The aim of the paper is this: Instead of presenting a provisional and necessarily insufficient characterization of what mathematical physics is, I will ask the reader to take it just as that, what he or she thinks or believes it is, yet to be prepared to revise his opinion in the light of what I am going to tell. Because this is precisely, what I intend to do. I will challenge some of the received or standard views about mathematical physics (...) and replace them by a more sophisticated picture, which takes into account the methodological and philosophical roots of mathematical physics in Göttingen. (shrink)

In recent years the works of Friedman, Howard and many others have made obvious what perhaps was always self-evident. Namely, that the philosophy of the logical empiricists was shaped primarily by Einstein and his invention of the theory of relativity, whereas Hilbert and his axiomatic approach to the exact sciences had comparatively little impact on the logical empiricists and their understanding of science — if they had any effect at all. This is in one respect quite astonishing, insofar as Einstein (...) himself confessed 1921 in his famous lecture before the Prussian Academy of Science that “without it [the axiomatic point of view] it would have been impossible for me to propound the theory of relativity”.2 Hence the simple question arises: why didn’t the logical empiricists pay more attention to Hilbert and his axiomatic point of view, than they in fact did? It is an aim of this paper to answer this question and in part to correct this one-sided view in the hypothetical or contra-factual sense that the logical empiricists would have done better, if they had paid somewhat more attention to Hilbert and his axiomatic approach to science. (shrink)

The paper deals with some of the developments in analysis against the background of Hilbert's contributions to the Calculus of Variations. As a starting point the transformation is chosen that took place at the end of the 19th century in the Calculus of Variations, and emphasis is placed on the influence of Dirichlet's principle. The proof of the principle (the resuscitation ) led Hilbert to questions arising in the 19th and 20th problems of his famous Paris address in 1900: theexistence (...) in a generalized sense, and theregularity of solutions of elliptic partial differential equations. By this new concept Hilbert pointed out two very important issues the history of which is closely tied up with the rise of modern analysis. Further on, Hilbert'stheorem of independence of the Calculus of Variations, an important contribution to its formal apparatus as well as to its field theory, is briefly discussed. But even as Hilbert published his first essential results, he was turning his attention to another area of mathematics that differs in an important respect from the Calculus of Variations:integral equations. Hilbert did so because he recognized that in this branch by its flexibility he was coming closer to his goal of an unifying methodological approach to analysis. (shrink)

Only recently has David Hilbert’s program to axiomatize the sciences according to the pattern of geometry left the shade of his formalist program in the foundations of mathematics.1 This relative neglect — which is surprising in view of the enormous efforts Hilbert himself had devoted to it — was certainly influenced by Logical Empiricists’ almost exclusively focusing on his contributions to the foundational debates. Ulrich Majer puts part of the blame for this neglect on Hilbert himself because “he failed to (...) make his position sufficiently clear, and he did not take much effort to promote his views beyond the narrow circle of mathematical physics in Göttingen.”. (shrink)

This paper addresses the historical context of Bertalanffy’s concept of Theoretical Biology, his early combattants, friends, teachers and the philosophical position of his critical reviewer Philipp Frank. I will describe the characteristics of his theory and how his ideas are embedded into the background discourse of the day. In the following five sections I will show that there are three main historical factors that shaped Bertalanffy’s intellectual views: First, his philosophical training with Schlick and Carnap, second, his close connection with (...) the biologists in the Prater-Vivarium, and third, his close contact to J.H. Woodger and, through him, with the organicists of the Theoretical Club in Cambridge. This narration also sheds some light on one of the founders of the Vienna Circle, Philipp Frank. I shall provide some historical data about his early interest in biology and discuss his position towards some basic problems in biology. (shrink)