Michael Heidelberger

The main claim of this talk is that mathematical physics and philosophy of physics are not different. This claim, so formulated, is obviously false because it is overstated; however, since no non-tautological statement is likely to be completely true, it is a meaningful question whether the overstated claim expresses some truth. I hope it does, or so I’ll argue. The argument consists of two parts: First I’ll recall some characteristic features of von Neumann’s work on mathematical foundations of quantum mechanics and will claim that von Neumann’s motivation and results are essentially philosophical in their nature; hence, to the extent von Neumann’s work exemplifies what is considered to be mathematical physics, mathematical physics appears as formally explicit philosophy of physics. The second argument is based on a rather trivial interpretation of what mathematical physics is. That interpretation implies that mathematical physics shares some key characteristic features with philosophy of physics which make the two almost indistinguishable.

It is widely held that the current debate on the mind-body problem in analytic philosophy began during the 1950s at two distinct sources: one in America, de- riving from Herbert Feigl's writings, and the other in Australia, related to writings by U. T. Place and J. J. C. Smart (Feigl [1958] 1967). Jaegwon Kim recently wrote that "it was the papers by Smart and Feigl that introduced the mind-body problem as a mainstream metaphysical Problematik of analytical philosophy, and launched the debate that has continued to this day" (Kim 1998, 1). Nonetheless, it is not at all obvious why these particular articles sparked a debate, nor why Feigl's work in particular came to play such a prominent part in it, nor how and to what extent Feigl's approach rests on the logical empiricism he endorsed

Alan Richardson, one of the editors of the present volume, dryly remarks in a footnote to the introduction: “Logical empiricism remains alive in philosophical memory chiefly by the significance of its death.” I think that this pertinent paradox can be enlarged to generally characterise the relation of present-day philosophy of science to logical empiricism : the more philosophy of science has struggled in the past to distance itself from central tenets of the movement of LE, the more it had to realise how close and how indebted it remains to LE and how much “post-positivism” itself willy-nilly keeps its spirit alive. Thus, there is the growing feeling that the identity of today’s philosophy of science is much more closely tied to LE, many manifestations to the contrary notwithstanding. The renewed interest in LE that has resulted from this insight must necessarily have lead to repercussions also on the appraisal of LE as a philosophical position. The once almost unanimous and rash condemnation of LE in the sixties and seventies is today followed by a prudent and broad-minded second look that tries to do fuller justice to the historical background and development. One can understand that for some of those who take the foregoing considerations seriously the news of LE’s death seems to be a little premature

Aus dem vielfältigen Werk von Hermann von Helmholtz versammelt diese Ausgabe die im engeren Sinne philosophischen Abhandlungen, vor allem zur Wissenschaftsphilosophie und Erkenntnistheorie, sowie Vorträge und Reden, bei denen der Autor seine Ausnahmestellung im Wissenschaftsbetrieb nutzte, um die Wissenschaften und ihre Institutionen in der bestehenden Form zu repräsentieren und zu begründen. Ein Philosoph wollte Helmholtz nicht sein, aber er legte der philosophischen Reflexion wissenschaftlicher Erkenntnis und wissenschaftlichen Handelns große Bedeutung bei. Vor allem bezog er, in der Regel ausgehend von seinen fachwissenschaftlichen Forschungen, in den verschiedensten Kontexten zu erkenntnistheoretischen und methodologischen Problemen der Wissenschaften Stellung. Bereits »Ueber die Erhaltung der Kraft« (1847) lässt erkennen, wie verwoben naturwissenschaftliche Grundlagenforschung und philosophische Grundlagenreflexion in seinem Werk sind. Die aus den frühen sinnesphysiologischen Forschungen hervorgegangene empiristische Wahrnehmungslehre trug ihm den Ruf ein, ein maßgeblicher Vertreter des Neukantianismus zu sein. Spätere Arbeiten v.a. zur Geometrie und Arithmetik – das zeigt die vorliegende Ausgabe – stellen jedoch eine radikale Absage an den konstitutiven Kern des Kantianismus (nämlich die Existenz synthetischer Urteile a priori) dar. Helmholtz’ philosophische Beiträge sind bisher in ihrer Vollständigkeit nicht annähernd so gut zugänglich wie sein naturwissenschaftliches Werk. Die Ausgabe enthält außerdem bibliographische Vorberichte zur Einordnung, detaillierte Namens- und Sachregister sowie mit 575 Einträgen für den Zeitraum zwischen 1842 und 2012 die erste umfassende Bibliographie von Helmholtz verfasster Werke überhaupt. »Ich glaube, dass der Philosophie nur wieder aufzuhelfen ist, wenn sie sich mit Ernst und Eifer der Untersuchung der Erkenntnissprocesse und der wissenschaftlichen Methode zuwendet. Da hat sie eine wirkliche und berechtigte Aufgabe.« Helmholtz in einem Brief um 1875

In this paper, I would like to show that considering technological models as they arise in engineering disciplines can greatly enrich the philosophical perspective on models. In fluid mechanics, (at least) three types of models are distinguished: mathematical, computer and physical models. Very often, the choice of a particular mathematical, computer or physical model highly affects the type of solutions and the computational time needed for it. Technological models not only aim at a correct description of the physical phenomena, but also for an efficient and accurate simulation. The problem arises how heterogeneous models of an engineering problem can be brought together and be compared to each other as regards their function and technological efficiency. There are two developments in the history of fluid mechanics that have greatly influenced the use of models in the field: The introduction of the concept of the boundary layer by Ludwig Prandtl in 1904 made it possible to apply ideal analytical solutions, which at the time were almost entirely based on Euler’s equations for inviscid fluids, to interesting real cases and to approximate the theoretical Navier-Stokes equations to practical engineering problems, i.e. to cases at high Reynolds numbers. This made it possible to link the empirical tradition of hydraulics with the theoretical tradition of analytical mechanics and therefore lead to a kind of equilibrium in the use of mathematical and physical models. In the 1970s the introduction of the computer has greatly pushed back the importance of both physical and mathematical (analytic) models alike without making them superfluous. There remain, however, three different ways to conceive of physical models in fluid mechanics, and thus of the experimental ingredient, depending on whether they are devised from an analytical, computational or measurement theoretical point of view. Yet even inside the tradition of computer simulation, different practices have formed according to the programming methods used. The choice of method either depends on considerations of efficiency in terms of costs and time, or on historically contingent factors, like availability of instruments and programming packages or the arbitrary choice of a forerunner. Seen from a technological point of view the factors that make models “autonomous agents” and thus (relatively) independent from theory depend on efficiency constraints. Models are means to solve problems in a certain practical perspective by the most efficient means available. To develop a model is a “fast and frugal way” to get to grips with a certain region of reality, whereas the theoretical approach stresses the importance of universal features.

In the foundations of Fechner's psychophysics, the concept of “functional relation” plays a highly relevant role in three different respects: (1) in respect to the principles of measurement, (2) in respect to the mind-body problem, and (3) in respect to the concept of a law of nature. In all three cases, it is important to explain the difference between a functional dependency of a variable upon another and a causal relationship between two (or more) variables. In all three respects, Ernst Mach developed Fechner's ideas further and tried to extend the lessons he had learned from using the concept of a functional relation in psychophysics to the whole of science. For all three cases, I explain why they are still relevant for psychophysics and philosophy today

In philosophischen wie nichtphilosophischen Darstellungen wird heutzutage der Ursprung des Leib-Seele-Problems überwiegend mit dem kartesischen Dualismus in Verbindung gebracht. Es wird die Meinung vertreten, daß erst durch Descartes’ Aufteilung des Menschen (und damit der Welt) in die beiden einander ausschließenden Substanzen der res extensa und der res cogitans das philosophische Grundübel in die Leib-Seele-Philosophie gekommen sei.1 Folgerichtig ist man fest davon überzeugt, daß sich das Problem nur lösen läßt, wenn man es an der Wurzel packt und konsequent Descartes’ ontologischen Dualismus verwirft. Ein Herumdoktern an den Symptomen nach Art des Okkasionalismus oder der Leibnizschen Lehre von der prästabilierten Harmonie wird demgegenüber als metaphysisch suspekt und aussichtslos angesehen. Zwar ist inzwischen die Hoffnung, durch bloßen Anti-Cartesianismus ans Ziel zu kommen, etwas geschwunden, nachdem man feststellen mußte, daß die anfänglich so vielversprechende Kritik des Behaviourismus an Descartes nicht zum Ziel führte. Und auch mit der nächsten, von der Identitätstheorie hervorgerufenen großen Welle der Descartes-Kritik sind die Lösungen bis heute nicht so befriedigend ausgefallen, wie man sie gerne hätte. Die Überzeugung ist aber weiterhin stark, daß eine Lösung für das Leib-Seele-Problem zuallererst die Verwerfung des kartesischen Dualismus erfordert.