Dedekind's major work on the foundations of arithmetic employs several techniques that have left him open to charges of psychologism, and through this, to worries about the objectivity of the natural-number concept he defines. While I accept that Dedekind takes the foundation for arithmetic to lie in certain mental powers, I will also argue that, given an appropriate philosophical background, this need not make numbers into subjective mental objects. Even though Dedekind himself did not provide that background, one can nevertheless (...) be found in the work of the neo-Kantian Ernst Cassirer on mathematical concept formation. (shrink)

Over the course of three books—Wandering Significance, Physics Avoidance, and most recently Imitation of Rigor—Mark Wilson seeks to rectify what he takes to be a century of error regarding analytic philoso-phy’s understanding of scientific theorizing. This is largely framed in terms of a sustained attack on what Wilson terms ‘theory T thinking’, which he uses to refer to a melange of philosophical tendencies that he argues fail to do justice to the nuances of how world–theory relations are forged in the (...) physical sciences. In its place, Wilson puts forward an intricate account of the shifting explanatory strategies scientists and mathematicians utilize, strategies that result in the morphing of the semantic import of our scientific terms. In the aftermath an important question emerges: what is to become of scientific realism? Despite numerous pronunciations of his own ‘stout’ realist stance, it remains unclear what Wilson’s position might actually entail. -/- I first sketch Wilson’s disputes with theory T thinking and demonstrate how his rejection of the main tenets of most contemporary realist accounts leaves a question as to what his own realist avowals could mean, further arguing that these are largely attempts to distance himself from any whiff of neo-Kantianism. In the remainder of the article, I turn to discuss a neo-Kantian account that I argue is both complementary to Wilson’s viewpoint and provides a foundation for a post-theory T realism: Ernst Cassirer’s account of concept-formation in the natural sciences. By fleshing out Cassirer’s notion of the transformation of the given and the particular role he attributes to theoretical idealization, I reconstruct his account in a way that draws out a number of fruitful parallels between his philosophy and Wilson’s. The upshot is that a post-theory T scientific realism can plausibly be brought into line with neo-Kantian conceptions. (shrink)

This paper compares Cohen’s Logic of Pure Knowledge and Cassirer’s Substance and Function in order to evaluate how in these works Cohen and Cassirer go beyond the limits established by Kantian philosophy. In his Logic, Cohen seeks to ground in pure thought all the elements which Kant distinguishes in empirical intuition: its matter (sensation) as well as its form (time and space). In this way, Cohen tries to provide an account of knowledge without appealing to any receptivity. In accordance with (...) Cohen’s project of reformulating the Kantian theory of sensibility, Cassirer undertakes in Substance and Function the task of developing an alternative doctrine of pure and empirical manifolds. But whereas Cohen analyzes the laws of pure thought, Cassirer aims to highlight the functional character of concepts in the development of modern mathematics and physics. I will discuss these two different approaches to the problems raised by Kantian philosophy and I will argue that Cassirer went further than Cohen in the project of critical idealism. (shrink)

The aim of this paper is make a contribution to the ongoing search for an adequate concept of the a priori element in scientific knowledge. The point of departure is C.I. Lewis’s account of a pragmatic a priori put forward in his "Mind and the World Order" (1929). Recently, Hasok Chang in "Contingent Transcendental Arguments for Metaphysical Principles" (2008) reconsidered Lewis’s pragmatic a priori and proposed to conceive it as the basic ingredient of the dynamics of an embodied scientific reason. (...) The present paper intends to further elaborate Chang’s account by relating it with some conceptual tools from cognitive semantics and certain ideas that first emerged in the context of the category-theoretical foundations of mathematics. (shrink)

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our (...) main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position towards the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals, nor whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity, and to exploit it in making sense of infinitesimals and related concepts. (shrink)

Abstract. In Dynamics of Reason Michael Friedman proposes a kind of synthesis between the neokantianism of Ernst Cassirer, the logical empiricism of Rudolf Carnap, and the historicism of Thomas Kuhn. Cassirer and Carnap are to take care of the Kantian legacy of modern philosophy of science, encapsulated in the concept of a relativized a priori and the globally rational or continuous evolution of scientific knowledge,while Kuhn´s role is to ensure that the historicist character of scientific knowledge is taken seriously. More (...) precisely, Carnapian linguistic frameworks, guarantee that the evolution of science procedes in a rational manner locally,while Cassirer’s concept of an internally defined conceptual convergence of empirical theories provides the means to maintain the global continuity of scientific reason. In this paper it is argued that Friedman’s neokantian account of scientific reason based on the concept of the relativized a priori underestimates the pragmatic aspects of the dynamics of scientific reason. To overcome this short-coming, I propose to reconsider C.I. Lewis’s account of a pragmatic the priori, recently modernized and elaborated by Hasok Chang. This may be<br><br><br><br><br><br><br><br><br><br&g t;<br><br><br><br><br><br>Keywords: Dynamics of reason, Paradigms, Logical Empiricism,Neokantianism, Pragmatism, Mathematics, Communicative Rationality. (shrink)

This paper reconstructs the major transformations in the Marburg neo-Kantian account of experience. By focusing on the problem of ‘conceptualism’, it traces connections between four issues that are central to the transcendental projects of the Marburg philosophers: the interpretation of Kant, the critique of experiential givenness, the account of objective cognition in science, and the relation between scientific and pre-scientific experience. My historical narrative identifies two shifts. The first is from Cohen's conceptualist answer to the threat of subjectivism to Cassirer's (...) functionalist answer to empiricism. The second is from Cassirer's conceptualism about scientific experience to his symbolic non-conceptualism about everyday perception. My reconstruction reveals the fate of neo-Kantian conceptualism to be linked to the fate of pre-scientific perception and suggests that the continuing significance of the Marburg philosophers lies in their responses to the coming apart of the manifest and the scientific image. (shrink)

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.

Ernst Cassirer’s epistemological trilogy – Substanzbegriff und Funktionsbegriff (1910), Zur Einsteinschen Relativitätstheorie (1921) and Determinismus und Indeterminismus (1937) – is well known to Western scholars, some of whom recently devoted a number of in-depth and interesting studies to Cassirer’s epistemology. Nonetheless, they overlooked aspects of Cassirer’s concept of idealisation and his model of science as found in his last epistemological work: Determinismus und Indeterminismus. In this essay I will consider these two almost disregarded aspects of Cassirer’s epistemology in order to (...) provide a better understanding of his idea of science. (shrink)

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...) with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)