THE CIRCULARITY OBJECTION

The first charge is that at the outset Perrin assumes that molecules exist while arguing that they exist. He derives equation (1), which he uses to obtain a value for Avogadro's number N and to see whether N is a constant, from equation (3), which presupposes the existence of mole­cules.

Reply

The argument presented here is only part of Perrin's reasoning, and indeed not the first part.^[116] In his book Atoms, long before he gets to this argument from Brownian motion, he devotes eighty-two pages to a devel­opment of atomic theory, giving chemical arguments in favor of the exis­tence of molecules. His 1909 article begins with a qualitative description of Brownian motion followed by qualitative arguments that Brownian motion is caused by collisions with molecules, and hence that molecules exist. In this article, he writes:

It was established by the work of M. Gouy (1888), not only that the hypo­thesis of molecular agitation gave an admissible explanation of the Brown­ian movement, but that no other cause of the movement could be imagined, which especially increased the significance of the hypothesis.^[117]

Gouy performed experiments in which he examined possible external causes of Brownian motion. These included vibrations transmitted to the fluid by passage of heavy vehicles in the street, convection currents pro­duced when thermal equilibrium was not yet attained, and artificial illu­mination of the fluid. When these and other external sources of motion were reduced or eliminated, the Brownian motion was not altered. Perrin concludes: “these [Brownian] particles simply serve to reveal an internal agitation of the fluid” (p.

Perrin offers a second argument from Brownian motion to molecules (pp. 514-515). Since the Brownian particles are continually accelerating and decelerating, they must be subject to forces exerted upon them, in such a way as to satisfy conservation of momentum. These forces are not present in the particles themselves, nor, as he argued earlier, are they produced by forces external to the fluid. Accordingly, he concludes, they must be produced by the perpetual motions of unobservable particles in the fluid itself.

These arguments for the existence of molecules are presented before Perrin's argument from the law of atmospheres given in section 1. Both involve eliminative-causal reasoning of the following sort:

Eliminative-causal argument:

(1) Given what is known, the possible causes of effect E (for example, Brownian motion) are C, C₁,...,C (for example, the motion of molecules, external vibrations, heat convection currents). (In probabilistic terms, given what is known, the probability is high that E is caused by one of the Cs cited.)

(2) C₁,...,C do not cause E (since E continues when these factors are absent or altered).

So probably

(3) C causes E.

Later, I shall consider whether such an argument is valid for molecules (or anything else). At the moment, I am claiming only that an argument of this type is employed by Perrin, and that it is employed prior to, and in addition to, the argument of section 1. Perrin offers additional arguments for molecules which are also independent of the law of atmospheres argument.¹¹

Accordingly, independently of his own law-of-atmospheres experi­ments on Brownian motion, Perrin presents both experimental and theo­retical arguments for the following claim:

H: Chemical substances are composed of molecules, the number N of which in a gram molecular weight of any substance is approximately 6 x 10²³.

Let b represent the information, other than the law-of-atmospheres con­siderations, on the basis of which Perrin infers H.

p(H/b) > k (4)

where k is some threshold of high probability, say 1/2.^{[118] [119]}

Now, on the basis of his law-of-atmospheres experiments, using equa­tion (1), Perrin claims that:

H': The calculation of N done by means of Perrin's experiments on Brownian particles, using equation (1), is 6 x 10²³, and this number remains constant even when various values in equation (1) are varied.

In H', the number N represents a number for Brownian particles. Perrin can be understood as assuming that, given both H and b, the probability of H' is (substantially) increased over what it is given b alone. That is, the probability that Perrin's experiments will yield result H' for Brownian par­ticles is greater given the assumption that molecules exist, and that their number in a gram molecular weight of a substance is constant and approx­imately equal to 6 10²³, than it is without this assumption. That is

p(H'/H&b) > p(H7b)

It follows that

p(H/H'&b) > p(H/b) (5)

assuming that neither p(H) nor p(H7b) is zero. In short, the probability of the molecular hypothesis H is (substantially) increased by H', the results of Per­rin's experiments with Brownian motion. From (4) and (5) we can conclude that the molecular hypothesis H is highly probable given H' and b, that is,

p(H/H'&b) > k

Perrin's argument, so represented, does not involve circularity. Even though Perrin derives the law of atmospheres (3) involving molecules from the assumption that molecules exist, and even though he derives H' from the law of atmospheres for molecules, H' itself does not state or presuppose that molecules exist or that Avogadro's number for molecules is 6 x 10²³. H' is established experimentally. On Perrin's view, given b, H' bestows substantial probability on H (which does state that molecules exist and that Avogadro's number for molecules is constant).

3.