The student of philosophy usually is not irritated by obscure formulations. On the contrary, reading the quoted passage he would presumably be convinced ...

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such (...) later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism. (shrink)

Hermann von Helmholtz’s work on perceptual science had a fundamental impact on Neo-Kantian movements in the late nineteenth century, and his influence continues to be felt in psychology and analytic philosophy of perception. As is widely acknowledged, Helmholtz denied that we can perceive mind-independent properties of external objects, a view I label Ignorance. Given his commitment to Ignorance, Helmholtz might seem to be committed to a subjectivism according to which we only perceive properties of our own representations. Against this, I (...) argue that for Helmholtz, the properties we perceive are not monadic properties of either the subject or the object. Rather, Helmholtz endorsed a relationalism about the properties we perceive: the properties of objects we perceive are all relational properties. I then suggest that once we take into account oft-neglected terminological distinctions in Helmholtz’s corpus, we are better able to make sense of his commitment to relationalism. (shrink)

The paper investigates Ernst Cassirer’s structuralist account of geometrical knowledge developed in his Substanzbegriff und Funktionsbegriff. The aim here is twofold. First, to give a closer study of several developments in projective geometry that form the direct background for Cassirer’s philosophical remarks on geometrical concept formation. Specifically, the paper will survey different attempts to justify the principle of duality in projective geometry as well as Felix Klein’s generalization of the use of geometrical transformations in his Erlangen program. The second aim (...) is to analyze the specific character of Cassirer’s geometrical structuralism formulated in 1910 as well as in subsequent writings. As will be argued, his account of modern geometry is best described as a “methodological structuralism”, that is, as a view mainly concerned with the role of structural methods in modern mathematical practice. (shrink)

In lieu of a programmatic argument about the general relations of history of science and philosophy of science, this essay offers a particular topic in the history of philosophy of science that should be of interest to both historians and philosophers of science. It argues that questions typical of contemporary history of science could illuminate the recent history of philosophy of science and analytic philosophy. It also suggests that the history of scientific philosophy is a particularly fruitful arena for historians (...) of science interested in issues of marginal science. (shrink)

The present paper is concerned with Helmholtz’s theory of measurement. It will be argued that an adequate understanding of this theory depends on how Helmholtz’s application of the concepts of perception and coincidence is interpreted. In contrast both to conventionalist and Kantian readings of Helmholtz’s theory, a more realistic interpretation will be suggested.

In spite of Ernst Cassirer’s criticisms of psychologism throughout Substance and Function, in the final chapter he issues a demand for a “psychology of relations” that can do justice to the subjective dimensions of mathematics and natural science. Although these remarks remain somewhat promissory, the fact that this is how Cassirer chooses to conclude Substance and Function recommends it as a topic worthy of serious consideration. In this paper, I argue that in order to work out the details of Cassirer’s (...) psychology of relations in Substance and Function, we need to situate it within two broader frameworks. First, I position Cassirer’s view in relation to the view of psychology and logic endorsed by his Marburg Neo-Kantian predecessors, Hermann Cohen and Paul Natorp. Second, I augment Cassirer’s early account of the psychology of relations in Substance and Function with the more mature view of psychology that he presents in The Philosophy of Symbolic Forms. By placing Cassirer’s account within these contexts, I claim that we gain insight into his psychology of relations, not just as it pertains to mathematics and natural science, but to culture as a whole. Moreover, I maintain that pursuing this strategy helps shed light on one of the most controversial features of his philosophy of mathematics and natural science, viz., his theory of the a priori. (shrink)

According to Michael Friedman, Ernst Cassirer’s “outstanding contribution [to Neo-Kantianism] was to articulate, for the first time, a clear and coherent conception of formal logic within the context of the Marburg School” (Friedman 2000, p. 30). In his paper “Kant und die moderne Mathematik” (1907), Cassirer argued not only that the new relational logic of Frege1 and Russell was a major breakthrough with profound philosophical implications, but also that the logicist thesis itself was a “fact” of modern mathematics. Cassirer summarizes (...) his evaluation of Russell’s work: Here logic and mathematics have been fused into a true, henceforth indissoluble unity; and from this inner connection there arises for each... (shrink)

Frege was the grandfather of analytical philosophy, Husserl the founder of the phenomenological school, two radically different philosophical movements. In 1903, say, how would they have appeared to any German student of philosophy who knew the work of both? Not, certainly, as two deeply opposed thinkers: rather as remarkably close in orientation, despite some divergence of interests. They may be compared with the Rhine and the Danube, which rise quite close to one another and for a time pursue roughly parallel (...) courses, only to diverge in utterly different directions and flow into different seas. Why, then, did this happen? What small ingredient into the thought of each was eventually magnified into so great an effect? (shrink)

A survey of the emergence of early analytic philosophy as a subfield of the history of philosophy. The importance of recent literature on Frege, Russell, and Wittgenstein is stressed, as is the widening interest in understanding the nineteenth-century scientific and Kantian backgrounds. In contrast to recent histories of early analytic philosophy by P.M.S. Hacker and Scott Soames, the importance of historical and philosophical work on the significance of formalization is highlighted, as are the contributions made by those focusing on systematic (...) treatments of individual philosophers, traditions, and periods in relation to contemporary issues (rule-following, neo-Fregeanism, contextualism, theory of meaning). (shrink)

This paper examines the anti-psychologism of Paul Natorp, a Marburg School Neo-Kantian. It identifies both Natorp’s principle argument against psychologism and the views underlying the argument that give it its force. Natorp’s argument depends for its success on his view that certain scientific laws constitute the intersubjective content of knowledge. That view in turn depends on Natorp’s conception of subjectivity, so it is only against the background of his conception of subjectivity that his reasons for rejecting psychologism make sense. This (...) interpretation of Natorp suggests that attention paid to late nineteenth century theories of subjectivity and philosophy of psychology could improve our understanding of the emergence of anti-psychologism in that period.Keywords: Paul Natorp; Marburg School; Neo-Kantianism; Psychologism; Subjectivity. (shrink)

Nineteenth-century scientist Hermann von Helmholtz’s peculiar wavering between empiricism and transcendentalism in his philosophy of science in general, and in his theory of perception in particular, is a much debated and well-documented topic in the history and philosophy of science. This contribution aims at providing a fresh angle on this classical issue, by considering Helmholtz’s account of differential consciousness against the background of a centuries-old philosophical debate between the empiricist tradition and the tradition of transcendental idealism. By placing Helmholtz’s psychology (...) against the background of a historical narrative stretching from Hume to Fichte, one can gain insight into the possible merits of his empirico-transcendentalism with regard to the problem of differentiation. More particularly, it is argued that Helmholtz’s psychology tilted towards transcendentalism when met with the classical theoretical problems of strict empiricism in dealing with the foundation of consciousness, most notably circularity and infinite regress. Without claiming that Helmholtz’s theorizing presented a self-conscious attempt to overcome the latter issues, his well-known wavering between perspectives in general, and his appropriation of the a priori in particular, might have served him well in avoiding the deadlocks of empiricism. As noted at the end, however, Helmholtz’s account produced complex philosophical problems of its own. (shrink)

The question of the applicability of mathematics is an epistemological issue that was explicitly raised by Kant, and which has played different roles in the works of neo-Kantian philosophers, before becoming an essential issue in early analytic philosophy. This paper will first distinguish three main issues that are related to the application of mathematics: indispensability arguments that are aimed at justifying mathematics itself; philosophical justifications of the successful application of mathematics to scientific theories; and discussions on the application of real (...) numbers to the measurement of physical magnitudes. A refinement of this tripartition is suggested and supported by a historical investigation of the differences between Kant’s position on the problem, several neo-Kantian perspectives, early analytic philosophy, and late 19th century mathematicians. Finally, the debate on the cogency of an application constraint in the definition of real numbers is discussed in relation to a contemporary debate in neo-logicism, in order to suggest a comparison not only with Frege’s original positions, but also with the ideas of several neo-Kantian scholars, including Hölder, Cassirer, and Helmholtz. (shrink)

Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this view, I focus on Hermann’s central claim that limited spatio-temporal, and even analogically causal, representations of events exist within an overall relational structure of entangled quantum mechanical states that defy any unified spatio-temporal description. (...) In my view, Hermann also advances an important transcendental argument that perspectival spatio-temporal representations of nature have their foundations in general relational networks that are not spatio-temporal. The key point is that the adoption of a perspectival system within the general network induces the representation but only for that context. These ideas are consistent with a perspectival subject–object principle in Kant and also with Weyl’s work on Lie groups and their representations. (shrink)

In this insightful study of the common origins of analytic and continental philosophy, Friedman looks at how social and political events intertwined and influenced philosophy during the early twentieth century, ultimately giving rise to the two very different schools of thought. He shows how these two approaches, now practiced largely in isolation from one another, were once opposing tendencies within a common discussion. Already polarized by their philosophical disagreements, these approaches were further split apart by the rise of Naziism and (...) the resulting emigration of all influential German-speaking philosophers except for Heidegger. Although the book gives a general overview of the philosophical issues of the period, the author pays special attention to the relationships among three key twentieth-century philosophers: Rudolf Carnap, Ernst Cassirer, and Martin Heidegger. (shrink)

Neo-Kantianism was an important movement in German philosophy of the late 19th century: Frederick Beiser traces its development back to the late 18th century, and explains its rise as a response to three major developments in German culture: the collapse of speculative idealism; the materialism controversy; and the identity crisis of philosophy.

This edition includes new essays by philosopher Michael Williams and literary scholar David Bromwich, as well as Rorty's previously unpublished essay "The ...

This collection, with contributions from leading philosophers, places analytic philosophy in a broader context comparing it with the methodology of its most important rival tradition in twentieth-century philosophy--phenomenology, whose development parallels the development of analytic philosophy in many ways. _The Analytic Turn _will be of great interest to historians of philosophy generally, analytic philosophers, and phenomenologists.

This is the first reprint, complete with a new introduction by John Slater.

Hermann von Helmholtz (1821-1894) participated in two of the most significant developments in physics and in the philosophy of science in the 19th century: the proof that Euclidean geometry does not describe the only possible visualizable and physical space, and the shift from physics based on actions between particles at a distance to the field theory. Helmholtz achieved a staggering number of scientific results, including the formulation of energy conservation, the vortex equations for fluid dynamics, the notion of free energy (...) in thermodynamics, and the invention of the ophthalmoscope. His constant interest in the epistemology of science guarantees his enduring significance for philosophy. (shrink)