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)

The ArgumentCassirer's analyses of twentieth-century physics from the perspective of the philosophy of science focuses on the concept of the object of scientific experience. Within his concept of functional knowledge, he takes a structural stance and claims that it is specifically this concept of the object that has paved the way for modern science. This article aims, first, to show that Cassirer's interpretation of Felix Klein's “Erlanger Programm” provided the impetus for this view. Then, it analyzes Kant's conception of objectivity (...) in order to examine whether Cassirer can rightfully claim that his view is a further development of transcendental principles. Finally, it is argued that it is Cassirer's concept of the object that enables him to integrate one decisive feature of scientific progress, namely, the increasinggeneralizationof the basic concepts of a science, into his conception of knowledge. This is illustrated in more detail through the example of the progression from Newton's mechanics to relativity theory. (shrink)

To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality, personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but the assignment of mathematics to informal reality is (...) not itself formally analysable, and it is dependent on social and personal construction processes. On these levels, absolute agreement cannot be expected. Starting from this point of view, repercussion of mathematical on social and personal reality, the historical development of mathematical modelling, and the role, use and interpretation of mathematical models in scientific practice are discussed. (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 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)

Whenever one reads internal histories of psychology what is covered is the establishment of a lab by Wundt in 1879 as the initiating act and then the breakaway movements of the 20th Century are discussed: Behaviorism, Gestalt Theory, Psychoanalysis, and most recently the Cognitive revival. However, Aron Gurwitsch described a perspective noted by Cassirer and first developed by Malebranche, which dates the founding of psychology at the same time as that of physics in the 17th Century. This external perspective shows (...) the dependency of psychology upon the concepts, methods and procedures of physics and the natural sciences in general up until the present time. Gurwitsch argues that this approach has blocked the growth of psychology and has assured its status as a minor science. He argued that the everyday Lifeworld achievements of subjectivity are the true subject matter of psychology and that a phenomenological approach to subjectivity could give psychology the authenticity it has been forever seeking but never finding as a naturalistic science. Some clarifying thoughts concerning this phenomenologically grounded psychology are offered, especially the role of desire. The assumption of an external perspective toward the history of psychology fostered the insights about psychology’s scientific role. (shrink)

In the paper I try, resolutely, to associate the open ended encyclopedic character of Cassirer's philosophy with the core part of this philosophy concerning symbolic formation. In this way I try to supplement and strengthen the anthropology that Cassirer formulated in AN ESSAY ON MAN. Finally I discuss the historical character and value of this anthropology.

The criteria for what is considered as science have been debated for a very long time. This article assumes the scientific nature of Theology as a given. This article discusses in three concentric circles the scientific nature of Theology and the type of contribution Theology can make. The first circle addresses the nature of science. This broader look at what is considered to be science sets the context for the ensuing discussion. Secondly, Theology as science is investigated. The criteria which (...) make Theology an indispensable part of the scientific project is identified as the ability to collaborate with other sciences based on a shared interest in reality and creation. Further, Theology as science has the ability to contextualise the products of scientific efforts to be relevant not only to the faith community but to society at large. Theology as science requires a critical self-reflection which does not only include a self-understanding but also a self-renewal. The third concentric circle focusses on the scientific nature of Theology as practised at the Faculty of Theology at the University of Pretoria. The Faculty of Theology endeavours to produce life-giving Theology. To prove itself to be scientific Theology needs to act credible by contributing to the wellness of society. (shrink)

On 11thOctober 2007, at the first international conference on Integrated History and Philosophy of Science (&HPS1) hosted by the Center for Philosophy of Science in Pittsburgh, Ernan McMullin (University of Notre Dame) portrayed a rather gloomy scenario concerning the current relationship between history and philosophy of science (HPS), on the one hand, and mainstream philosophy, on the other hand, as testified by a significant drop in the presence of HPS papers at various meetings of the American Philosophical Association (APA).

An overview of the history of the concept of matter highlights the fact that alternative modes of explanation were successively employed. With the discovery of irrational numbers the initial conviction of the Pythagorean School collapsed and was replaced by an exploration of space as a principle of understanding. This legacy dominated the medieval period and had an after-effect well into modernity—for both Descartes and Kant still characterized matter in spatial terms. However, even before Galileo the mechanistic world view slowly entered (...) the scene—the world as chaos, particles in motion. Elevating movement to become the guiding principle in our understanding of matter dominated the main tendency of modern physics until the (end of the) 19th century. The discovery of irreversible processes (radio-activity for example) directed 20th century physics towards an exploration of the meaning of energy-operation. It turned out that even within 20th century physics long-standing legacies prevailed, because an account of the nature of matter continued to be torn apart by atomistic and holistic views—confronted by the problem of constancy and change (radical transformability versus persistence). Concrete, material reality exceeds the scope of any single mode of explanation—an insight that also serves a better understanding of the wave-particle duality. (shrink)

The basic tendencies in the conceptual history of the 'subject' within Russian intellectual history are presented. This backgrounds a closer analysis of S. Trubetskoj's concept of 'conciliar consciousness', including the problems and aporiae connected with it. It will be shown that and how this conception depends on assumptions from prekantian metaphysics and therefore ignores the Kantian account of subjectivity.

The basic tendencies in the conceptual history of the 'subject' within Russian intellectual history are presented. This backgrounds a closer analysis of S. Trubetskoj's concept of 'conciliar consciousness', including the problems and aporiae connected with it. It will be shown that and how this conception depends on assumptions from prekantian metaphysics and therefore ignores the Kantian account of subjectivity.

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)

Ludwik Fleck is a pioneer of the contemporary social constructionist trend in scientific theory, where his central concept of thinking style has become standard fare. Yet the concept is too often misunderstood and simplified with serious consequences not only for Fleck studies. My essay situates Fleck’s concept of thinking style in the historical context of the 1920s and ‘30s, when the notion of style was first applied to the natural sciences, in order to illustrate the uniqueness of Fleck’s concept among (...) the uses of style by his contemporaries and, finally, to examine the epistemological, methodological, and political consequences of this distinction. (shrink)

A Christian approach to scholarship, directed by the central biblical motive of creation, fall and redemption and guided by the theoretical idea that God subjected all of creation to His Law-Word, delimiting and determining the cohering diversity we experience within reality, in principle safe-guards those in the grip of this ultimate commitment and theoretical orientation from absolutizing or deifying anything within creation. In this article my over-all approach is focused on the one-sided legacy of mathematics, starting with Pythagorean arithmeticism (“everything (...) is number”), continuing with the geometrization of mathematics after the discovery of irrational numbers and once again, during the nineteenth century returning to an arithmeticistic position. The third option, never explored during the history of mathematics, guides our analysis: instead of reducing space to number or number to space it is argued that both the uniqueness of these two aspects and their mutual coherence ought to direct mathematics. The presence of different schools of thought is highlighted and then the argument proceeds by distinguishing numerical and spatial facts, while accounting for the strict correlation of operations on the law side of the numerical aspect and their correlated numerical subjects (numbers). Discussing the examples of 2 + 2 = 4 and the definition of a straight line as the shortest distance between two points provide the background for a brief sketch of the third alternative proposed (inter alia against the background of an assessment of infinity and continuity and the vicious circles present in contemporary mathematical arithmeticistic claims). (shrink)