Michael Heidelberger

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.

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.

This article deals with Moritz Schlick's critical realism and its sources that dominated his philosophy until about 1925. It is shown that his celebrated analysis of Einstein's relativity theory is the result of an earlier philosophical discussion about space perception and its role for the theory of space. In particular, Schlick's "method of coincidences" did not owe anything to "entirely new principles" based on the work of Einstein, Poincaré or Hilbert, as claimed by Michael Friedman, but was already in place before these principles were developed. The first part of the article is devoted to Alois Riehl's critical realism—a neo-Kantian variant which rejects the dominant interpretation of the thing-in-itself as a mere limiting concept and takes empirical theories of space perception into consideration. The second part deals with the central role of "Psychological Parallelism" for Riehl and its integration with Kant's epistemology. In the third part it is shown that Schlick's theory of knowledge is based on Riehl's intricate reworking of Kantian epistemology, physiological psychology, theory of sense perception and philosophy of mathematics. The conclusion stresses the position of the unity of consciousness in Riehl's philosophy which Schlick admittedly cannot cope with

Since the late 1950s one of the most important and influential views of post-positivist philosophy of science has been the theory-ladenness of observation. It comes in at least two forms: either as a psychological law pertaining to human perception (whether scientific or not) or as conceptual insight concerning the nature and functioning of scientific language and its meaning. According to its psychological form, perceptions of scientists, as perceptions of humans generally, are guided by prior beliefs and expectations, and perception has a peculiar holist character. In its conceptual form it maintains that scientists’ observations rest on the theories they accept and that the meaning of the observational terms involved depends upon the theoretical context in which they occur. Frequently, these two versions are combined with each other and give rise to a constructivist view of scientific knowledge (I shall use the term “constructivism” roughly in the same way as Golinski [1998, chap. 1]). According to this outlook, our experience is categorized and preconditioned by prior belief since the process of gaining knowledge through science always involves the use of concepts from some theory or other. This view can easily be strengthened to serve as the cornerstone of a constructivist and anti-empiricist account of science: The categories in terms of which we carve up our experience are not read off from the external world but follow from prior theoretical commitments.

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.

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.