This paper explores some of the constructive dimensions and specifics of human theoretic cognition, combining perspectives from (Husserlian) genetic phenomenology and distributed cognition approaches. I further consult recent psychological research concerning spatial and numerical cognition. The focus is on the nexus between the theoretic development of abstract, idealized geometrical and mathematical notions of space and the development and effective use of environmental cognitive support systems. In my discussion, I show that the evolution of the theoretic cognition of space apparently follows (...) two opposing, but in truth, intrinsically aligned trajectories. On the epistemic plane, which is the main focus of Husserl’s genetic phenomenological investigations, theoretic conceptions of space are progressively constituted by way of an idealizing emancipation of spatial cognition from the concrete, embodied intentionality underlying the human organism’s perception of space. As a result of this emancipation, it ultimately becomes possible for the human mind to theoretically conceive of and posit space as an ideal entity that is universally geometrical and mathematical. At the same time, by synthesizing a range of literature on spatial and mathematical cognition, I illustrate that for the theoretic mind to undertake precisely this emancipating process successfully, and further, for an ideal and objective notion of geometrical and mathematical space to first of all become fully scientifically operative, the cognitive support provided by a range of specific symbolic technologies is central. These include lettered diagrams, notation systems, and more generally, the technique of formalization and require for their functioning various cognitively efficacious types of embodiment. Ultimately, this paper endeavors to understand the specific symbolic-technological dimensions that have been instrumental to major shifts in the development of idealized, scientific conceptions of space. The epistemic characteristics of these shifts have been previously discussed in genetic phenomenology, but without devoting sufficient attention to the constructive role of symbolic technologies. At the same time, this paper identifies some of the irreducible phenomenological and epistemic dimensions that characterize the functioning of the historically situated, embodied and distributed theoretic mind. (shrink)

The author of the article analyses the historical and philosophical principles used by B. Russell, L. Couturat, E. Cassirer, H. Heimsoeth, W. Kabitz, B. Jansen, D. Mahnke and others to interpret the relation between logic and metaphysics in the philosophy of G. W. Leibniz. The article proves that the approach of W. Kabitz is a significant regression compared to the approach of E. Cassirer due to the ignoring of Leibniz's contribution to the history of logic, methodology and theory of cognition, (...) as well as due to the too narrow modernised understanding of logic. The author disagrees with the interpretation of B. Jansen, who based Leibniz's philosophy on non-cholastic pre-established harmony. The disadvantage of D. Mahnke's approach is, in the author's opinion, a failure to understand that synthesis for the sake of synthesis can never be creative, and the construction of a universal philosophical system can never be the goal of true philosophical creativity. (shrink)

The reflection on the preconditions and evolution of science has played a decisive role in the development of Ernst Cassirer's philosophy, contributing to its functional and thus inherently pluralistic and holistic view of knowledge. To present Cassirer's conception of physics as an open symbolic formation enables us to reveal and study the radical features of his epistemological model: (1) the fundamental process of generating sense-units and meaning in its constitutive character for each attempt of objectification, (2) its driving and structuring (...) dynamics that touches and transforms all elements of knowledge, the a priori included, (3) the strategies of justification that allow maintaining the claim of truthfulness in spite the fact that Cassirer's open model integrates contingency and transitoriness as an inherent part of knowledge. It thus becomes clear that Cassirer's term 'symbol' cannot be reduced to its habitual representational acceptation, for its key theoretical function is to overcome the inconsistencies of dualistic epistemological models. It is this re-orientation, a kind of 'second Copernican revolution', that allows Cassirer to go beyond traditional dichotomies and to propose a larger frame in which to appreciate the diversity of human understanding. (shrink)

The ArgumentRecent archival research has brought about a new understanding of the import of Einstein's puzzling remarks (1916) attributing a physical meaning to general covariance. Debates over the scope and meaning of general covariance still persist, even within physics. But already in 1921 Cassirer identified the significance of general covariance as a novel stage in the development of the criterion of objectivity within physics; an account of this development, and its implications, is the primary task undertaken in his monograph of (...) “epistemological considerations” on the theory of relativity. Cassirer's assessment is correct: general covariance, understood as an injunction against dynamical theories with background elements, is a “limiting heuristic principle” guiding Einstein's fundamental conception of a “complete field theory”; as such, it underlies a “separation principle” built into the conceptual framework of the EPR criticism of quantum mechanics. In conclusion, a further parallel is noted: mutual recognition that the principle of general covariance is but a form of “anthropomorphism.”. (shrink)

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. (shrink)

Leibniz propôs mais de um conceito para descrever filosoficamente a substância. Ironia instrutiva, esta pluralidade que tem por fim uma explicação unificada da realidade culminou em uma definição dos componentes fundamentais do mundo – as mônadas – como unidades que abrigam a multiplicidade. Estas substâncias, bem como a sua função essencial de se exprimirem mutuamente, apenas se tornam plenamente inteligíveis quando observamos os conceitos anteriores, de que a filosofia madura de Leibniz herdou algumas intuições. Guiando-nos pelas obras-chave do filósofo e (...) físico alemão, procuraremos retraçar esse percurso intelectual, a fim não de esboçar um hipotético sistema seu, mas de _unificar_ o tratamento que ele dispensou à _unidade_. Tal hipótese de leitura concorda fundamentalmente com aquela sustentada por Michel Fichant, mas traz pontuais acréscimos ou desacordos, que serão indicados neste artigo. (shrink)

The aim of this paper is to analyze Dimitry Gawronsky’s doctrine of actual infinitesimals. I examine the peculiar connection that his critical idealism establishes between transcendental philosophy and mathematics. In particular, I reconstruct the relationship between Gawronsky’s differentials, Cantor’s transfinite numbers, Veronese’s trans-Archimedean numbers and Robinson’s hyperreal numbers. I argue that by means of his doctrine of actual infinitesimals, Gawronsky aims to provide an interpretation of calculus that eliminates any alleged given element in knowledge.

Marburg Neo-Kantianism has attracted substantial interest among contemporary philosophers drawn by its founding idea that the success of advanced theoretical science is a given fact and it is the task of philosophical inquiry to ground the objectivity of scientific achievement in its a priori sources (Cohen and Natorp 1906, p. i). The Marburg thinkers realized that recent advances and developments in the mathematical sciences had changed the character of Kant’s transcendental project, demanding new methods and approaches to establish the objectivity (...) of the latest insights into physical reality. Hermann Cohen, one of the founders of the Marburg School, attempted to base the objectivity of science on the concepts of .. (shrink)

The late nineteenth- and early twentieth-century debate over ‘internal’ and ‘external’ relations is well explored, as far as its course in Britain is concerned. F. H. Bradley’s idealistic internalism, on the one hand, and Bertrand Russell’s realistic externalism, on the other, were at the center of this debate. Less well known, however, is that there was also a discussion about relations in the United States at the time. The central figures in this discussion were Edward Gleason Spaulding and John Dewey. (...) Like Russell, Spaulding advocated a realist-inspired externalism, while Dewey criticized this viewpoint from a pragmatist perspective. The aim of the present paper is to reconstruct the exchange between Spaulding and Dewey and to elaborate the specifics of this exchange. In doing so it will emerge, among other things, that, in contrast to Bradley’s idealist rejection of externalism, Dewey’s pragmatist attempt at a refutation was more in line with common sense and science and that Spaulding’s version of externalism differed markedly from Russell’s in its strong empirical orientation. Overall, an undeservedly forgotten chapter in the history of early twentieth-century American philosophy is revisited and reassessed. (shrink)

: Few texts summarize and at the same time compound the challenges of their author's philosophy so sharply as Hermann Cohen's Das Prinzip der Infinitesimalmethode und seine Geschichte (1883). The book's meaning and style are greatly illuminated by placing it in the scientific, political, and academic context of late-nineteenth century Germany. As this context changed, so did both the reception of the philosophy of the infinitesimal and of the Marburg school more generally. A study of this transformation casts significant light (...) on the political relevance of the philosophy of science in theWilhelmine era. As a means of following this development across time, Cohen's text is read through its changing reception in the philosophy of his closest disciple, Ernst Cassirer. (shrink)

The ArgumentBiology, understood in turn-of-the-century Germany to include psychology, held a central but enigmatic place in the philosopher Ernst Cassirer's work. From his earliest studies with Hermann Cohen through his long engagement with the theoretical biology of Jakob von Uexküll and Adolf Meyer-Abich, Cassirer consistently used the history and practice of biology to examine and delineate a set of characteristic tensions between the natural and cultural sciences. This paper examines Cassirer's treatment of this theme by addressing two contrasting interpretations he (...) gave — in hisPhilosophy of Symbolic Forms and in hisEssay on Man — to the benchmark case from empirical psychology of the “talking” horse “Clever Hans.” The original case involved the horse's ability to signal answers to remarkably complex questions by stamping its hooves, an ability that ultimately appeared to rest on a capacity to detect extremely minute unintentional movement cues in its auditors as it reached the appropriate answer. Due to both Cassirer's shifting description of the case within his philosophy and the case's inherent polyvalence, Cassirer's remarks provide a useful window onto the social, epistemological, and stylistic meaning of his “unified” philosophy of human culture and science. (shrink)

This article offers a reconstruction of Derrida’s critique of Leibniz. It suggests that in attempting to fit Leibniz into his conception of the history of metaphysics and the all-embracing notion of logocentrism that underwrites it, Derrida presupposes two regimes of logocentrism: one subjective, the other theological. Subsumed into this second mode, Derrida casts Leibniz as a progenitor of structuralism and the new sciences and technologies of information in order to expose their logocentric foundations. However, in doing so, he ends up (...) sidelining the aspect of Leibniz’s ideas that anticipates the specificity of the new epoch of writing he claims to historicise. The article goes on to argue that to grasp this specificity one must look beyond the “expressivist” schema of exterior representation, which Derrida draws from Husserl’s theory of meaning, and instead look to Leibniz’s own formal-combinatorial concept of expression, which exceeds Derrida’s critical framework. (shrink)

In the present paper, the author aims at laying the foundations of a symbolics of technical gesture, according to the thesis that symbolic faculty is another face of the technological one, and that they are both in truth two sides of the same coin. Accordingly, the author suggests to rename the whole dimen-sion as “meta-environmentality”. The analysis is carried out on the basis of a specific comparison between Cassirer’s definition of “animal symbolicum” and its scientific consistence in the light of (...) modern palaeontology. “Animal symbol-icum” is here compared with Leroi-Gourhan’s homo technologicus, and Cassi-rer’s ideas on human identity tested starting from paleoanthropological data. The result of the inquiry lead us to recognize the urgency of integrating Cassi-rer’s argument with the primacy of the technological capacity, but a deep anal-ysis of the characterizing attributes of the latter compels us to uphold the symbolic attitude of the technological dimension. The author then sketches a basic description of the guidelines of a symbolic theory of technology, and tries to show how the basic elements of such an approach were familiar both to Cassirer and Leroi-Gourhan. As a consequence of the whole theory, the author elaborates a chronological analysis of human identity, whose basic result is the determination of the future as main temporal dimen-sion of human acting. (shrink)

The article attempts to reconsider the relationship between Leibniz’s and Kant’s philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called “transformation principle”, the very same principle that thinkers such as Helmholtz or Poincaré applied in a more (...) general form in their celebrated philosophical writings about geometry. The first two parts of the article try to show that Leibniz’s and Kant’s philosophies of geometry, despite their differences, appear to be preoccupied with the common problem of the impossibility to grasp conceptually the intuitive difference between two figures (such as a figure and its scaled, displaced or mirrored copy). In the third part, it is argued that from the perspective of Hausdorff’s philosophical-geometrical reflections, this very same problem seems to find a more radical application in Helmholtz’s or Poincaré’s thought experiments on the impossibility of distinguishing distorted copies of our universe from the original one. I draw the conclusion that in Hausdorff’s philosophical work, which has received scholarly attention only recently, one can find not only an original attempt to frame these classical arguments from a set-theoretical point of view, but also the possibility of considering the history of philosophy of geometry from an uncommon perspective, where especially the significance of Kant’s infamous appeal to “intuition” can be judged by more appropriate standards. (shrink)

In 1912, Ernst Cassirer contributed to the special issue of the Kant-Studien that honored Hermann Cohen's retirement—his mentor and teacher, and the recognized founding father of the so-called 'Marburg school' of Neo-Kantianism. In the context of an otherwise rather conventional presentation of Cohen's interpretation of Kant, Cassirer made a remark that is initially surprising. It is “anything but accurate,” he wrote, to regard Cohen's philosophy as focused “exclusively on the mathematical theory of nature,” as is usually done. A reconstruction of (...) the genesis of Cohen's thought, Cassirer continued, would already refute this interpretation. Actually, “[t]he... (shrink)

This paper offers an introduction to Hermann Cohen’s Das Princip der Infinitesimal-Methode, and recounts the history of its controversial reception by Cohen’s early sympathizers, who would become the so-called ‘Marburg school’ of Neo-Kantianism, as well as the reactions it provoked outside this group. By dissecting the ambiguous attitudes of the best-known representatives of the school, as well as those of several minor figures, this paper shows that Das Princip der Infinitesimal-Methode is a unicum in the history of philosophy: it represents (...) a strange case of an unsuccessful book’s enduring influence. The “puzzle of Cohen’s Infinitesimalmethode,” as we will call it, can be solved by looking beyond the scholarly results of the book, and instead focusing on the style of philosophy it exemplified. Moreover, the paper shows that Cohen never supported, but instead explicitly opposed, the doctrine of the centrality of the ‘concept of function’, with which Marburg Neo-Kantianism is usually associated. (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)

the domain of Art critique and becoming a philosophical argument. How can we think of Perspective as symbolic Form? Is Perspective really a symbolic form? Why is Perspective so important? Because at the beginning of the Modern Age, Perspective as spiritual figure grounds many symbolic or even many scientific constructions. We could we say that perspective open the foundation of modern science as such. The “Geometrization” of Vision, beginning with perspective, will be for us the interpretative key in order to (...) understand the Modern Age as a whole. This understanding will allow us to understand the anthropologic dimension arising from the Modern Age, called „Perspectivism“. Assuming that perspective was neither only an invention of painting nor of geometry nor of philosophy, taken as singular fields of human inquiry, we will try to sketch the genesis of “perspective” from an interdisciplinary point of view. By doing so, we will also try to fix its deep significance for the anthropology of the Modern Age. Living and feeling in a perspectival world is the real invention of the Modern Age, one that overcame the closed Cosmos of the Middle Ages in order to reveal to mankind its own potential. Our interdisciplinary approach will proceed from many points of view and converge on the idea of a new kind of human experience. Such an interdisciplinary approach will open new questions about our present time. Are we justified in thinking of our experience today as perspectival? What does it mean today to think from perspectives in the manifold dimensions of our living and to face to the complexity of our times? (shrink)

The paper is devoted to an overview of Cassirer’s work both as historian of philosophy and historian of science. Indeed, the “intelletcual cooperation” between history of philosophy and history of science represents an essential feature of Cassirer’s style of philosophizing: while the roots of a wide exploration stretching from Renaissance thought to modern physics go back to the Neo-Kantianism of the Marburg School, the results of a similar cross-fertilization of research fields have deeply contributed to shaping new standards of inquiry. (...) Cassirer’s relationship with the Warburg milieu in Hamburg and late in his life with the American intellectual scenario are surely worthy of closer investigation. Distinguished scholars such as Meyerson, Brunschvicg, Burtt, Koyré, Metzger, Lovejoy, Kristeller, have disussed, appreciated, critizised Cassirer’s still today fascinating studies devoted to Pico della Mirandola, Galileo, Newton, Leibniz, to mention but a few. To explore some of these aspects focusing both on affinities and differences within a cosmpolitian intellectual community can provide a better understanding of philosophy and history of science in the first half of 20th century. Cassirer’s legacy requires, therefore, a new assessment. (shrink)

Resumen En el presente trabajo analizo el concepto de cuerpo en los escritos maduros de Leibniz. En el marco del debate contemporáneo acerca del estatus de la sustancia corpórea examino el entramado de las tres nociones sobre las que se construye la metafísica leibniziana de los cuerpos, a saber, la de materia prima, la de cuerpo orgánico y la de extensión. En cada caso evalúo el estatus ontológico que Leibniz les reconoce así como el papel que cumplen en su metafísica.In (...) this paper I examine the concept of body in Leibniz’s mature writings. In the context of the contemporary debate on the status of the corporeal substance, I analyze the relation between the three notions from which he builds his metaphysics of bodies, namely, the primary matter, the organic body, and the extension. For each case I evaluate their ontological status and the role they play in his metaphysics. (shrink)

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)

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...) calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. (shrink)

Starting from an analogy with Quine’s two dogmas of empiricism, I offer a critique of two dogmas of analytic historiography: the belief in a cleavage between the justification of a ph...

Gottfried Wilhelm Leibniz (1646–1716) was one of the great thinkers of the seventeenth and eighteenth centuries and is known as the last “universal genius”. He made deep and important contributions to the fields of metaphysics, epistemology, logic, philosophy of religion, as well as mathematics, physics, geology, jurisprudence, and history. Even the eighteenth century French atheist and materialist Denis Diderot, whose views could not have stood in greater opposition to those of Leibniz, could not help being awed by his achievement, writing (...) in his Encyclopedia, “Perhaps never has a man read as much, studied as much, meditated more, and written more than Leibniz… What he has composed on the world, God, nature, and the soul is of the most sublime eloquence. If his ideas had been expressed with the flair of Plato, the philosopher of Leipzig would cede nothing to the philosopher of Athens.” (Vol. 9, p. 379) Indeed, Diderot's mood was almost despairing in a remark from another piece, which also has a great deal of truth in it: “When one compares the talents one has with those of a Leibniz, one is tempted to throw away one's books and go die quietly in the dark of some forgotten corner.” More than a century later, Gottlob Frege, who fortunately did not cast his books away in despair, expressed similar admiration, declaring that “in his writings, Leibniz threw out such a profusion of seeds of ideas that in this respect he is virtually in a class of his own.” (“Boole's logical Calculus and the Concept script” in Posthumous Writings , p. 9) The aim of this entry is primarily to introduce Leibniz's life and summarize and explicate his views in the realms of metaphysics, epistemology, philosophical theology, and natural philosophy. (shrink)