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Bertrand Russell on Bosocovich’s Theory
Bertrand Russell says:

“There are, speaking broadly, three great types of dynamical theory. There is the doctrine of hard extended atoms, for which the theory of impact is the appropriate weapon. There is the doctrine of the plenum, of an all-pervading fluid, for which the modern doctrine of the ether— the theory of Electricity, in fact— has at last partially forged the necessary weapons. And finally, there is the doctrine of unextended centres of force, with action at a distance, for which Newton supplied the required Mathematics. Leibniz failed to grasp these alternatives, and thus, from his love of a middle position, fell between, not two, but three stools. His view of impact as the fundamental phenomenon of Dynamics should have led him to the theory of extended atoms, supported by Gassendi, and, in his own day, by Huygens. His belief in the plenum and the fluid ether should have led him to the second theory, and to the investigation of fluid motion. His relational theory of space, and his whole doctrine of monads, should have led him, as it led Boscovich, Kant1 and Lotze, to the theory of unextended centres of force. The failure to choose between these alternatives made his Dynamics a mass of confusions. The true Leibnizian Dynamics is not his own, but that of Boscovich2. This theory is a simple development of the Newtonian Dynamics, in which all matter consists of material points, and all action is action at a distance. These material points are unextended like the monads, to which Boscovich appeals as analogous3; and in order to preserve their mutual independence, it is only necessary to regard the attraction or repulsion as due to the perception of one monad by the other, which, as a matter of fact, Leibniz actually does. Why, then, was this theory not that of Leibniz ?

“There was, I think, to begin with, in later life, a personal reason. Leibniz had quarrelled with Newton concerning the Calculus, and he did not choose to admit that Newton had anything to teach him4. He therefore rejected gravitation as an ultimate account of things, giving as his reason that action at a distance is impossible. But this personal reason can only have operated after the publication of the Principia in 1687, by which date Leibniz had constructed both his philosophy and his Dynamics. It becomes necessary, therefore, to search for more objective reasons.

“Leibniz rejected atoms, the vacuum, and action at a distance.

“His grounds for these three rejections must be now examined.

“(1) Against extended atoms he had, I think, fairly valid grounds. These are best set forth in his correspondence with Huygens, who maintained atoms. (See G. M. II. pp. 136, 145, 155—7). In the first place, the extended atom is composed of parts, since extension is repetition; it cannot, therefore, afford a metaphysical solution of the composition of matter. Moreover, if the laws of motion are to be preserved, the atom must be perfectly elastic, which is impossible since it must also be perfectly hard, and can contain no " subtle fluid." Again there is a breach of the law of continuity in assuming infinite hardness and absolute indivisibility to emerge suddenly when a certain stage is reached in division. And primitive rigidity is, in any case, a quality wholly without reason, and therefore inadmissible. In short, infrangible atoms would be a perpetual miracle. These arguments have been urged many times since, and are, one may suppose, on the whole valid.

“(2) With regard to the vacuum, Leibniz relied mainly on the argument from what he called metaphysical perfection. He admitted that a vacuum is conceivable (N. E. 157; G. V. 140), but held that, wherever there is room, God might have placed matter without harm to anything else. Since, generally, the more existence the better, God would not have neglected the opportunity for creation, and therefore there is matter everywhere (D. 240, 253; G. VII. 356, 378). This principle of metaphysical perfection will be discussed later; for the present I confine myself to less theological arguments. A very weak argument, which Leibniz sometimes permits himself, is, that there could be no sufficient reason for determining the proportion of vacuum to filled space, and therefore there can be no vacuum at all (D. 253; G. II. 475; VII. 378). The only argument which attempts to be precise is one which is fatally unsound. If space be an attribute, Leibniz says, of what can empty space be an attribute (D. 248; G. VII. 372) ? But space, for him, is a relation, not an attribute; his whole argument against the view that space is composed of points depends, as we shall see in Chapter IX., upon the fundamental relation of distance. He has, in fact, no valid arguments whatever against a vacuum. He seems to regard a belief in it as necessarily associated with a belief in extended atoms—" atoms and the void " are always spoken of together. In fact, when action at a distance is rejected, the two are necessarily connected; since unextended atoms must act at a distance, if there is to be any dynamical action at all5.

“(3) This brings me to Leibniz's grounds against action at a distance. I cannot discover, on this point, anything beyond vulgar prejudice. Both on this and on the previous point, his immediate followers, under the influence of Newton, abandoned the views of their master, which seem to have been mainly due to a lingering Cartesian prejudice. The spatial and temporal contiguity of cause and effect are apparently placed on a level. " A man will have an equal right to say that anything is the result of anything, if that which is absent in space or time can, without intermediary, operate here and now" (D. 115; G. IV. 507). With regard to time, though a difficulty arises from continuity, the maxim may be allowed; but with regard to space, it is precluded, as a metaphysical axiom, by the denial of transeunt action. For since nothing really acts on anything else, there seems no possible metaphysical reason why, in monads which mirror the whole universe, the perception of what is distant should not be a cause, just as much as the perception of what is near. There seems, therefore, in Leibniz's system, no metaphysical ground for the maxim; and in his time (which was that of Newton), there was certainly no dynamical ground. The denial of action at a distance must, therefore, be classed as a mere prejudice, and one, moreover, which had a most pernicious effect upon the relation of Leibniz's Dynamics to his Metaphysics.”

Russell’s References

From A critical exposition of the philosophy of Leibniz, Bertrand Russell, George Allen and Unwin, London, original 1900, third impression (second edition) 1949, p 90- 92

1 That Kant's theory of space in the Metaphysische Anfangsgrunde der Naturwissenschaft is different from that of the Kritik, has been often observed. See Vaihinger's Commentar, p. 224 ff.

2 Theoria Philosophiae Naturalis. See esp. Part I, § 138 ff.

3 Venetian edition of 1763, p. xxv. Boscovich differs from Newtonian Dynamics chiefly in assuming that, at very small distances, the force between two particles is repulsive. He differs from the Newtonian philosophy by regarding action at a distance as ultimate.

4 It has even been suggested— and the suggestion appears very probably correct— that Leibniz never took the trouble to read the Principia. See Guhrauer, op. cit. Vol. I. p. 297.

5 On one minor point, however, namely the possibility of motion in a plenum, Leibniz is unquestionably in the right. Locke had maintained that there must be empty space, or else there would be no room for motion. Leibniz rightly replies (N. E. pp. 53—4; L. 385; G. V. 52), that if matter be fluid, this difficulty is obviated. It should indeed be obvious, even to the non-mathematical, that motion in a closed circuit is possible for a fluid. It is a pity philosophers have allowed themselves to repeat this argument, which a week's study of Hydrodynamics would suffice to dispel. The complete answer to it is contained in what is called the equation of continuity.

G. M. = Leibnizens mathematische Schriften, herausgegeben von C. J Gerhardt. Halle, 1850- 63.

G.M. II. 136 I confess that I have difficulty in understanding the reason of such infrangibility (as that of atoms), and I believe that for this effect we should have to have recourse to a kind of perpetual miracle.

G.M. II 145 There is no absurdity in giving different degrees of rigidity to different bodies; otherwise we could prove by the same reason that bodies must have a zero or an infinite velocity... There are other inconveniences about atoms. For example, they could not be susceptible of the laws of motion, and the force of two equal atoms, which impinged directly with equal velocities, would have to be lost; for it seems that only elasticity makes bodies rebound.

G.M. II 156 Matter, according to my hypothesis, would be divisible everywhere and more or less easily with a variation which would be insensible in passing from one place to another neighbouring place; whereas, according to the atoms, we make a leap from one extreme to the other, and from a perfect incohesion, which is in the place of contact, we pass to an infinite hardness in all other places. And these leaps are without example in nature.

G.M. II 157 There is no last little body, and I conceive that a particle of matter, however small, is like a whole world, full of infinity of still smaller creatures.

D. = The Philosophical Works of Leibnitz, with notes by George Martin Duncan. New Haven, 1890.

N. E. = New Essays concerning human understanding by Gottfried Wilhelm Leibnitz, together with an Appendix consisting of some of his shorter pieces, translated by Alfred Gideon Langley. New York and London, 1896.

G = Die philosophischen Schriften von G. W Leibniz, herausgegeben von C. J Gerhardt, Berlin, 1875 - 90.

L. = Leibniz: The Monadology and other philosophical writings, translated, with introduction and notes, by Robert Latta. Oxford, 1898.