or to what extent his argument depends upon his metaphysics of esse and essence, and whether, for instance, a different theory of the relation between esse and essence, e.g., that of Thomas Aquinas, might be able to provide accidents with some measure of interiority of essence, which Dietrich denies to accidents but which difference in disposition, we can count those differences. But recalling that an accident is nothing more than a disposition of a substance, then any difference in how the substance is disposed just is a numerical difference in accidents. Therefore a substance that is now more white, now less white is disposed differently; and therefore more white and less white are numerically distinct. 27 This is different than conceiving of intensification of qualities in terms of perfection according to the analogy with generation. Rather, Dietrich is taking generation not as something merely to be compared to, but as the model or exemplar of what intensification is. Is Dietrich with this argument implicitly responding to the perfection model of qualitative intensification? It is not easy to decide this question, mainly because Dietrich otherwise does appear to acknowledge that more intense qualities are distinguished from less intense as perfect from imperfect. This need not entail by any means that intensification must be understood in terms of a motion of perfection, that is, a perfecting, but it does provide some cause for doubt in this case. 28 The comparison perhaps breaks down with respect to corruption, unless it is considered that the intrinsic qualitative decrease of a substance would be the passage from adulthood into senility. DIETRICH OF FREIBERG ON INTENSIFICATION 19 would otherwise allow for a numerical-identity preserving account of qualitative intensification.

4. ‘More and less’ as privative and relative properties of qualities There might be some concern that Dietrich in this first argument is begging the question against his opponents, by merely asserting and insisting that intensification is strictly an intrinsic qualitative increase, thus ruling out without any real argument any accounts of intensification in terms of the addition of some extrinsically advening form. There can be no such concern, however, in the second of his arguments to be considered here. This argument turns upon his efforts to prove, in effect, that degrees of intensity are properties of a quality, in the strict Porphyrian sense, with the result that there cannot be a change of property or degree without there also being a change of essence of the quality as well; and hence, that any difference in degree of intensity entails a numerical difference in qualities as well. In addition, however, by arguing in this manner Dietrich in effect is attempting to establish (and not merely assume) his basic understanding of just what intensification is, namely, that it is an intrinsic qualitative increase. For, by arguing first, that more and less and hence degrees of intensity are properties of a quality, he can then infer that therefore, degrees of intensity are intrinsic to the essence of the quality. Now Dietrich believes that in order to show that more and less are properties of quality it is sufficient to show that they are certain privative and relative ‘modes’, inasmuch as these modes of signifying are distinctive of properties. An argument for the same point is taken from the proper signification of these modes, which are named ‘more’ and ‘less’. For besides what was said above concerning the signification of these modes (namely, that in their proper sense they signify certain qualitative modes according to the intensification and remission of the quality itself and that such intensification and remission is only a certain intrinsic qualitative increase with respect to intensification, or with respect to remission, a certain intrinsic qualitative decrease), besides this, I say, it must be considered that in their signification about the intensification and remission of a quality they most principally signify certain privative as well as relative modes, because of which they are designated properties and per se passions of quality by the Phi- losopher in the book Categories. For these modes of signifying, namely to 20 B.F. CONOLLY

signify privatively or relatively, are in some manner proper to all per se passions and properties of things, as is clear from inspecting any of the doctrinal sciences.29 For the sake of brevity we shall pass over the questionable reference to Aristotle,30 and simply grant to Dietrich that it is evident from “an inspection of any of the doctrinal sciences,” that the modes of signifying privatively or relatively are proper to properties. In any event, while it is almost self-evident that more and less signify something relative, as Dietrich himself points out,31 it is by no means obvious that they should be privative. Dietrich, however, believes that he can show that these terms are essentially privative in their mode of signifying by tracing their meaning back to their logical root, principle and measure: Now that such is the signification of these modes, which are called ‘more’ and ‘less’, is clear. For in the genus of quality, like and unlike, the differences of which are more and less, are, I say, all species of one and of many, and the first genera of them are one and many. Now according to the Philosopher, in Metaphysics X, the ratio of these genera (which are one and many), and of all their differences and species, consists in a certain privation, which is clear from their first root. For more and less are differences of likeness and unlikeness; unlikeness, however, is a species of many.

29 DIETRICH OF FREIBERG, De magis et minus, § 26, p. 64, 71-83: “Sumitur autem eiusdem ratio ex propria significatione horum modorum, qui nominantur magis et minus. Praeter hoc enim, quod supra dictum est de significatione istorum modorum, videlicet quod in sua propria significatione important quosdam modos qualitativos secundum intensionem et remissionem ipsius qualitatis et quod huiusmodi intensio et remissio non est nisi intraneum quoddam crementum qualitativum quoad intensionem vel quoad remissionem quoddam intraneum qualitativum decrementum, praeter hoc, inquam, consi- derandum, quod in sua significatione circa intensionem et remissionem qualitatis princi- palissime important quosdam modos privativos simul et respectivos, propter quos principaliter assignantur proprietates et per se passiones qualitatis a Philosopho in libro Praedicamentorum. Isti enim modi significandi, scilicet significare privative vel respective, quasi proprii sunt omnibus per se passionibus et proprietatibus rerum, ut patet inspiciendo in singulis doctrinalibus scientiis.” 30 The reference is difficult to reconcile with the Philosopher’s text (cf. Categories, 8, 10b26-11a14); this suggests that Dietrich was perhaps working with some unknown (to me) commentary on the Categories or at least reading the Categories through some distinctive interpretive lenses, such as that of the modists or Averroists. In any case, neither the commentaries of Albertus Magnus nor of Averroes on the Categories, both of which Diet- rich would have known, suggest this line of thought. 31 DIETRICH OF FREIBERG, De magis et minus, § 26, p. 65, 100-101: “Quod autem importent etiam respectus aliquos, quasi per se notum est. Magis enim album dicitur magis album in respectu minus albi et e converso.” DIETRICH OF FREIBERG ON INTENSIFICATION 21

But the root, principle and measure of multitude is one, the ratio of which consists in privation.32 It is perhaps not difficult to see how more and less can be considered as differences of both likeness and unlikeness. They are differences in the genus of likeness in that A is more like B than C is, which is less like B than A is. More and less thus differentiate A’s and B’s likenesses, respectively, to C. In a similar manner and correlatively, more and less differentiate A’s and B’s unlikeness to C. Furthermore, inasmuch as likeness is a species of one, and unlikeness is a species of many, it follows that both likeness and unlikeness are essentially privative. This is because, first, the ratio of one consists in privation; it follows that likeness, as a species of one, is therefore essentially privative. Further- more, since unlikeness is a species of many, and since ‘the root, principle, and measure of multitude is one’, it follows that unlikeness is therefore also essentially privative. Inasmuch, then, as more and less are differences of likeness and unlikeness, it follows therefore that they, too, are essentially privative in their signification. If we can accept Dietrich’s argument that more and less signify relatively and privatively, he can then draw his conclusion: Hence like and unlike, more and less and such [things] indicate no real nature pertaining to quality with respect to what is principally and formally signified

32 DIETRICH OF FREIBERG, De magis et minus, § 26, pp. 64, 84 – 65, 92: “Quod autem talis sit significatio istorum modorum, qui dicuntur magis et minus, patet. In genere enim qualitatis simile et dissimile, quarum differentiae sunt magis et minus haec, inquam omnia sunt species unius et multi et prima eorum genera sunt unum et multa. Secundum Philosophum autem in X Metaphysicae horum generum, quae sunt unum et multa, et omnium suarum differentiarum et specierum ratio in quadam privatione consistit, quod patet ex prima eorum radice. Magis enim et minus sunt differentiae similitudinis ; dissimilitudo autem est species multi; multitudinis autem radix, principium et mensura est unum, cuius ratio in privatione consistit.” Cf. THOMAS AQUI- NAS, In Metaph., IV, 3, § 567: “Cum igitur ista scientia consideret unum et idem, aequale et simile, necesse est quod consideret opposita his, scilicet multum, alterum sive diversum, dissimile, et inaequale, et quaecumque alia reducuntur ad illa, sive etiam ad unum et pluralitatem.”; In Metaph., V, 11, § 907: “Partes autem unius sunt idem, quod est unum in substantia: et simile, quod est unum in qualitate: et aequale, quod est unum in quantitate. Et e contrario partes multitudinis sunt diversum, dissimile et inaequale.” For more on Dietrich’s understanding of both one and many, see DIETRICH OF FREIBERG, De natura contrariorum, ed. R. IMBACH, Opera Omnia II, Hamburg 1982, §§11-17, pp. 92-97. On Dietrich’s notion of unum, see J.A. AERTSEN, Medieval Philosophy as Transcendental Thought. From Philip the Chancellor (ca. 1225) to Francisco Suárez, Leiden / Boston 2012, pp. 327-329. 22 B.F. CONOLLY

by these names; they signify no real nature, I say, pertaining to the quality to which they are attributed in such or such degree of intensification and remission, just as is the case for great and small in quantity, according to the Philosopher in Metaphysics V, which do not signify anything really added onto a quantity. And so it is clear that these modes, which are more and less, designate certain privative modes pertaining to quality.33 Having thus established that more and less are privative and relative, and treating as evident that to signify privatively and relatively are marks of properties, Dietrich can conclude that more and less are therefore properties of qualities. Furthermore, having reminded us, this time with abundant support from Aristotle, that there is no motion to anything relative and privative, he can then infer further that there is in particular no motion to properties, inasmuch as to signify privatively and relatively is, again, a distinctive mark of properties.34 Consequently, if there is such motion, that is, if there is a change in a property, there would have to be a change in that of which the property is a property, that is a change in essence, since properties follow from the essence. Hence, it is further argued with respect to the main point that since the often said modes pertain to the genus of quality with respect to its intensification

33 DIETRICH OF FREIBERG, De magis et minus, § 26, p. 65, 92-99: “Secundum hoc autem simile et dissimile, magis et minus et talia circa qualitatem nullam realem naturam important quantum ad id, quod principaliter et formaliter significatur his nominibus, nullam, inquam, realem naturam important circa qualitatem, cui attribuntur in tali vel tali gradu intensionis et remissionis, sicut se habet magnum et parvum in quantitate secundum Philosophum in V Metaphysicae, quae non important aliquid realiter superad- ditum quantitati. Et sic patet, quod hi modi, qui sunt magis et minus, designant quosdam modos privativos circa qualitatem.” Cf. ARISTOTLE, Metaph., V, 13, 1020a14-26. The comparison with quantities is useful for understanding his meaning here: to say that four is greater than three adds nothing real to four as such. Analogously, then, if we were to assert that snow is more white than is milk, whereas milk is more white than teeth, nothing real in either case is added to the white of milk. The comparatives more and less here are both relative and privative inasmuch as implicit in the assertion is the distinction among whitenesses: the white of snow is not the white the milk, which again is also not the white of teeth. 34 It should be noted that Dietrich is not bringing to a conclusion a first argument when he asserts that there is no motion or change to privative and relative things, and then moving on to a second, further argument. Rather, he needs this first step to establish that there is no motion to properties. Only then can he draw his conclusion that there is no motion to more and less, which are properties of quality; and from here establish that numerical identity is not preserved because property follows the essence, so that a change in property requires a change in essence. DIETRICH OF FREIBERG ON INTENSIFICATION 23

and remission and so, as was said, they signify their thing privatively and relatively, hence, I say, they have the nature of properties and a property of a quality is designated by the Philosopher,35 insofar as it is called ‘more’ and ‘less’. Now there is no motion in any genus with respect to properties and their per se passions primarily and principally and by themselves. If consequently there is change in such things, because the motion or change is an acquisition through itself and primarily of the part after the part of the genus in which there is motion or change, for instance, in quantity, in quality, and in location.36 Therefore, and in particular, since more and less, and hence, degrees of intensity, are properties of qualities, there can be no motion to degrees of intensity. Change in property, in particular, a change in degree of intensity, requires a change in the essence of the quality itself. Therefore, when change occurs from less white to more white in the same individual of a substance, one and numerically the same whiteness is not changed according to the said property, that is, according to more and less. Rather, the subject is changed according to the acquisition of whiteness of one degree, and the loss of whiteness of another degree. And so it is necessary that there be numerically distinct whitenesses: that which is more intense, and that which is less intense or remitted, which is the main point.37 An analogous example taken from the category of quantity may help to illustrate further Dietrich’s conclusion here: if even and odd are to be considered properties of numbers, then there is no motion, primarily and per se from even to odd, as Socrates adds one egg to the number of eggs in his basket; rather, the motion is from, e.g., six to seven. Motion

35 ARISTOTLE, Categories, 8, 10b26-11a14. 36 DIETRICH OF FREIBERG, De magis et minus, § 27, p. 65, 3-12: “Ex hoc autem ulterius arguitur ad propositum, quia ex hoc, quod saepe dicti modi pertinent ad genus qualitatis quantum ad intensionem et remissionem ipsius et secundum hoc, ut dictum est, important rem suam privative et respective, secundum hoc, inquam, habent naturam proprietatum et assignatur a Philosopho proprietas qualitatis secundum magis dici et minus. Non est autem motus in aliquo genere quoad proprietates et per se passiones suas primo et principaliter et per se, si consequenter se habet transmutatio in huiusmodi, ex hoc, quod motus sive transmutatio est acquisitio per se et primo partis post partem illius generis, in quo est motus seu transmutatio, puta in quantitate, qualitate et loco.” 37 DIETRICH OF FREIBERG, De magis et minus, § 27, pp. 65, 13 – 66, 19: “Ergo, quando fit transmutatio de minus albo in magis album in eodem individuo substantiae, non transmutatur una et eadem numero albedo secundum dictam proprietatem, id est secundum magis et minus, sed subiectum transmutatur secundum acquisitionem albedinis secundum unum gradum et deperditionem albedinis secundum alium gradum. Et sic necessarium est esse aliam et aliam albedinem numero eam, quae est magis intensa, et eam quae est minus intensa sive remissa, quod est propositum.” 24 B.F. CONOLLY from even to odd can therefore be regarded here as only accidental to the real motion, which pertains to the underlying quantities. (For there can be no even or odd without the underlying quantities.) The argument, if we grant it to Dietrich, not only establishes what he wants, namely, that numerical identity is not preserved in the intensification and remission of qualities, it does so in a manner that is consistent with, and indeed affirms and even establishes, his notion of intensification as being an intrinsic qualitative increase. If Dietrich is correct, nothing can be extrinsically added to the quality that will change the property while the underlying quality remains somehow invariant. Rather, if there is a change that affects the property this can only be because the underlying quality has itself been varied essentially and therefore numerically, that is, in such a way that the initial quality departs, to be replaced by a newly acquired quality that has a different property, namely, a different degree of intensity.38 With this argument Dietrich has certainly turned our attention to the question of what exactly these degrees of intensity are in relation to their intensified qualities.39 That they are properties is even at the surface a reasonable answer, all the more so if we find his arguments to be cogent; and if we accept that they are properties then this is a very good case indeed for the numerical diversity of intensified and remitted qualities. The cogency of the argument, however, depends

38 Cf. the third argument of THOMAS DE BAILLY against the identity theory in his Quodlibet III, q. 15, “Cum caritas intenditur, utrum gradus minus intensus corrumpatur essentialiter,” ed. P. GLORIEUX, Paris 1950, pp. 208-217, especially 210. The argument presented there by Thomas de Bailly is very similar to Dietrich’s argument but does not go into the detail that would show that the white in more white does not really differ from more white: “Album non differt realiter a minus albo nec a magis albo; immo album in minus albo est idem realiter cum minus albo, et eodem modo album in magis albo est idem realiter cum eo; ergo non potest intelligi, cum aliquis movetur de minus albo in magis album, quod fiat variatio secundum magis et minus album quia etiam fiat secundum essentiam albedinis et sic non potest intelligi quod corrumpatur minus album quin corrumptatur realiter ipsum album, nec quod introducatur magis album nisi etiam introducatur album, quia neutrum istorum est aliud essentialiter quam album.” 39 To some extent this question would require us to revisit what appears to be the earlier question (which Dietrich does not address) namely, whether intensification and remission are to be accounted for in terms of the inesse or participation of the quality in its subject, wherein the quality itself remains intensively invariant, or in terms of a latitude of degrees intrinsic to the quality and in some manner determined and actualized. Neither theory is particularly conducive to the addition theory; perhaps inesse could be construed in a manner consistent with it. DIETRICH OF FREIBERG ON INTENSIFICATION 25 on what can only be seen as the obscure argument that more and less are essentially privative, and therefore on the fundamental privativeness of both one and many. But even if we were to grant Dietrich the privativeness of one and of many, more needs to be said about whether or to what extent likeness and unlikeness can be called species of many; and even if so whether the privativeness of many is sufficient to determine likeness and unlikeness to be also essentially privative. Similarly then for more and less. There is distinction involved in the rationes of all these terms, to be sure; but it remains a question as to whether the privation implicit in distinction so overwhelms all other conceptual content in these terms as to determine them to be essentially privative. Despite such concerns as these, Dietrich’s claim that degrees of intensity are properties of qualities remains at least plausible; to that extent his argument is persuasive. But there is a further problem if not with the argument, at least with the result. For since property follows from the essence, the definition of which is given by the species, then if the degree of intensity is a property of some quality (e.g., green, so that greens that differ by degree of intensity thus have distinct properties), it follows that qualities differing by degree of intensity differ not only numerically (which is what Dietrich has argued for) but also specifically, which is more than what he was arguing for. This would be so even with respect to numerically the same underlying subject, e.g., Socrates, whose whiteness intensifies or remits depending on how much time in the sun he has been getting, those whites that differ in degree of intensity differ not only numerically (as per Dietrich’s argument) but also specifically. This consequence is of course not absurd in itself, but it does pose some interesting and difficult questions concerning the relations among, e.g., colors: do two whites differing only in degree of intensity differ in the same way as do white and green? Perhaps degrees of intensity are not so much properties as they are specific differences, in which case Dietrich’s argument, above, would have to be reformulated and re-evaluated.40

40 That qualities differing by degrees differ not only in number but also in species goes well beyond the arguments and results of other defenders of the succession theory. If this analysis is correct, then he perhaps undermines his own doctrine, in that while it may be impossible for two qualities differing only in number to be in the same subject at the same time — indeed this is a version of the incompossibility of the termini of motion argument — it is not impossible that two qualities that differ in species be in the same 26 B.F. CONOLLY

Dietrich’s strategy in both these arguments is in any case both admi- rable and thought-provoking. By drawing our attention to the differences between accidents and substance, and again, by examining what precisely these degrees of intensity are in relation to the qualities that they characterize, he is able to address and undermine one of the fundamental assumptions underlying those theories that insist upon the preservation of numerical identity through the process of intensification. This, again, is the assumption that such intensification takes place by means of the progressive accumulation of extrinsically advening forms. By establishing that, on the contrary, intensification must be intrinsic, and by clarifying that what he means by intrinsic here cannot be confused with the doctrine of the latitude of forms, Dietrich thus makes more plausible that such identity is not preserved.41

5. The succession theory of intensification and actual infinity As was mentioned in the introduction, perhaps the most important of the non-theological objections to the succession theory is that in any such intensification or remission of a quality there will be entailed an infinity of forms.42 For, as long as the intensification is assumed subject. That is, it is no longer the case that less white and more white differ only in number (and thus become subject to the incompossibility argument); rather, they differ also in species. On the other hand, even if successionists have to give up the incompossibility argument, this still has no real bearing on any of Dietrich’s own argument, and thus the strength of his position as established by those arguments. 41 Dietrich offers a fourth argument, which, like the third shows that intensification and remission, that is, more and less, are essential to a quality, but this time by showing that they cannot be accidental to a quality. That more and less cannot be accidental to a quality stems from the understanding that having accidents requires having parts; but a quality, for example, white, is said to have parts only by speaking per accidens. That is, it is said to have parts only insofar as its subject, an individual substance, has parts. In itself, that is, considered apart from its subject, it is simple. Therefore, the intensification of the quality must be in the quality as a whole; and, as Dietrich explains, De magis et minus § 28, p. 66, 26-27: “Quidquid autem positivum secundum rationem totius vel in eo, quod simplex est, inest, hoc ad essentiam pertinet vel est solum proprietas rei.” Since they are essential, more white will therefore differ essentially from less white; and those things that differ by essence cannot be numerically the same. 42 Perhaps the most important of the theological objections to the succession theory pertains to the gift of charity: it is maintained that charity can be corrupted only by a mortal sin. Yet the succession theory maintains that as charity is increased or intensified, the prior less intense charity is completely replaced by the newly arriving more intense charity. Such complete replacement appears to entail in effect the corruption of the prior DIETRICH OF FREIBERG ON INTENSIFICATION 27 to be a continuous motion or change from the remitted form to the intensified form, it was argued that to every ‘now’ in the time of the intensification there would correspond a distinct degree of intensity; but because time is infinitely divisible, it follows that there would be an infinity of nows and therefore an infinity of such degrees. There- fore, if it is thought that the intensification of a quality entails a succession of numerically distinct qualitative forms, it would follow that any such intensification will involve an infinity of forms. A particularly clear account of the objection can be found in Her- vaeus Natalis’ Quodlibet II, question 2: It is argued that if the intensified and remitted were diverse forms really differing then in any alteration there would be infinite forms really differing, because if the intensified and remitted differ really, there are as many diverse forms really differing in the alteration as there are differences according to more and less. But the differences according to more and less are infinite, therefore, etc. The major is clear because more and less are related just as are the intensified and remitted. The minor is clear because there are as many differences according to more and less as there are nows that can be understood to be in the time of the alteration, because in the time of alteration there are no two nows in which the movable is equally intensely altered; but in any time there can be understood infinite nows. Therefore, etc. 43 less intense charity. But again, charity can be corrupted only by mortal sin; yet the succession theory seems to require that charity can be and is corrupted by the arrival of a more intense charity. Dietrich does not appear to have anything to say in response to this objection. 43 HERVAEUS NATALIS, Quodlibet II, Venice 1513 (reprint, Ridgewood, N.J. 1966), fol. 58vB: “Arguitur quod, si intensum et remissum essent diuerse forme realiter differentes, quod in qualibet alteratione essent infinite forme realiter differentes, quia si intensum et remissum differunt realiter, tot sunt diuerse forme realiter differentes in alteratione quot sunt differentie secundum magis et minus. Sed differentie secundum magis et minus sunt infinite, ergo etc. Maior patet quia magis et minus se habent sicut intensum et remissum. Minor patet quia tot sunt differentie secundum magis et minus quot nunc possunt accipi in tempore alterationis, quia in tempore alterationis non est dare duo nunc in quibus mobile sit eque intense alteratum, sed in quolibet tempore possunt accipi infinita nunc, igitur etc.” See also the very similar version of the argument found in HER- VAEUS NATALIS, Quodlibet VI, q. 11, “Utrum aliquod accidens suscipiat magis et minus?,” fols. 135rA-135vB: “Secundo, non [reading non for modo] videtur verum esse quod dicunt, quia quando fit ex remisso intensum corrumpatur prior forma et nova introducatur, quia si non potest eadem forma numero esse intensa et remissa, sequeretur quod in eadem alteratione essent infinite forme numero. Hoc autem est inconueniens, ergo etc. Maiorem probo quia dum aliquid calefit non est dare in tempore calefactionis duo nunc in quibus fit equaliter intensum vel remissum, ergo quot nunc possunt accipi in tempore alterationis tot sunt ibi differentie secundum intensum et remissum. Sed in 28 B.F. CONOLLY

That it is impossible for motion to pass through an infinity of forms is established by Aristotle in Physics VI, where numerous arguments are offered whereby passage through an actual infinity is seen to be impossible;44 and since passage through an actual infinity is impossible, it appears to be necessary to surrender the succession of forms — or, as we shall see, deny the continuity of motion. It is therefore a formidable objection to the doctrine. Defenders of the succession theory respond to this objection in two different ways. First, there are those, like Thomas de Bailly, who accept the premise that intensification is a continuous motion and furthermore, that the succession theory does indeed entail an infinity of forms, but who then argue that the potential infinity thus entailed is not contrary to the Aristotelian prohibition against actual infini- ties.45 The other approach is that taken by Dietrich of Freiberg (perhaps uniquely among medieval philosophers), who responds to this objection first by denying that intensification is continuous, and then therefore denying that it entails passage through an infinity of forms, actual or otherwise. Dietrich’s response is certainly dialectically bold and highly effective — leaving aside for the moment the question of the cogency of his arguments — inasmuch as it disarms the identity theorists of one tempore alterationis possunt accipi infinita nunc, ergo sunt ibi infinite differentie secundum intensum et remissum, ergo si intensum et remissum non possunt esse idem numero, in tali alteratione erunt infinite forme diuerse numero.” For discussion of the dubious attribution of the text to Hervaeus Natalis, see P. GLORIEUX, La littérature quodlibétique, Paris 1935, vol. 2, p. 139. Glorieux suggests that the author should be found among the teachers or students of Hervaeus. For a different opinion, however, see R. FRIEDMAN, “Dominican Quodlibet Literature, ca. 1260-1330,” in: C. SCHABEL (ed.), Theological Quodlibeta in the Middle Ages: The Fourteenth Century, Leiden 2007, pp. 401-492, especially 433-445. A version of the argument is also mentioned by JACQUES THÉRINES, in his Quodlibet II, q. 14, “Utrum caritas augmentata sit eadem numero que prius?,” ed. P. GLO- RIEUX, Paris 1958, pp. 292-293: “Tertio quia aliter sequeretur quod in qualibet alteratione uel in quolibet augmento essent infinite forme numero differentes; et sic in quolibet motu esset pertransire infinita mutata esse in actu, quod est inconveniens, et contra Philoso- phum VI Physicorum.” See also JOHN QUIDORT, Quodlibet I, q. 8, “Utrum aliquid positivum possit produci a non ente? ,” ed. A.J. HEIMAN, in: J.R. O’DONNELL (ed.), Nine Medieval Thinkers, Toronto 1955, pp. 284-286, who also offers a version of the objection in his arguments against the succession of forms. 44 ARISTOTLE, Physics, VI, 10; see also Physics, III, 5-10. 45 THOMAS DE BAILLY, Quodlibet III, q. 15, “Cum caritas intenditur, utrum gradus minus intensus corrumpatur essentialiter?,” ed. by P. GLORIEUX, Paris 1950, pp. 208-217. DIETRICH OF FREIBERG ON INTENSIFICATION 29 of their best arguments against the succession theory. Dietrich offers two arguments against the notion that intensification is a continuous motion. The first argument considers whether the component or con- stituent parts of a continuum are in potency or in act. Dietrich argues that they must be in potency, but then argues that any of the degrees of quality passed through in the course of intensification, and hence the component parts of the motion of intensification, must be in act. Intensification therefore cannot be a continuous motion.46 His second argument turns upon the impossibility of instantaneous motion or change. For if intensification were continuous, then the transition from any one such degree to the next one immediate to it in continuous succession would take place in an instant.47 Because medieval physics does not allow change to take place in an instant, it follows that all change must occur over a determinate length or duration of time; from this it further follows that the succession of degrees is not continuous but proceeds in a step-wise manner.48 The first argument addresses certain fundamental assumptions about time and motion. To begin, then, if we could compare ‘temporal parts’ of a continuous motion with the spatial parts of a

46 See DIETRICH OF FREIBERG, De natura et proprietate continuorum, ed. R. REHN, Opera Omnia III, Hamburg 1983, pp. 249-273, ch. 2, pp. 254, 75 – 255, 78: “Num- quam enim tale corpus secundum dictum transitum inveniretur actu calidum eo, quod gradus caloris secundum suam intensionem tali transitu erit ens in potentia.” Note that reducing each degree of intensity to being in potency, in the course of the motion, is just what Thomas de Bailly does in order to preserve continuity of motion. This first argument therefore appears to be a response directed at Thomas de Bailly (or at least to some proponent of the succession of forms theory who responds to the infinity objection by maintaining that intensification entails only a potential infinity of degrees). Dietrich will argue against this position by maintaining that motion itself requires that the different degrees of quality passed through in the intensification be in act; and it is because the degrees of quality are in act that the motion of intensification cannot be continuous. 47 DIETRICH OF FREIBERG, De natura et proprietate continuorum, ch. 2, p. 255, 78-81: “immo talis transitus, ex quo ponitur continuus, necessario esset in instanti, quia in tali transitu ipsa mutata esse sunt indivisibilia. Quilibet etiam gradus caloris habet esse in indivisibili ex hypothesi; transitus autem indivisibilium, videlicet ubi solum sunt indivisibilia, est in instanti.” 48 This line of reasoning would be equally effective against those who, like Dietrich, defend the “succession of forms” theory of intensification, but who, unlike Dietrich, maintain that such motion is continuous, as it is against those who maintain the numerical identity of the intensified or remitted form. In other words, Dietrich is requiring that any “succession of forms” theory of intensification entail the corresponding thesis concerning the discrete motion of intensification. 30 B.F. CONOLLY

continuous line, the medievals introduce a technical term, mutatum esse, the ‘state of having changed’ or perhaps ‘moment of change’ to correspond to the point on a line which conjoins two parts of line. That is, in a continuous motion or change, it is the mutatum esse that conjoins two temporal parts, as it were, of the motion. Like a point on the line, the mutatum esse is indivisible. But, again like a point on the line, it is a terminus of two otherwise distinct parts (viz., the beginning of one and the end of another). This of course involves the mutatum esse in certain problems. For, with regard to the point on a line, Dietrich asks “how can one and the same indivisible thing, for example, a point, belong to the substance that is one part , and similarly belong to the substance that is another part, which parts are conjoined to each other in the same point, if a point indicates in its essence something really positive of absolute essence?”49 Because the answer to Dietrich’s question is that such is impossible, this accounts for why a point is understood as merely a privation: “For nothing one and the same in number in the genus of positive beings belongs to two natures distinct in number.”50 The problem and solution for the mutatum esse of continuous motion must be analogous. It is not, properly speaking, a privation in the manner that a point on a line is. But it comes considerably short of being considered a positive being, which is to say, it is not a being in act: “Such an indivisible thing, namely, the mutatum esse, does not have any fixed being, but its being consists in a certain transition; and so it is not a being in act, just as any indivisible thing in a continuum is in potency only, unless it were signified in act.”51

49 DIETRICH OF FREIBERG, De natura et proprietate continuorum, ch. 1, § 5, p. 252, 34-38: “Quomodo enim unum et idem indivisibile, puta punctus, est de substantia unius partis, et similiter est de substantia alterius partis, quae partes ad invicem in eodem puncto continuantur, si punctus indicat in sua essentia aliquid reale positivum absolutae essentiae.” 50 DIETRICH OF FREIBERG, De natura et proprietate continuorum, ch. 1, § 5, p. 252, 33-34: “Nihil enim unum et idem numero de genere entium positivorum est duarum naturarum numero distinctarum.” For added emphasis Dietrich (p. 252, 42-43) also cites Euclid’s definition of a point as that of which there is no parts. 51 DIETRICH OF FREIBERG, De natura et proprietate continuorum, ch. 2, § 5, p. 253, 27-30: “Huiusmodi indivisibile, scilicet mutatum esse, non habet aliquod esse fixum, sed consistit esse suum in quodam transitu: et ideo non est aliquod ens actu, sicut et quodlibet indivisibile in continuo est solum potentia, nisi actu significetur.” DIETRICH OF FREIBERG ON INTENSIFICATION 31

Dietrich offers an argument for why, on the contrary, the degrees of quality, which are passed through over the course of an intensification, must all be beings in act, that is, why they cannot be merely beings in potency. He explains: Having been changed (mutatum esse) does not have a fixed being, [...] but rather is, so to speak, a kind of otherness of the movable in respect of the passiones in which motion occurs. Now the Philosopher proves in Physics IV that motion is not otherness. However, everything that is other is other in respect of something, namely, some form or passion. From this it follows that a movable thing in motion actually participates in such a passion. For something is not ‘one and another’ or ‘this and that’ except through some being in act. And so it is necessary that in locomotion the movable thing actually be in a place. Similarly in alteration, it is necessary that it participate in act in the quality according to which it is altered, and so concerning the others.52 In other words, each degree of quality must be assumed to be other than any other degree in the succession; if there is no difference among the successive degrees then there cannot be said to be any motion. But something is different or other only through some being in act. Therefore, it is necessary, at any given moment in the course of any motion, that the movable or alterable thing be in act. In local motion, this means that at any given moment in the motion the movable thing must be in some place; in alteration, this means that at any given moment the alterable thing must participate some quality in act. To maintain the degrees of quality in the course of the intensification are beings in potency only, as would have to be the case if intensification were a continuous motion and if the degrees of quality were comparable to the mutata esse of continuous motion, then there would

52 DIETRICH OF FREIBERG, De natura et proprietate continuorum, ch. 2, § 5, pp. 253, 27 – 254, 41: “Huiusmodi indivisbile, scilicet mutatum esse, non habet aliquod esse fixum [...], sed solum est, ut sic loquamur, alteritas quaedam mobilis secundum passiones in quibus est motus. Probat autem Philosophus in IV Physicorum, quod motus non est alteritas; omne autem quod est alterum, est aliquo alterum, aliqua videlicet forma vel passione. Ex hoc sequitur, quod mobile in motu participet actu talem passionem. Non enim aliquid est aliud et aliud vel alterum et alterum nisi per aliquid actu ens. Et ideo oportet in motu secundum locum, quod mobile actu sit in loco. Similiter in alteratione necessarium est actu participare qualitatem, secundum quam alteratur, et sic de aliis.” Dietrich makes use of similar reasoning in at least one other context, namely, in his argument for why the possible intellect cannot be the image of the Trinity in the soul. See DIETRICH OF FREIBERG, De visione beatifica, ed. B. MOJSISCH, Opera Omnia I, Hamburg 1977, §1.1.1, p. 16, 36-38. 32 B.F. CONOLLY be no motion at all. For, as Dietrich argues, there would not be the requisite otherness distinguishing one moment of the intensification from the next, and motion requires precisely such otherness, which is possible only if the degrees of quality are beings in act. Therefore, either (i) the motion is continuous and the degree of quality in any given intensification is in effect a mutatum esse, in which case, no degree of quality within the course of the transition will be a being in act, but a being in potency only; or, (ii) the degree of quality is a being in act, in which case the motion cannot be continuous, i.e., motion is discontinuous.53 The former is impossible, since motion or change requires that the degrees of quality that are passed through in the intensification are in act; it therefore remains that intensification must be discontinuous. As mentioned above, Dietrich offers a second argument for the discontinuity of intensification. This argument turns upon the notion that if intensification were a continuous motion, then the change from one degree to the next would have to be in an instant: Indeed, such a transition, since it is posited as continuous, necessarily would be in an instant, because in such a transition the mutata esse are indivisible. For54 any degree of heat has to be in [something] indivisible, by the hypoth- esis; but the transition of indivisibles, that is, where there are only indivisibles, is in a instant. Therefore it is necessary for such a body, if it is posited that it is changed according to itself as a whole from a lesser heat to a greater heat, that in such a transmutation, in which something actually hot is to be found, it would remain in act according to some time in some degree of heat, and so such a transition and transmutation will not be continuous, and consequently, neither will be motion.55

53 This, again, is because the degree of quality, as a positive being in act, and neither a being in potency nor a privation, cannot conjoin two distinct parts of the motion or change, as it were, in the manner required for that motion to be continuous. This is because the degree of quality is assumed to be indivisible, and nothing in the realm of positive beings can be part of two distinct entities at the same time. 54 Reading enim for etiam. 55 DIETRICH OF FREIBERG, De natura et proprietate continuorum, ch. 2, § 9, p. 255, 78-86: “Immo talis transitus, ex quo ponitur continuus, necessario esset in instanti, quia in tali transitu ipsa mutata esse sunt indivisibilia. Quilibet enim gradus caloris habet esse in indivisibili ex hypothesi; transitus autem indivisibilium, videlicet ubi solum sunt indivisibilia, est in instanti. Necesse est igitur tale corpus, si ponatur secundum se totum transmutari de minore calore usque ad maiorem, quod in huiusmodi transmutatione, in qua invenitur actu calidum, stet actu secundum aliquod tempus in aliquo gradu caloris, et sic huiusmodi transitus et transmutatio non erit continua, et per consequens non erit motus.” DIETRICH OF FREIBERG ON INTENSIFICATION 33

Since instantaneous change from one degree to the next is impossible, it follows that each successive degree endures for some positive non- zero period of time, however small that may be. Furthermore, since each degree occupies some non-zero period of time, the number of such temporal divisions corresponding to the successive degrees within the time-frame of the intensification must be finite. From this it further follows that there is a minimum degree of quality in any such change (i.e., the degrees of quality themselves are not infinitely divisible in the sense that it is not the case that between any two degrees no matter how close there can always be found another degree). For otherwise, if there were no minimum qualitative difference between successive degrees, then the intensification would never arrive at its terminus in a finite time. Hence, intensification, far from being continuous, proceeds instead in a discontinuous and stepwise manner.56 Taking both arguments together, the result is a remarkable theory of motion: for it follows that in intensification, (i) each degree is a being in act and (ii) each degree is maintained for some minimal non-zero duration of time, so that the intensification takes place in a stepwise manner. It further follows that the degrees themselves are neither infinite in number nor infinitely divisible. Instead, there is and must be a minimum difference in degrees, however inaccessible to our senses this minimum may be,57 so that qualitative intensification

56 Walter Burley, perhaps the most famous proponent of the ‘succession of forms’ theory of qualitative intensification, has different concerns here. Within a similar frame- work, Burley, who wants to preserve the continuity of motion, accepts an infinite series of qualitative degrees. That is, he does not attempt to show that there is no infinity of actual beings, which is what Dietrich has done. The underlying question separating these two approaches to the problem appears to be whether there could be a way of thinking of a continuum wherein any degree within a continuous qualitative change could be a being in act. Dietrich understands the mutatum esse as a term, and thus as a part of a temporal part, as it were, of the change. If this is considered instead as a limit, and therefore, perhaps, not necessarily as a part, there might be some room to grant actuality to the degrees of quality in continuous qualitative change. See E. SYLLA, “Infinite Indivisibles and Continuity in Fourteenth-Century Theories of Alteration,” in: N. KRETZMANN (ed.), Infinity and Continuity in Ancient and Medieval Thought, Ithaca 1982, pp. 231-257. 57 See DIETRICH OF FREIBERG, De natura et proprietate continuorum, ch. 2, p. 255, 89-92: “Nec obstat iam dictis, si quis opponat, quod chorda sonante, si quis trahat digi- tum vel aliquid simile per longitudinem chordae, videtur enim continuus sonus et conti- nue transire de gravi in acutum vel de acuto in gravem.” Dietrich’s response is found in the next paragraph (§ 11, p. 255, 95-101): “Ad primum istorum dicendum, quod sonus 34 B.F. CONOLLY will proceed through a series of very small, but finite, qualitative leaps, resulting in a motion that is discrete, stepwise and discontinuous.58 In this way, Dietrich not only responds to the ‘actual infinity’ objection with a well-reasoned reply, but thus introduces a provoca- tive theory of change that challenges some fundamental assumptions about the continuity of motion.

6. Concluding remarks There is more to the ‘actual infinity’ objection than the number of forms that must be passed through in the process of intensification. The objection argues further that without continuity there is no way for the succession theorists to account for the unity of motion, so that the intensification from white of degree d1 to degree dn would not be one motion, as defined by its endpoints d1 and dn, but several, indeed some large albeit finite number of motions, depending upon the talis chordae non est vere continuus, quamvis secundum sensum sic videatur. Unde sic se habet, sicut dictum est iam de calore, si corpus ponatur calefieri secundum se totum. Non enim huiusmodi vadunt in infinitum, sed in talibus invenitur aliquid minimum, puta quod faciat calorem in tali gradu intensionis, et aliqua minima portio chordae vel exten- sionis, quae generet sonum in tali gradu gravitatis vel acuminis.” 58 That the position defended by Dietrich was not unknown amongst his contemporaries is clear from a couple of sources at least. First, as was noted in a footnote above, John Quidort argues that the succession theory entails the absurd consequence of discontinuous motion. Second, see also HERVAEUS NATALIS, Quodlibet II, q. 13, “Utrum in qualibet alteratione infinitae formae differentes sint sive si remissum et intensum realiter differunt?,” fol. 59rB, who expressly considers the discontinuity of intensification as a response to the actual infinity objection: “Tertio sic. Quia Philosophus in VI Physics ubi probat quod ante quodlibet mutatum esse est mutari et ante mutari mutatum esse in motu, et hoc in infinitum dicit sic. Eadem autem demonstratio et in non continuis. Accipiemus enim tempus in quod est motus, etc. Et sic videtur dicere quod non oportet quod alteratio sit continua sed propter continuitatem motus requiritur unitas formae, et non propter aliud. Ergo videtur quod non requiritur in alteratione unitas formae. Quarto sic. Quia ut dicunt continuitas proprie dicta non est nisi in quantitate dimensiva sed alteratio non dicit tale quantitatem, igitur etc.” Although Hervaeus’ discussion of the succession of forms theory is long and detailed, and especially valuable for his treatment of those proponents of the succession theory of intensification who respond to the infinity objection by attempting to provide an account of the continuity of motion that is consistent with the succession theory (as is the case with, for example, Thomas de Bailly), his reply to this response to the infinity objection lacks clarity and perhaps indicates that he was not directly familiar with an authoritative version (such as that by Dietrich) of the argument. DIETRICH OF FREIBERG ON INTENSIFICATION 35 minimum difference and duration of the degrees of quality. Dietrich does not, it appears, address this part of the objection, let alone offer a response to it. Whether he needs to, however, is a question that will be saved for another occasion.59 Of course, and in any case, Dietrich’s theory of discontinuous and stepwise motion with respect to the intensification of qualities is dependent upon his doctrine of the succession of forms; and it was suggested earlier (but not discussed) that his arguments for the latter appear to be dependent upon his distinctive doctrine of esse and essentia. If we are not persuaded by his arguments for these latter posi- tions, then his arguments for the discontinuous motion of intensification can scarcely stand. But even if we are not persuaded by Dietrich’s arguments, his discussion of the problem of the intensification of qualities remains valuable nevertheless. His unusual approach to the problem draws our attention to several fundamental assumptions concerning the differences between substance and accidents and the relation between them, as well as to the relation between qualities and their degrees of intensity. His analysis of motion at the very least likewise causes us to question our assumption concerning the continuity of motion. The breadth of perspective thereby gained can only lead to a clearer assessment of the problem itself and enables us also to evaluate better the numerous and various proposed solutions.60

Brian F. CONOLLY Bard College at Simon’s Rock Great Barrington, MA 01230 [email protected]

59 See the discussion of this objection and the response by THOMAS DE BAILLY, Quod- libet III, q. 15, “Cum caritas intenditur, utrum gradus minus intensus corrumpatur essentialiter?,” ed. P. GLORIEUX, Paris 1950, pp. 208-217. Thomas de Bailly emphasizes the unity of the subject, and thus responds to the objection in a manner that is adequate, and which would pose no inconsistencies were it to be appropriated by Dietrich. 60 I would like to thank the referees of RTPM for their comments.