Polanyi's presagement of the incommensurability concept

Kuhn and Feyerabend have little to say about the thought of Michael Polanyi, and the secondary literature on Polanyi's relation to them is meagre. I argue that Polanyi's view, in Personal knowledge and in other writings, of conceptual frameworks ‘segregated’ by a ‘logical gap’ as giving rise to controversies in science foreshadowed Kuhn and Feyerabend's theme of incommensurability. The similarity between the thinkers is, I suggest, no coincidence.     

De-synthesizing the relative a priori

This paper considers the question whether the notion of the relative apriori, central to Michael Friedman’s transcendentalist programme for philosophy of science, is available also to philosophers who reject appeals to a synthetic a priori. After tracing the rediscovery of the relative a priori and delineating its potential, the question is considered whether Friedman’s arguments against Quinean naturalism and Carnap’s attenuated logicism tell against a conception of philosophy as scientific metatheory that combines logical and empirical inquiries. Finding an opening here it is argued that this conception can also help itself to the notion of a relative a priori which, it is agreed, is central to historically informed theorising about science.     

Historical evolution of the concept of homotopic paths

Conclusions The historical evolution of the homotopy concept for paths illustrates how the introduction of a concept (be it implicit or explicit) depends upon the interests of the mathematicians concerned and how it gradually acquires a more satisfactory definition.In our case the equivalence of paths first meant for certain mathematicians that they led to the same value of the integral of a given function or that they led to the same value of a multiple-valued function. (See for instance [Cau], [Pui], [Rie].) Later this dependency upon given functions is dropped (by Jordan for surfaces, by Riemann and most explictly by Poincaré) and this leads to a concept which depends only upon the manifold. It thus becomes a concept which belongs to topology.As a consequence of this hesitant evolution, there was at first a confusion between concepts and hence no attention to relations between them. At a later stage these relations were investigated, as for instance the fact that homotopy equivalence implies homology equivalence: in1882, Klein gave an example of a closed curve on a surface which is the boundary of a part of the surface but could not be shrunk to a point. In 1904, Poincaré explicitly said that this curve is homologue à zéro (null homologous), but not équivalent à zéro (null homotopic). Poincaré obtains the homologies from the fundamental group by allowing changes in the order of the terms in the équivalences. This means also that the equivalences imply homologies but not vice versa.From a methodological standpoint, this situation of using properties without asking about relations between them or without even properly defining them is reminiscent of mathematics of a century earlier. An example is the way differentiability was used for the differentiation of functions without consciously questioning the properties of this concept until in the nineteenth century examples were given by Bolzano (1834), Weierstrass (1872), Riemann (1854) and others of functions which are continuous but nowhere differentiable [Kli].Another example is the use eighteenth-century mathematicians made of series without inquiring about the validity of the operations they used on them. Another aspect which had its influence was the success of algebraic methods in topology which explains the preference for theories with base point and constrained deformation even though free deformation is a more natural concept.As we can see the evolution of the homotopy concept for paths did not progress without impediments. It also had an influence on the evolution of the abstract group concept and the basic principle of equivalence. These aspects make it a history which is not only intrinsically interesting (how did homotopic paths come to be?), but also because it illustrates relations between different branches of mathematics.     

Goethe's Archetype and the romantic concept of the self

This paper attempts to illuminate Goethe's concept of an archetype by setting it alongside the concept of the self that was being articulated at the same time, also by writers of the Romantic movement. The Romantic concept of the self expresses a new concept of the self as a 'core' plus an expression of the core: and it is the same 'core plus expression' idea that is embodied in the Goethean archetype. Goethe's archetype is not simply a 'plan'. It is a kind of agent at the heart of a thing, striving for self expression, and to this end driving the thing's development. Both Romantic self and archetype reflect the wider attempt to reinstate the concept of action in our understanding of things and happenings in general. The root idea of there being at the heart of a living thing an agent pursuing a goal remains in the modern concept of the organism.     

On assessing the relative performance of default predictions

We compare the accuracy of default predictions as, for instance, produced by professional rating agencies. We extend previous results on partial orderings to nonidentical sets of obligors and show that the calibration requirement virtually rules out the possibility of some partial orderings and that the partial ordering based on the ROC curve is most easily achieved in practice. As an example, we show for more than 5,000 firms rated by Moody's and S&P that these ratings cannot be ranked according to their grade distributions given default or nondefault, but that Moody's dominate S&P with respect to the ROC criterion and the Gini curve.     

Herman Boerhaave and the element-instrument concept of Fire

La théorie générale du contrôle et de la communication, mieux connue sous le nom de ‘cybernétique’, est habituellement considérée comme le fruit des recherches liées à la deuxième guerre mondiale aux Etats-Unis, menées principalement par le mathématicien américain Norbert Wiener (1894–1964). Dans le cadre de son travail pour l'armée, Wiener a développé une théorie générale des régulations. Nous nous intéressons aux origines de la théorie générale des régulations en Allemagne (Allgemeine Regelungskunde), montrant qu'elle prend naissance dans un contexte bien différent.

Hermann Schmidt (1894–1968), le principal acteur dans ce domaine en Allemagne, bien que physicien de formation, formula sa version de la théorie du contrôle à la fin des années 30, grâce aux différents systèmes de régulation qu'il était amené à étudier au bureau des brevets du Reich (Reichspatentamt). A partir de l'analyse d'une combinaison de facteurs contextuels, nationaux, politiques et contingents, nous proposons une explication de la moindre influence de la théorie de Schmidt.     

Forecasting relative quality

This paper develops a model to forecast the likely quality rating of new automobiles. A scheme is devised and implemented for 1982 whereby the probability that a specific model will have one of five quality ratings is computed. The quality ratings are based on the trouble index computed by Consumer Reports based on a survey of its subscribers. A multinomial logit specification is used whereby the relative probability that a given level of quality is realized is a function of previous quality ratings, the location of the manufacturer of the automobile, the size of the automobile and the list price (or port-of-entry prices, in the case of imports). The forecast results when compared in a qualitative way to actual 1982 quality ratings prove to be acceptable.     

Chemical mutagenesis in relation to the concept of the gene

Zusammenfassung Die vorliegende Arbeit gibt einen Überblick über neuere Untersuchungen chemischer Mutationsauslösungen mit besonderer Betonung der Induktion von Chromosomenbrüchen in Pflanzen und Rückmutationen beiNeurospora. Die Arbeit zeigt, dass jedes Allel ein charakteristisches Mutationsverhalten zeigt, das durch die Reaktion auf physikalische und chemische Mutagene definiert wird. Diese Ergebnisse werden unter dem Aspekt diskutiert, dass ein Gen die Einheit der Funktion, Rekombination und Mutation darstellt.     

A new concept of the alkaline oxidation of uric acid

Zusammenfassung Früher veröffentlichte Arbeiten über die alkalische Oxydation der Harnsäure wurden ergänzt durch eine Untersuchung über die Struktur von Uroxansäure sowie der Zwischenprodukte, die im alkalischen Oxydationsgemisch auftreten. Die Resultate führen zu einer grundlegend neuen Auffassung über den Mechanismus der Abbaureaktion (Schema II). Uroxansäure ist ein Imidazolidon (XIII) und nicht ein offenkettiges Diureid (III); das vonBehrend formulierte Zwischenprodukt II hingegen, dem man bisher in der alkalisch-chemischen sowie auch in der enzymatischen Harnsäureoxydation eine Schlüsselstellung einräumte, muss durch offenkettige Verbindungen ersetzt werden (XIV, XV, X), in denen das zentrale C-Atom auf die frühere Harnsäure-position 4 zurückgeführt werden kann.     

Geminus and the concept of mean motion in Greco-Latin astronomy

Conclusion Geminus account of lunar motion in chapter 18 of hisIntroductio astronomiae is, in our view, an important contribution to Greco-Latin astronomy because, in attempting to reconstruct arithmetically (the parameters of) the Moon's motion in longitude, he undermines the task astronomers had hitherto set for themselves. This undermining of a commonly acknowledged view of the purpose of astronomy is articulated in a whole new set of questions concerning the nature and place of both observation and mathematical reasoning in the science of the heavens. Yet, one must not overlook the fact thatGeminus reconstruction also indicates resources for addressing these questions. Of these resources, the most powerful proved to be the idea that irregular motion could be quantified as a systematic departure from a mean motion, and the idea that observational data could be organized and structured by means of genetic arithmetical reconstructions.But, since we limit our attention to extant treatises and decline to speculate about works or parts of works that have not survived, we must say that it would takePtolemy to discern the new direction for astronomy thatGeminus opened up and to pursue it. In part, this involved straightening out the conflated conception of mean motion in chapter 18 — the qua arithmetic mean daily displacement can only be anapparent lunar motion in longitude and not one the Moonreally makes, but the same need not be true of the qua periodic mean daily displacement — and determining its proper relation to real and apparent planetary motion. Indeed,Ptolemy's genius lay, we think, in seeing that even though, in assimilating Babylonian astronomy, earlier and contemporary Greco-Latin writers betrayed a confused, inconsistent, and unsophisticated grasp of the proper role of arithmetic, geometry, and observation in astronomical argument [seeBowen 1994], the solution lay in a mathematical reconstruction of the observed celestial motions, in which mean motion played an essential role.     

On the relative position of the centromere of chromosome 3 inDrosophila melanogaster

Zusammenfassung HomozygoteDrosophila-melanogaster-Weibchen, genetisch markiert mit scarlet (st), Kinked (Ki) und pink peach (P^p) wurden bestrahlt, um Compound-3-Chromosomen herzustellen. Es wurden ausschliesslich st/st- und P^p Ki/Ki(?) P^p-Compoundchromosomen gefunden. Dies zeigt, dass das Zentromer links der Markierung Kinked liegt.

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This work was supported by Schweizerischer Nationalfonds zur Förderung der wissenschaftlichen Forschung.