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Naturalistic approaches to explaining the living world led to intense controversies over whether free will and consciousness could be explained away as illusions in a mechanistic brain. Huxley and his colleagues argued that we were automata blindly obeying the laws of physics, chemistry, and biology. They denied that consciousness and volition had independent existence and concluded that the universe was fundamentally deterministic. Maxwell protested that the reality of free will was the most basic fact of our experience, both in our day to day life and in our participation in a society of morally-responsible individuals. His famous “demon,” best known as a thought experiment in thermodynamics, also functioned as an argument for how human souls could have meaningful effects in a world of uniform laws. Consciousness became the wedge issue on which naturalistic and theistic scientists began to profoundly split. The question was whether consciousness was a scientific fact on which theories could be built, or whether it was an epiphenomenon in need of explanation in other terms.

One of the most basic elements of Victorian (and, indeed, modern) scientific practice was the expectation that nature functioned according to fixed laws, which never varied in time or place. This uniformity of natural laws provided both a goal for scientific practice and a methodological guide. Both theistic and naturalistic scientists made the case that uniformity could only be expected and justified in their worldview, and used the concept as grounds for attacking their opponents. Maxwell and Huxley each spent significant energy describing, justifying, and searching for a uniform world, and in their work we can see the close binding of uniformity to their religious outlooks. The use and conceptualization of natural laws in scientific practice was very similar across the theistic/naturalistic border. Uniformity also touched closely on the problem of reconciling miracles and science, and this chapter examines Victorian theological approaches to that issue.

One of the most contentious issues with which the emerging naturalism had to grapple was the question of what, if anything, was beyond science’s grasp. Both naturalists and theists accused each other of making unsupportable claims of absolute knowledge about the world, and of intellectual arrogance. However, in practice, both sides agreed quite closely about the limits of scientific investigation and knowledge, and tied the establishment of those limits to their naturalistic or theistic worldview. One important example was the question of the origin of the universe. Surprisingly, human ignorance of this question was justified in very similar terms by both groups. Maxwell and Huxley undertook sophisticated analyses of the limits of science - Huxley through his articulation of agnosticism, Maxwell through his work on scientific models. The limits of science question was not solely a rhetorical debate, and appeared in important ways in scientific practice.

The myth of inevitable conflict between science and religion grew out of a genuine battleground - the control of educational institutions in Britain. Huxley and the scientific naturalists were frustrated by the close alliance between the universities and the established church, and fought tirelessly to create a space for science education free of any theological control. Figures such as the evangelical Maxwell moved comfortably in these Anglican institutions and saw it as critical that science be taught in the larger context of traditional liberal arts. Despite this deep split, Maxwell and Huxley found themselves at one point volunteering to teach for the same school - the Working Men’s College, a project of the controversial theologian F.D. Maurice. The surprising circumstance of the agnostic and the evangelical teaching science under the guidance of Christian Socialists helps tease out the actual issues involved in the control of Victorian science education.

This introductory chapter describes Maxwell’s and Huxley’s backgrounds, particularly the formation of their views on and experience with religion. It shows the variety of “religion” present in the Victorian period: it is necessary to distinguish personal religiosity, institutional religion, and Anglican theology. Huxley argued strongly for a distinction between religion and theology, and aimed his rhetorical weapons against the latter with great precision (though this was not always appreciated by his readers). Maxwell’s religious background blended Episcopalian, Presbyterian, and evangelical thought, which shows the spectrum of belief and practice in Victorian Britain. His training and career, heavily influenced by the natural theology tradition, demonstrates how theistic science functioned in a deeply religiously environment while still promoting science. Further, the established Church of England played a powerful role in education and employment in the sciences, and Maxwell and Huxley show how careers in science were significantly shaped by an individual’s relationship to the many forms of Christianity in play.

Analogy was a crucial conceptual tool for Victorian natural philosophers, who regarded the physical world less in terms of material bodies than formal relationships. Thus, even as they aimed for verisimilitude in their theoretical models, James Clerk Maxwell and Michael Faraday used analogical figures freely, for they understood nature itself to be structured around analogical relations. Like Maxwell, Algernon Charles Swinburne wrote an undergraduate essay on the subject of analogy, conceiving it as fundamental to both scientific advancement and poetic production, where its logic of equivalence subsumes not only metaphor but also rhythm and rhyme. Swinburne’s poems “Before the Mirror” and “Sapphics” dramatize the replacement of the traditional notion of metaphor by the structures of formal analogy.

The previous chapter laid the foundation for the argument that the central controversy in the control of Victorian science education was not religion, but rather sectarianism and dogmatism. Closer inspection of Huxley’s attacks on theology and the established church, particularly through his narratives of the history of religion, shows that the fundamental point of contention was the issue of the compulsion of belief. He argued that the practice of science could only be done in a space of intellectual liberty, which certain theological institutions had been working to constrain. Huxley’s Church Scientific then, can be seen less as a fortress against God and more as a space for free inquiry where theists could be quite comfortable. Maxwell’s evangelical values are then examined to show their unexpected overlap with Huxley’s defense of liberty: hostility to institutional authority, avoidance of compulsion, and commitment to individual decision-making. The naturalistic and theistic values here also converge on the role of the Bible in education.

For Heinrich Hertz and most of his contemporaries and precursors from the 17th century on, mechanics was not just one among many more recent areas of physics. It was the basic discipline of physics. In a weak sense this meant that mechanics was a perfect model for other disciplines, and in a stronger sense it meant that the ultimate goal of physics was to give mechanical explanations of all natural phenomena. Electromagnetism gradually led to the decline of the mechanistic world view and ironically Hertz was among the contributors to this tendency. Indeed, in Hertz's theoretical papers on James Clerk Maxwell's theory he did not give any mechanical explanation of the electromagnetic phenomena, but having introduced some basic physical ideas and operational definitions of the fields he treated the theory from an axiomatic, mathematical point of view.

This chapter discusses three methodologies proposed by James Clerk Maxwell that can be used in situations where there is insufficient evidence to establish a theory, or indeed, in some cases, no theory at all to establish. The first is called a “method of physical analogy,” the second “an exercise in mechanics,” and the third a “method of physical speculation.” Philosophers and scientists concerned with general questions of methodology too often focus entirely on methods of proving or establishing theories. But, Maxwell emphasizes, there are more scientific activities involving theorizing than are dreamed of in these philosophies. Maxwell is right and the three different methodologies he presents are important and liberating ones for philosophers as well as scientists to consider.

This chapter presents the views of James Clerk Maxwell. For instance, in his inaugural lecture at King’s College London, he claimed that ‘As physical science advances we see more and more that the laws of nature are not mere arbitrary and unconnected decisions of Omnipotence, but that they are essential parts of one universal system in which infinite Power serves only to reveal unsearchable Wisdom and eternal Truth’. He also believed that people should ‘not be led into other men’s ways of thinking under the pretence of studying science’, and that the quest to comprehend the world as a meaningful whole could never be considered an achieved state.

This chapter appraises one aspect of how Samuelson adopted the methods of physics for economics. Samuelson is considered a leader in adopting the concepts of optimization with constraints to economics. The chapter grasps the source of this principle in the little used and obscure writings of the physicist James Clerk Maxwell. It prices Samuelson from the angles of physics and mathematics. Samuelson reasoned in terms of physical axioms and their order. In economic analysis, the terms ‘price’ and ‘quantity’ are used to replace such concepts as ‘pressure’ and ‘volume’ from physics. From the area of classical mechanics, Samuelson borrowed the law of conservation of (mechanical) energy. This conservation model has been a workhorse in modern economics in optimization problems, and shows no sign of weakening in the 21st century.

James Clerk Maxwell and George Eliot advanced probabilistic approaches to describe invisible phenomena to which they could not apply more traditional empirical methods. Maxwell asserted that the movements of molecules could only be understood statistically and questioned the absolute truth of the second law of thermodynamics by proposing a subjectively unlikely but still statistically possible distribution of molecules. For George Eliot, thinking probabilistically allowed for a sympathetic approach to others while still allowing for the contingencies of character. Like Maxwell, she was interested in the points of intersection between personal belief and statistical likelihood, and from that probabilistic stance she reframed novelistic coincidences as statistically possible events in Daniel Deronda.

This chapter analyzes the role of mechanical modeling in nineteenth-century physics, showing how precisely mechanical models were used to enhance scientific understanding. It discusses the work and ideas of William Thomson (Lord Kelvin), James Clerk Maxwell, and Ludwig Boltzmann, who advanced explicit views on the function and status of mechanical models, in particular, on their role in providing understanding. A case study of the construction of molecular models to explain the so-called specific heat anomaly highlights the role of conceptual tools in achieving understanding and shows that intelligibility is an epistemically relevant feature of mechanical models. Next, the chapter examines Boltzmann’s Bildtheorie, an interpretation of mechanical models that he developed in response to problems and criticisms of the program of mechanical explanation, and his associated pragmatic conception of understanding. The final section discusses the limitations of mechanical models and Ernst Mach’s criticism of the mechanical program.

The first atomic theory is credited to Democritus of Abdera, who lived in the 5th century BC. The actual development of the kinetic theory of gases accordingly took place much later, in the 19th century. With his transfer equations, James Clerk Maxwell had come very close to an evolution equation for the distribution function, but this last step must beyond any doubt be credited to Ludwig Boltzmann. The equation under consideration is usually called the Boltzmann equation, but sometimes the Maxwell-Boltzmann equation. Rudolf Clausius took kinetic theory to a mature stage with the explicit recognition that thermal energy is but the kinetic energy of the random motion of the molecules and the explanation of the first law of thermodynamics in kinetic terms. In any case there remained the important unsolved problem of deducing the second law of thermodynamics, the basis of the modern idea of irreversibility in physical processes.

This chapter explores how German economists and statisticians of the historical school viewed the idea of social or statistical law as the product of confusion between spirit and matter or, equivalently, between history and nature. That the laws of Newtonian mechanics are fully time-symmetric and hence can be equally run backwards or forwards could not easily be reconciled with the commonplace observation that heat always flows from warmer to cooler bodies. James Clerk Maxwell, responding to the apparent threat to the doctrine of free will posed by thermodynamics and statistics, pointed out that the second law of thermodynamics was only probable, and that heat could be made to flow from a cold body to a warm one by a being sufficiently quick and perceptive. Ludwig Boltzmann resisted this incursion of probabilism into physics but in the end he was obliged, largely as a result of difficulties presented by the issue of mechanical reversibility, to admit at least the theoretical possibility of chance effects in thermodynamics. Meanwhile, the American philosopher and physicist C. S. Pierce determined that progress—the production of heterogeneity and homogeneity—could never flow from rigid mechanical laws, but demanded the existence of objective chance throughout the universe.

This chapter focusses on James Clerk Maxwell, who at age 14 produced a scientific paper that was read to the Royal Society of Edinburgh. A few years later it was followed up by a second paper, ‘On the Equilibrium of Elastic Solids’, resulting from an experiment where he shone a beam of polarized light into a twisted cylinder of gelatin. The then 18-year-old Maxwell discovered that as the light shone through the stressed jelly, the strain patterns became visible to the naked eye, and had thereby invented a technique widely used by engineers until it was eventually superseded by computer modelling. While Maxwell never achieved the kind of celebrity accorded to Newton or Darwin, his achievements were not lost on his successors. Twentieth-century physicists have described Maxwell as among ‘the most penetrating intellects of all time’.

The most remarkable feature of the physical content of Heinrich Hertz's book Principles of Mechanics is that it is a mechanics without forces. The concept of force and, in particular, of gravitation acting at a distance was introduced by Isaac Newton. This was strongly criticised by the Cartesians who argued that all interactions could and should be explained in terms of contact forces. Hertz's view of the relation between the concept of force and the concept of constraint was a total reversal of that of Siméon-Denis Poisson and William Rowan Hamilton. According to Hertz, connections are the physically primary concept and forces are only derived idealized epiphenomena. This reversal was part of a larger rejection of Laplacian physics. This chapter also discusses James Clerk Maxwell's theory of electromagnetism, distance forces, arguments against atomism, and the emergence of energetics as an alternative to an atomistic, force-based mechanical conception of physics.