Michael Heidelberger

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.