Lydia Patton

Ernst Mach’s philosophical ideas were warmly received in America, which already had a pragmatist tradition close to Machian empiricism and budding schools of philosophy, psychology, and physics more or free of the neo-Kantian influences which were a strong academic competitor to the spread of empiricism in Europe. The founding pragmatists Charles Sanders Peirce and William James engaged directly with Mach and Paul Carus, the editor of the Monist and publisher of the Open Court press actively translated and published Mach’s works for the American public. A generation later when members of the Vienna Circle sought Academic posts in elite American universities, the ground was well prepared for their arrival as Holton and Stadler have described. Beneath the surface however, the American reaction to Mach was not one of naïve admiration but fairly staunch criticism, which Mach himself appreciated and welcomed. Peirce was highly critical of Mach’s mechanics in a review and Peirce famously described Mach’s empiricism as akin to riding a horse to death. In some ways, Peirce himself had anticipated aspects of Mach’s views on mind and body, a surprising discovery I made recently. Even Carus, who declared himself an admirer, was highly critical of Mach’s theory of economy of thought. James, too, who admired Mach greatly, had major disagreements with Mach on so-called sensations of innervation in psychology, and although’s James’ own radical empiricist essays owed much to Mach’s neutral monist ideas in the Analysis, James broke away from what he saw as Mach’s excessive physical reductionism, rejecting the monism about nature that was Mach’s trademark. In short Mach’s ideas acted as a stimulus to American thinkers, but they had their own tradition and they were able to resist his authority and contribute in reverse to Mach’s own refinement of his positions.

The paper aims to investigate some aspects of Ernst Mach’s epistemology in the light of the problem of human orientation in relation to the world (Weltorientierung), which is a main topic of Western philosophy since Kant. As will be argued, Mach has been concerned with that problem, insofar as he developed an original pragmatist epistemology. In order to support my argument, I firstly investigate whether Mach defended a nominalist or a realist account of knowledge and compare his view to those elaborated by other pragmatist thinkers, such as W. James, H. Vaihinger and H. Poincaré. Secondly, the question of what does it mean, for Mach, to orient ourselves in science is addressed. Finally, it will be argued that, although Mach tried to keep his epistemology restricted to a mere operational and economical account of science, that question involves the wider plane of practical philosophy.

Ernst Mach’s positivism, it is argued in this paper, may be regarded as a version of pragmatist philosophy of science. Already James’s biographer Perry detected such tendencies in Mach and this is confirmed here by close attention to Mach’s early works, esp. History and Root of the Principle of the Conservation of Energy and The Science of Mechanics. Both Mach’s principle of the economy of thought and his principle of scientific significance are shown to bear out his pragmatism. A similar conclusion is shown to hold for the philosophy of Wilhelm Jerusalem already long before he became the translator of James’s Pragmatism into German. But while Jerusalem early on relied perhaps even more than Mach on evolutionary theory for promptings of pragmatist insights, he soon too linked them, as Mach had all along, to broadly sociological observations concerning the condition of human cognition.

Mach has long been an important figure in the history of relativity, but the nature of his role has remained controversial. This essay contributes to this discussion by connecting Mach’s critical philosophical perspective more fully to his diverse experimental research and pedagogical contributions to mechanics, and charting his changing presentations of these over some time. In particular, linking Mach’s early research in sense perception and psychophysics to his conceptual critiques of mechanics offers new perspectives on relativist physics in general and Einstein’s debts to Mach in particular. Mach’s early work on the Doppler effect, together with studies of visual and motor perception explored subtle interrelations between physiology, physics and psychology, and offered new approaches to physiological space and time. These informed the critical conceptual attacks on Newtonian absolutes that Mach famously outlined in The Science of Mechanics in 1883, as well as his positive account of the fundamental laws of physics in terms of experimental propositions and definitions. Mach’s critiques helped form a foundation for later work in electrodynamics in which he did not participate. Yet revisiting Mach’s early work will suggest he was still more important to the development of new approaches to inertia and gravitation than has been commonly appreciated. In addition to what Einstein later called “Mach’s principle,” I argue that a thought experiment on falling bodies in Mach’s Science of Mechanics also provided a point of inspiration for the happy thought that led Einstein to the equivalence principle.

This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the attempt to interpret general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general relativity is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others

In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and infinitesimals do not entail the paradoxes of the infinitesimal and continuum. Essential to that defense is an interpretation, developed in the paper, of Cohen's positions in the PIM as deeply rationalist. The interest in developing this interpretation is not just that it reveals how Cohen's views in the PIM avoid the paradoxes of the infinitesimal and continuum. It also reveals some of what is at stake, both historically and philosophically, in Russell's criticism of Cohen.

Some commentators on Hermann Cohen have remarked on what they take to be a puzzle about the origins of his mature anti-psychologism. When Cohen was young, he studied a kind of psychology, the Völkerpsychologie of Moritz Lazarus and Heymann Steinthal, and wrote apparently psycholgistic accounts of knowledge almost up until the moment he first articulated his anti-psychologistic neo-Kantianism. To be sure, Cohen's mature anti psycholgism does constitute a rejection of certain central commitments of Völkerpsychologie. However, the relation between Völkerpsychologie and Cohen's mature anti-psychologism is not one of straightforward opposition. This paper argues that Cohen had significantly less distance to travel than it appears to get from his early Völkerpsychologie to his mature anti-psychologism. In particular, this paper argues that Cohen always had an anti-psychologistic account of knowledge, even during the period when he was studying Völkerpsychologie, and further, that key features of his Völkerpsychologie partly shaped his mature account of knowledge. Finally, the paper identifies how Cohen’s views did change over the transition from his völkerpsychological period to his later anti-psychologism. It thus identifies what changes in Cohen’s views do need to be explained.

hilosophy of history and history of philosophy of science make for an interesting case of “mutual containment”: the former is an object of inquiry for the latter, and the latter is subject to the demands of the former. This article discusses a seminal turn in past philosophy of history with an eye to the practice of historians of philosophy of science. The narrative turn by Danto and Mink represents both a liberation for historians and a new challenge to the objectivity of their findings. I will claim that good sense can be made of “working historical veins of possibility” (contrary to how the phrase was originally intended) and that already Danto and Mink provided materials (although they did not quite advertise them as such) to assuage fears of a constructivist free-for-all.

Baruch Spinoza’s (1632–77)Tractatus theologico-politicus (1669 or 1670) caused outrage across the Dutch Republic, for it obliterated the carefully installed separation between philosophy and theology. The posthumous publication of Spinoza’s Ethica, which is contained in his Opera posthuma (1677), caused similar consternation. It was especially the mathematical order in which the Ethica was composed that caused fierce opposition, for its mathematical appearance gave the impression that Spinoza’s heretical teachings were established demonstratively. In this essay, I document how the Dutch physician, local politician, and amateur mathematician and experimenter Bernard Nieuwentijt (1654–1718) attempted to physico-mathematically and methodologically counter the threats posed by Spinoza’s program. Nieuwentijt tried to defend the authority of the scriptures in times at which they came under attack by the new philosophy and by the emerging sciences that were gradually winning terrain. The crux of his defense consisted in delineating a modest epistemology, a “learned ignorance,” that would cure Spinoza’s followers of their pansophical aspirations, on the one hand, and remove the conflict between the Bible and reason, on the other. The specific way in which he sought to accomplish this distinguished him from Dutch Reformed thought, or so I will argue.

In the Critique of Pure Reason, Kant describes schematism as a (A141/B180–1). While most commentators treat this as Kant's metaphorical way of saying schematism is something too obscure to explain, I argue that we should follow up Kant's clue and treat schematism literally as Kunst. By letting our interpretation of schematism be guided by Kant's theoretically exact ways of using the term Kunst in the Critique of Judgment we gain valuable insight into the nature of schematism, as well as its connection to Kant's concerns in the third Critique.

The text- and argument-focused histories of philosophy that we have are mainly interested in teasing out the details of the positions taken on philosophical issues by individual philosophers. But this is a long way from having a historical explanation of the larger-scale trajectory of philosophical development. An empirical history of philosophy, however, examines the institutionalized places and venues for philosophical work that provide a rich, shared structure for the promotion of particular sorts of work. Mid-twentieth-century philosophers of science such as Herbert Feigl and Philipp Frank knew what they were doing—they were creating the space to promote certain sorts of work in venues such as the Institute for the Unity of Science and the Minnesota Center for Philosophy of Science and, ultimately, in publication venues such as Daedalus and the Minnesota Studies in Philosophy of Science. Here the engine of progress is the institution-building activity of committed philosophers making a space within the institutional structures of philosophy for their own projects and other projects aligned with them and transmitting these as live philosophical projects to the next generation.