Ludwig Boltzmann is one such thinker. He is largely responsible for the fact that the second law of thermodynamics has become associated with the concept of entropy. Boltzmann worked with thermodynamics generally, and with statistical approaches to physics. His work is in many ways foundational to certain subtopics within physics.
In approaching statistical definitions in physics, Boltzmann touched upon a central topic in the philosophy of science in general, the underdetermination of theories. Both hypothetically and in practice, we are confronted with competing theories, and in some cases, more than one theory fits the data. Our choice of theory, then, in such circumstances cannot be made by the data or with regard to the data. Boltzmann wrote, in 1899, that
we remain faithful to our principle that for the time being we are not aiming at a single best account of science, but that we regard it as expedient to try as many accounts as possible, each of which has its peculiar advantages but also its drawbacks. Again we must focus our main attention on avoiding all inconsistencies and logical mistakes and on not smuggling in tacit concepts or assumptions, and ensure on the contrary that we become most clearly aware of all hypotheses we rely on.
In arguing against Schopenhauer’s assertion that the law about the conservation of matter, a law often associated with the name Lavoisier, is true and knowable a priori, Boltzmann wrote in 1905 that
doubts about this law have arisen in connection with the behavior of radium. I am convinced that these experiments too will confirm the law, but that proves the law to be other than a priori: were it not to hold, we could retort nothing from a logical point of view.
Correctly foreseeing that the radium example, what we now understand to be the decay of an unstable isotope, would not violate the law, but rather refine our understanding of it as the conservation of matter and energy, Boltzmann indicated its empirical nature. (Lavoisier was probably not the first to stumble upon the conservation of mass, but he publicized it and so his name became associated with it.) Despite his emphasis upon mathematical methods, Boltzmann maintained that physics had an essentially empirical aspect:
Thus we must change all laws of thought in such a way that they lead everywhere to the same goal, that they correspond to experience and that overshooting the mark is kept within proper bounds. Even if this ideal will presumably never be completely realized, we can nevertheless come nearer to it, and this would ensure cessation of the disquiet and the embarrassing feeling that it is a riddle that we are here, that the world is at all and is as it is, that it is incomprehensible what is the cause of this regular connection between cause and effect, and so on. Men would be freed from the spiritual migraine that is called metaphysics.
We see here a connection between Boltzmann’s more technical results - dealing with the dynamics of molecules and their speeds, especially in gasses - and contact with questions of philosophical interest - it is a riddle that we are here, it is a riddle that the world is at all, and it is a riddle that the world is as it is and is not otherwise. He hoped, not to answer such questions or solves such riddles, but rather to sidestep them by directing physics as a whole toward empiricism. To some extent, Boltzmann may have here anticipated logical positivism and the Vienna Circle - to the extent that we can interpret him to be saying that such riddles and questions do not need to be answered, but rather need to be recognized as nonsense. Allan Janik and Stephen Toulmin offer a synopsis of Boltzmann’s work. They write that the influence of Kant and of Heinrich Rudolf Hertz
is evident also in the ideas of Ludwig Boltzmann, the man who founded the “statical mechanics” which lies at the basis, not only of the twentieth-century approach to thermodynamics, but of the modern attitude toward theoretical physics generally. Boltzmann took Hertz’s account of mechanics as defining a system of “possible sequences of observed events,” and made it the starting point for a general method of theoretical analysis in physics itself. He did so, by treating each independent property of a physical system as defining a separate coordinate in a multidimensional system of geometrical coordinates. All the possible locations of each separate body in the physical system, for instance, were ordered along three spatial “axes of reference”; all values of, say, temperature along another axis; all values of, say pressure, along a fifth; and so on. The totality of theoretical “points” in the resulting multidimensional coordinate system gave one a representation of the “ensemble of possible states” of the physical system in question; and any actual state could be defined, by specifying the particular point in this “multidimensional space” whose coordinates correspond to the actual values of all the variables. The general problem for statistical mechanics was then to discover mathematical relations governing the frequencies with which - on various assumptions and conditions - the actual states of a physical system would be distributed among its possible states; and, so, to compute the relative probabilities of finding the system, in actual fact, in one overall physical state rather than another.
There may be some hint of an internal tension in Boltzmann’s thought. On the one hand, he wants to be a hard-nosed empiricist and deal only with the data given to us by experience. On the other hand, he wants to create a matrix to cover all possible situations, including those which have not been experienced; in fact, his matrices may easily include configurations - states of affairs - which have never and will never be actualized. While there is a standard empiricist defense for talk about such unrealized possibilities - this defense will argue that such discourse is still meaningful because criteria for verification exist - , these uninstantiated possible states of affairs also present a opportunity to sneak some metaphysical thought into physics. And Boltzmann does not like metaphysics.
John Blackmore sees a slightly different type of internal tension in Boltzmann’s thought. Blackmore writes:
As a physicist, one might naturally suppose that he considered what he called methodology of science more important than natural philosophy, but in fact, as the reader has no doubt already observed, judged in terms of what he actually taught, the opposite was the case. He increasingly taught the ideas of Schopenhauer, Kant, and Brentano on logical, epistemological and ontological topics. He was never quite sure what natural philosophy was, but his lectures became much closer to traditional philosophy than to methodology of science. In short, Boltzmann may have compartmentalized what we would call his intellectual outlook into an expanding series of more or less isolated cells starting with science and what he thought was methodology of science and gradually extending to and through physiology, biology, and Darwinism on the one side and various forms of epistemology, ontology, and “metaphysics” on the the other. It may be no wonder that he had such a hard time obtaining peace of mind or a coherent, inclusive philosophy or world view. One compartment of thought seemingly didn’t know what the other compartments were doing.
The tension Blackmore sees between Boltzmann’s science and Boltzmann’s scientific methodology - between the way Boltzmann did physics and the way he talked about physics - is reflected in the way Boltzmann simultaneously endorses aspects of Schopenhauer’s philosophy while rejecting Schopenhauer’s hypothesis about the rational foundation for the second law of thermodynamics.
