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De Zeventiende Eeuw. Jaargang 12 (1996)

De Zeventiende Eeuw. Jaargang 12

(1996)– [tijdschrift] Zeventiende Eeuw, De–rechtenstatus Auteursrechtelijk beschermd

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The Philosophical Foundations of Huygens 's Atomism
Gianfranco Mormino

Huygens's conception of matter is commonly regarded as an eclectic hybrid combining Cartesian and Gassendistic arguments;1. this widespread analysis is chiefly supported by two elements of truth: on one hand Huygens recalls the idea of a subtle matter, whose different classes, characterized by a specific size and mobility of the particles, account for phenomena like light, magnetism, electricity and gravity; on the other he rejects the identity of space and body and assumes the existence of atoms, that is perfectly hard and indivisible bodies moving in the vacuum. Such a description implies a negative evaluation of the depth and coherence of his view, whose failure, according to modern historians, is evident in the controversy with Leibniz: Huygens's obstinate defence of rigid, rebounding atoms against the criticisms of the German philosopher would show the naivety of his approach to the foundations of natural philosophy, which leads him to an ‘illogical’, ‘dogmatical’2. position.

In this paper, which mainly deals with Huygens's conception of atomism and its close relationship with his peculiar interpretation of mechanistic philosophy, I will try to argue against the above mentioned analysis on the grounds that: firstly, it fails to account for the evolution of Huygens's thought, which attains atomism only in the end of his life, after a close confrontation with the problems raised by his own researches about collision and the mechanism of propagation of light; secondly, it improperly overestimates Huygens's debt to his great French predecessors, whose opinions he never accepted with the passive easiness of an eclectic; thirdly, it leads to identify Gassendi's antitypia, an occult property, insusceptible of any experimental verification, with Huygens's perfect hardness, which depends on the contrary on the principles of conservation of motion; lastly, it perpetuates the commonplace about the weakness (or even the absence) of Huygens's philosophy, a judgment which, in my opinion, leads to a major misunderstanding of his role in the Scientific Revolution. In spite of its multifarious and rigorous ‘technicality’, Huygens's scientific activity is always supported by a definite philosophical orientation, which is shown by his predilection for physico-mathematical subjects, by his firm refusal of teleological explanations as well as of occult causes and, finally, by his keen sense for the possibilities and limits of human knowledge. This attitude, however, is very rarely expressed in the works which were published during his lifetime; the reason whereof, I think, mainly lies in his dislike for the scholastico-dialectical model of scientific writing and in his admiration for the pure and concise style of the great mathematicians of the Antiquity (in particular his beloved Archimedes): Huygens's scientific treatises do not describe false paths, do not confute his opponents' theories or justify the methods he himself employed, but just contain the strict development of consequences flowing from the hypotheses. But this does not at all entitle his commentators to neglect the thought structures

underlying his sectorial researches and justifying their methods and goals. Even while apparently stressing the worthiness of scientific enterprise in itself, as for example when he vindicates his own merits in having correctly described how hard bodies collide,3. Huygens does not forget that a causal explanation is still to be found and that the choice of hypotheses depends on philosophical considerations: no deductive proceeding can find its own foundation in itself but has to derive it from a philosophically-oriented experience. Huygens's last years of activity, in particular, are marked by a broader presence of extra-mathematical and speculative interests, which do not involve a weaker commitment to properly scientific researches, but at the same time allow us to suppose the opening of a new phase in his thought and make us regret that it could not last more than a few years. In his writings and correspondence dating 1686-87 to 1694 we can find scattered reflections about: a) the development of science in his century (with particular reference to Galileo and Descartes) and his own historical role in it; b) the ornatus of the world and the degree of ontological variety it presents, with reference to God's aims and potentia ordinata, which are to be detected in finite beings; c) the infinity of space, resting on considerations derived from Renaissance and Copernican thought, although not implying its immobility; d) glory, immortality and other classical philosophical themes about which, for example in Cosmotheoros and Pensees meslees, he follows in Cicero's and La Mothe le Vayer's footsteps; e) the cosmological meaning of conservation principles, until then employed only in particular domains and with heuristic purposes. Even his reaction to Newton's Principia is in a certain sense naturphilosophisch and consists more of a closer analysis of general concepts than of the definition of different mechanical laws to oppose to Newton's ones. Noteworthily, in his last years Huygens focused his thought upon the two canonical concepts of any mechanistic philosophy: matter and motion. In his defence of atomism and of a general relativity principle he shows a new and more consistent awareness of the kind of problems a natural scientist should face and of the kind of solutions he can rightfully offer, in short the definition of an ideal of rationality. Of course I am not thereby assuming that the Dutch thinker contrived an out and out philosophical system; I only want to stress his deep involvement in the philosophical and methodological debate in the second half of the seventeenth century, out of which his work would lose any meaning.

Huygens's critics to Descartes's ‘res extensa’

In 1669, at the end of his researches about collision, Huygens was still uncertain about the physical cause of the transmission of motion; both elasticity and hardness could account for perfect rebound but the choice between these two possible explanations could not influence in any way his perfect physico-mathematical treatment of impact, which deals with abstract bodies.4. His interest in the constitution of real bodies gets deeper in occasion of his researches about the mechanism of propagation of light; not even in this domain, however, he attains an unambiguous determination of physical matter. On one hand the finiteness of the speed of light makes him think that its propagation has to be explained by the compression and restitution of the particles of ether, which should therefore be elastic and divisible

in infinitum. On the other hand he cannot exclude that motion is communicated ‘in instanti vel indivisibili tempore communicari (quod necesse est) quandoquidem quo duriora sunt corpora quae habemus, hoc est quo minus a figura recedunt minusque restituuntur, hoc est, quo minori tempore motum communicant, eo melius leges nostras reflexionis servent’5.: a possibility which opens the way to the existence of simple, perfectly hard bodies.6. In his writings and letters preceding the end of the '80s there is thus no sign of adhesion to any definite theory of matter; a fortiori he could not be ranked in the number of the atomists. Huygens's only certainty concerns the erroneousness of the Cartesian definition of the essence of body, which excludes hardness; in his opinion that conception leads astray, since it perfectly fits to empty space.7. If body cannot be reduced to extension, likewise impenetrability cannot flow from simple dimensionality, as Descartes (who was following on this point the Aristotelian tradition, or rather one Aristotelian tradition) had thought.8. Even more decidedly than Gassendi9. Huygens thinks that the Cartesian argument is meaningless and holds that bodies, in order to prevent each other from occupying the same place at the same time, need to be endowed with an essential property different from the extensio in longum, latum et profundum. He writes to the French Cartesian Denis Papin:

‘Je ne comprens pas comment vostre idée de l'etendue enferme aussi la resistence et l'impenetrabilitè des corps, car ce dire trivial que non datur dimensionum penetratio n'a point de sens legitime.’10.

The contradictoriness of Descartes's theory of matter clearly appears in the determination of the shape of the particles of his second element;11. on one hand he thinks that they are rounded off and made spherical by continual collisions, on the other he states that they can push other particles, thus implicitly admitting that they offer resistance.12. But whence can this resistance derive, if it is not inherent to matter? And how can it have a finite degree? Once again, as it was the case with the collision theory, Huygens is led to deepen his views by the incongruity of Descartes's assumptions: there is no possible alternative to mechanical corpuscularism, the ‘vraye & saine Philosophie’13. which makes use of ‘Principes qui n'excedent pas la portée de nostre esprit’14. and prescribes to explain the occult causes of natural phenomena ‘atomorum seu minimorum quorundam corpusculorum varijs motibus occursibusque’,15. ‘secundum democriti sententiam’.16. Any philosophy introducing corpuscula as causal agents has to explain: 1) what grounds the individuality of bodies; 2) what maintains the shape of bodies; 3) what allows bodies to push each other. The only possible solution is to attribute durities insuperabilis to bodies; therefore, in the Appendix to his Discours de la Cause de la Pesanteur, Huygens openly supports the theory of atoms and void:

‘Pour ce qui est du vuide, je l'admets sans difficulté, & mesme je le crois necessaire pour le mouvement des petits corpuscules entre eux. n'estant point du sentiment de Mr. Des Cartes, qui veut que la seule étendue fasse l'essence du corps; mais y adjoutant encore la dureté parfaite, qui le rende inpenetrable, & incapable d'estre rompu ni écorné.’17.

This statement is soon criticized by Papin, who reaffirms Descartes's objections to atomism and keenly underlines the contrast between atomism and mechanism, retorting upon Huygens the accusation of employing non-mechanical principles:

‘Une autre chose qui me fait de la peine c'est [...] que vous croyez que la dureté parfaitte est de l'essence du corps: il me semble que c'est lá supposer une qualité inhaerente qui nous eloigne des Principes Mathematiques ou Mechaniques.’18.

In his Discours, as a matter of fact, Huygens had written he could not believe that Newton admitted attraction as ‘une qualité inherente de la matiere corporelle [...] parce qu'une telle hypothese nous eloigneroit fort des principes Mathematiques ou Mechaniques.’19.

The argument devised by Papin in order to show the contradiction between the atomistic conception of matter and a sound mechanism bears a great resemblance to the one employed some years before by Henry More (though with quite different purposes):20.

‘Un atome quelque petit qu'on le prenne est pourtant composé de parties reellement distinctes et les unes hors des autres: la moitié orientale est reellement distincte de la moitié occidentale: de sorte que si je donne un coup seulement à la partie orientale pour la pousser vers le Midy, il n'ij a aucune raison Mechanique qui m'oblige à croire que la partie occidentale ira aussi du mesme costé.’21.

Following the Lucretian tradition, the Gassendist François Bernier had already observed that if the absolute cohesion of atoms is denied, ‘tous les corps, quels qu'ils soient, seront [...] egalement aisez à diviser’22. and no solidity or resistance whatever will be possible. Huygens's reply, offhand at first sight, consists of the simple attribution of hardness to matter; being essentially inherent to it, hardness cannot contrast with the ‘veritables principes naturels’.23. He does not actually deny the difficulty, but rather points out that it would undermine Descartes's corpuscular theory, too: any resistance to division in compound bodies has to be ultimately grounded on the originary resistance of simple parts. Descartes himself, in endowing the bodies of his second element with the capability of keeping their own shape and of mutually interacting while colliding, surreptitiously introduces hardness as an essential property;24. but, according to Huygens, he was wrong in posing it as finite, since there is only one matter and nothing can determine it to possess a particular degree of hardness. Any corpuscularism, Huygens means, is nothing else but atomism. Papin admits, but only hypothetically, that ‘si la matiere a essentiellement quelque dureté cette dureté doibt estre invincible’;25. nevertheless, ‘pour s'en tenir absolument aux Principes de Mechanique il faut croire que la matiere d'elle mesme n'a aucune liaison de parties, et que la dureté qui s'eprouve en certains corps ne vient que du mouvement des liqueurs environnantes, qui pressent les parties moins agitées les unes contre les autres.’26. Against this objection Huygens devised a definitive counterexample27. which Papin will not be able to confute: on his elusive reply, essentially based on the articles 4, 11 and 20 of the Second Part of Principia Philosophiae, Huygens simply comments:

‘En fin un corps n'est pas corps selon moy s'il n'a en soy de quoy maintenir son etendue, et je ne vois pas que l'etendue elle mesme puisse servir a cela. Et quand cela seroit vos corps ne pourroient pourtant estre tous que parfaitement liquides, par ce qu'aucune force de pression par dehors ne pourroit empescher qu'au moindre attouchement un tel corps ne changeast de figure, mais cela est contraire a l'experience.’28.

The letter with this answer was not sent until one year later; Cartesianism, in Huygens's opinion, was becoming obsolete and there was no reason to go on with the controversy.

Huygens vs. Leibniz

Huygens's open declaration of atomism in his Discours de la Cause de la Pesanteur attracted also the attention of Leibniz, who had abandoned that theory more than 20 years before; his high esteem for the older Dutch colleague (‘Parmy tous ceux, qui ont jamais soustenu les atomes, personne l'a fait avec plus de connoissance de cause, et y a apporté plus de lumieres, que vous’29.) spurred him to raise the question in the letter of April 11, 1692. Bodies cannot be infrangible, he remarks, without ‘une espece de miracle perpetuel’;30. perfect hardness is an occult quality, ‘laquelle estant accordée, on passeroit bientost à d'autres suppositions semblables, comme à la pesanteur d'Aristote, à l'attraction de Mons. Neuton, à des sympathies ou antipathies et à mille autres attributs semblables’.31. Shortly later he sent his Animadversiones in partem generalem Principiorum Cartesianorum to Huygens, with an explicit invitation to discuss the arguments against atomism contained in that work, where he had criticized the inadequacy of Descartes's attacks.

Leibniz's first objection consists of two arguments which tend to demonstrate the incompatibility of atomism with Huygens's mechanistic beliefs and with the metaphysical principles governing the system of Nature, respectively. Essential hardness does not derive from motion and cannot therefore be reduced to mechanical causes;32. it consequently presupposes God's intervention, and a perpetual one, too. The argument is specifically aimed at Huygens, according to whom we cannot find any truth in nature, unless we assume the existence of bodies ‘dans lesquels on ne considere aucune qualité ni aucune inclination à s'approcher les uns des autres, mais seulement des differentes grandeurs, figures, & mouvements.’33. But, he replies, ‘il faut premierement que ce soient des corps’,34. that is separate beings able to maintain their dimensions and shape. Impenetrability is necessarily a non-mechanical, irreducible quality, since it is precisely the foundation of mechanistic causality and the condition of the intelligibility of natural phenomena.

Moreover Leibniz states that an infinite originary hardness cannot be accepted, because it contrasts with the principles of continuity and variety. Matter, he thinks, is heterogeneous35. and divisible par tout, et plus ou moins facilement, avec une variation, qui seroit insensible dans le passage d'un endroit à un autre endroit voisin’,36. while Huygens's perfectly hard bodies, located in a perfectly yielding space, would originate a leap,37. thus excluding the existence of all intermediate degrees of divisibility, as required by the great order of Nature. But the uniqueness of matter, Huygens says, is much more consonant with the simplicity of the machina mundi and with the exigencies of our understanding than Leibniz's multiplication of the degrees of hardness. It is not uniformity, then, but rather variety that raises conceptual problems to him, as the following passage shows: ‘Ce qui me fait a moy le plus de peine dans la supposition des atomes, c'est que je suis obligè de leur attribuer à chacun quelque figure et qu'elle [sic] sera la cause de la varietè infinie

de ces figures.’38. Assuredly, it is impossible to draw information about the world from God's essence, but we may accept the result of His free creating will as a datum manifested by our senses: ‘Mais quelle est la cause des differentes figures du sable de la mer, lequel j'admire toutes les fois que j'en regarde avec le microscope, chaque grain estant un caillou de cristal, qui ne croit ni ne diminue et a estè tel qui scait par combien de siecles. C'est que le Createur les a fait une fois naitre telles, et de mesmes pour les atomes.’39. This Calvinistic-oriented theological voluntarism does not contrast with mechanism, since they operate at different levels of natural philosophy; Huygens's mechanism (unlike Descartes's one) is essentially critical and does not allow us to find out hypotheses of research, which must be derived from experience, but only to exclude those which our understanding cannot accept, as, for example, horror vacui or attraction at a distance.

Also the discussion about the second objection involves the question of the variety of Creation, a further proof of the philosophical nature of this debate. In his Animadversiones Leibniz remarks that perfect cohesion cannot derive ‘ex nuda quiete’,40. as Descartes had thought, i.e. from the tendency of bodies to persist in their state; otherwise one might also demonstrate that two bodies ten feet apart would maintain the same distance forever, which is absurd. One should rather inquire the reason why the impulsion on one part of a rigid body causes the movement of the whole body. The atomists say that the parts of a continuous body cannot be separated: cohesion is nothing else but simple, perfect, essential unity, that is absence of empty spaces within the parts of matter. But if two bodies touch one another along their surfaces, they will originate an indestructible continuum, a larger atom which no force could ever split; this would cause a progressive and unceasing concretion of the parts of matter ‘instar pilae nivis per nivem provolutae, ac tandem futurum [est], ut omnia in plusquam adamantinam duritiem coaelescant et aeterna glacie obtorpescant, quando causa coalitionis datur, dissolutionis non datur’:41. a phenomenon we have no experience of. The atomists could reply that the surfaces of atoms cannot adhere one to another, for example by attributing a spherical shape to all atoms; but this would really be a ‘grand postulatum’.42. Huygens's answer, however, precisely goes in that direction: first of all, atoms move too swiftly to allow their surfaces to touch for a sufficient time and precisely enough to come to relative rest; more deeply, the creation of flat surfaces would imply a definite teleological intention on God's part, which is epistemologically improper to be admitted and is never to be detected in nature: ‘Vous n'avez qu'a regarder les grains de sable avec un microscope et à voir si vous y trouvez de surfaces exactement plattes.’43. According to Leibniz, God would have acted in view of a particular aim, that is avoid cohesion, if he had not created flat surfaces, which are the simplest shapes one can imagine; in this kind of questions, he adds, ‘on ne doit avoir egard non seulement à ce qui est, mais encore à ce qui est possible.’44. This last consideration is remote from Huygens's patterns of thought:45. we must not assume a priori an infinite variety in Creation, but rather confine ourselves to experience and reason, which show that ‘il est bien plus facile de former quelque surface indeterminee comme en cassant un corps, que d'en former une exactement platte.’46. And this markedly probabilistic attitude is often to be found in his last writings, first of all in the posthumous Cosmotheoros.

Leibniz's third criticism concerns the conservation of relative motion in colli-

sion; like Mariotte, Wallis and Fatio de Duillier, he thinks that, in case of symmetrical impact, perfectly hard bodies would lose their whole motion and come to rest in the point of collision, as it happens with perfectly soft bodies, since elasticity only can make them rebound. According to him, this point is the core of the issue, the definitive argument against atomism, and he wonders how Huygens, who had first discovered the laws of collision, can defend the resilience of inflexible bodies.47. In fact, Huygens promises to explain his view ‘un jour’48. but his answer is not to be found in his letters to Leibniz nor in other writings he published during his lifetime. He just points out that elasticity, whose mechanism consists of compression and restitution of component bodies, cannot of course be attributed to simple bodies, since they have no dislocable parts;49. but Leibniz rather thinks that ‘une particelle de la matiere, quelque petite qu'elle soit, est comme un monde entier, plein d'une infinité de creatures encor plus petites’50. and that ‘il n'y a point de dernier petit corps.’51. Elasticity, though in different degrees, is thus present in all matter.52. The impasse is evident and Leibniz could easily think that his arguments had prevailed.53. Modern historians generally think that Huygens did not actually have a solution or, at least, that there are no sufficient elements to guess it; and it might be argued that the definitive decline of the hypothesis of perfectly hard atoms has not encouraged any philological or historical effort to understand Huygens's point of view.

Traces of a solution can however be found in Codex Hugeniorum 7A; in a passage written before the controversy with Leibniz, Huygens explains that hard bodies differ from soft ones since, in mutual collision, ‘leur vitesse continue tousjours sans estre interrompue ni diminuée, et partant il n'est pas estrange qu'ils rejalissent’;54. if they were at rest in the point of collision, their rebound would be impossible: ‘les atomes en se rencontrant demeureroient toutes collees ensemble et ne composeroient pas une matiere liquide comme elles font.’55. Rebound cannot be a new motion, which, as Leibniz and Mariotte rightfully think, would have no cause; it is rather the continuation of the motion which made the bodies collide: ‘Non enim desinit aut cessat motus, utque in restitutis, sed tantummodo determinatio mutatur.’56.

From a dynamical point of view impenetrability is thus a ‘neutral cause’; it explains rebound (that is an instantaneous change of direction) without any loss or gain of speed; in the impact of indeformable bodies no deceleration happens and relative motion is conserved. The alternative resulting from the controversy with Leibniz cannot be eluded: if bodies are divisible in infinitum, the mechanism of elasticity (that is compression and restitution) goes as well in infinitum, and can no more be imagined or understood, at least not as a mechanism; if, on the contrary, simple bodies exist, one must admit that they can instantaneously rebound, otherwise relative motion would get lost. Huygens's solution, though evidently straining the principle of inertia, is the only possible one in a mechanical philosophy, since it allows to attribute individuality, persistence and activity to the parts of matter without introducing any mind-like property. That's why Descartes himself, in Huygens's opinion, could not help admitting essential hardness. Huygens's concept of infrangibilité is an original contribution to the development of atomism: while Gassendi and his followers, in accord with the ancient sources, accepted antitypia as the very essence of matter, Huygens realizes that the indivisibility of atoms

cannot be explained by mechanical reasons; yet, he refuses to abandon it, as if it were an occult quality, and rather attributes to it the role of only causal agent in the world and of guarantee of the principle of conservation of relative motion.


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