Abstract
Let us begin by reviewing our main results to this point. In Chap. 2 it was argued that it is possible to give a probabilistic justification of induction. In Chap. 5 it was argued that a probabilistic argument, resembling an inductive argument, can also be given for the reality of some unobservable entities. The type of inference used in arguments of this sort was called an “Eddington-inference”. But, it was also argued that if Eddington-inferences were to furnish us with good reason to believe in the unobservable entities postulated by specific scientific theories, they needed to be supplemented with a means of determining that one theory about the behaviour of observables was more likely to be true than another. It was argued that the notion of the independence of theory from data was able to do this. The viability of that notion for the task at hand was defended in Chap. 6.
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Notes
- 1.
See Maxwell “Molecules” reprinted in Maxwell on Molecules and Gases edited by Elizabeth Garber, Stephen G. Brush and C. W. Francis Everett, (MIT Press, 1986), pp.137–155.
- 2.
See Maxwell “Molecules” in Garber, E et al., op cit, p.139.
- 3.
Maxwell, op cit, p.140.
- 4.
Maxwell, op cit, p.141.
- 5.
Maxwell’s wording suggests that he is relying on IBE at this point, but it seems there is a plausible route from the phenomenon of diffusion to the conclusion that the particles are in motion that does not use IBE. Maxwell says that when he opens the stopper on a flask containing a strongly smelling substance, “fairly quickly” it becomes possible to smell the substance from some distance away. This certainly would seem to indicate that once the stopper on the flask had been removed, the particles comprising the substance contained therein were in motion: they moved from the mouth of the flask to distant points in the lecture theatre. But now, unless the act of removing the stopper from the flask imparted motion to the particles, the law of the conservation of energy assures us the particles must surely have also been in motion prior to the stopper being removed. This argument assumes the law of conservation of energy, but this would appear to be something that can be confirmed without having to appeal to any problematic form of IBE. And so we seem to have a possible route to the conclusion that the particles were in motion, prior to the removal of the stopper, that does not rely on problematic IBE.
- 6.
See Maxwell, op cit, p.139.
- 7.
The present author has also argued that the reasons available to Maxwell gave him probabilistic reason to prefer the hypothesis that all masses conformed to Newton’s laws. (Explaining Science’s Success, ch 6.)
- 8.
Maxwell, op cit, p.142. Boyle’s Law is perhaps more commonly expressed as the law that, for any given mass of gas, pressure is inversely proportional to volume. However, it is plain that the law Maxwell is here referring to as “Boyle’s Law” entails that pressure will be inversely proportional to volume for a given mass of gas.
- 9.
See Maxwell, loc cit.
- 10.
Maxwell, loc cit.
- 11.
See J. P. Joule “On the Existence of an Equivalent Relation between Heat and the Ordinary Forms of Mechanical Power” in Philosophical Magazine, 3 27 (1845), pp.205–207.
- 12.
See Albert Einstein “On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular Kinetic Theory of Heat” reprinted in Investigations on the Theory of the Brownian Movement edited by R. Furth (Dover Publications, 1956), pp.1–18
- 13.
Einstein, op cit, p.1.
- 14.
Einstein, op cit, p.3.
- 15.
The formula Einstein derived can be expressed as follows:
$$ \mathrm{N}=\left(1/{\mathrm{x}}^2\right)\left(\mathrm{RT}/3\pi \eta r\right)\tau $$Where N is Avogadro’s Number, Spiltx2Spigt is the mean square displacement of a particle over some unit of time τ, R is the gas constant, T is the temperature in degrees Kelvin, η is the viscosity of the liquid, and r is the radius of the particles. This expression of the formula comes from “Einstein, Perrin and Avogadro’s Number – 1905 Revisited” by Ronald Newburgh, Joseph Peidle and Wolfgang Rueckner American Journal of Physics, 74, 478 (2006).
- 16.
Stokes’ Law can be expressed as F d = 6πμRV, where F d is the force required to move a sphere of radius R at velocity V through a fluid of viscosity μ.
- 17.
Boyle’s law states that, for an ideal gas at constant temperature, pressure is inversely proportional to volume, that is, P = k1(1/ V), where P is pressure, k1 is a constant, and V is volume. Charles’ Law states that when pressure is held constant, volume is directly proportional to temperature, at constant pressure, V = k2 T, where V is volume, k2 is a constant and T is absolute temperature. Avogadro’s Law states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules. This law can be stated as K = V/n, where K is a constant equal to RT/P, where R is the universal gas constant, T is absolute temperature and V is volume.
An objection might be raised at this point. Our overall aim is to show that there is a good, purely probabilistic, argument for the existence of molecules. The results established by Einstein are a step on the way to that conclusion. Einstein uses the general ideal gas law PV = nRT, but this is derived from, among other things, Avogadro’s law which makes reference to the number of molecules in a gas. It might be objected that if we have good grounds for saying that Avogadro’s Law is true, then we must already have good grounds for saying that there are molecules (since Avogadro’s Law makes reference to the number of molecules in a gas.) But if we already have good grounds for saying molecules exist, is not the subsequent work of Perrin, for example, thereby rendered superfluous? And if we do not already have good reason for Avogadro’s Law, is not the subsequent reasoning rendered unsound?
However, this objection fails. On the view advocated here, the “No-coincidental agreement” inference has a role in establishing the existence of unobservable entities. For this inference to work, we must be led via an Eddington inference together with non ad-hoc hypotheses to entities that have the same causal powers as those postulated by our explain theory. So, for our purposes, it is sufficient that Avogadro’s Law not be ad hoc. And, it surely is not ad hoc: it provides a natural explanation of Gay-Lussac’s Law that at any given temperature and pressure the ratio between the volumes of reacting gases and their product can be expressed in simple whole numbers. Gay-Lussac’s law evidently could be established by enumerative induction.
- 18.
Perrin’s main work summarizing the results of his findings is his Atoms (Constable and Company, London 1916).
- 19.
See W. Salmon Reality and Rationality edited by P. Dowe and M. Salmon, (Oxford University Press, 2005), esp. pp.3–60.
- 20.
See Salmon, op cit. A summary of the results obtained by the use of the different methods is given in Perrin’s Atoms, p.206. There Perrin lists thirteen different methods. The lowest value obtained (from a technique involving energy radiated in radioactivity) is 6.0 × 1023. The highest is 7.5 × 1023, from a technique involving “critical opalescence”. The latter value would seem to be something of an outlier from the others. Perrin comments that the degree of agreement between the various methods is so remarkable “the real existence of the molecule is given a probability bordering on certainty.” (p.207).
- 21.
See Perrin, op cit, pp.90–94.
- 22.
Note that n and n* refer to the “density of the particles” in the sense of the number of them to be found in a given volume of space. So, n will take a very high value if there are, for example, very many of the particles in a cubic centimetre. But D refers to the density of the substance out of which the particles are made. So, D will have a higher value if the particles are made out of, say, lead rather than aluminium.
- 23.
The derivation, and the formula, both contain reference to temperature in degrees Kelvin. But this need not be taken as assuming that heat is the kinetic energy of tiny particles. The term “T” that appears in the formula could be taken merely as a measure of the kinetic energy of the particles. So then LA might, for example, tell us how, at a given average kinetic energy, the density of a quantity of randomly moving ping pong balls diminishes with height.
- 24.
Again, assuming “T” to refer to kinetic energy.
- 25.
See Perrin, op cit, pp.101–103.
- 26.
See Perrin, op cit, Chapter IV.
- 27.
See Perrin, op cit, p.123. Perrin remarks: “This remarkable agreement proves the rigorous accuracy of Einstein’s formula and in a striking manner confirms the molecular theory.”
- 28.
See Perrin, op cit, pp.104–106.
- 29.
See P. Achinstein The Book of Evidence, (Oxford University Press, 2001), Chap. 12 “Evidence for Molecules: Jean Perrin and Molecular Reality”, pp.243–265, esp. p.244.
- 30.
See for example my Realism and Explanatorily Priority (Kluwer Academic Publishers, 1997) and “The Explanatory Role of Realism” in Philosophia, v 29 (2002), pp.35–56.<?spieprPar123?>
- 31.
See B. van Fraassen “The Perils of Perrin, in the hands of philosophers”, Philosophical Studies, v 143 (2009), pp.5–24.
- 32.
See van Fraaasen, op cit. p.8. Van Fraassen discusses the significance of an “Atwood Machine”, and of a mechanism consisting of two masses joined by a spring, as devices for measuring mass.
- 33.
See van Frassen, op cit, p.11.
- 34.
See Stathis Psillos “The View from Within and the View from Above: Looking at van Fraassen’s Perrin” in W. J. Gonzalez (ed), Bas van Fraassen’s Approach to Representation and Models in Science, Synthese Library 368., (Springer, Dordrecht: 2014).
- 35.
See Mixture and Chemical Combination and Related Essays by Pierre Duhem, edited and translated with an Introduction by Paul Needham, Boston Studies in the Philosophy of Science, v 223, (Kluwer Academic Publishers, 2002), p.92.
- 36.
Psillos, op cit. Gouy’s findings are in L. Gouy “Le Mouvement Brownien et le Mouvement Moleculaires” in Revue Generale des Sciences Pures et Appliquees, v 6, pp.1–7.
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Wright, J. (2018). Eddington Inferences in Science – 1: Atoms and Molecules. In: An Epistemic Foundation for Scientific Realism. Synthese Library, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-030-02218-1_7
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