Michael Heidelberger

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

In 1874, the French philosopher Émile Boutroux wrote a dissertationon the contingency of the laws of nature that highly influenced academic philosophy during the French Third Republic and led to a more hypothetical view of the natural sciences and mathematics. Boutroux took over the concept of contingency from the neo-Kantian philosopher Eduard Zeller who had insisted against Hegel on the role of contingency in history, and carried it over to nature. From this he tried to show that the sciences are hierarchically structured such that each layer is irreducible to its more basic predecessor. He also distinguished between two kinds of natural laws in a way very similar to Nancy Cartwright in the1980s. It is finally shown that Boutroux’s view on the nature of mathematics as a hypothetical science had a strong impact on Poincaré.

Preface to Volumes 1 and 2 Lorenz Krüger xv Introduction to Volume 1 Lorraine J. Daston 1 I Revolution 1 What Are Scientific Revolutions? Thomas S. Kuhn 7 2 Scientific Revolutions, Revolutions in Science, and a Probabilistic Revolution 1800-1930 I. Bernard Cohen 23 3 Was There a Probabilistic Revolution 1800-1930? Ian Hacking 45 II Concepts 4 The Slow Rise of Probabilism: Philosophical Arguments in the Nineteenth Century Lorenz Krüger 59 5 The Decline of the Laplacian Theory of Probability: A Study of Stumpf, von Kries, and Meinong Andreas Kamlah 91 6 Fechner’s Indeterminism: From Freedom to Laws of Chance Michael Heidelberger 117 7 The Saint Petersburg Paradox 1713-1937 Gerard Jorland 157 8 Laplace and Thereafter: The Status of Probability Calculus in the Nineteenth Century Ivo Schneider 191 9 Emile Borel as a Probabilist Eberhard Knobloch 215 III Uncertainty 10 The Domestication of Risk: Mathematical Probability and Insurance 1650-1830 237 11 The Objectification of Observation: Measurement and Statistical Methods in the Nineteenth Century Zeno G. Swijtink 261 12 The Measurement of Uncertainty in Nineteenth-Century Social Science Stephen M. Stigler 287 IV Society 13 Rational Individuals versus Laws of Society: From Probability to Statistics Lorraine J. Daston 295 14 Decrire, Compter, Calculer: The Debate over Statistics during the Napoleonic Period Marie-Noelle Bourguet 305 15 Probability in Vital and Social Statistics: Quetelet, Farr, and the Bertillons Bernard-Pierre Lécuyer 317 16 Paupers and Numbers: The Statistical Argument for Social Reform in Britain during the Period of Industrialization Karl H. Metz 337 17 Lawless Society: Social Science and the Reinterpretation of Statistics in Germany, 1850-1880 Theodore M. Porter 351 18 Prussian Numbers 1860-1882 Ian Hacking 377 19 How Do Sums Count? On the Cultural Origins of Statistical Causality M. Norton Wise 395.

The following article treats the 'applicational turn' of modern fluid dynamics as it set in at the beginning of the 20th century with Ludwig Prandtl's concept of the boundary layer. It seeks to show that there is much more to applying a theory in a highly mathematical field like fluid dynamics than deriving a special case from a general explanatory theory under particular antecedent conditions. In Prandtl's case, the decisive move was to introduce a model that provided a physical/causal conception of viscous flow at high Reynolds numbers. It facilitated an approximate solution to the Navier-Stokes equations, which in turn gave rise to many special applications. After a detailed account of Prandtl's achievement, the article discusses the role of the physical model and its experimental and mathematical significance. It is shown that the mathematical simplification provided by the physical model greatly expanded the explanatory capacity of the theory which the Navier-Stokes equations alone could not provide.

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.

Wenn hier Fechners Philosophie als „wissenschaftlich-philosophische Weltauffassung“ bezeichnet wird, dann soll damit gesagt werden, dass Fechner mit seiner Philosophie einen wissenschaftlichen Anspruch verfolgt hat und dass sie tatsächlich auf einem weltanschauungsfreien Fundament ruht. Ich möchte sogar so weit gehen zu behaupten, dass Fechner damit zur Tradition der „wissenschaftlichen Philosophie“ des 19. Jahrhunderts zu rechnen ist, deren folgenreichstes späteres Produkt im 20. Jahrhundert der logische Empirismus darstellt. Der „Wiener Kreis“ als die bekannteste Schule dieser Tradition bediente sich (in seinem Manifest von 1929) des Ausdrucks „Wissenschaftliche Weltauffassung“, um sich von allen spekulativen Weltanschauungen abzugrenzen.

In the 19th century, "Psychophysical Parallelism" was the most popular solution of the mind-body problem among physiologists, psychologists and philosophers. (This is not to be mixed up with Leibnizian and other cases of "Cartesian" parallelism.) The fate of this non-Cartesian view, as founded by Gustav Theodor Fechner, is reviewed. It is shown that Feigl's "identity theory" eventually goes back to Alois Riehl who promoted a hybrid version of psychophysical parallelism and Kantian mind-body theory which was taken up by Feigl's teacher Moritz Schlick.

The physiologist and neo-Kantian philosopher Johannes von Kries (1853-1928) wrote one of the most philosophically important works on the foundation of probability after P.S. Laplace and before the First World War, his Principien der Wohrscheinlich-keitsrechnung (1886, repr. 1927). In this book, von Kries developed a highly original interpretation of probability, which maintains it to be both logical and objectively physical. After presenting his approach I shall pursue the influence it had on Ludwig Wittgenstein and Friedrich Waismann. It seems that von Kries's approach had more potential than recognized in his time and that putting Waismann's and Wittgenstein's early work in a von Kries perspective is able to shed light on the notion of an elementary proposition.