Dr. Anouk Barberousse
Chargée de recherches (Junior researcher)
Institut d'Histoire et de Philosophie des Sciences et des Techniques UMR 8590
CNRS - Université Paris 1 - ENS
13 rue du Four
F-75006 Paris
France fax : (33) (0)1 43 25 29 48
http://www-ihpst.univ-paris1.fr/  

A case of irrationality?

As soon as Maxwell published his first paper on the kinetic theory of gases in 1860, he noted that a major consequence of its principles, namely the equipartition theorem, conflicted with known empirical data about the specific heats of poly-atomic gases. In spite of the theory being empirically refuted, he and Boltzmann went one developing it. According to the main current logical-philosophical accounts of belief change, they should have given up their theoretical enterprise and change their beliefs about the promise of the kinetic theory of gases. However, for all we know, they did not change their beliefs and placed more and more confidence in the theory.

The specific heats problem illustrates a not-so-seldom tension between philosophical theories and the historical actions of scientists. My aim in this paper is to twofold. First, I show that this historical episode is best analyzed by taking the actors’ beliefs and other epistemic attitudes into account, and not just the internal development of the theory. The specific heats problem is less an abstract problem for the kinetic theory than a problem about the analysis of Maxwell’s and Boltzmann’s views on the dynamics of scientific theorizing. Second, I propose an analysis of Maxwell’s and Boltzmann’s epistemic attitudes about the kinetic theory that is (i) informed by philosophical theories of belief change, and (ii) coherent with the hypothesis that they were not guilty of irrationality.

I contend that the relevant philosophical theories for this case are those about the coherence of belief sets of a agents vis a vis empirical data and the dynamics of belief change rather than conceptions about theory confirmation or refutation. The problem is not that the kinetic theory of gases, and later statistical mechanics, is a fruitful theory in spite of its being refuted by data about specific heats. Several scientific theories have survived in such a situation, first of all Newtonian mechanics. Their overall empirical success and fruitfulness were outweighing the local empirical challenge they were facing. In the specific heats case, the problem is rather to understand why Maxwell and Boltzmann still had faith in the kinetic theory although one of its main direct consequence (the equipartition theorem) conflicted with empirical data. Textual evidence in Maxwell’s and Boltzmann’s writings shows that they were worried by the specific heats problem; it makes up a good basis for an unusual, but revealing, case-study about scientists’ epistemic attitudes toward their theories.  

Several theories have been proposed in order to understand the dynamics of belief, namely, to state how an agent should change her beliefs upon receiving new data. The so-called ‘AGM theory’ (Alchourrón et al., 1985) proposes postulates of belief change the consequence of which is that Maxwell and Boltzmann were irrational to go on with kinetic theory. Proposals have been made to amend the AGM framework and to open it to other epistemic states than only beliefs. However, none of them is able to clearly establish Maxwell’s and Boltzmann’s rationality.  

From Maxwell’s and Boltzmnn’s writings, it appears that their epistemic states were distributed along several axes of uncertainty. They were constantly evaluating every relevant theoretical hypothesis and set of empirical data according to a variety of ‘epistemic scales’ measuring degrees of epistemic entrenchment. I show that during the 1860s, we can infer from Maxwell’s papers that his opinion comprised the following valuations. First, he thought that the applicability of the principles of mechanics to microscopic objects was highly plausible, even if the analogy from the visible to the invisible is problematic from his own point of view. He was profoundly convinced of the truth of the atomic hypothesis, and this conviction was the mainspring of his investigation. As far as the ‘mechanical analogy’ is concerned, namely the hypothesis that the gaseous molecules are reasonably similar to billiard balls, Maxwell’s explicit aim is to assess its plausibility; however, the conclusion of his 1860 paper is reserved. Finally, he scaled the available empirical data from fully acceptable to severely doubtful. I give more details about the way Maxwell conceives of the consequences of these items.

Such a detailed study shows that the expression ‘acceptance of a theoretical hypothesis’ is highly ambiguous, and that its meaning crucially depends on the type of hypothesis considered. As these hypotheses are not connected, a faithful formalization of Maxwell's epistemic state in the 1860s should not be based on a single belief set, but rather on distinct hierarchies of belief sets.

In order to build up an analysis of the specific heats problem as it is understood in this paper, I insist that the conditional nature of the elements of scientists' epistemic states should be taken seriously: almost all propositions considered by scientists are conditional, of the form: 'If such theory or hypothesis or such empirical data is correct, then …'. From the detailed analysis of Maxwell’s and Boltzmann’s papers, I suggest that the unconnected hierarchies formed by the propositions accepted by a scientist derive from this conditional nature, as well as from the various degrees of acceptance which are assigned to the antecedents. Boltzmann, in a 1895 paper, discusses the various modes of this conditional dependence, underlining the fact that even if a proposition is true if another one is, in a case where one does not know if the antecedent is true, one should not retain from attempting to develop the consequences of the consequent.  

From my historical study, I make some further suggestions about how to represent a scientist’s epistemic state in view both the results of the case-study and the available philosophical theories. I insist that the sources of belief change, as well as of theory change, should be precisely identified in each historical situation in order to avoid misrepresentations of the scientists’ epistemic states. Finally, I propose to introduce the notion of a ‘dynamic component’ of epistemic states in order to account for the full rationality of Maxwell’s and Boltzmann’s enterprise.