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. (shrink)

Abstract. The aim of this paper is to reconstruct the debate on Begriffstheorie between Ernst Cassirer, the Swe¬dish philosopher Konrad Marc-Wogau, and, virtually, Moritz Schlick. It took place during in the late thirties when Cassirer had immigrated to Sweden. While Cassirer argued for a rich “constitutive” theory of concepts, Marc-Wogau, and, in a different way, Schlick favored “austere” non-con¬sti¬¬tutive theories of concepts. Ironically, however, Cassirer used Schlick’s account as a weapon to counter Marc-Wogau’s criticism of his rich con¬¬sti¬tu¬¬tive theory of (...) concepts. With the help of modern Formal Concept Theory (FCT) it can be shown, however, that Marc-Wogau’s argument is flawed. (shrink)

The paper discusses neo-Kantian commentaries on Russell's views on logic and the philosophy of mathematics at the beginning of the twentieth century. Although Russell and the neo-Kantians had similar philosophical interests at this time, their views were usually incompatible. First, I examine the differences between Russell's A Critical Exposition of the Philosophy of Leibniz and Cassirer's Leibniz' System in seinen wissenschaftlichen Grundlagen. Second, I discuss the critiques of the logicist programme presented by the neo-Kantians Paul Natorp, Ernst Cassirer and Jonas (...) Cohn. They argued that Russell's attempt to deduce the number concept from the class concept is a petitio principii. Russell replied that the sense in which every object is ‘one’ must be distinguished from the sense in which ‘one’ is a number. I claim that Russell was wrong in dismissing the neo-Kantian argument as an elementary error. Neo-Kantians understood the logicist definition of number in terms of the neo-Kantian movement to which they belonged; that is to say, although the notion ‘a class with one object’ does not presuppose the number ‘one’ if one accepts the logicist definition of number, it will presuppose it if one advocates a neo-Kantian theory of number. (shrink)

En este trabajo nos proponemos estudiar los vínculos que Cassirer establece entre los conceptos de causalidad, invariancia y sistematicidad en el conocimiento de la física. Para ello, comenzaremos considerando el marco general en el que se inscribe el análisis que Cassirer realiza. Este marco es el provisto por el método trascendental. En segundo lugar, consideraremos el principio de causalidad de Kant a la luz de su distinción entre principios constitutivos y principios regulativos de la experiencia. Luego, discutiremos las dificultades que (...) Cassirer encuentra en la doctrina kantiana de la causalidad. Más adelante nos referiremos al sistema de los enunciados de la física, para poder así determinar el modo en el que se relacionan los conceptos de causalidad, invariancia y sistematicidad. (shrink)

The notion of idealization has received considerable attention in contemporary philosophy of science but less in philosophy of mathematics. An exception was the ‘critical idealism’ of the neo-Kantian philosopher Ernst Cassirer. According to Cassirer the methodology of idealization plays a central role for mathematics and empirical science. In this paper it is argued that Cassirer's contributions in this area still deserve to be taken into account in the current debates in philosophy of mathematics. For extremely useful criticisms on earlier versions (...) I am grateful to B.P. Larvor and another anonymous journal referee. CiteULike Connotea Del.icio.us What's this? (shrink)

(2000). CASSIRER, SCHLICK AND ‘STRUCTURAL’ REALISM: THE PHILOSOPHY OF THE EXACT SCIENCES IN THE BACKGROUND TO EARLY LOGICAL EMPIRICISM. British Journal for the History of Philosophy: Vol. 8, No. 1, pp. 71-106.

Este ensaio busca oferecer uma coleção de materiais historiográficos, em sua maior parte traduzidos do alemão, a bem da contextualização mais detalhada do papel de Moisés Mendelssohn no debate filosófico alemão da segunda metade do XVIII, em especial no que concerne à provável influência de suas reflexões em Kant e Hegel. Inicio com a consideração das novidades trazidas à tona por M. Serres no que concerne à interpretação de Leibniz, e o faço com o intuito de introduzir em sentido amplo (...) a problemática da _característica universal_, que servirá de fio condutor neste percurso. Tal introdução me permite definir alguns dos termos mediante os quais observaremos o debate entre Kant e Mendelssohn, a começar com a análise de alguns aspectos do concurso sobre a cientificidade da metafísica proposto pela Academia de Ciências da Prússia em 1762, e em seguida com a observação, mesmo que sumária, de alguns outros momentos importantes do contato entre ambos os filósofos. Meu objetivo é ilustrar a posição mendelssohniana, mesmo que de maneira introdutória, no intuito de se lançar alguma luz sobre seu projeto crítico de impor limites à razão teórica da matemática clássica e à razão prática da mística cabalística – diapasão em que se exercita a mágica e o fascínio do ideário da característica universal – o que promete, por sua vez, iluminar tanto alguns aspectos fundamentais do projeto da _Crítica da Razão Pura_ de Kant quanto da _Ciência da Lógica_ de Hegel. À guisa de conclusão relatarei, mesmo que de maneira episódica e sumária, aspectos da _querela do panteísmo_ e indicaremos brevemente como Kant e Hegel, de maneiras opostas, a ela reagiram. (shrink)

O autor estuda o impacto de Kant na filosofia analítica contemporânea e na respetiva historiografia, desde Frege, Russell e o positivismo lógico vienense, até a algumas reformulações mais recentes do problema kantiano sobre a distinção entre o analítico e o sintético, e a possibilidade do sintético a priori, como é o caso, entre outras, da de Quine e da de Kripke. Discute as razões que estão na origem do retorno a Kant na filosofia analítica desde os anos cinquenta do século (...) passado até aos nossos dias, e mostra que esse retorno se centrou na atualidade do problema referido e das respetivas implicações. (shrink)

What I want to point out is the “meaning change” that Friedman ascribes to terms and principles, which he calls a priori, in the transition from the old framework to the new: -/- 'This captures the sense, in particular, in which there has indeed been a ”meaning change” in the transition from the old framework to the new: even if the same terms and principles reappear in the new framework they do not have the same meaning they had in the (...) old' (Friedman 2001, p. 99, ft. 37). -/- Following Friedman, we should admit that the same words possess different meanings in different frameworks. In fact, terms and principles that are empirical in an old framework may shift to constitutive status in the new framework, and vice- versa. If Friedman’s account seemed to entrust the prospective rationality of science to constitutive a priori principle, the notion of meaning change suggests instead that Friedman’s argument upholds the Kuhnian account of incommensurability, while we were expecting he aimed to mitigate it. As he clearly states in the passage to follow: -/- 'The later framework is not translatable into the earlier framework, of course, simply because the concepts used in formulating the later framework have not yet come into existence' (Friedman 2001, pp. 98-99). -/- Friedman’s account purports to emphasize that a transition from empirical laws to principles, and vice-versa, should imply a conceptual shift. But is “meaning change” the appropriate expression that may describe such a conceptual shift? What does the word “concept” mean for Friedman? How are concepts related to the meaning of terms? What does the “meaning” mean in Friedman’s view? What is the relation between terms and theories? Does theory change entail a meaning change of scientific terms, that is, do terms determine theory change (i.e. difference in theories is ipso facto difference in terms)? Recently, some specialists (Tsou 2010, for instance) have stressed Friedman’s notion of constitutive a priori principle in light of Putnam’s positive account of apriority. Friedman's and Putnam’s notions of relativized a priori are presented as similar insofar as they both affirm the existence of principles in science, which are revisable and relativized to a particular body of knowledge. However, the similarities do not take into account that Friedman ascribed a meaning change to coordinating principles that are constitutive of the new framework. Could Putnam subscribe such a meaning change? This paper aims to analyse Friedman’s notion of constitutive a priori principle in relation to the problem of meaning change by taking into account Putnam’s theory of meaning and his notion of framework principle. (shrink)

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this endeavor (...) can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

Sie ist eine systematische und dialektische Auseinandesetzung mit Kants Architektonik der reinen Vernunft in der Kritik der reinen Vernunft. Damit zeigt Sie uns an, dass die Kritik der reinen Vernunft sich mit der Unterscheidung von Anschauung und Begriffen als eine Aufklärung einer praktischen Zweckmäßigkeit unserer Vernunft vorstellt.

The aim of this paper is to show that a comprehensive account of the role of representations in science should reconsider some neglected theses of the classical philosophy of science proposed in the first decades of the 20th century. More precisely, it is argued that the accounts of Helmholtz and Hertz may be taken as prototypes of representational accounts in which structure preservation plays an essential role. Following Reichenbach, structure-preserving representations provide a useful device for formulating an up-to-date version of (...) a (relativized) Kantian a priori. An essential feature of modern scientific representations is their mathematical character. That is, representations can be conceived as (partially) structure-preserving maps or functions. This observation suggests an interesting but neglected perspective on the history and philosophy of this concept, namely, that structure-preserving representations are closely related to a priori elements of scientific knowledge. Reichenbach’s early theory of a relativized constitutive but non-apodictic a priori component of scientific knowledge provides a further elaboration of Kantian aspects of scientific representation. To cope with the dynamic aspects of the evolution of scientific knowledge, Cassirer proposed a re-interpretation of the concept of representation that conceived of a particular representation as only one phase in a continuous process determined by pragmatic considerations. Pragmatic aspects of representations are further elaborated in the classical account of C.I. Lewis and the more modern of Hasok Chang. (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)

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)

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. (...) Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method. (shrink)

Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these objections. We (...) argue that while propensity theories face challenges, these challenges do not undermine their validity as prospective interpretations of probability in science. (shrink)

Ernst Cassirer’s book Substanzbegriff und Funktionsbegriff is a difficult book for contemporary readers to understand. Its topic, the theory of concept formation, engages with debates and authors that are largely unknown today. And its “historical” style violates the philosophical standards of clarity first propounded by early analytic philosophers. Cassirer, for instance, never says explicitly what he means by “substance-concept” and “function-concept.” In this article, I answer three questions: Why did Cassirer choose to focus on the topic of concept formation? What (...) did Cassirer mean in contrasting “substance-concepts” and “function-concepts”? How does Cassirer’s polemic against traditional theories of concept formation lead to the distinctive philosophy of mathematics that he defends in the book? I argue that Cassirer’s contrast between substance-concepts and function-concepts includes a series of interrelated contrasts—contrasts that touch on issues in logic, metaphysics, epistemology, and the theory of objectivity. Cassirer’s defense of mathematical structuralism flows out of a progressively unfolding and intricate argument that begins with epistemological problems in the theory of concept formation. (shrink)

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...) an inter-weaving of methodological and epistemological considerations. The latter aspect illustrates how philosophical concerns can grow out of mathematical practice, as opposed to being imposed on it from outside. It also sheds new light on the legacy and the lasting significance of logicism today. (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)

This paper addresses a number of closely related questions concerning Kant's model of intentionality, and his conceptions of unity and of magnitude [Gröβe]. These questions are important because they shed light on three issues which are central to the Critical system, and which connect directly to the recent analytic literature on perception: the issues are conceptualism, the status of the imagination, and perceptual atomism. In Section 1, I provide a sketch of the exegetical and philosophical problems raised by Kant's views (...) on these issues. I then develop, in Section 2, a detailed analysis of Kant's theory of perception as elaborated in both the Critique of Pure Reason and the Critique of Judgment; I show how this analysis provides a preliminary framework for resolving the difficulties raised in Section 1. In Section 3, I extend my analysis of Kant's position by considering a specific test case: the Axioms of Intuition. I contend that one way to make sense of Kant's argument is by juxtaposing it with Russell's response to Bradley's regress; I focus in particular on the concept of ‘unity’. Finally, I offer, in Section 4, a philosophical assessment of the position attributed to Kant in Sections 2 and 3. I argue that, while Kant's account has significant strengths, a number of key areas remain underdeveloped; I suggest that the phenomenological tradition may be read as attempting to fill precisely those gaps. (shrink)

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. (shrink)

The vicissitudes of mathematical reason in the 20th century Content Type Journal Article Pages 1-6 DOI 10.1007/s11016-011-9556-y Authors Thomas Mormann, Department of Logic and Philosophy of Science, University of the Basque Country UPV/EPU, Donostia-San Sebastian, Spain, Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

One of the key events in the relations between the Central European philosophers and those of the Nordic countries was the Second International Congress for the ...

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)

This article argues that Ernst Cassirer's views about the concept of substance and his views on mythic consciousness are applicable to the concept of race. By analyzing examples from the most influential and representative racial theories, this article shows that the concept of race functions like the concept of substance whereby random, large-scale, and irreducibly complex phenomena is explained through the deterministic behavior of a smaller, material, constituent part. Given that mythic consciousness explains causality in the same way, this substance-mode (...) explanation of becoming can also be termed “mythic.” Further, under this substance/racial understanding of personhood, humans have no agency to determine their own fates. It is this fatalism that Cassirer railed against in The Myth of the State. In place of this substance (racial) understanding of personhood, and as this article will describe, Cassirer argued for a “functional” (cultural) understanding of personhood. (shrink)

In this paper, I shall discuss the assumption that Kant’s method in the Critique of Pure Reason is a transcendental analysis of experience. In order to do this, I will consider the conception of transcendental analysis that Marburg Neo-Kantianism powerfully introduced into Kant interpretation. I shall first develop a general model of transcendental analysis in the Marburg sense. I shall then ask whether this is a suitable model for the interpretation of the first Critique. Kant’s distinction between the analytic and (...) synthetic method in the Prolegomena seems to contradict this, given that it is a distinction between two different mathematical methods of demonstration. However, I shall argue that any such reading is incompatible with the Critique, and that transcendental analysis is indeed a legitimate interpretative model for understanding Kant. I shall finally turn to Strawson’s conception of descriptive metaphysics, which has strong affinities to Kant and the Marburg school. Most importantly, Strawson helps us to understand three significant aims at which transcendental analysis is directed. Finally, comparing transcendental analysis to dominant conceptions of analysis in philosophy, I shall argue that it constitutes a variety of philosophical analysis sui generis. (shrink)

In recent years, Reichenbach's 1920 conception of the principles of coordination has attracted increased attention after Michael Friedman's attempt to revive Reichenbach's idea of a "relativized a priori". This paper follows the origin and development of this idea in the framework of Reichenbach's distinction between the axioms of coordination and the axioms of connection. It suggests a further differentiation among the coordinating axioms and accordingly proposes a different account of Reichenbach's "relativized a priori".

A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.

Although logicism played a significant role in Carnap's philosophical thinking, the relation of his philosophy of mathematics to the main tenets of the logicist tradition is complex and variable. is paper examines one aspect of this relation by discussing the following question: What elements of Carnap's Logical Syntax of Language, if any at all, indicate a real commitment to that tradition? It will be shown that although important aspects of Frege-Russell logicism are incorporated into the framework developed in that book, (...) it is nonetheless impossible to define a position within that framework which deserves to be called “typically logicist“. (shrink)

(2012). Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians – Two Recently Discovered Documents. British Journal for the History of Philosophy. ???aop.label???. doi: 10.1080/09608788.2012.692665.

In early major works, Cassirer and Schlick differently recast traditional doctrines of the concept and of the relation of concept to intuitive content along the lines of recent epistemological discussions within the exact sciences. In this, they attempted to refashion epistemology by incorporating as its basic principle the notion of functional coordination, the theoretical sciences' own methodological tool for dispensing with the imprecise and unreliable guide of intuitive evidence. Examining their respective reconstructions of the theory of knowledge provides an axis (...) of comparison along which to locate Cassirer's Neo-Kantianism and Schlick's pre-positivist empiricism, and an immediate background of contrast to the subsequent rise of logical empiricism. For in the absence of intuition all our knowledge is without objects and therefore remains entirely empty. (Kant A62/B87) And how awkward is the human mind in diving the nature of things when forsaken by the analogy of what we see and touch directly? (Boltzmann 1895). (shrink)

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. (shrink)

In A Philosophical Defense of Culture, Shuchen Xiang draws on the Confucian philosophy of "culture" and Ernst Cassirer's philosophy of symbolic forms to argue for the importance of "culture" as a philosophic paradigm. A defining ideal of Confucian-Chinese civilization, culture (wen) spans everything from natural patterns and the individual units that make up Chinese writing to literature and other refining vocations of the human being. Wen is thus the soul of Confucian-Chinese philosophy. Similarly, as a philosopher who bridged the classical (...) age of German humanism and postwar modernity, Cassirer implored his and future generations to think of humankind in terms of their culture and to think of the human being as a "symbolic animal." The philosophies of culture of these two traditions, very much compatible, are of urgent relevance to our contemporary epoch. Xiang describes the similarity of their projects by way of their conception of the human being, her relationship to nature, the relationship of human culture to nature, the importance of cultural pluralism, and the role of the arts in human life, as well as the metaphysical frameworks that gave rise to such conceptions. Combining textual exegesis in classical Chinese texts and an exposition of Cassirer's most important insights against the backdrop of post-Kantian philosophy, this book is philosophy written in a cosmopolitan mode, arguing for the contemporary philosophical relevance of "culture" by drawing on and bringing together two different but strikingly similar streams in our world tradition. (shrink)

L’enjeu de cet article est d’exposer les principaux aspects du débat philosophique contemporain autour de la conception de l’ a priori de Michael Friedman. Ce dernier a défendu l’existence de principes constitutifs a priori permettant de coordonner la structure mathématique des théories physiques avec l’expérience sensorielle. Bien qu’il s’appuie sur la conception cassirérienne de l’ a priori pour défendre une continuité entre les structures mathématiques des théories, Friedman, dans la lignée d’Hans Reichenbach, conçoit ces principes constitutifs comme révisables en fonction (...) des changements de théories physiques. Cette conception des principes constitutifs s’est vu reprocher un certain arbitraire dans le choix de ses principes, mais également son insuffisance et son simplisme pour décrire la manière avec laquelle les théories physiques s’appliquent à l’expérience. Enfin, il ne semble pas que l’on puisse, comme Friedman, réduire l’ a priori d’Ernst Cassirer à son rôle régulateur, puisque celui-ci concevrait également des principes constitutifs alternatifs à ceux de Reichenbach. (shrink)

Há muitos pontos de concordância entre Frege e os neokantianos. Isso vale especialmente para os representantes do neokantismo da teoria do valor ou do Sudoeste alemão na tradição de Hermann Lotze. Não discutiremos aqui todos os aspectos dessa proximidade; de acordo com o tema que propomos, ficaremos restritos à filosofia da matemática. A primeira parte do artigo tratará da relação entre aritmética e geometria, mostrando surpreendentes semelhanças entre Frege e o neokantiano Otto Liebmann. A segunda parte discutirá as diferentes recepções (...) do logicismo de Frege por Jonas Cohn, Paul Natorp, Heinrich Rickert, Ernst Cassirer e Bruno Bauch. (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)

At the turn of the twentieth century, Helm and Ostwald were the most prominent supporters of so-called ‘energetics’, which aimed to unify all physics by employing the sole concept of energy, without relying on mechanical models. This paper argues that Cassirer's interest in the history of the energy principle and the energetic controversy is entangled with the main themes of his philosophy of physics up to the 1920s: the opposition between the a priori and the a posteriori and the substance-concept (...) and the function-concept. These interwoven motifs are not always easy to disentangle. The paper suggests that Cassirer's interpretation of the energy principle can serve as a guiding thread that runs through Cassirer's philosophy of physics up to the 1920s. (shrink)

Neo-Kantianism emerged over the course of the 1860s and it occupied a leading position in the German universities from the 1870s until the First World War. Demands for getting "back to Kant" had become common since the early 1860s, and these demands were discussed in the meetings of the Philosophical Society of Berlin (Philosophische Gesellschaft zu Berlin; PGB), which was the international organization of Hegelians. In this paper I address some reactions among the PGB members to the 1860s Kant revival. (...) The journal "Der Gedanke", the organ of the PGB, reported closely how Kant returned to the spotlight of German philosophy. The reactions of the PGB members to the Kant revival was not only critical. Over the course of the 1860s the interest on Kant among the members grew little by little. (shrink)

In a famous passage (A68/B93), Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought (...) that Frege's priority principle is close to (or at least derivable from) Kant's. I argue that it is not. Nevertheless, there was a gradual historical development that began with Kant's priority thesis and culminated in Frege's new logic. (shrink)

This review of contemporary discussions of Kantian philosophy of mathematics is timed for the publication of the essay Kant’s Philosophy of Mathematics. Volume 1: The Critical Philosophy and Its Roots (2020) edited by Carl Posy and Ofra Rechter. The main discussions and comments are based on the texts contained in this collection. I first examine the more general questions which have to do not only with the philosophy of mathematics, but also with related areas of Kant’s philosophy, e. g. the (...) question: What is intuition and singular term? Then I look at more specific questions, e. g.: What is the subject of arithmetic and what is the significance of diagrams in mathematical reasoning? As a result, the reader is presented with a fairly complete overview of modern discussions which can be used as an introduction to the problem field of Kant’s philosophy of mathematics. (shrink)