Descartes: Principia philosophiae : [1644 - 1994]

by Jean-Robert Armogathe, Giulia Belgioioso

Atti del Convegno per il 350 anniversario della pubblicazione dell'opera; Parigi, 5 - 6 maggio 1994, Lecce, 10 - 12 novembre 1994

724 pages, Paperback

First published January 1, 1996

Reviews

[William Bies · Rating 5 out of 5]

There are two remote sources of the mathematical physics of today: Plato, in the Timaeus, and Descartes’ magnum opus, the Philosophia Principiæ of 1644. Perhaps someday this recensionist will have occasion to comment on the former once his Greek is up to par, but for now it will suffice to take a look at the latter. What Descartes really does here beyond the trite res extensa – res cogitans distinction is to conceive a novel paradigm by which to render the world intelligible. True, there are no equations in the present work, but by expressly proclaiming geometry the key to a physical understanding of the phenomena Descartes implicitly mathematizes the world. When Bernoulli and Euler, a century later, derive their partial differential equations of hydrodynamics, they are only following in Descartes’ footsteps and realizing his dream. But more than this, the very enterprise of mathematical physics itself is here envisioned for almost the first time – discounting Plato! – and receives its justification. After Riemann and Einstein, we have better reason than ever to hold geometry the prototype of everything in the material world. So, it would not be too much to declare virtually all present-day theoretical physicists Descartes’ heirs, however little survives of the seventeenth-century rationalist’s naïve concrete models.

The standard scholarly edition of Descartes’ works available in English translation in two volumes by John Cottingham, Robert Stoothoff and Dugald Murdoch is actually an abridgment based upon the rather dubious procedure of abstracting the passages supposedly relevant to philosophy from the whole text, which is about the physics and the philosophy together, and printing only those, cutting it down to about one-third the length of the original Latin. To get around this difficulty one is fortunate to have the present bilingual edition from the Felix Meiner Verlag, which reproduces the unabridged Latin text along with a translation into German. The extensive Einleitung by Christian Wohlers, rather than seek merely to paraphrase the lengthy document, does a nice job of elucidating for the inexpert reader the meaning of what Descartes is up to, philosophically speaking: the role of geometry, his dualism and model of causality, ontology and the centrality of language and, lastly, what remains of Cartesian physics today. In addition, Wohlers affixes fifty pages of endnotes and a detailed Latin-German index. Wohlers’ concluding paragraph is worth quoting here in full:

Was bleibt von Descartes’ Physik? Was die Inhalte betrifft, nichts – denn auch die oben angedeutete historische Verbindung zwischen der Cartesischen Wirbeltheorie und der heute noch gültigen Theorie der Entstehung des Sonnensystems ist – wie die überwiegende Anzahl der in den Principia angeführte Theoreme! – keine genuine Cartesische Theorie, sondern mehr ein (unter anderem auch) Cartesisches Motiv, das woanders wiederkehrt. Es is nicht ausgeschlossen, daß andere Motive an anderen Stellen der Physik eine Wiedergeburt feiern werden; aber es ist in der Rückschau immer leicht, vermeintliche Vorbilder gegenwärtiger Ideen zu entdecken, der eine Wiederkehr erkennen will. Was sollte von Descartes’ Inhalten der Physik eine Wiederkehr erfahren? Die gefurchteten Partikel? Aber bei aller Neigung, sich über die bizarren Einzelheiten der Cartesischen Physik zu mokieren: die von ihm vertretene Einheit der Physik ist auch heute, und heute mehr denn je, für die Physik eine dringendere Aufgabe als sie es für die Philosophie jemals gewesen ist; und es wäre zu wünschen, daß die Wege, die Descartes beschreitet, um diese Einheit herzustellen, von Physikern nicht weniger als von Philosophen erneut nachvollzogen würden – denn wenn das Unbehagen, das jeden Leser des beginnenden 21. Jahrhunderts bei der Lektüre der Cartesischen Principia befallen dürfte, diesen Leser anderseits auch in die Lage versetzt, den systematischen Anspruch zu begreifen, den allein man in der heutigen Zeit noch »Philosophie« nennen sollte – denn ein Philosoph ist man nicht, wenn man Bücher liest, die »philosophisch« genannt werden – , wo wird dieses Werk auch heute noch, wenn auch nicht sein, so doch wenigstens ein Ziel erreicht haben. Man kann berechtigte Zweifel daran hegen, ob Descartes, wenn er in diese Welt zurückkehrte, seine Physik mit seiner Philosophie als so eng verbunden würde ansehen wollen, wie er es tat, als er im 17. Jahrhundert die Principia verfaßte. Aber es gehört nur wenig Phantasie dazu, sich auszumalen, was ihm Unbehagen bereiten würde an der Wissenschaft, die man heute betreibt. Zu erkennen, was an die Stelle der von Descartes so leidenschaftlich bekämpften Scholastik getreten ist, könnte – wie mir scheint – durchaus der Beginn einer notwendigen Revision des abendländischen Denkens sein. [pp. lxvi-lxvii]

In this review we shall comment on what may appear striking to the modern reader, familiar with the course that mathematical physics took subsequent to Descartes, without aiming at anything like a thorough analysis. For indeed one could write a whole book on the subject, and in any event Wohlers provides a quite satisfactory 65-page introduction in the present edition to which anyone interested may be referred.

Descartes asserts that all extension is to be thought of as having the same mass-density. If the nature of a body consists solely in its extension and not in anything else, such as cohesion, weight or color, how can one distinguish between kinematics and dynamics? Yet Descartes certainly has a dynamics, though not entirely correct according to classical mechanics as we now understand it, otherwise he could not have a concept of momentum and he could not posit rules of motion governing collisions as he does on pp. 151-155. NB, the non-existence of the vacuum is definitional [pp. 109-111]. Descartes supposes that space must always be geodesically complete.

If, according to Descartes’ definition, motion properly speaking is only relative motion at the border between two neighboring bodies [pp. 121-123], it is hard to see how momentum can be uniquely defined, as momentum is proportional to velocity with respect to a fixed inertial frame. In other words, how can one derive an invariant concept of velocity from the set of relative velocities between neighboring bodies?

Descartes gets into trouble with motions that involve convergence or divergence, because his extension is not supposed to be compressible or dilutable [p. 135]; he appeals to an indefinite division of the body into countlessly many smaller pieces all of which move around in such a way that they can apparently take up more or less space (meaning that parts of other bodies either intervene or depart). But then, if the body is really an uncountable aggregate of points, why would we say that is extended? Measure-theoretically this is difficult to imagine, as he concedes.

Not clear how Descartes can say that one can derive true and certain results from merely fictional premises [p. 223]. True, in logic a false premise can have a true conclusion, but we would not speak of knowledge in this situation. Isn’t Descartes disingenuous, anyway, in opposing church teaching to what one must presume he considers the simple, natural explanation of the formation of world on his theory, and suggesting that the latter is fictional while the former is true? Descartes holds that it is more fitting and orderly for God to create the world fully formed in an instant, rather than for it to evolve from a chaotic undifferentiated beginning [p. 225]. Granted, in either case, the laws of nature are observed at every instant after time zero. But the latter case seems more natural, in that things acquire their structure for inherent reasons instead of having it imposed by fiat.

The whole of Part III is a wonderfully imaginative confabulation, garishly pursued into the smallest details. Descartes’ approach resembles that of kinetic theory of the Fokker-Planck equation for hard spheres in the dense limit (Enskog), with three species. At the threshold between mythology and modern mechanics. It seems somewhat tasteless for Descartes to spin his explanations out at such great length, given that they are neither demonstratively constructed models nor supported by observation except in the most casual, impressionistic terms, without any quantitative analysis. There are too many just-so stories. But one can sense all along how thrilling it must have been for the first time to construct a system of the world on a mechanical basis that, in principle, reduces all phenomena to aspects of the solutions to a deterministic differential equation.

Descartes’ physics falls apart in Part IV. While his astronomy in Part III is, for the most part, quasi-plausible upon superficial inspection, his explanations of terrestrial phenomena look more and more strained and arbitrary, just as, Popper complains, Marxists and Freudians can account for just about anything by their theories. No alternative hypothesis whatsoever considered, no argumentative force, just free-wheeling associations. In particular, his whole system seems very much more unconvincing when it treats chemistry than celestial mechanics or ballistics, as it is hard to see how the forces he entertains could lead to very much specificity in chemical bonds. After all, his particles have a tendency to become ground down into featureless spheres. It is not even very easy to see how, on his principles, the specific gravity of bulk materials can range over such a wide interval (greater than a factor of thirty). In particular, one fails to see how his particles could bind together into molecules, as opposed to being packed together by an external pressure (unlike what is the case with Epicurus’ atoms, there are no hooks).

Descartes’ enthusiasm is comparable to Boyle’s over his discovery of the explanatory possibilities inherent in corpuscularianism, even though at the time few, if any, results had hitherto been obtained. Moreover, let us caution that Descartes’ application is incompatible with his principles, strictly speaking. Just as Lucretius implicitly assumes dynamical interactions alongside his atoms and the vacuum, Descartes often speaks of his particles possessing properties other than mere extension and motion, which he in no way derives from anything more fundamental, such as hardness and in the case of acids versus bases. Moreover, like the ancient atomists, who supposed that their atoms could be very large, even visible, Descartes’ particles can be very different in size and the larger ones susceptible to bending, deformation, elastic restorative forces etc.

Contra Bohr, Descartes supposes that plant and animal life can be explained on the very same principles already introduced [pp. 601-603]. The organic is not a higher stage or potency of the inorganic, as with Schelling.

This reviewer finds it somewhat unnerving how complacent Descartes—supposedly the most rigorous of philosophers—can be, in that for him it is sufficient that his theory has an appropriate answer to every question regarding the invisible bodies, even if they did not exist or if God had arranged things differently than we imagine. This stance reminds one of Epicurus’ indifference [equipollence]; for the latter, it is enough to amass a number of possible explanations, among which it scarcely matters which is true; all we want is to calm our anxiety over dependence on the will of the gods. Also, it is striking how convinced Descartes is that scientific explanation should be easy (even when being applied to the microscopic domain, where we have no prior experience) and should have no need to avail itself of principles that are not already known to us from our experience of macroscopic phenomena. A typical illustration of Descartes’ arrogance:

Nec sane ullus mihi videtur excogitari posse alius modus, secundum quem variorum istorum vorticum motus sibi mutuo minus adversentur. [Nor does it seem to me that there could be any way of explaining how these different vortices would hinder one another’s motions less, p. 251]

Throughout: no mathematical formulae or derivations whatsoever, and (apart from a handful of minor cases) no numerical data either. In other words, what we are used to in the theoretical physics handed down to us from the latter half of the nineteenth century, the confrontation between theory and experiment as a vital part of the research process, does not exist for Descartes, even in a nascent stage.

Re. psychology in Part I: 1) Descartes equates thought with the empirical self [p. 17]. How can one erect a metaphysics in which the absolute ego is missing? 2) Both intellect and will are involved in judgment [p. 41]. For Descartes, the will is the sole source of error. His explanation does seem to hit upon something deep: we err because the will has a natural tendency to go beyond what we know clearly and distinctly, so as to embrace everything.

So much for a miscellaneous overview of contents. Let us cycle back to the question that stands at the front of this review: what is Descartes’ value then from a contemporary point of view? Wohlers sees continuing interest in Descartes’ physics in its systematicity, even though all of its particular models have been superseded. Let us enlarge on the point with which he closes the passage from his introduction quoted above. What is the problem with western thought in its latest phase that stands silently behind the concern expressed? Is it just academic overspecialization, or something deeper? Our society suffers from a baleful concatenation of disciplinary fragmentation (which Henry James, for one, is among the first to rue in his prescient The Dynamo and the Virgin of 1900) and preoccupation with instrumental reason (for which see our review of Max Horkheimer’s Eclipse of Reason).

How could a return to a more Cartesian perspective help? Systematicity implies concern for the whole. At least in principle, one should be more disposed to remember the top-level phenomena that go forgotten when one narrows down one’s focus to an all-but-complete fixation one what is technologically achievable. When the latter becomes paramount, inhumanity sets in. For instance: isn’t in virto fertilization as a solution to the problem of infertility a neat technical marvel (and note well, it is a serious problem when everything is reduced to a mere problem!)? Yes, but what one elides is the fact that, in order for the existing procedures to be maximally efficient and cost-effective, one conceives many more embryos than can be brought to term and just freezes or discards the surplus. To conceive a human being in order to kill it is a horror beyond imagining to any sane person.