Determinismus und Indeterminismus in der modernen Physik is one of Cassirer’s least known and studied works, despite his own assessment as “one of his most important achievements”. A prominent theme locates quantum mechanics as a yet further step of the tendency within physical theory towards the purely functional theory of the concept and functional characterization of objectivity. In this respect DI can be considered an “update”, like the earlier monograph Zur Einsteinschen Relativitätstheorie: Erkenntnistheoretische Betrachtungen, to Substanzbegriff und Funktionsbegriff, a (...) seminal work considering only classical and pre-relativistic physics. But how does DI cohere with the three volumes of The Philosophy of Symbolic Forms providing a systematic survey of symbolic meanings in diverse aspects of culture, each with its own mode of “objectification” via self-created signs and images? Cassirer’s “phenomenology of cognition” via distinct types of symbolic form locates Dirac’s Principles of Quantum Mechanics as an exemplar within physical theory of purely symbolic thought, a realm of pure relations and their correlated meanings. In particular, Dirac’s characterization of the new notion of “physical state” in quantum mechanics by a “symbolic algebra of observables” severed from particular representations points to a limiting pole of the Bedeutungsfunktion, the third and highest mode of symbolic formation. (shrink)

The aim of this paper is to reconstruct a peculiar debate between Ernst Cassirer and the Swedish philosopher Konrad Marc-Wogau on Begriffstheorie that took place in the late thirties of the 20th century. This debate may be conceived as sort of ersatz of the discussion between Cas sirer's Neokantian Begriffstheorie on the one hand, and logical empiricist accounts on the other, in particular Schlick's Begriffstheorie as presented in his Allgemeine Erkenntnislehre. Although Schlick did not participate in personam in the (...) discussion that took place between Cassirer and Marc-Wogau, one may consider him as a “virtual” participant of the debate, since his Begriffstheorie played an important role in the background, in particular for Cassirer. More precisely, I'd like to show that the debate can be read as a dispute on the feasibility of a “rich” account of Begriffstheorie, favored by Cassirer, and the necessity of restricting Begriffstheorie to an “austere” approach whose protagonists were Marc-Wogau and Schlick, although in a quite different ways. More generally, the debate on Begriffstheorie exemplifies the complex interactions — and non-interactions — between three important currents of scientific philosophy, namely, the Marburg Neokantianism of Cassirer, the scientifically minded philosophers of the Uppsala School, and, indirectly, the Logical Empiricism of the Vienna Circle. (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)

The main thesis of this paper is that Pap’s The Functional A Priori of Physical Theory (Pap 1946, henceforth FAP) and Cassirer’s Determinism and Indeterminism in Modern Physics (Cassirer 1937, henceforth DI) may be conceived as two kindred accounts of a late Neo-Kantian philosophy of science. They elucidate and clarify each other mutually by elaborating conceptual possibilities and pointing out affinities of neo-Kantian ideas with other currents of 20th century’s philosophy of science, namely, pragmatism, conventionalism, and logical empiricism. (...) Taking into account these facts, it seems not too far fetched to conjecture that under more favorable circumstances Pap could have served as a mediator between the “analytic” and “continental” tradition thereby overcoming the dogmatic dualism of these two philosophical currents that has characterized philosophy in the second half the 20th century. (shrink)

Constructivism is at the heart of a pedagogical philosophy going back to Vico, whose view of the interrelationship of the arts and sciences sought to reconstitute the classical paideia. The Vichian idea that human beings can only know the truth of what they themselves have made has theoretical and practical consequences for Vico's pedagogy and view of the university. Vico's ideas on education are extended in the modern period by such thinkers as Cassirer, Piaget and Bateson. At the basis (...) of Cassirer's pedagogical philosophy is his theory of the symbol, the symbol being a universal and transcendent modality in culture. The result of this unifying theory is that symbolism, which is pervasive across the disciplines, provides a moral and ethical means for integrating communication about teaching. Cassirer's thought is compatible with Piaget's, which emphasizes the pluralism of experience and the role of dynamic learning in the construction of meaningful order. Piaget's constructivism assumes that an operational bridge exists to link together the hard sciences, the human sciences, and the historical disciplines. This systems view of epistemological matters is similar in many respects to the one advanced by Gregory Bateson, which is explored in the paper's final section. (shrink)

Ernst Cassirer, 2011, Symbolische Prägnanz, Ausdrucksphänomen und „Wiener Kreis“, Nachgelassene Manuskripte und Texte, vol. 4, ed. Christian Möckel, 478pp., Hamburg, Felix Meiner Verlag.

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 Anglo-Saxon philosophy of science there is strong conviction that idealist philosophy of science on the the one hand and serious science and philosophy of science on the other do not go well together. In this paper I argue that this sweeping dismissal of the idealist tradition may have been too hasty. They may be some valuable insights for which it is striving. A promising case in question is provided by Ernst Cassirer’s Neo-Kantian „Critical Idealism“ that he put forward (...) in the first decades of the past century, or so I’d like to argue. (shrink)

Philosophy and Phenomenological Research, Volume 103, Issue 2, Page 466-472, September 2021.

In the first third of this century Cassirer was one of the leading, most influential philosophers of the German-speaking world. He was the respected opponent of such giants as Husserl, Russell, Schlick, Heidegger or Carnap who left their mark on the philosophical landscape until this very day. One might recall his discussion with Schlick on the philosophical relevance of Einstein’s relativity theory in the first decade of this century. Carnap reported to have received essential ideas for the Logical Construction (...) of the World from Cassirer and other neo-Kantians; or, to recall a more spectacular event concerning Cassirer’s philosophy, one might mention the famous “Davos disputation” with Heidegger in 1929 which seems to have been a major philosophical event for the audience. (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)

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 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)

According to Cassirer, humanity is defined by the activity of the spirit. In other places, he attempts to explain the transition from ›life‹ to ›spirit‹, but this proj- ect seems hampered by his taking spirit to be a phenomenon of consciousness. Plessner’s »aesthesiology« opens up an alternative route. He discloses the mean- ing of ›spirit‹ or ›understanding‹ by an inquiry concerning the work of the senses in the context of behavior. This paper shows that for Plessner behavior is closely (...) related to its environment while at the same time not restricted to a biological programme. (shrink)

Though the relationship between Goethe, Cassirer and Levi-Strauss has been explored extensively, the focus usually lies on questions of genealogy. This article aims for a different course: Building on the notable similarities between Goethe’s discussion of morphology, Levi-Strauss’ structuralistic approach and Cassirer’s philosophy of symbolic forms we will investigate the epistemological similarities between the three authors. They can be found in a specific form of humanism (or anti-humanism) which connects questions on the conditions of the world and its (...) accessibility with the more global question of humankind and its place within the natural world, thus, by virtue of a specific interpretation of the concept of transformation, opening the door for new approaches which have recently been discussed as ontological turn. (shrink)

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be (...) useful in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle. (shrink)

© The Authors [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] book Space, Number, and Geometry from Helmholtz to Cassirer is a reworked version of Francesca Biagioli’s PhD thesis. It aims ‘[to offer] 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’. More precisely, Biagioli concentrates on how the Marburg school of neo-Kantianism dealt with what may (...) be called ‘Helmholtz’s challenge’ to the classical Kantian thesis that the geometry of space is necessarily Euclidean. To be precise, besides the Marburg current, SNG also deals with some other neo-Kantians, among them the realist neo-Kantian Alois Riehl and the South-West German neo-Kantian Bruno Bauch.According to SNG, the Marburg revision of the Kantian theory of space opened the door to a new way... (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)

One can extrapolate from the art of language instruction to discover methods applicable across the disciplines in higher education. The paradigm presented by language instruction is applicable throughout the arts and sciences. If cultivated—and there are institutional pressures working against it—such an art can impact the languages and codes of the individual disciplines so as to advance the research mission of scholars in those fields; it can also favor the interrelationships between the disciplines. How the student learns another language (L2) (...) is comparable to the process of learning a scientific discipline. (shrink)

Quine’s classical classic interpretation succinctly characterized characterizes Carnap’s Aufbau as an attempt “to account for the external world as a logical construct of sense-data....” Consequently, “Russell” was characterized as the most important influence on the Aufbau. Those times have passed. Formulating a comprehensive and balanced interpretation of the Aufbau has turned out to be a difficult task and one that must take into account several disjointed sources. My thesis is that the core of the Aufbau rested on a problem that (...) had haunted German philosophy since the end of the 19th century. In terms fashionable at the time, this problem may be expressed as the polarity between Leben and Geist that characterized German philosophy during the years of the Weimar Republic. At that time, many philosophers, including Cassirer, Rickert and Vaihinger, were engaged in overcoming this polarity. As I will show, Carnap’s Aufbau joined the ranks of these projects. This suggests that Lebensphilosophie and Rickert’s System der Philosophie exerted a strong influence on Carnap’s projects, an influence that is particularly conspicuous in his unpublished manuscript Vom Chaos zur Wirklichkeit. Carnap himself asserted that this manuscript could be considered “the germ of the constitution theory” of the Aufbau. Reading Chaos also reveals another strong but neglected influence on the Aufbau, namely a specific version of neutral monism put forward by the philosopher and psychologist Theodor Ziehen before World War I. Ziehen’s work contributed much to the invention of the constitutional method of quasi-analysis. -/-. (shrink)

Abstract. El objetivo de este documento es elucidar el papel de las idealizaciones en el conocimiento matemático inspirado por algunas ideas del filósofo neo-kantiano Ernst Cassirer. Usualmente, en la filosofía de la ciencia contemporánea se da por hecho que el tema de la idealización se refiere únicamente a las idealizaciones en las ciencias empíricas, en particular en la física. Por el contrario, Cassirer afirmó que la idealización de las matemáticas, así como en las ciencias tiene la misma base (...) conceptual y epistemológica. Precisamente, su "tesis de la identidad" es analizada al investigar una variedad de ejemplos de idealizaciones tomadas del álgebra, la topología, la teoría de red y la geometría física. Las idealizaciones en matemática, así como en el conocimiento físico se puede caracterizar por la introducción de elementos ideales que conducen a completaciones. En ambas áreas estos elementos ideales desempeñan esencialmente el mismo papel, es decir, sustituyen una variedad incompleta de objetos mediante una variedad conceptual completa “idealizada. (shrink)

One can extrapolate from the art of language instruction to discover methods applicable across the disciplines in higher education. The paradigm presented by language instruction is applicable throughout the arts and sciences. If cultivated—and there are institutional pressures working against it—such an art can impact the languages and codes of the individual disciplines so as to advance the research mission of scholars in those fields; it can also favor the interrelationships between the disciplines. How the student learns another language (L2) (...) is comparable to the process of learning a scientific discipline. (shrink)

In A Parting of the Ways Michael Friedman proposed to conceive the contemporary divide between analytic philosophy (AP) and continental philosophy (CP) as the outcome of the bifurcation between the Neokantians of Heidelbarg and Marburg. According to Friedman, Carnap can be characterized as the executor of the Marburg school, while Heidegger is to be considered as the heir of the Southwest Neokantianism. In this paper it is argued that Carnap was much closer to the Southwest Neokantianism than usually recognized. To (...) some extent, Carnap’s project in the Aufbau may be described as an attempt to modernize the Neokantian approach of the Southwest school with the help of modern relational logic. This entails that Carnap cannot be lined so easily with the Marburg school as Friedman assumes. (shrink)

Der Körper hat Konjunktur. Als ausgestellter, verfüg- und verführbarer begegnet er uns täglichim Übermaß. Es war nur eine Frage der Zeit, bis im Spiel der sich in den Wissenschafteneinander ablösenden turns auch ein corporeal (oder body) turn ausgerufen würde. Dabeibleibt im genannten turn der Gegenstand der Untersuchung nicht selten reduziert auf das, wasman im deutschen Sprachgebrauch »Körper« nennt: ein physisches Substrat, das wie ein Dingunter Dingen beschreibbar ist. Gegen diese Verkürzung stellt der Begri des »Leibes«,spätestens seit Edmund Husserl, eine präzise (...) theoretische Intervention in die wissenschaftlicheund philosophische Diskussion um Körper und Körperlichkeit dar: Dem objektiv beobachtbaren Körper, den wir haben, wird der lebendige Leib, der wir sind, gegenübergestellt. Diesem »Leib«, seiner Geschichte, seinen Varianten und seinem Versprechen gehen dieAutoren der vorliegenden Beiträge nach. Inhaltsübersicht Emmanuel Alloa/Thomas Bedorf/Christian Grüny/Tobias Nikolaus Klass: Einleitung I. Der Leibbegriff in der Phänomenologie Emmanuel Alloa / Natalie Depraz: Edmund Husserl – „Ein merkwürdig unvollkommenkonstituiertes Ding“ – Stefan Kristensen: Maurice Merleau-Ponty I – Körperschema undleibliche Subjektivität – Emmanuel Alloa: Maurice Merleau-Ponty II – Fleisch und Dierenz – David Espinet: Martin Heidegger – Der leibliche Sinn von Sein – Thomas Bedorf: EmmanuelLevinas – Der Leib des Anderen – Karel Novotný: Körper, Leib, Aektivität in Jan Pato č kasPhänomenologie der natürlichen Welt – Julia Scheidegger: Michel Henry – TranszendentaleLeiblichkeit – Jörg Sternagel: Bernhard Waldenfels – Responsivität des Leibes – Kerstin Andermann: Hermann Schmitz – Leiblichkeit als kommunikatives Selbst- und Weltverhältnis II. Zur Geschichte des Leibbegris Emmanuel Alloa: Archaische Leiblichkeit. Die griechische Antike und die Entdeckung desKörpers – Theresia Heimerl: Der Leib Christi und der Körper des Christen: Körper und Leib alszentrale Problemzonen des Christentums – Marc Rölli: Philosophische Anthropologie im 19. Jahrhundert – Zwischen Leib und Körper – Tobias Nikolaus Klass: Friedrich Nietzsche – Denkenam „Leitfaden des Leibes“ – Andreas Cremonini: Sigmund Freud – Der gelebte vs. derphantasmatische Leib – Uta Noppeney: Kurt Goldstein und Frederik Buytendijk – Der Leib-Begri in der organismischen Biologie – Volker Schürmann: Max Scheler und Helmuth Plessner– Leiblichkeit in der Philosophischen Anthropologie – Marion Lauschke: Ernst Cassirer und AbyWarburg – Kulturanthropologie III. Grenzen und Kritik des Leibbegris Christian Grüny: Theodor W. Adorno – Soma und Sensorium – Ulrich Johannes Schneider: Michel Foucault – Der Körper und die Körper – Burkhard Liebsch: Paul Ricoeur – Das leiblicheSelbst begegnet dem Widerstand des Anderen – Mirjam Schaub: Gilles Deleuze – Was weiß ein„Körper ohne Organe“ vom Leib? – Kathrin Busch: Jean-Luc Nancy – Exposition und Berührung– Shaun Gallagher: Embodiment: Leiblichkeit in den Kognitionswissenschaften – Marie-Luise Angerer: Gender und Performance – Ist leibliche Identität ein Konstrukt? – Thomas Bedorf/Selin Gerlek: Praxistheorien – Leibkörperliche Praktiken im Vollzug. (shrink)

Der Antirepräsentationalismus behauptet, es sei an der Zeit, das auf dem Begriff der Repräsentation basierende Paradigma der Philosophie zu verabschieden. Die von Rorty und anderen propagierte Unterscheidung von Repräsentationalismus und Antirepräsentationalismus beruht jedoch auf einem verkürzten Repräsentationsbegriff als Spiegelung. Der Begriff der Repräsentation, so wie er in der Philosophie und Wissenschaft gebraucht wird, hat nur wenig mit Spiegelung zu tun. Statt den Begriff der Repräsentation mit Hilfe der Spiegelungsmetapher zu explizieren, sollte man Repräsentation als strukturerhaltende Abbildung konzipieren. Dadurch lassen sich (...) die für den Repräsentationsbegriff wesentlichen pragmatischen Aspekte der Reduktion und Induktion von Komplexität explizieren. Der Zusammenhang der gegenläufigen Aspekte Reduktion und Induktion wird an Beispielen aus der Konstitution extensiver Größen sowie an Cassirers Theorie der Konstitution von Erkenntnis und Wirklichkeit erörtert. Man sollte daher den Begriff der Repräsentation nicht aus dem philosophischen Diskurs eliminieren, sondern versuchen, die Ansätze einer allgemeinen pragmatischen Repräsentationstheorie auszubauen. (shrink)

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)

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. (shrink)