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)

Employing the ideas of modern mathematics and biology, seen in the context of Ernst Cassirer's "Symbolic Forms, the author presents an entirely new and novel solution to the classical mind-brain problem. This is a "hard" book, I'm sorry, but it is the problem itself, and not me which has made it so. I say that Dennett, and, indeed, the whole of academia is wrong.

The Marburg neo-Kantians argue that Hermann von Helmholtz's empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz's account raises the 'problem of validity' (Gueltigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz's and Ludwig Wittgenstein's Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the (...) necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz's original account. (shrink)

From the 1930s through the 1970s, C. H. Waddington attempted to reunite genetics, embryology, and evolution. One of the means to effect this synthesis was his model of the epigenetic landscape. This image originally recast genetic data in terms of embryological diagrams and was used to show the identity of genes and inducers and to suggest the similarities between embryological and genetic approaches to development. Later, the image became more complex and integrated gene activity and mutations. These revised epigenetic landscapes (...) presented an image of how mutations could alter developmental pathways to yield larger phenotypic changes. These diagrams became less important as the operon became used to model differential gene regulation. (shrink)

We like Euclidean geometry because we are men [sic], and have eyes and hands, and need to operate a concept of space that will be independent of orientation, distance and size. Lucas, A Treatise on Time and Space.

We develop a new understanding of the historical horizon of event ontology. Within the general area of the philosophy of nature, event ontology is a still emerging field of investigation in search for the ultimate materialist ontology of the world. While event ontology itself will not be explicated in full mathematical details here, our focus is on its conceptual interrelation with the dominant current of Idealism in Western thought approached by us as a problem in the history of ideas. Our (...) presentation is designed to be accessible to a wider audience. We especially highlight the deep connection between event ontology and postmodernism in general, and the post-war French philosophers Althusser, Foucault, Deleuze, and Guattari in particular, who are viewed as main sources for current and future programs of abstract materialism. (shrink)

This paper examines the points of disagreement between Petrus Camper and J. W. von Goethe regarding the existence of the inter-maxillary bone in humans as the link between man and the rest of nature. This historical case illustrates the fundamental role of aesthetic judgements in scientific discovery. Thus, I shall show how the eighteenth century discovery of the inter-maxillary bone in humans was largely determined by aesthetic factors—specifically, those sets of assumptions and criteria implied in the aesthetic schemata of Camper (...) and Goethe. I argue that the relevance of scientifically ascertainable morphological properties that count as evidence for the existence of bona fide anatomical structures depend on the aesthetic schema adopted by the communities assessing the classification. At the same time, I propose and explain mechanisms by which aesthetic considerations might determine the acceptability of empirical claims about the world. Based on the reconstruction of the arguments of Camper and Goethe, I conclude that aesthetic considerations play a substantive role in both the generation and preliminary evaluation of scientific hypotheses. This paper suggests a complementary relation between the mediation of aesthetic criteria in theory choice and in scientific discovery in that while aesthetic considerations in theory choice lead to conservatism; in the context of discovery they often lead to innovation. (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)

Ernst Haeckel and Emil du Bois-Reymond were the most prominent champions of Darwin in Germany. This essay compares their contributions to popularizing the theory of evolution, drawing special attention to the neglected figure of du Bois-Reymond as a spokesman for a world devoid of natural purpose. It suggests that the historiography of the German reception of Darwin’s theory needs to be reassessed in the light of du Bois-Reymond’s Lucretian outlook.

In this paper we examine aspects of Canguilhem’s philosophy of biology, concerning the knowledge of life and its consequences on science and vitalism. His concept of life stems from the idea of a living individual, endowed with creative subjectivity and norms, a Kantian view which “disconcerts logic”. In contrast, two different approaches ground naturalistic perspectives to explore the logic of life and the logic of the living individual in the 1970s. Although Canguilhem is closer to the second, there are divergences; (...) for example, unlike them, he does not dismiss vitalism, often referring to it in his work and even at times describing himself as a vitalist. The reason may lie in their different views of science. (shrink)

Philosophy of biology is often said to have emerged in the last third of the twentieth century. Prior to this time, it has been alleged that the only authors who engaged philosophically with the life sciences were either logical empiricists who sought to impose the explanatory ideals of the physical sciences onto biology, or vitalists who invoked mystical agencies in an attempt to ward off the threat of physicochemical reduction. These schools paid little attention to actual biological science, and as (...) a result philosophy of biology languished in a state of futility for much of the twentieth century. The situation, we are told, only began to change in the late 1960s and early 1970s, when a new generation of researchers began to focus on problems internal to biology, leading to the consolidation of the discipline. In this paper we challenge this widely accepted narrative of the history of philosophy of biology. We do so by arguing that the most important tradition within early twentieth-century philosophy of biology was neither logical empiricism nor vitalism, but the organicist movement that flourished between the First and Second World Wars. We show that the organicist corpus is thematically and methodologically continuous with the contemporary literature in order to discredit the view that early work in the philosophy of biology was unproductive, and we emphasize the desirability of integrating the historical and contemporary conversations into a single, unified discourse. (shrink)

The living forms represented in this paper are sets of parts that spontaneously increase in organization. Their organizations are measured by an information-theoretic function derived from the work of Boltzmann and Shannon. We briefly review its derivation in the context of the troubled role of mathematics in biology, and then define the function. We illustrate its nature by measuring the 22 different organizations of a set of eight things; and we facilitate its use by defining the parameters that determine an (...) amount of organization. The measure is then applied to show that the organization of limb pairs on free-living arthropods, based on data given by Cisne, confirms a pattern of increasing organization in their evolution from the Cambrian era to the present. Further applications measure the changes in organizations of ideal (theoretical) life forms, and contrasting changes in inanimate systems. Our main results represent the reproduction of unicellular organisms, and the formation of hierarchies, as processes of increasing organization. (shrink)

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

The 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)

Like other sciences, biosemiotics also has its time-honoured archive, consisting, among other things, of writings by those who have been invented and revered as ancestors of the discipline. One such example is Jakob von Uexküll who has been hailed as a precursor of semiotics, developing his theory of “sign” and “meaning” independently of Saussure and Peirce. The juxtaposition of “sign” and “meaning” is revelatory because one can equally legitimately claim Uexküll as a hermeneutician in the same way as others having (...) claimed him as a semiotician. Such a novel temptation can be justified by Uexküll’s prolonged obsession with Sinn and Bedeutung since his first book in 1909. This paper attempts to reconstruct the immediate intellectual horizon of Uexküll’s historicity, a discursive space traversed by his contemporaries Frege and Husserl, in order to see how Uexküll’s discussions of Zeichen and Gegenstand, Sinn and Bedeutung, were informedby other philosophers of language, and to establish Uexküll as a phenomenological hermeneutician in the tradition of Husserl, Heidegger and Gadamer. To forestall and counter possible criticism that hermeneutics is primarily concerned with textual interpretation, while Uexküll is at most an interpreter of animal life, the paper will discuss his unfinished parody of the Platonic dialogue Meno, which is entitled Die ewige Frage: Biologische Variationen über einen platonischen Dialog (1943). It is through such textual practice that one witnesses the emergence of an Uexküll who embodies at once the addressee exercising his understanding of ancient texts as well as the second addresser recoding his explanation to another group of targeted addressees. This textual practice already goes beyond the confines of biology and in fact involves the linguistic pragmatics of rhetoric and speech act. (shrink)

According to the instrumentalism of Friedman and Machlup it is irrelevant whether the explanatory principles or “assumptions” of a theory satisfy any criterion of “plausibility,” “realism,” “credibility,” or “soundness.” In this view the main or only criterion for selecting theories is whether a theory yields empirically testable implications that turn out to be consistent with observations. All we should require or expect from a theory is that it is a useful instrument for the purpose of prediction. Considerations of the “efficiency” (...) of a theory for the purpose of ordering our experiences are permitted, but considerations of “plausibility” are not. “Explanatory assumptions” are not really explanatory in the sense that they claim to represent underlying causal processes in reality; they only serve to generate, by deduction, implications that are in accordance with as many observations as possible. (shrink)

Since Darwin's theory of evolution by natural selection, the idea of descent with modification came to dominate systematics, and so the study of morphology became subgugated to the reconstruction of phylogenies. Reinstating the organism in the theory of evolution (Ho & Saunders, 1979; Webster & Goodwin, 1982) leads to a project inrational taxonomy (Ho, 1986, 1988a), which attempts to classify biological forms on the basis of transformations on a given dynamical structure.Does rational taxonomy correspond to thenatural system that Linnaeus and (...) his contemporaries as well as all pre-Darwinian morphologists had in mind? Here, we examine how rational taxonomy and the natural system can coincide in the dynamics of processes generating forms during development, which conferexclusivity, genericity androbustness to the forms that do exist. We use the example of segmentation, especially inDrosophila, as an illustration to explore the implications of rational taxonomy for evolution and systematics, and the relationship between ontogeny and phylogeny. (shrink)

This paper discerns two types of mathematization, a foundational and an explorative one. The foundational perspective is well-established, but we argue that the explorative type is essential when approaching the problem of applicability and how it influences our conception of mathematics. The first part of the paper argues that a philosophical transformation made explorative mathematization possible. This transformation took place in early modernity when sense acquired partial independence from reference. The second part of the paper discusses a series of examples (...) from the history of mathematics that highlight the complementary nature of the foundational and exploratory types of mathematization. (shrink)

It is a well-known fact that Ernst Cassirer was inspired by his colleague, the biologist Jakob von Uexkiill at the university of Hamburg. This paper claims this inspiration was double—affecting both Cassirer's philosophical anthropology and Cassirer's epistemology of biology, but in two rather different ways. Thus, the paper intends to shed light on a corner of the history of the development of German thought of the interwar period. It may also have an actual interest because both Cassirer and Uexkiill enjoy, (...) for the time being and each in their way, a renaissance, e.g. in the recent field of biosemiotics. (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)

Although Cassirer's four-volume Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit has long been highly regarded as an example of historical scholarship — Cassirer was awarded the golden Kuno-Fischer Medal of the University of Heidelberg in July 1914 for the first two volumes — its importance for understanding his theoretical position seems to have gone unrecognized. In the English-speaking world it is, unfortunately, only known through the fourth volume, and when this appeared in English in 1950 it met (...) with a negative, even hostile, reception. (shrink)

This article presents a new argument concerning the relation between Kant’s theory of race and aspects of the critical philosophy. It argues that Kant’s treatment of the problem of the systematic unity of nature and knowledge in the Critique of Pure Reason and the Critique of the Power of Judgment can be traced back a methodological problem in the natural history of the period – that of the possibility of a natural system of nature. Kant’s transformation of the methodological problem (...) from natural history into a set of philosophical problems proceeds by way of the working out of his own problem in natural history – the problem of the natural history of the human races – and specifically the problem of the unity in diversity of the human species, in response to which he develops a theory of race. This theory of race is, further, the first developed model of the use of teleological judgment in Kant’s work. The article thus argues that Kant’s philosophical position on the sy... (shrink)

Reply to Fred Crowe's Note on 'The History That is Written' (in this issue of jdma).

By inserting the dialogue between Einstein, Schlick and Reichenbach into a wider network of debates about the epistemology of geometry, this paper shows that not only did Einstein and Logical Empiricists come to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but also that in their lifelong interchange, they never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his ”measuring rod objection” against (...) Weyl. On the contrary, Logical Empiricists, though carefully analyzing the Einstein–Weyl debate, tried to interpret Einstein’s epistemology of geometry as a continuation of the Helmholtz–Poincaré debate by other means. The origin of the misunderstanding, it is argued, should be found in the failed appreciation of the difference between a “Helmholtzian” and a “Riemannian” tradition. The epistemological problems raised by General Relativity are extraneous to the first tradition and can only be understood in the context of the latter, the philosophical significance of which, however, still needs to be fully explored. (shrink)

The very idea of a general philosophy of science relies on the assumption that there is this thing called science —as opposed to the various individual sciences. In this programmatic piece I make a case for the claim that general philosophy of science is the philosophy of science in general or science as such. Part of my narrative makes use of history, for two reasons. First, general philosophy of science is itself characterised by an intellectual tradition which aimed to develop (...) a coherent philosophical view of science, qua a part of culture with distinctive epistemic features and a distinctive relation to reality. But, second, this tradition went through some important conceptual shifts which re-oriented it and made it more sensitive to the actual development of science itself. The historical narrative focuses on three such moments: the defining moment, associated with Aristotle, and two major conceptual turns, related to Kant and Duhem. The pressures on the very idea of a general philosophy of science that followed the collapse of the macro-models of science that became popular in the 1960s, the pressures that lay all of the emphasis on fragmentation and not on integration, can be dealt with by a new synthesis within general philosophy of science of the constitutive and the historical, in light of the intellectual tradition that has defined it. (shrink)

On rencontre encore cette idée d'une triple révolution: Copernic, Darwin, Freud. La première phase fera l'objet de nos réflexions. Elle a été conçue par Freud comme une blessure au narcissisme humain. « Le narcissisme universel des hommes, leur amour d'eux-mêmes, nous dit Ricœur expliquant Freud, a, jusqu'à présent, subi trois sévères coups de la part de la science: ce fut d'abord la position centrale de la terre qui fut contesée par Copernic, puis … « Freud lui-même nous dit que pour (...) l'homme pré-copernicien » la position centrale de la terre indiquait qu'elle jouait un rôle dominant dans l'univers et concordait avec la tendance qu'il avait à se considérer comme maître du monde «. Et à l'époque de Freud des historiens de la science abondèrent dans le même sens: au « moyen âge », la terre et l'homme étaient au centre de l'univers et cette position était la plus honorable. (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)

_ Source: _Volume 47, Issue 3, pp 429 - 448 Taxonomy is our response to the proliferating variety of the natural world on the one hand, and the principle of unrelieved universality on the other. From Aristotle, through Porphyry to Linneaus, Kant and others, thinkers have struggled to develop taxonomies that could order what we know and also what we do not yet know, and this essay is a reflection on the existential desire that propels this effort. Porphyry’s tree of (...) logic is an exhaustive account of the things we can say about the sort of beings we are; Linneaus’s system of nature reaches completion in the classification of humans; Kant discovers a way to have natural and logical forms coincide in the thought of natural purpose and purposiveness. The stakes are high. When we order the world, we order ourselves: when we enter the taxonomy, it enters us and confronts us with our judgments of kind, race and kin. (shrink)

On the basis of a comparative analysis of the biosemiotic work of Jakob von Uexküll and of various theories on biological holism, this article takes a look at the question: what is the status of a semiotic approach in respect to a holistic one? The period from 1920 to 1940 was the peak-time of holistic theories, despite the fact that agreement on a unified and accepted set of holistic ideas was never reached. A variety of holisms, dependent on the cultural (...) and disciplinary contexts, is sketched here from the works of Jan Smuts, Adolf Meyer-Abich, John Scott Haldane, Kurt Goldstein, Alfred North Whitehead and Wolfgang Köhler. In contrast with his contemporary holists, who used the model of an organism as a unifying explanatory tool for all levels of reality, Jakob von Uexküll confined himself to disciplinary organicism by extending the borders of the definition of “organism” without any intention to surpass the borders of biology itself. The comparison reveals also a significant difference in the perspectives of Uexküll and his contemporary holists, a difference between a view from a subjective centre in contrast with an all-encompassing structural view. Uexküll’s theories are fairly near to J. S. Haldane’s interpretation of an organism as a coordinative centre, but even here their models do not coincide. Although biosemiotics and holistic biology have different theoretical starting points and research-goals, it is possible nonetheless to place them under one and the same doctrinal roof. (shrink)

The project behind this and the following1 special issue of Angelaki first assumed concrete form in the shape of a three-day international conference, “Continental Philosophy and the Sciences,” hel...

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)

Homology continues to be a concept of central importance in the study of phylogenetic relations, but its relation to ontogenetic processes remains problematical. A definition of homology in terms of equivalent morphogenetic processes is defined and applied to the comparative study of tetrapod limbs. This allows for a consistent treatment of relations of similarity and difference of appendage structure in vertebrates, and the distinction between fishes fins and tetrapod limbs in terms of the concept of equivalence is described. The role (...) of genes can also be clarified in this context, in particular the influence of the Hox 4 complex in determining digit character and the homeotic transformations that arise from changes in their expression patterns. It is argued that these observations are not compatible with the notion of homology between individual digits (I, II, III, etc.) across the tetrapods, and that homology cannot be consistently identified with gene action. The relations between homology and the properties of the morphogenetic limb field are discussed. (shrink)