by
Gavin Ardley
Philosophical studies, Vol. VII, pp. 83-100, December, 1957
Whatever one may think of the merits and demerits of the Cartesian system one must acknowledge the great vitality of the Cartesian principles. They were launched with a passion, a sincerity, an engagement rarely equalled. The principles in some way met a deeply-felt need stirring in many breasts in the 17th century; a half-unconscious aspiration which many struggled to articulate and expressed in a variety of ways. Bacon, Galileo, Descartes, each in his own way helped to formulate and create the new order, and in doing so stimulated the general appetite for it so that it grew apace. Descartes prepared the ground, Galileo planted the tree, Bacon looked after the `public relations'. The scientific age is the outcome of their work. These men were themselves too close to things to see clearly the consequences of what they were doing; some of these consequences would have greatly surprised them. Could Descartes, for instance, personally the most `existentialist' of philosophers, have foreseen that his principles would give rise to a diametrically opposite regime: that forcing the radical separation and disengagement of man and the material world would lead to a state of brittle `facts' and shallow `emotions', and would provoke the contemporary `existentialist' reaction?
The interpretations of Descartes' intentions and the real nature of his system are legion. Many critics seem to find an initial difficulty in deciding whether or not to take the Cartesian mechanical order literally. Mechanism, so their thoughts run, seems strange, but has not physical science proved its validity? Hence the common ambivalence in discussing the Cartesian philosophy. Not daring to discard the notion of a mechanical universe completely, and yet not wishing to accept it as the whole truth, critics endeavour to steer clear of each extreme. But the mere avoidance of extremes is not sufficient; to bring clarity and conviction we must go beyond uneasy compromise to find a via media which exists in its own right; we must discover the positive truth of the matter before we can profitably discuss variant interpretations. When we find the truth we shall have gained a vantage point from which we shall see both mechanism and anti-mechanism as paths leading down on each side to gloomy depths of nihilism.
When St. Thomas Aquinas surveyed the whole course of philosophical speculation he saw only two basic aberrations: one is to attribute too much independence to creatures; the other is to allow them too little. The truth, as Thomas discerned it, is that creatures are dependent on God and yet not servile, i.e., they are nothing without God and yet with God they are something in their own right. The world is hierarchical, nature is a great society. God did not create a self-sufficient world and then retire; nor is God a puppetmaster pulling all the strings so that creatures only seem to do things but in reality it is God who does everything. The first aberration is `materialism' or `mechanism'; the second is 'spiritism' and is exemplified in Berkeley. As Thomas sees the situation, God in his infinite power freely created the world, but he made creatures with their own natures; by virtue of his infinite wisdom he thereafter respects the natures of his creatures and sustains and enlivens them in accord with those natures. God is power and wisdom together: exaggerate the role of power, the divine freedom, and diminish the role of the divine wisdom, and we destroy the reality of the world and make God and the world alike unintelligible; diminish the role of the divine freedom, and we throw the reality of the world on to an inscrutable eternal "matter", which course too makes God and the world alike unintelligible. Only at the point of balance of divine freedom and reason, of creaturely dependence and autonomy, can we find rationality and truth.
From this central point we may diverge in either direction, but on further scrutiny we find that in going to the extremes the opposites turn out to be the same thing. It makes only a verbal (and possibly emotional) difference whether we ascribe a series of events to an unknowable origin which we call `matter' or to an unknowable origin which we call `infinite power'. In each case all we can know is the series of events; what lies behind them we do not know, we cannot even speak significantly of it. Our expectation of the series' continuance in the future in the same familiar pattern as in the past is one which we may think baffles explanation (the "induction problem" of the empiricists) or may think needs no explanation (the solution of linguistic analysis); or we may conceal the problem by an ascription of permanent properties to matter, or by what in the context is a gratuitous ascription of `goodness' to the infinite power (both of which verbal devices, the first typified by the atomists, the second by Berkeley, manifestly beg the question). Herakleitos and Parmenides on closer inspection turn out to be a single person saying the same thing in two languages, and both ultimately preaching the doctrine of negation.
Our view of God's nature and our view of the constitution of the world are indissolubly linked together. Any view of God's nature other than Thomas's balance of power and wisdom leads inevitably to Nominalism; and Nominalism is the home of nihilism, the repository of all error.
The world, as Thomas sees it, consists of a great society of creatures exercising real but secondary causation, pursuing divers purposes in accord with their natures, motivated by love on many different planes, hierarchically governed; the whole universal Society guided providentially by an all wise and all powerful deity whose nature we dimly see by analogy with the structure and operation we perceive in the world. This general scheme of things appears to be the only possible scheme of the world: shift from it in either direction and we are launched on a downhill slide to nothingness.
When we examine the Cartesian philosophy we find that Descartes tends to oscillate verbally between the two aberrant extremes indicated above: sometimes he uses the language of extreme materialism and ascribes the course of the world exclusively to natural law; at other times he prefers the language of total surrender to an omnipotent and inscrutable deity whose reason and purpose, if any, are quite beyond us. The opposition between these two formulations (corresponding to Le Monde and Meditations respectively) is only apparent. They both amount to the same thing: a planar world, ultimately a succession of events, occurring in recurrent patterns and successions, their ground or origin quite unknowable.
It might appear then that the Cartesian philosophy is merely another aberrant system: one of the long line of such systems which Thomas discerned running through philosophical speculations in all ages. But the astounding works performed by those contemporary with and coming after Descartes who tacitly accepted the Cartesian world-system, forbids any such easy dismissal.
One of the advantages of studying the history of the sciences is that we gain a perspective. The Cartesian problem in isolation might be thought well-nigh insoluble. But considering the opinions of the precursors of Descartes, and taking up the pregnant suggestions of the neo-Kantism interpretations of the exact sciences in our own times, we may be able to reach a solution of the Cartesian enigma.
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Planar Cosmologies
On the grounds adduced above we shall take as our datum point that the cosmology of the philosophia perennis in principle delineates the real structure of the universe (and indeed is the only formulation which does not succumb to reductio ad absurdum); that Plato, Aristotle, Thomas, have laboured to trace out that cosmology; that their insights have revealed it more and more truly; that at least the broad lines laid down are sure, and that further insight will confirm and deepen the perennial doctrine.
Granted this, then what are we to think of the cosmology of the Nominalist group centred on the University of Paris in the 14th century; the disciples of that dark figure, William of Ockham, whose sinister shadow falls across the centuries up to our own day? The two outstanding members of the movement, Buridan and Oresme, laid down the principal articles of the Nominalist system of the world: a self-sufficient autonomous universe; no governmental hierarchy; all things on the one plane. Conducive to these principles, they were at pains to stress God's initial creative activity rather than continuing Providence; to see things coming immediately from the divine freedom without reference to the divine wisdom[1]; they advocated the inertial theory of locomotion, thus promoting the notion of dumb mechanical behaviour[2]; dismissed the intelligences from the skies, and maintained the homogeneity of celestial and terrestrial realms (an essential equation in the Nominalist scheme); argued for the diurnal rotation of the Earth on its axis, so tending to give the Earth the same status as the other bodies of the universe[3]; and compared the universe to a clock.[4] This Parisian Nominalist cosmology is an adumbration of the mechanical universe devoid of purpose with mind as a detached spectator which was gradually to become generally accepted by the 17th century.
This planar system is, from one point of view, manifestly an eccentric cosmology linked with an aberrant theology. If it had not been for subsequent events it is likely that the Parisian cosmological school would have gone down in history as merely another of the many aberrations which have their day and are forgotten in the course of time.
So too with Copernicus: some shrewd geometrical manipulation of planetary orbits combined with an amiable excursion into Pythagorean number mysticism would have earned for its author an honourable but modest place in the long line of philosophical astronomers. But the heliocentric system was seized upon by the Nominalists as a triumphant weapon in the campaign of general levelling: the Earth was released from subservience to the revolving heavens; the universe had no longer a chain of command or any preferred bodies, but all were on the one level of excellence. As Galileo put it long afterwards:
"As for the Earth, we strive to ennoble and perfect it, whilst we make it like to the celestial bodies, and as it were place it in heaven, whence your philosophers have exiled it."[5]
It is evident that some people must have seen quite other uses for these innocent and even quaint speculations: like the astute business entrepreneur who, by a flash of intuition, sees vast commercial possibilities in the contrivance of some harmless inventor whose long-suffering friends have hitherto thought merely a bore; or, more appositely, like the traveller in the African darkness of a former day who comes upon a group of innocent children playing with some rough glassy pebbles, who recognises these as raw diamonds, brings them to Europe, has them cut and polished, and so acquires a set of brilliant jewels to grace a diadem; a transformation of character and purpose so great as to be well-nigh incredible to the simple children whose artless playthings they had once been.
Projection
What a number of people in the 17th century seem to have dimly perceived was that if the universe were treated in thought as if it were of the planar constitution then, with a little ingenuity, it could be re-furbished in thought in an exact and mathematical manner and treated in practice in these terms. As the shapeless pebble is cut along precise geometrical planes to yield the sparkling diamond, so a new order can be projected on to the world.
The drill sergeant can, over a limited area of life, impress his uniform patterns of movement on his human material, at least as far as externals are concerned; the ballet does the same sort of thing with more exuberance; Machiavelli laid down maxims by which the astute prince could manipulate his subjects; modern urban life must of necessity be rigidly stylised in a multitude of ways, as in the traffic laws; the animal trainer may discipline his charges and induce in them remarkable patterns of behaviour unknown to the state of nature. Nonetheless there are obvious limits to the rigid manipulation of living beings, especially humans; the material is pliable in some things but intractable in others. This is not so with inanimate objects; here there are limitations but no revolts. The sculptor finds the marble obedient to his will; the brickmaker experiences no rebellion from the clay when he presses his uniform ingots; the surveyor traces his triangles and parallels of latitude on a submissive land. Inanimate nature is remarkably plastic and compliant to our behests. This fact is relevant when we seek to deal with the world in terms of any a priori philosophical system.
Our understanding of the world is never finished; we can always penetrate further into its nature. While we view things under limitations or with an admixture of error or misrepresentation or deception, we must perforce see the world to that extent blurred or distorted or deformed. The pursuit of truth means the gradual sharpening of the focus and elimination of this deformation; in the meanwhile we took through a refracting medium. This is all the more so when done by deliberate policy, when we project some pre-determined order.
We may regard Oresme's cosmology as erroneous. But the fact remains that if we narrow our horizon then we can look upon the universe as a piece of clock-work; the world is like a clock when viewed through Oresme's eyes. Oresme qua cosmologist projects his system on the world as a projectionist does his shadow show on the screen. By embracing the planar system Oresme and his friends thereafter bent the world to the terms of that system; inertia, celestial-terrestrial parity, and so on are the instruments of that bending; not invincibly so they could have passed on to a wider perspective, a more wholly adequate system, could have climbed out of Nominalism; but while arrested under the dominance of their principles they moulded their understanding of the world's events accordingly and systematised them on that basis. While we entertain errors, aberrations, pre-determined notions, we ipso 'facto project them on to the world.
The projective process is not always a merely external and passive reception. Sometimes there is an inner moulding as well as an external impression. With human regimentation there is quite evidently an impress not merely on the enforced mode of behaviour but on the nature itself. Unless of very strong character, people tend to become dreary and hopeless automata if they are made to conform to an oppressive and dreary routine. The performance of an actor is enhanced, his genius is called forth, by a responsive audience. Animals, like dogs and horses, are very susceptible to sympathetic treatment. In the inanimate world can we detect a similar sensitivity? The fact that there is no clear line of demarcation between animate and inanimate makes this not unplausible. Is the beauty of the crystal dependent on the sympathy and response of the beholder? Is beauty merely excluded temporarily from purview in treating the crystal as a space-lattice for X-ray analysis or is there a more active withdrawal and atrophy of its aesthetic character and a yielding and conformity to the geometrical probing of its investigator? The viruses seem to look two ways: they will respond as complex molecular lattices or as virulent organisms according to the demands made upon them. Is it merely fanciful to think that the old mahogany chair makes a warm if dumb response to one who treasures it, but withdraws into a wretched subjection when a chemist prepares to analyse its patina?
Whatever we may think of the possibility of an inner response of the inanimate world towards conformity to what is projected on it, there can be little question of its external passive obedience within wide limits. A corpuscular-minded physicist will "find" corpuscles in a beam of electrons; his wave-minded colleague will "find" waves; the stream will likewise oblige the wielder of the Schrödinger y wave equation which subsumes the wave and the corpuscular properties. The inanimate world is singularly tractable and docile to those who have learnt the rudiments of the art of leading it. Compare Galileo's remark:
"When the geometrical philosopher would observe in concrete the effects demonstrated in abstract, he must defalcate the impediments of matter; and, if he knows how to do that, I do assure you, the things shall jump no less exactly than arithmetical computations"[6]
If Oresme is determined to interpret the universe as a kind of clock then, while he restricts himself to his own chosen ground, he will not find any protesting voice from the bodies of the universe; he can `save the appearances' with impunity on his own field. So too with Copernicus: restricting his view to the mere geometry of the universe he encountered no resistance to the heliocentric pattern from the bodies so regimented.
The egalitarian world-picture was taken up avidly in the 17th century and has remained the generally accepted scientific world-order ever since. If in fact the universe is the sort of hierarchy which Aristotle and Thomas believed it to be then the systematic projection of the levelled out scheme of things is, in a sense, a régime of ruthless tyranny: a romantic spirit might be tempted to wonder if the seemingly insensate physical universe is really suffering from this long repression; this enforced alienation from the world of mind and love and purpose; if it is crying out in some dumb way for justice, for recognition.
The new men of the 17th century were oblivious to any gentler and more sympathetic natural philosophy; they were concerned rather to conquer nature. It is only in the last half-century that many people have come to recognize at all clearly the role of projective processes in this conquest, and the fact that such processes enter fundamentally into forming the structure of the exact sciences. Henri Poincaré unfolded the theme in terms of conventions of measurement and definitions; C. I. Lewis in terms of active attitudes directed pragmatically; P. W. Bridgman with the operational principle; Wittgenstein and the categories of language; Sir Arthur Eddington and Procrustean beds; and behind them all, the stiff archetypal figure of Kant.[7] Equipped with this principle of interpretation we can look back to the 14th century and recognize the groundwork of the new order projected by the Nominalist cosmologists as a planar cosmology; to Descartes, and observe its clarification as a mathematical order; to Galileo as the operative genius who consummated the new order in his exact mathematical laws.
The Cartesian projection
At the age of 23 Descartes had a vision of a marvellous new science: his subsequent writings would seem to be a series of attempts to unfold and expound his discovery, and recruit others to his cause. In his early exposition, the unpublished Le Monde, he advances rather baldly the general scheme of a levelled-out mechanistic universe. In the later Meditations he expounds the theme with more subtlety and circumspection and instead of dogmatic assertion he sets out to convince his readers. Finally, in the Principles, he endeavours to set out his new science in a systematic order of propositions. As a prelude to the Meditations he published the Discourse on Method which is his philosophical testament and an `existential' document of the first order.
It is customary to consider the Cartesian system as a metaphysical doctrine, as something ontological. Viewed as such it is full of paradoxes and largely indefensible. But if we suppose that its prime significance is projective (albeit Descartes himself may have been far from clear about its purport), then we may discern more reason in it; matters obscure or even absurd when viewed ontologically may now appear clear.
In Le Monde Descartes sketched a highly ingenious scheme of the universe in terms of matter and natural law. It was nonetheless arbitrary and unconvincing and he did not publish it. In the Meditations, which he did publish, he deepened and enriched the scheme and laboured to render it more generally acceptable; he changed from the language of matter and its laws to the equivalent (although seemingly more familiar and orthodox) language of immediate divine omnipotence; by counselling systematic doubt he sought to disengage his readers' allegiance from the familiar order of the universe; by the cogito principle he solicited their assent to the withdrawal of mind from matter, established a firm isolated vantage point for mind, and made mind the spectator (or more properly the doppelgänger) of a purely material world; to form this world he made an ingenious appeal to the divine guarantee and on these credentials he projected forward a phantasm, a mathematical continuum of extension which, he claimed, was the true nature of matter. In the ordering of mathematical extension Descartes at last found the triumphant use for mathematics which had delighted him by premonition from his youth (Discours, Pt. I).
As an objective ontological analysis of the world the programme of the Meditations will not survive serious scrutiny. But its form: a series of meditative exercises designed to carry the mind of the reader on step by step until a re-orientation to the universe is accomplished, and the nature of its doctrines, all show it to be a more carefully contrived presentation of that same `miraculous' new outlook on the universe adumbrated in Le Monde. Nor need we doubt the sincerity of Descartes' professions: he wrote with burning zeal and transparent honesty, and the contrivances of argument are manifestly designed to accomplish the all-important re-orientation of his readers away from vulgar experience towards the proposed new exact ordering of things. The new vision is not for all: initiation into the esoteric lore is for the chosen few (Discours, II); and these must be led and exhorted stage by stage to see the light. The image of Plato's cave inevitably comes to mind; but the Sun of Descartes is not the Sun of Plato.
The Meditations makes a decisive step forward from Descartes' predecessors. Descartes tacitly confirms the leveled-out universe of Oresme and Buridan, but adds to the earlier projection the decisive element of mathematical manipulation. Descartes himself made little progress in the employment of the new mathematical order: that is where the great triumphs of Galileo lay. Descartes created a new army: its successful deployment was the work of others.
The new cosmology
When in Le Monde Descartes charted his scheme of the universe he devoted himself to making the planar measurable order credible, and let his imagination run freely on the possible origins and evolution of such a world.
He first disengages our natural judgement of the world by a plausible argument designed to illustrate the difference between our sentiments and the things which produce them (notwithstanding that the point he is making rests on the contrast with the cases where our senses do not misrepresent the situation - Le Monde I); by this means he endeavours to reconcile us to the paradoxical thesis that the world is really very different from what our senses tell us it is; he is preparing the way for the mechanical model of the universe.
He proceeds to construct his model; he fills his nouveau Monde completely with matter of various degrees of fineness leaving no void. (If the essence of matter is extension then to say there is extension without matter would be a contradiction in terms). He goes on to lay down on semi-intuitive grounds the laws of this new matter: laws professedly given by God and in terms of which the new universe functions; laws which, as he will explain later in the Discours, are so evident that to assent to them no more is needed than simply to understand them: viz., inertia, conservation of total motion on collision, and the centrifugal effect of circular motion (Le Monde, vii); laws whose precise derivation he does not now, nor will he later, reveal explicitly because of the possible jealousy of critics (cf. Discours V, opening passage et al.)[1]
Descartes imagines a primeval condition of rest; God gave to the assemblage of matter the first fillip. The ensuing exchange of motion between the particles leads, he argues, not to a state of chaos, but to the formation of vortices. At the centre of each vortex fine (or fiery) matter accumulates and thus is formed a star. One of these is our Sun. Around the Sun rotate massive bodies formed by accretion; these are the planets, and one of them is the Earth.
Whatever the initial condition of the universe, even if it be the most confused chaos the poets can describe, the parts will sort themselves out by the operation of the laws of nature, and a universe like our own will gradually evolve spontaneously. Our universe is the only possible final one.[2]
The unknown X
The model of the universe proposed in Le Monde is a purely mechanical one, devoid of mind and purpose: mind is a spectator, not a participant (cf. Discours V). God gave the first fillip; thereafter the bodies composing this universe have continued obedient to the laws of nature. The only cause remaining of Aristotle's four causes is the efficient cause, and this in its isolation lingers on merely as a vestige: a mathematical order does not partake of cause in any intelligible sense. Providence and purpose are rigorously excluded from the Cartesian world. We shall discuss this causal situation later: for the present, let us consider Descartes' invocation of God. He requires God to give the first fillip, i.e., to set the whole universe in motion; a totality of motion which, by Descartes' 2nd Law, is conserved thereafter. After his initial intervention God leaves the universe to sort itself out following the laws which he has ordained: laws which Descartes lays down dogmatically in Le Monde but which in Discours V, he suggests are, concurrently with their impression on nature, impressed likewise on our minds in the form of innate notions; notions which, by their clarity on introspective reflection, can be known to all mankind. The certainty, the immutability, and the continued operation of these laws of nature is guaranteed by God's infinite power and changelessness (Le Monde Ch. vii); or, as Descartes expresses the matter in the Meditations, his perfection and goodness. In this way, through the impression of laws on matter, we can reconcile the changing world with the unchanging God. In Le Monde there is no suggestion of any real delegation of powers to matter; there is no hierarchical master-servant relation; no real secondary causes exercised by matter; we can speak of the total autonomy conferred on matter, or the total attribution to God, indifferently; but we cannot operationally combine the two in any intelligible manner in the Cartesian scheme. In Le Monde then, the universe of matter is envisaged as governed by blind laws. God is invoked as a guarantor of these laws by virtue of his power, and of their continuance by his changelessness.
In the Meditations Descartes suggests an apparently different interpretation of the situation (Meds. iii; cf. Princ. i, 21). There he envisages the course of time "divided into an infinity of parts, each of which is in no way dependent on any other. . . . In truth, it is perfectly clear and evident to all who will attentively consider the nature of duration that the conservation of a substance, in each moment of its duration, requires the same power and act that would be necessary to create it, supposing it were not yet in existence; so that it is manifestly a dictate of the natural light that conservation and creation differ merely in respect of our mode of thinking and not in reality."
This is employed by Descartes as an argument to the existence of God. God, it seems, recreates the world at each successive moment of time in the new configuration required by that moment. The fall of a stone, for instance, would be something like a moving picture show: really a series of still re-creations, but giving the appearance of continuity. The natural laws find no mention here: they are subsumed into the habitual patterns of God's activity.
In Le Monde there is total attribution to matter and natural law; in the Meditations there is complete and immediate dependence on God, the world having no autonomy of any kind.
Is there any real contradiction between these two? On reflection it would seem not. For the Cartesian "matter" of Le Monde would appear to be only a metaphor, a vehicle for natural law, or rather a personification of natural law itself (Descartes' analysis in the Meditations of "matter" as extension is a clarification of this point). "Natural law" is mathematically clear and intelligible; it prescribes a certain pattern or order of events. When Descartes' abstract "material" bodies interact they do so in obedience to mathematical laws; the laws are the gist of the situation. To speak of `matter' and `cause' in this abstract content is misleading.[3] It was left to Berkeley to exorcise the ghost of `matter ' from the phantasmal world which Descartes had created. `Cause' had a more tenacious hold; in spite of being obscurantist in this context, it was retained by Descartes, Locke, and Berkeley, and was only finally banished by Hume. One wonders that a Hume did not appear long before. With the atrophying of cause in Descartes' hands the ascription of the natural laws to `God' is fundamentally unintelligible. The ultimate meaning or origin or basis of Cartesian natural law remains inscrutable. At the most we could attribute its reign to an unknown X. Descartes calls X 'God', but this is surely meretricious. Such a theology is profoundly meaningless; it would be a God whose only operative attribute is unlimited power or irresponsible will devoid of any reason we can recognize, one who is so possessive that he dictates arbitrarily even the eternal verities, one whose nature is utterly beyond us (if indeed we can even speak of 'nature' in such a situation), with whom we could enjoy no community of reason or love. Both the universe and God on such a basis would be un-knowable.[4] X, the unknown behind the scenes, may equally well be called 'God', or immutable 'natural law', or `eternal matter'; whatever we call it, its content is nothing. David Hume was properly contemptuous of all such mystification.[5]
In writing Le Monde Descartes was concerned to expound his new order of nature in a simple and direct manner and called X by the name of natural law. 1n the Meditations he presents the system again in what he undoubtedly believes is a more illuminating and convincing guise, and here he changes the name of X to God. The only real advantage of the term 'God' here is emotive; it gives a credibility in the mind to the reign of law and ensures more respect for the immutability of law; it answers the inductive problem by cloaking it in an alleged divine wisdom, or rather it appears to do so. The Cartesian 'divine wisdom' or 'goodness' evaporates when examined. The terms merely disguise the problem inherent in any Nominalist philosophy. The Nominalist world and the nature of God envisaged as the first principle of such a world are alike irrational and nihilist. But regarded not as metaphysics but as a programme of projection of a phantasmal substitute for the real world, the scheme becomes more intelligible.
The body-mind parallelism
Descartes' intuitive procedure by which he professed to find certainty for the external geometrical order in the innate contents of his mind, may be compared to a film projectionist, looking at his film in the projector rather than at the screen on which he projects the image: he is entitled to take the correspondence for granted. Descartes claims that the mind knows itself more easily than it does objects. From the common-sense point of view, from the point of view of rational philosophy, this is absurd. Descartes could only justify it by supposing that God implants the ideas in the mind to correspond to the external order; but such an occasionalist metaphysics is shallow and sophistical, and when pursued further is arid. If, however, we regard the new order as projective rather than ontological we have no need to resort to this desperate expedient of occasionalism. We project a predetermined order, hence the prior knowledge and the necessary character of the new science. There is no puzzle about this and no need to invoke a mysterious psycho-physical parallelism. Descartes was very alive to the a priori character of the new science; but his misguided theory of innateness kept him thereafter a prisoner; he failed to see that there must also be an a posteriori facet: what is projected must be governed by experience, by the response of the world to our ordering. Having created his phantasmic mathematical extension Descartes' genius grew fitful. Galileo, with a less conscious metaphysical formulation, far surpassed Descartes in practice. It was Galileo, not Descartes, who discovered the new philosopher's stone to transmute the leaden metal of the universe into mathematical gold.
But one thing which Descartes did with his continuum has been an invaluable asset ever since: he evolved a new mode of geometrical analysis: he married extension with algebra and made his brilliant advance into co-ordinate geometry. The Euclidean geometry grew by abstraction out of the forms of the material world of common experience and was held bound by figures; it was a heavy and inflexible system for the new order. Descartes, having emancipated himself from the old world of thought, proceeded to emancipate himself from its geometry. He employed in its stead an untrammelled system of algebraic symbols representing positions in 2 or 3 dimensional space. The final emancipation of co-ordinate geometry was not achieved until the 19th century when n-dimensional geometries were introduced: it was an unwitting archaism of Descartes and his immediate successors that they limited themselves to the 3 dimensions of space as we experience it. Multi-dimensional geometry could have been employed from the beginning: the Cartesian phantasmic order being our own creation properly knows no bounds except ultimate expediency.
Cause
Aristotle distinguished the four causes to be found in any practical situation, e.g., in building a house: the final cause, the purpose for which the house is intended, providing the motivation for the whole building operation; the material cause, the stones, wood, etc., of which it is to be built; the formal cause, the plan or design by which it is built; and the efficient cause, the activity of the builder in setting up the components. In doing so Aristotle was not distinguishing four separate or even separable causes, but one situation with four facets. To isolate any one of these four causes is to deprive it of meaning and render the other three nugatory. The Aristotelian analysis illumines real substantial situations. In the abstraction of mathematics it does not appear that any such analysis can be significant; mathematics is effectively [a-causal].[6]
The Cartesian projection of a mathematical order of extensions is properly a-causal for this reason. Descartes himself effectively excluded from his model universe all but one of the four causes; he retained efficient cause. The efficient cause for Descartes in its isolation is ghostly and vestigial and is appealed to virtually only to attempt to explain how God controls the events of the world; a very ambiguous `explanation' as we saw above. Between the events themselves Descartes usually recognises that there is no real causal connection but only regularities of succession as ordained by God and following the patterns of the `laws of nature'. Any Nominalist scheme of things making the world a series of events dependent immediately on a God who is infinite Will only, must come to the same point. The Nominalist God is a sort of puppet-master or Prospero conjuring up illusions; he is himself wholly arbitrary and inscrutable to us, albeit he deigns to order events with a visible regularity.
Berkeley's world scheme is of this very type. For Berkeley there are no substantial bodies, no real secondary causes, in fact no world in any intelligible sense, but only a series of impressions or `ideas'. His God is an infinitely powerful Prospero. The laws of physical science are, for Berkeley, the records of the habitual succession of the acts of this mysterious and unknowable conjurer.
David Hume saw very clearly that in a world whose only attribute is regular concomitance of events, the ascription of these events to an unknown X or God is quite gratuitous. Hume had a higher standard than his Nominalist predecessors; he saw very clearly that the God of Descartes and Berkeley was an imposture, a caricature, an idol. His atheism was a protest against false theologies. He was probably himself in a state of almost invincible ignorance concerning the true nature of the world and God as envisaged by Aristotle and Thomas.
Cause and God with Descartes are then merely fragments of the ontological order which accidentally strayed into Descartes' new mathematical projection (there to bring confusion ever since). The criterion of "clear and distinct" is the badge of this new order, a criterion applicable to the mathematical; whereas dim intimations of the shapes of things, rough and ready regularities (except in the heavens where precision reigns), the operation of real causes, and an analogical but true knowledge of God, is the substance of the Aristotelian-Thomist order of being. Descartes was not himself very clear about what he was doing and did not adequately discriminate the two orders; he needlessly embarrassed himself by retaining in an alien context old items of philosophical furniture (encouraged too, perhaps, by deference to the susceptibilities of his readers). Emancipation has come slowly; only after three centuries have there been any serious attempts to unravel these twisted strands.
The gradual attrition and disappearance of the notion of cause in the exact sciences in the last century or so should not be surprising; it was written into the Cartesian mathematical projection, but it took two centuries before the fact came to be generally recognized. The relevance of cause is in inverse proportion to the phenomenal character or abstractness or exactness of the science. The more concerned with regular succession or the more mathematical, the more a-causal it is. The more concrete and practical and approximate and singular, the more concerned we are with weak but genuine agents, the more fully are we committed to cause; not merely an attenuated 'efficient cause' but the totality with the four aspects which Aristotle traced out.
The Anonymity of the Cartesian world
When Descartes projected his mathematical phantasm he created an order devoid of purpose, of love, and of individuality. The entities of his universe are profoundly anonymous. The name is the symbol of individuality, or personality. 'What is your name?' is the ancient formula of the catechist. Men have names. By association with men so have individual dogs, houses, trees, ships, etc. But a Euclidean triangle has no individual name; there is no individuality in mathematics. By substituting a mathematical order for the real world, Descartes destroyed the individual, the unique. He is the creator of the swarms of identical electrons, quanta, etc., of the modern era. He is the spiritual father of the age of mass-production.
GAVIN ARDLEY
University of Auckland
[1] The novelty of exact "laws" as distinct from the more elastic "principles" of Aristotelian physics is characteristic of the new order of embodied mathematics.
[2] The Cartesian spontaneous evolution to equi-finality bears some similarity to the open-system theory of Ludwig von Bertalanffy, although it is doubtful if the Cartesian universe is an `open system' in Berlalanffy's sense. See his Problems of Life, and the article General System Theory, in BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE, 1950.
[3] Newton used the language of cause, but its rôle would seem to be with him a mental aid rather than something constitutive. The Newtonian system transformed from its "force" formulation into "energy" terms sheds its casual expression without, it would seem, any ascertainable loss. Similarly, the notion of `matter' has become a non-entity in modern physics.
[5] Cf. Pascal's remark:
"I cannot forgive Descartes. In all his philosophy he would have been quite willing to dispense with God. But he had to make Him give a fillip to set the world in motion; beyond this, he has no further need of God.” – Pensées, 77.
[6] It may be held that in mathematics there is only one cause, the formal cause. But the term cause is better avoided entirely in such a situation; its employment can only be misleading.
[1] Cf. Nicole Oresme, Le Livre du Ciel et du Monde, ed. Menut and Denomy, 69 d. This remarkable commentary on the De Caelo is an early manifesto of the modern scientific weltanschauung; it deserves to be more widely known.
[4] Oresme 71 a.
[5] Dialogo dei Massimi Sistemi (Firenze 1632) p. 29. Giorgio de Santillana's English translation (Chicago 1953) p. 40.
[6] Dialogo p. 202, de Santillana p. 222.
