Marij Van Strien

Bohm’s interpretation of quantum mechanics has generally been received as an attempt to restore the determinism of classical physics. However, although this interpretation, as Bohm initially proposed it in 1952, does indeed have the feature of being deterministic, for Bohm this was never the main point. In fact, in other publications and in correspondence from this period, he argued that the assumption that nature is deterministic is unjustified and should be abandoned. Whereas it has been argued before that Bohm’s commitment to determinism was connected to his interest in Marxism, I argue for the opposite: Bohm found resources in Marxist philosophy for developing a nondeterministic notion of causality, which is based on the idea of infinite complexity and an infinite number of levels of nature. From ca. 1954 onwards, Bohm’s conception of causality further weakened, as he developed the idea of a dialectical relation between causality and chance.

Bohr’s work in quantum mechanics posed a challenge to philosophers of science, who struggled with the question of whether and to what degree his theories and methods could be considered rational. This paper focuses on Popper, Feyerabend, Lakatos and Kuhn, all of whom recognized some irrational, dogmatic, paradoxical or even inconsistent features in Bohr’s work. Popper, Feyerabend, and Lakatos expressed strong criticism of Bohr’s approach to quantum physics, while Kuhn argued that such criticism was unlikely to be fruitful: progress in science is generally not made through philosophical reflection. Feyerabend’s criticism of Bohr gradually weakened, as he gained a more detailed understanding of the development of Bohr’s views on quantum mechanics, and this went together with an increasingly critical view of normative philosophy of science and was instrumental to his conversion to ‘anarchism’. This paper aims to show that quantum mechanics played a central role in their debates and disagreements on the rationality of science and the possibility of a normative philosophy of science.

The theory of quantum mechanics has often been thought to show an affinity with logical empiricism: in both, observation plays a central role, and questions about what is unobservable are dismissed. However, there were also strong tensions between the logical empiricism of the Vienna Circle and implications drawn from quantum physics. In the 1920s and 1930s, many physicists thought that quantum mechanics revealed a limit to what could be known scientifically, and this opened the door to a wide range of speculations, in which quantum mechanics was connected with free will, organic life, psychology, and religion—speculations in which many leading quantum physicists were engaged. Members of the Vienna Circle, such as Frank and Schlick, looked at quantum mechanics for a confirmation of their empiricist views, but they were at the same time critical about these wider implications drawn from quantum mechanics, which in their eyes were connected with broader mystical and irrational trends in society. They engaged in particular with the views of Bohr and Jordan, both of whom expressed a sympathy for logical empiricism while at the same time arguing for claims that proved hard to reconcile with the scientific world conception of the Vienna Circle.

According to Ernest Nagel, determinism is central to the scientific enterprise. Faced with the claim that determinism fails in quantum mechanics, Nagel proposed a notion of determinism which does not rely on a fundamental level of description, and can play a role in different scientific disciplines irrespective of their reducibility to physics. Nagel argues that determinism ultimately plays the role of a guiding principle in scientific research. In this way, Nagel argues that determinism has an enduring relevance in all domains of science, from quantum physics to the social sciences.

When David Bohm published his alternative theory of quantum mechanics in 1952, it was not received well; a recurring criticism was that it formed a reactionary attempt to return to classical physics. In response, Bohm emphasized the progressiveness of his approach, and even turned the accusation of classicality around by arguing that he wanted to move beyond classical elements still inherent in orthodox quantum mechanics. In later years, he moved more and more towards speculative and mystical directions. This paper aims to explain this discrepancy between the ways in which Bohm’s work on quantum mechanics has been received and the way in which Bohm himself presented it. I reject the idea that Bohm’s early work can be described as mechanist, determinist, and realist, in contrast to his later writings, and argue that there is in fact a strong continuity between his work on quantum mechanics from the early 1950s and his later, more speculative writings. In particular, I argue that Bohm was never strongly committed to determinism and was a realist in some ways but not in others. A closer look at Bohm’s philosophical commitments highlights the ways in which his theory of quantum mechanics is non-classical and does not offer a way to avoid all ‘quantum weirdness’.

In the mid-eighteenth century, it was usually taken for granted that all curves described by a single mathematical function were continuous, which meant that they had a shape without bends and a well-defined derivative. In this paper I discuss arguments for this claim made by two authors, Emilie du Châtelet and Roger Boscovich. I show that according to them, the claim follows from the law of continuity, which also applies to natural processes, so that natural processes and mathematical functions have a shared characteristic of being continuous. However, there were certain problems with their argument, and they had to deal with a counterexample, namely a mathematical function that seemed to describe a discontinuous curve.

This paper aims to show that the development of Feyerabend’s philosophical ideas in the 1950s and 1960s largely took place in the context of debates on quantum mechanics. In particular, he developed his influential arguments for pluralism in science in discussions with the quantum physicist David Bohm, who had developed an alternative approach to quantum physics which (in Feyerabend’s perception) was met with a dogmatic dismissal by some of the leading quantum physicists. I argue that Feyerabend’s arguments for theoretical pluralism and for challenging established theories were connected to his objections to the dogmatism and conservatism he observed in quantum physics. However, as Feyerabend gained insight into the physical details and historical complexities which led to the development of quantum mechanics, he gradually became more modest in his criticisms. His writings on quantum mechanics especially engaged with Niels Bohr; initially, he was critical of Bohr’s work in quantum mechanics, but in the late 1960s, he completely withdrew his criticism and even praised Bohr as a model scientist. He became convinced that however puzzling quantum mechanics seemed, it was methodologically unobjectionable – and this was crucial for his move towards ‘anarchism’ in philosophy of science.

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.

During the period 1860-1880, a number of physicists and mathematicians, including Maxwell, Stewart, Cournot and Boussinesq, used theories formulated in terms of physics to argue that the mind, the soul or a vital principle could have an impact on the body. This paper shows that what was primarily at stake for these authors was a concern about the irreducibility of life and the mind to physics, and that their theories can be regarded primarily as reactions to the law of conservation of energy, which was used among others by Helmholtz and Du Bois-Reymond as an argument against the possibility of vital and mental causes in physiology. In light of this development, Maxwell, Stewart, Cournot and Boussinesq showed that it was still possible to argue for the irreducibility of life and the mind to physics, through an appeal to instability or indeterminism in physics: if the body is an unstable or physically indeterministic system, an immaterial principle can act through triggering or directing motions in the body, without violating the laws of physics.

In this paper I examine the foundations of Laplace's famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace's statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace's determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace's determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation.

The recent discovery of an indeterministic system in classical mechanics, the Norton dome, has shown that answering the question whether classical mechanics is deterministic can be a complicated matter. In this paper I show that indeterministic systems similar to the Norton dome were already known in the nineteenth century: I discuss four nineteenth century authors who wrote about such systems, namely Poisson, Duhamel, Boussinesq and Bertrand. However, I argue that their discussion of such systems was very different from the contemporary discussion about the Norton dome, because physicists in the nineteenth century conceived of determinism in essentially different ways: whereas in the contemporary literature on determinism in classical physics, determinism is usually taken to be a property of the equations of physics, in the nineteenth century determinism was primarily taken to be a presupposition of theories in physics, and as such it was not necessarily affected by the possible existence of systems such as the Norton dome.

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.

The development of rigorous foundations of differential calculus in the course of the nineteenth century led to concerns among physicists about its applicability in physics. Through this development, differential calculus was made independent of empirical and intuitive notions of continuity, and based instead on strictly mathematical conditions of continuity. However, for Boltzmann and Poincaré, the applicability of mathematics in physics depended on whether there is a basis in physics, intuition or experience for the fundamental axioms of mathematics—and this meant that to determine the status of differential equations in physics, they had to consider whether there was a justification for these mathematical continuity conditions in physics. For this reason, their ideas about continuity and discreteness in nature were entangled with epistemology and philosophy of mathematics. They reached opposite conclusions: Poincaré argued that physicists must work with a continuous representation of nature, and thus with differential equations, while Boltzmann argued that physicists must ultimately take nature to be discrete.