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Bertrand Russell on Boscovich'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. |