This chapter explores Ernst Mach’s philosophy of scientific knowledge as an original form of pragmatism. Mach recognised science as a deeply historical phenomenon and scientific knowledge as path-dependent, thoroughly fallible, and far from ever closed. Conceptual perplexities, he held, can only be resolved by historical-comparative investigations. What merits thinking of Mach as a pragmatist, I will argue, is his insistence, as a philosopher, on the ultimately practical orientation of all thought as a matter both of fact and norm, and, as a historian of science, on the need to investigate the specific problem situations out of and in response to which concepts and theories developed. Last but not least, the practical orientation of his philosophy found expression in his allegiance to the ideal of enlightenment.

I analyse the relation of two important doctrines of Ernst Mach’s epistemology – namely the theory of the elements, exposed in The Analysis of Sensations, and the economy of thought, mainly explored in Knowledge and Error and elsewhere – to his historical-critical approach. After discussing Erwin Hiebert’s seminal work on Mach’s philosophical use of the history of science, I defend the thesis that there is a more profound, structural relationship between Mach’s conception of history and the anti-metaphysical remarks which open The Analysis of Sensations and introduce his theory of the elements. Finally, I contend that this can provide novel insights into the doctrine of the economy of thought.

Although the received view of Ernst Mach comported well with Mach’s historical influence on members of the Vienna Circle , it is inadequate, and it is now giving way to a more realistic and nuanced ‘neutral monist’ view. I defend the neutral monist tradition and show that it is actually a form of scientific realism, not positivism. I also argue that it is more in line with Mach’s contemporary reception, and that it leads to the views of American Realists, as well as to the views of our contemporary neutral monists. I start with a characterisation of some tenets of neutral monism in general, many of which were shared by William James and Bertrand Russell, both deeply influenced by Mach. I then detail the evidence for these views in Mach’s texts (including his notebooks and other documents). Seeing Mach as a kind of realist also casts much light on his scientific views and corrects a number of historical misconceptions regarding both atomism and Mach’s philosophy of space and time. Finally, I discuss Mach’s place in the neutral monist movement of James, Russell, and the American Realists, and the revival of these views in recent philosophy of mind.

This chapter analyses the careers of two distinct narratives about Mach’s philosophical legacy that prevailed among German-speaking physicists and philosophers for more than a generation. Planck’s polemic against Mach sired the idea of a Machian philosophical system that was irreconcilable with modern physics, Boltzmann’s legacy foremost. But Planck also bereaved Mach’s positivism of its naturalist foundation and identified it straight with phenomenalism. In contrast, many Austrians considered the epistemologies of Mach and Boltzmann as even mutually supportive for a defence of empiricist indeterminism. Taking positivism in its original, more general understanding, they underscored Mach’s broader anti-metaphysical and empiricist stance, eventually adopting him as a standard-bearer for the new movement of Logical Empiricism. While these understandings were not necessarily tied to a positive or negative assessment, they often amounted to simplifications, transformations, or even contortions of Mach’s thinking, which made it increasingly difficult to declare oneself in Mach’s footsteps and simultaneously to advocate scientific modernism.

The aim of this chapter is to provide a thorough account of the fact that Ernst Mach and Friedrich Nietzsche are often associated with each other in the specialised literature on the history of philosophy and the philosophy of science. I argue that the consistency which can be discovered between them is much more substantial than one may imagine. On the basis of their conception of knowledge and truth, it is possible to outline a complete parallelism between their approach to the issue concerning our intellectual relationship with the external world. In fact, Mach and Nietzsche dealt with the very same questions and indeed pursued a common general aim, namely the elimination of worn-out conceptions from the world of modern culture. Furthermore, I will maintain that Mach’s and Nietzsche’s research interests converge on the classic problem of realism versus anti-realism, and that it is in the light of this particular issue that their own views can be compared.

Ernst Mach’s Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit is now widely regarded as occupying a pivotal position in his oeuvre. Erik C. Banks called it a ‘roman à clef’. More generally, it is safe to say that the law of energy conservation played a central role in Mach’s thought. He frequently referred to it in his publications to illustrate how science works. This chapter has a two-fold aim. First, it sets his reflections on energy conservation against the background of its nineteenth-century history. Mach appears as a particularly astute observer of his own time. Second, it relates Mach’s comments on the law to his overall philosophy. Although in the second half of the nineteenth century the importance of the law of energy conservation was generally acknowledged, there was no consensus on what the law actually meant. Its name, discoverer, formulation, justification, and implications were all subject to debate. Mach was at the same time a participant in this debate (interpreting the law of energy conservation) and a commentator on it (interpreting debates on the law of energy conservation). In the process, he developed a new understanding of scientific meaning as grounded in communication, practice, and history.

Ernst Mach’s works have often been interpreted as presenting some version of idealism, such as phenomenalism. However, Erik C. Banks’ recent case for the rival neutral monist reading seems persuasive. But it still leaves a problem: how to explain why so many intelligent and thoughtful readers, some of them sympathetic to Mach, thought of him instead as some kind of idealist. I set out the major factors which tempt people into reading Mach thus and assess the strengths and weaknesses of these two readings.

Psychophysics as Mach understood it could be explained in several ways. This reflects the central conundrum that psychophysics held the potential to resolve: the communication of an individual’s subjective experience. This chapter surveys the many ways in which Mach described psychophysical experiences, from demonstrations on his Bösendorfer grand piano to differential equations. These descriptions were often multi-modal, using sound and images in tandem. Mach also employed analogies, mathematical derivations, and descriptions of the subjective experience of such phenomena as accommodation, acceleration, and visual after-images. A comparison of how Mach discusses psychophysics in popular lectures, scientific publications, and personal correspondence suggests that he made a number of assumptions about how best to communicate scientific ideas to different audiences. Further, this chapter argues that Mach’s techniques of presentation/argumentation, celebrated both in his time and subsequently, went far towards cultivating a psychophysical imaginarium similar to a mind’s eye. That is, by asking his readers or listeners to imagine specific psychophysical experiences, Mach established the broad outlines of a new way of thinking about subjectivity.

Ernst Mach’s appeal to the ‘economy of science’ has sometimes been interpreted as an overarching principle of minimisation, promoting the increasing simplification of scientific knowledge via principles that increase calculating power without adding substantively to the knowledge embedded in empirical facts. There is a growing literature arguing for a more robust understanding of Mach’s ‘economy of science’. Machian ‘economy’ appeals to the continuity between scientific experiences and concepts, but also to the increasing complexity of scientific concepts, building on connections between what Mach called world-elements or sensation-elements. Mach’s account emphasises not only continuities between experiences that allow for simplification, but also areas of divergence that promote the branching of scientific concepts and methods. I emphasise the roles of abstraction, pragmatism, and history in Mach’s economy of science and argue that these elements allowed Mach to investigate the productive tension between creative and conservative moments in the history of science.

There is a familiar narrative of the development from Ernst Mach’s 'positivism' to the more sophisticated 'neo-positivism' of the Vienna Circle, with language analysis and formal logic as additional ingredients. But we also see an alternative historiography telling of the rise and decline of scientific philosophy and the genetic theory of learning from Mach to the Vienna Circle. Recent research on Mach uncovers a more complex and multifaceted influence and pluralist reception of his work within the Vienna Circle based on a general appreciation of his empiricism and his idea of the unity of science. This chapter reconstructs the complex and diverse reception of Mach by main members of the Vienna Circle, showing the inherent pluralism based on the common anti-Kantian and 'late Enlightenment' consensus between empiricism and pragmatism, with Mach figuring as a critic of 'school philosophy' and a pioneer of contemporary history and philosophy of science. The thesis of a strong positive reception and further development and extension (regarding language and logic) of Mach’s doctrines with a critical distance vis-à-vis academic metaphysical philosophy is demonstrated as a manifestation of Mach’s function as a role model and predecessor of Viennese Logical Empiricism from the 'First Vienna Circle' to the heyday of the Schlick Circle.

Ernst Mach and William James were personal friends and intellectual allies. Might there have been an American pragmatist influence on Logical Positivism via James’s influence on Mach? I explore the relationship between these two friends, arguing that, if anything, Mach’s instrumentalism about science actually influenced James more than James’s pragmatism influenced Mach. What is more, empirical and not philosophical issues dominated their intellectual exchanges, and I examine the three topics about which they most frequently engaged one another: the role of the semicircular canals in the perception of bodily orientation, the question of whether there is a distinctive 'feeling of effort' (Innervationsgefühl), and the nature of visual spatial perception. The debate over the Innervationsgefühl is particularly interesting because James apparently convinced Mach to reverse his position on the matter. In short, we remember Mach as a master experimentalist and James as a philosophical populariser, so it is a surprise to learn that the main philosophical influence apparently flowed from Mach to James, while the main influence when it comes to matters of empirical interest actually flowed the other way.

This chapter examines the changing relations between Mach’s epistemology and his mechanics to offer a new perspective on the diverse respects in which Einstein built on Mach’s work. Considering Mach’s early psychophysical research on sensations of space and time indicates foundations both for Mach’s later research on physical space and time and for his search for an epistemology capable of encompassing conceptions and perceptual experience, but also psychology, physics, and psychophysics, as well as the social world: all knowledge. I show that Mach’s critical studies of mass and inertia emerged from his perceptual studies and were intimately linked to bodily experience and experiment. Considering his well-known Mechanics indicates that Mach sought to train the imagination as well as stimulate critique in the attacks on absolutes that are now usually taken to define his anti-metaphysical empiricism. I argue that while celebrating the role of Mach’s criticism, Einstein remained unaware of the extent to which his initial approach to general relativity was shaped by a pedagogical thought experiment on action and reaction in which Mach linked gravitation and acceleration. Finally, when he turned explicitly to epistemology, rather than emphasising positivist empiricism, Mach offered a study of the psychology of research in practice.

I examine Mach’s views on how analogy is used in natural science. Omissions of key parts of the text in translations and reprints of his 1904 paper on the topic have contributed to a lack of understanding of what he said and thus to a lack of appreciation of his views. I distinguish two different kinds of analogies that he discusses: in the common use of the term, an analogy is drawn between two objects and is feature-based. In the powerful use made of it in the historical case studies he refers to in talking about analogy in natural science, an analogy is drawn between two systems of concepts, and so opens up a role for scientific laws and principles to play in analogies.