Online research in philosophy

The founders of the Marburger Schule of Neo-Kantianism, Hermann Cohen and Paul Natorp, laid an emphasis upon a Platonic understanding of mathematics and logic as the paradigmatic epistemological basis of philosophy. Their successors, namely Ernst Cassirer and Nicolai Hartmann, made obvious, however, that new biological thinking can have a strong influence on ontology as well as on the theory of knowledge. They could show that biology was no longer to be treated as a metaphysical system in that pejorative meaning of metaphysics which Kant had so severely been opposing. Against the anti-realistic approach of the older neo-Kantians who wanted to eliminate Kant's thing-in-itself (Ding an sich), both Cassirer and Hartmann returned to a form of realism by way of Hegel's philosophical results and reflections on his method. This makes clear that their realism is still to be taken as a more of less monistic idealism. However, considering that modern biology as an antimetaphysical force became influential in their system for the first time and that it did so in two different but - on second thoughts - complementary ways, it becomes clear that it was necessary to change the paradigms of any neo-Kantian philosophy. Cassirer proved this by his development as a philosopher with a strong historical impetus while Hartmann as a more systematical philosopher only pointed in that direction.

An autobiographical account of a formative experience -- Cassirer's philosophy of symbolic forms -- Art and science as supplementing forms -- The parting of the ways and the divide in organizational theory -- Cassirer in the light of neuroscience -- Bringing Cassirer into organizations -- The institution as a symbolic form.

We seek to elucidate the philosophical context in which the so-called revolution of rigor in inifinitesimal calculus and mathematical analysis took place. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at that 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. Expressed in terms of modern mathematics, the Marburg philosophers saw the introduction of both infinitesimals and limits as completions whose prototype was Dedekind's of the rational number system resulting in the real numbers. At least partially,, this idea of "completions" can be captured in terms of a category-theoretical description of the conceptual development of modern mathematics. The feasibility of such a modern reformuation may be taken as evidence that the philosophical resources of Marburg neo-Kantianism may be of interest even for contemporary philosophy of mathematics.

Summary The paper considers Ernst' Cassirer's standpoint with reference to Euclidean geometry and the complementarity principle of quantum theory, interpreted as a choice between a causal description and a space-time description. The acceptance of the complementarity principle by Cassirer not only lands him off the Kantian path slightly, but it also leads him to some contradictions and incompatibilities within his own system of thought. 1. Accepting complementarity, Cassirer cannot still hold that there is an infinite hierarchy of objective levels as he does towards the end of hisDeterminismus; and 2. accepting complementarity, Cassirer cannot still hold on to the observability principle of Leibniz.

My purpose in this paper is to look at Cassirer’s relation to critical philosophy from a new perspective. Most discussions concerning Cassirer’s Kantianism have so far centered on his relation to neo-Kantianism and the Marburg school. My focus will not be on neo-Kantianism but on Cassirer’s notion of a “critique of culture.” In an often cited paragraph from the introduction to The Philosophy of Symbolic Forms , Cassirer says that his aim is to broaden Kant’s critical approach to all various forms of culture, to language as well as myth and art, and thus to transform the “critique of reason” into the “critique of culture.” I will explore Cassirer’s concept of the “critique of culture” and suggest that it can best be understood by placing it in the context of early twentieth century German philosophy. More precisely, I will aim to show that Cassirer’s critique can be seen as an effort to find a middle path between Lebensphilosophie and the positivism of the Vienna Circle.

Biographical material.--Descriptive and critical essays on the philosophy of Ernst Cassirer.--The philosopher speaks for himself.--Bibliography of the writings of Ernst Cassirer.

Idealist Heresies in Philosophy of Science: Cassirer, Carnap, and Kuhn. As common wisdom has it, philosophy of science in the analytic tradition and idealist philosophy are incompatible. Usually, not much effort is spent for explaining what is to be understood by idealism. Rather, it is taken for granted that idealism is an obsolete and unscientific philosophical account. In this paper it is argued that this thesis needs some qualification. Taking Carnap and Kuhn as paradigmatic examples of positivist and postpositivist philosophies of science it is shown that these accounts share important features with Cassirer's idealist philosophy of science developed in the first half of this century. As it turns out, often Cassirer is more modern than those classical philosophers of (post)posivitist philosophy of science. For instance, Quine's criticism against Carnap's empiricist philosophy of science launched in Two Dogmas of Empiricism is anticipated by Cassirer for several decades.

According to Kant, pure intuition is an indispensable ingredient of mathematical proofs. Kant‘s thesis has been considered as obsolete since the advent of modern relational logic at the end of 19th century. Against this logicist orthodoxy Cassirer’s “critical idealism” insisted that formal logic alone could not make sense of the conceptual co-evolution of mathematical and scientific concepts. For Cassirer, idealizations, or, more precisely, idealizing completions, played a fundamental role in the formation of the mathematical and empirical concepts. The aim of this paper is to outline the basics of Cassirer’s idealizational account, and to point at some interesting similarities it has with Kant’s and Peirce’s philosophies of mathematics based on the key notions of pure intuition and theorematic reasoning, respectively.

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 ..

One of the most important philosophical topics in the early twentieth century ? and a topic that was seminal in the emergence of analytic philosophy ? was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant.