In his Zur Einstein’schen Relativitätstheorie, Ernst Cassirer presents relativity theory as the last manifestation of the tradition of the “physics of principles” that, starting from the nineteenth century, has progressively prevailed over that of the “physics of models.” In particular, according to Cassirer, the relativity principle plays a role similar to the energy principle in previous physics. In this article, I argue that this comparison represents the core of Cassirer’s neo-Kantian interpretation of relativity. Cassirer pointed out that before and after (...) Kant, the history of physics presents significant instances in which the search for formal conditions that the laws of nature must satisfy preceded and made possible the direct search for such laws. In his earlier years, Cassirer seems to have regarded principles like the energy principle, the relativity principle, and the principle of least action as a constitutive but provisional form of a priori, imposing specific limitations on the form of the allowable laws of nature. Only in his later years, by attributing an autonomous status to these statements of principle, did Cassirer attribute a definitive but merely regulative meaning to the a priori. This does not impose specific requirements on natural laws but only a motivation to search for them. (shrink)

A full appreciation for Ernst Mach's doctrine of the economy of thought must take account of his direct realism about particulars (elements) and his anti-realism about space-time laws as economical constructions. After a review of thought economy, its critics and some contemporary forms, the paper turns to the philosophical roots of Mach's doctrine. Mach claimed that the simplest, most parsimonious theories economized memory and effort by using abstract concepts and laws instead of attending to the details of each individual event (...) or experiment. For Mach, the individual case never truly repeated in all of its uniqueness, nor was all of the individual detail of a physical element adequately captured in abstract laws and schemata, however necessary these were for the pursuit of science. As can be shown from specific passages, some already published, some not, Mach's elements included physical qualia in nature similar to Russell's unsensed sensibilia, which existed even where there were no conscious observers. An argument will be presented to make the case that Mach believed in the mind-independent elements from the 1870s on, while other aspects of his thought evolved over time; I have thus dated the references to reflect this historical progression. I concentrate on Mach's ontology, as it bears on economy of thought, not his epistemology per se, which might well have been restricted to observable elements/sensations. After his own conversion to neutral monism, in the 1920s, Bertrand Russell echoed Mach's call for a 'future science' capable of handling the 'intrinsic character' of qualitative data directly without the excessive abstraction of physics. (shrink)

It is commonly thought that before the introduction of quantum mechanics, determinism was a straightforward consequence of the laws of mechanics. However, around the nineteenth century, many physicists, for various reasons, did not regard determinism as a provable feature of physics. This is not to say that physicists in this period were not committed to determinism; there were some physicists who argued for fundamental indeterminism, but most were committed to determinism in some sense. However, for them, determinism was often not (...) a provable feature of physical theory, but rather an a priori principle or a methodological presupposition. Determinism was strongly connected with principles of causality and continuity and the principle of sufficient reason; this thesis examines the relevance of these principles in the history of physics. Moreover, the history of determinism in this period shows that there were essential changes in the relation between mathematics and physics: whereas in the eighteenth century, there were metaphysical arguments which lent support to differential calculus, by the early twentieth century the development of rigorous foundations of differential calculus led to concerns about its applicability in physics. The thesis consists of six papers. In the first paper, "On the origins and foundations of Laplacian determinism", I argue that Laplace, who is usually pointed out as the first major proponent of scientific determinism, did not derive his statement of determinism directly from the laws of mechanics; rather, his determinism has a background in eighteenth century Leibnizian metaphysics, and is ultimately based on the law of continuity and the principle of sufficient reason. These principles also provided a basis for the idea that one can find laws of nature in the form of differential equations which uniquely determine natural processes. In "The Norton dome and the nineteenth century foundations of determinism", I argue that an example of indeterminism in classical physics which has attracted attention in philosophy of physics in recent years, namely the Norton come, was already discussed during the nineteenth century. However, the significance which this type of indeterminism had back then is very different from the significance which the Norton dome currently has in philosophy of physics. This is explained by the fact that determinism was conceived of in an essentially different way: in particular, the nineteenth century authors who wrote about this type of indeterminism regarded determinism as an a priori principle rather than as a property of the equations of physics. In "Vital instability: life and free will in physics and physiology, 1860-1880", I show how Maxwell, Cournot, Stewart and Boussinesq used the possibility of unstable or indeterministic mechanical systems to argue that the will or a vital principle can intervene in organic processes without violating the laws of physics, so that a strictly dualist account of life and the mind is possible. Moreover, I show that their ideas can be understood as a reaction to the law of conservation of energy and to the way it was used in physiology to exclude vital and mental causes. In "The nineteenth century conflict between mechanism and irreversibility", I show that in the late nineteenth century, there was a widespread conflict between the aim of reducing physical processes to mechanics and the recognition that certain processes are irreversible. Whereas the so-called reversibility objection is known as an objection that was made to the kinetic theory of gases, it in fact appeared in a wide range of arguments, and was susceptible to very different interpretations. It was only when the project of reducing all of physics to mechanics lost favor, in the late nineteenth century, that the reversibility objection came to be used as an argument against mechanism and against the kinetic theory of gases. In "Continuity in nature and in mathematics: Boltzmann and Poincaré", I show that the development of rigorous foundations of differential calculus in the nineteenth century led to concerns about its applicability in physics: through this development, differential calculus was made independent of empirical and intuitive notions of continuity and was instead based on mathematical continuity conditions, and for Boltzmann and Poincaré, the applicability of differential calculus in physics depended on whether these continuity conditions could be given a foundation in intuition or experience. In the final paper, "Determinism around 1900", I briefly discuss the implications of the developments described in the previous two papers for the history of determinism in physics, through a discussion of determinism in Mach, Poincaré and Boltzmann. I show that neither of them regards determinism as a property of the laws of mechanics; rather, for them, determinism is a precondition for science, which can be verified to the extent that science is successful. (shrink)

This is the second of a series of essays on the development and reception of Wilhelm Ostwald’s energetics. The first essay described the chemical origins of Ostwald’s interest in the energy concept and his motivations for seeking a comprehensive science of energy. The present essay and the next discuss his various attempts, beginning in 1891 and extending over almost 3 years, to develop a consistent and coherent energetic theory. A final essay will consider reactions to this work and Ostwald’s replies, (...) and will also seek to evaluate his program of research. Ostwald’s project – to reconstruct physics and chemistry “as a pure energetics” – is worth attending to for several reasons: first, because Ostwald did ground-breaking work in chemistry (he was awarded a Nobel Prize in 1909 for his studies in catalysis and rates of reaction); second, because an important school of physical chemistry formed around him at Leipzig, a school that promoted his ideas; and, finally, because he was a prominent and vigorous participant in debates at the end of the nineteenth century concerning the proper course of physical theory. (shrink)

The reversibility problem (better known as the reversibility objection) is usually taken to be an internal problem in the kinetic theory of gases, namely the problem of how to account for the second law of thermodynamics within this theory. Historically, it is seen as an objection that was raised against Boltzmann's kinetic theory of gases, which led Boltzmann to a statistical approach to the kinetic theory, culminating in the development of statistical mechanics. In this paper, I show that in the (...) late nineteenth century, the reversibility problem had a much broader significance - it was widely discussed and certainly not only as an objection to Boltzmann's kinetic theory of gases. In this period, there was a conflict between mechanism and irreversibility in physics which was tied up with central issues in philosophy of science such as materialism, empiricism and the need for mechanistic foundations of physical theories, as well as with concerns about the heat death of the universe. I discuss how this conflict was handled by the major physicists of the period, such as Maxwell, Kelvin, Duhem, Poincaré, Mach and Planck, as well as by a number of lesser-known authors. (shrink)