A medieval Arabic analysis of motion at an instant: the Avicennan sources to the forma fluens/fluxus formae debate

The forma fluens/fluxus formae debate concerns the question as to whether motion is something distinct from the body in motion, the flow of a distinct form identified with motion (fluxus formae), or nothing more than the successive states of the body in motion, the flow of some form found in one of Aristotle’s ten categories (forma fluens). Although Albertus Magnus introduced this debate to the Latin West he drew his inspiration from Avicenna. This study argues that Albertus misclassified Avicenna’s position, since Albertus could not conceptualize motion at an instant, whereas it is claimed here this was the very position Avicenna adopted. The paper includes an overview of Albertus’s discussion and a brief survey of the Avicennan sources upon which Albertus drew. The heart of the paper treats Avicenna’s analysis of motion at an instant. Avicenna’s general argument was that since spatial points have no extremities, nothing in principle prevents a moving object from being at a spatial point for more than an instant, understood as a limit. It is then argued that Avicenna had the philosophical machinery to make sense of a limit, albeit not in mathematical terms, but in terms of an Aristotelian potential infinite. The first and foremost topic of classical and medieval physics is the concept of motion (Grk. kinēsis, Arb. h ̇ araka, Lat. motio). Within the complex of issues and problems associated with motion, the question ‘in which category does motion itself belong?’ occupied a position of considerable importance in scholastic natural philosophy. In the Latin tradition the problem was most typically framed in terms of whether motion should be characterized as a forma fluens or a fluxus formae. AQ1 Albertus Magnus, it would seem, philosophically introduced this topic into Latin natural philosophy in his commentary on Text 4, Book 3 of Aristotle’s Physics. Yet, as Albertus himself admits, the immediate historical origins of this debate are found in the writings of the Arabic philosophers Avicenna and Averroes.1 * Department of Philosophy, University of Missouri-St Louis, 599 Lucas Hall (MC 73), One University Blvd, St Louis, MO 63121–4400, USA. Email: [email protected]. I would like to acknowledge the National Endowment for the Humanities, the University of Missouri Research Board and the University of Missouri, St Louis Center for International Studies, whose support made this project possible. Many thanks go to Jules Janssen for allowing me a preview of the relevant chapters in the forthcoming edition of the ‘Marinus’ Latin translation of Avicenna’s Physics. I am also grateful for the extremely helpful comments made by two anonymous reviewers, comments which certainly have helped improve the content and accessibility AQ5 of this study. As always any shortcoming are my own. 1 Ahmad Hasnawi, in his recent study ‘Le Statut catégorical du mouvement chez Avicenne: Contexte grec et postérité médiévale latine’, in De Zénon d’Élée à Poincaré : Recuil d’études en homage à Roshdi Rashed (ed. R.Morelon and A. Hasnawi), Les Cahiers duMIDEO, Volume 1, Louvain-Paris, 2004, 607–22, translates BJHS 39(2): 1–17, June 2006. f British Society for the History of Science doi:10.1017/S0007087406007941 This study starts by looking briefly at how Albertus frames this debate. He does so by investigating five approaches to the conceptualization of motion, which he claims to have drawn from Avicenna. Included within these five approaches are the forma fluens and fluxus formae characterizations of motion. Albertus maintains that Averroes espoused the former and Avicenna the latter position. I next quickly consider Avicenna’s own historical catalogue of the various ways in which motion had been conceptualized. Albertus admits this was the precursor for his own characterizations. The heart of the paper considers to what extent Albertus has properly classified Avicenna’s position concerning the characterization of motion. More specifically I suggest that Albertus and subsequent historians of science have misclassified Avicenna’s characterization of motion. Of the five approaches, Albertus canvasses one which he virtually rejects out of hand as feeble or unsound (sententia debilis), for it takes motion to be a univocal term and so a category in itself that subsumes the various types of motion. I contend that the position is not as untenable as Albertus would have one believe. There are textual and philosophical grounds in the writing of Avicenna for thinking that he may have endorsed such a view. Albertus addresses the question ‘in which category does motion itself belong?’ by delineating five ways of conceptualizing motion. First, one may consider motion by reference to its mover. In this respect motion would fall within the category of action. Second, one may consider motion by reference to what is moved or the mobile. In this respect motion would fall within the category of passion. Third, one may consider motion by reference to its final end or goal (finis et terminus) or, to be more exact, to the successively acquired stages of a moving thing during its process towards its ultimate end. On this account motion is not considered to be essentially different from the end to which it is directed, but only differs from it in its mode of being. In this respect motion is identical in essence with the end it attains, so motion is an equivocal term, since motion’s different ends fall under the distinct and irreducible categories of quantity, quality and place. This is the idea of a forma fluens, which Albertus ascribes to Averroes. Fourth, one may again consider motion by reference to its end or goal. But instead of characterizing motion with respect to any of Aristotle’s categories, one views it simply as a ‘means leading to a categorical result ’ (via ad rem praedicamenti) or a ‘principle leading to it ’ (principium ad ipsam). Motion, on this account, is a certain type of imperfection. It is not the complete or perfect possession of a given end but only a means to that end, and so does not strictly speaking exist, or at least does not fully exist. However, since the categories only contain things that exist, motion itself cannot be subsumed under one of the recognized categories. In this respect motion is in a certain sense outside any categorical classification, so the only reality it has is as a for the first time in a modern language the relevant Avicennan text, at ̇ -T ̇ abı̄‘ ı̄yāt, as-samā‘ at ̇ -t ̇ abı̄‘ ı̄ II.2. Although Hasnawi’s article and mine treat the same topic, the two articles do not repeat one another. Instead it is to be hoped they complement one another. 2 Albert Magnus, Opera Omnia (ed. Wilhem Kübel), Volume 4, Part 1, Physica (ed. Paul Hossfeld), Aschendorff, 1987, III, 1, 3, 150–6. 3 Albertus Magnus, op. cit. (2), 150. 81–151. 5. 4 Albertus Magnus, op. cit. (2), 151. 5–15. 5 Albertus Magnus, op. cit. (2), 151. 16–52. 2 Jon McGinnis