Signs, toy models, and the a priori: from Helmholtz to Wittgenstein

The Marburg neo-Kantians argue that Hermann von Helmholtz’s empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz’s account raises the ‘problem of validity’ (Gültigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz’s and Ludwig Wittgenstein’s Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz’s original account.     

Atomism, Poincaré and Planck

Planck's change in attitude to the question of whether atomic hypotheses were scientifically accessible, is discussed. It is argued contra Holton, that Planck's change in attitude to this question did not signal a methodological shift towards realism. The point of doing this is not just to investigate a significant episode in the history of quantum theory, but also to use the episode as a case study in support of a broader historical thesis. This thesis is that there was a widespread late-nineteenth century methodological tradition which motivated the change in status of certain ontological claims — e.g., that atoms exist — from ‘inaccessible to science’ to ‘scientifically acceptable’ even though those claims were not strictly ‘observable’. This methodological tradition is a hybrid of positivist and realist views. Thus, contrary to one popular view, the fin de siécle triumph of atomism is not to be seen as a triumph for a realist view of science Poincare's views are also used as an illustration.     

Newton's early computational method for dynamics

On December 13, 1679Newton sent a letter toHooke on orbital motion for central forces, which contains a drawing showing an orbit for a constant value of the force. This letter is of great importance, because it reveals the state ofNewton's development of dynamics at that time. Since the first publication of this letter in 1929,Newton's method of constructing this orbit has remained a puzzle particularly because he apparently made a considerable error in the angle between successive apogees of this orbit. In fact, it is shown here thatNewton's implicitcomputation of this orbit is quite good, and that the error in the angle is due mainly toan error of drawing in joining two segments of the oribit, whichNewton related by areflection symmetry. In addition, in the letterNewton describes quite correctly the geometrical nature of orbits under the action of central forces (accelerations) which increase with decreasing distance from the center. An iterative computational method to evaluate orbits for central forces is described, which is based onNewton's mathematical development of the concept of curvature started in 1664. This method accounts very well for the orbit obtained byNewton for a constant central force, and it gives convergent results even for forces which diverge at the center, which are discussed correctly inNewton's letterwithout usingKepler's law of areas.Newton found the relation of this law to general central forces only after his correspondence withHooke. The curvature method leads to an equation of motion whichNewton could have solvedanalytically to find that motion on a conic section with a radial force directed towards a focus implies an inverse square force, and that motion on a logarithmic spiral implies an inverse cube force.     

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.     

Public scientific testimony in the scientific image

In this paper, I draw on philosophy of science to address a challenge for science communication. Empirical research indicates that some people who trust a meteorologist's report that they are in the path of a storm do not trust a climate scientist's report that we are on a path to global warming. Such selective skepticism about climate science exemplifies a more general challenge:

The Challenge of Selective UptakeLaypersons who generally accept public scientific testimony nevertheless fail to accept public scientific testimony concerning select, equally well warranted, scientific hypotheses.

A prominent response arising from the novel interdisciplinary science of science communication is a principle called Consensus Reporting. According to this principle, science reporters should, whenever feasible, report the scientific consensus or lack thereof for a reported scientific view.However, philosophy of science may offer a different perspective on the issue. This perspective is critical insofar as it indicates some inadequacies of Consensus Reporting. But it is also constructive insofar as it guides the development of an alternative principle, Justification Reporting, according to which science reporters should, whenever feasible, report aspects of the nature and strength of scientific justification or lack thereof for a reported scientific view. A central difference between these proposals is that Consensus Reporting appeals to the authority of the scientists whereas Justification Reporting appeals to the authority of scientific justification. As such, Justification Reporting reflects the image of science.The paper considers the philosophical and empirical motivation for Justification Reporting and its limitations. This includes prospects and problems for implementing it in a way that addresses The Challenge of Selective Uptake. From a methodological point of view, the paper illustrates how empirically informed philosophy of science may help address challenges for science communication.     

Conventionalism in Reid’s ‘geometry of visibles’

The subject of this investigation is the role of conventions in the formulation of Thomas Reid’s theory of the geometry of vision, which he calls the ‘geometry of visibles’. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid’s ‘geometry of visibles’ and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the construction and assignment of its various properties, especially metric properties, and this fact undermines the claim for a unique non-Euclidean status for the geometry of vision. Finally, a suggestion is offered for trying to reconcile Reid’s direct realist theory of perception with his geometry of visibles.While Thomas Reid is well-known as the leading exponent of the Scottish ‘common-sense’ school of philosophy, his role in the history of geometry has only recently been drawing the attention of the scholarly community. In particular, several influential works, by N. Daniels and R. B. Angell, have claimed Reid as the discoverer of non-Euclidean geometry; an achievement, moreover, that pre-dates the geometries of Lobachevsky, Bolyai, and Gauss by over a half century. Reid’s alleged discovery appears within the context of his analysis of the geometry of the visual field, which he dubs the ‘geometry of visibles’. In summarizing the importance of Reid’s philosophy in this area, Daniels is led to conclude that ‘there can remain little doubt that Reid intends the geometry of visibles to be an alternative to Euclidean geometry’;¹ while Angell, similarly inspired by Reid, draws a much stronger inference: ‘The geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764 ...’² The significance of these findings has not gone unnoticed in mathematical and scientific circles, moreover, for Reid’s name is beginning to appear more frequently in historical surveys of the development of geometry and the theories of space.³Implicit in the recent work on Reid’s ‘geometry of visibles’, or GOV, one can discern two closely related but distinct arguments: first, that Reid did in fact formulate a non-Euclidean geometry, and second, that the GOV is non-Euclidean. This essay will investigate mainly the latter claim, although a lengthy discussion will be accorded to the first. Overall, in contrast to the optimistic reports of a non-Euclidean GOV, it will be argued that there is a great deal of conceptual freedom in the construction of any geometry pertaining to the visual field. Rather than single out a non-Euclidean structure as the only geometry consistent with visual phenomena, an examination of Reid, Daniels, and Angell will reveal the crucial role of geometric ‘conventions’, especially of the metric sort, in the formulation of the GOV (where a ‘metric’ can be simply defined as a system for determining distances, the measures of angles, etc.). Consequently, while a non-Euclidean geometry is consistent with Reid’s GOV, it is only one of many different geometrical structures that a GOV can possess. Angell’s theory that the GOV can only be construed as non-Euclidean, is thus incorrect. After an exploration of Reid’s theory and the alleged non-Euclidean nature of the GOV, in 1 and 2 respectively, the focus will turn to the tacit role of conventionalism in Daniels’ reconstruction of Reid’s GOV argument, and in the contemporary treatment of a non-Euclidean visual geometry offered by Angell ( 3 and 4). Finally, in the conclusion, a suggestion will be offered for a possible reconstruction of Reid’s GOV that does not violate his avowed ‘direct realist’ theory of perception, since this epistemological thesis largely prompted his formulation of the GOV.     

Eating and drinking induced by cerebral-ventricular injections in rats with lesions in the lateral hypothalamus

Résumé Par des lésions bilatérales hypothalamiques on a rendu des rats aphagiques et adipsiques. Durant la période de convalescence, on a injecté dans le ventricule latéral du pentotal de sodium (ce qui normalement fait manger les animaux) et une solution saline hypertonique (qui normalement les fait boire). On a trouvé qu'après les lésions les rats ne réagissent que lorsqu'ils sont redevenus capables de manger et de boire spontanément.

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This work was supported in part by a grant from the National Institute of Neurological Diseases and Blindness, No. NB 01941, of the National Institutes of Health, U.S. Public Health Service, Bethesda, Maryland; by a grant from the National Science Foundation, No. GB-4594, Washington, D.C.; and the Fund for Research and Teaching of the Department of Nutrition, Harvard School of Public Health, Boston, Massachusetts.     

Poincaréan intuition revisited: what can we learn from Kant and Parsons?

This paper provides a comprehensive critique of Poincaré’s usage of the term intuition in his defence of the foundations of pure mathematics and science. Kant’s notions of sensibility and a priori form and Parsons’s theory of quasi-concrete objects are used to impute rigour into Poincaré’s interpretation of intuition. In turn, Poincaré’s portrayal of sensible intuition as a special kind of intuition that tolerates the senses and imagination is rejected. In its place, a more harmonized account of how we perceive concrete objects is offered whereby intuitive knowledge is consistently a priori whatever the domain of application.     

Über das Problem der Welkekrankheiten bei Pflanzen

Summary Lycomarasmin is a plasma poison produced byFusarium lycopersici Sacc., the pathogen of tomato wilt. In a dilution of 10^–2 and 10^–3 mol it causes a pathological wilting of tomato plants and usually disturbs their water balance; in a dilution of 10^–4 mol it only disturbs the latter.In the present paper, we develop the theory that in sufficient concentration lycomariasmin damages or destroys thesemipermeability of the plasma boundary layer.In a dilution of 10^–2 and 10^–3 mol of lycomarasmin the semipermeability of the plasma membranes iscompletely destroyed. Thus on the one hand the conditions for osmotic pressure disappear and irreversible pathological wilting appears, and on the other hand cellular fluid passes into the transpiration current of the cell-membrane and leads to a momentary excess humidity, particularly in the leaf-tissues, and thus also to a momentaryexcess transpiration.The water-deficit regularly observed in wilt-literature is therefore not the cause of pathological wilting but, just as the wilting itself, a consequence of the distruction of the semipermeability of the plasma boundary layer.In a dilution of 10^–4 mol lycomarasmin apparently only affects the permeability of the exterior plasma boundary layer forwater, but not for sugars etc. Therefore it only produces an excess of fluid in the leaf tissues and thus an excess transpiration, but no definite inactivation of the plasma membrane and therefore also no pathological wilt.     

Ein Beweis für das Vorhandensein des Knotpunktpotentials am Herzmuskel

Summary After administration of methoxamine, a synthetic sympathomimetic amine, a change in the transmembrane potential, suggestive of the presence of a junction potential between two cardiac cells, was observed in the guinea-pig's ventricular muscle.

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Durch die dankenswerte Unterstützung derPharmacological Research Foundation (Yakurikenkyu-kai, Tokyo) wurde diese Arbeit ermöglicht.     

Cytogenetics of South American akodont rodents (Cricetidae). V. Segregation of chromosome No. 1 polymorphism inAkodon molinae

Summary Akodon molinae is polymorphic with 2n=42, 43, 44, where the metacentric autosome No. 1 is homologous to 2 acrocentrics 1a and 1b. Matings between 2n=43 heterozygotes 1/1a, 1b gave a surplus of 1/1 offspring, a moderate reduction of heterozygous and a strong reduction of homozygous 1a, 1b/1a, 1b offspring. The latter type also has a highly reduced fertility.This work was supported by grants from the Consejo Nacional de Investigaciones Científicas y Técnicas, the Comisión de Investigaciones Científicas de la Provincia de Buenos Aires and the Organización de Estados Americanos.     

Die Wirkung von Na3[Ca-DTPA] auf den Glykogengehalt von Niere und Leber der Ratte

Summary DTPA, a derivative of EDTA, in doses of 1, 2, 4, and 8 mmoles kg^–1/d ^–1 causes a histochemically detectable increase of glycogen in the kidneys and a decrease of glycogen in the liver of rats. Furthermore, a severe damage of the intestinal mucosa has been demonstrated; its possible relevance for the pathogenesis of the other findings is discussed.     

Heterogeneity of the Fourth International Standard for Insulin by gel-chromatography on sephadex

Resumen Se sometieron cristales del Cuarto Patrón Internacional de Insulina a gel-cromatografía por Sephadex. Se determinó que previa a la hormona, eluye una zona de proteínas de mayor peso molecular, cuya posición de elución corresponde a proinsulina y compuestos intermedios. Su área representa un 4.5% del área total. Se demuestra así la heterogeneidad de dichos cristales, y se sugiere que el Quinto Patrón sea sometido a gel-cromatografía durante su preparación. Este procedimiento daría a dicho Patrón una mayor homogeneidad y potencia.     

Pierre Duhem’s epistemic aims and the intellectual virtue of humility: a reply to Ivanova

David Stump (2007) has recently argued that Pierre Duhem can be interpreted as a virtue epistemologist. Stump’s claims have been challenged by Milena Ivanova (2010) on the grounds that Duhem’s ‘epistemic aims’ are more modest than those of virtue epistemologists. I challenge Ivanova’s criticism of Stump by arguing that she not distinguish between ‘reliabilist’ and ‘responsibilist’ virtue epistemologies. Once this distinction is drawn, Duhem clearly emerges as a ‘virtue-responsibilist’ in a way that complements Ivanova’s positive proposal that Duhem’s ‘good sense’ reflects a conception of the ‘ideal scientist’. I support my proposal that Duhem is a ‘virtue-responsibilist’ by arguing that his rejection of the possibility of our producing a ‘perfect theory’ reflects the key responsibilist virtue of ‘intellectual humility’.     

Über die Funktion der Lorenzinischen Ampullen der Selachier

Summary The afferent impulses from the ampullae ofLorenzini ofScyllium show, both in the intact animal and in the isolated preparation, a steady discharge at constant temperature with a frequency reaching a maximum at an average of 20° and decreasing continuously at higher and lower temperatures. The discharge stops between 5° and 30° on the average. Rapid cooling causes a temporary rise in frequency, while rapid warming causes a temporary drop in frequency. While the ampullae are not sensitive to a mechanical stimulus, they react definitely to a change in temperature of 0.05°C. The ampullae thus behave like the cold receptors of the homoiotherms.     

Künstliche Niere mit Kapillarsystem für den Stoffaustausch

Summary A particularly efficient removal of urea and similar substances by dialysis in an artificial kidney is obtained if both blood and dialyzing liquid are allowed to flow in countercurrent through channels a few hundredths of a mm thick and separated from each other by a membrane about 1/100 of a mm thick. In order practically to realize the flow required, about two thousand of these narrow channels, each of a length of about 2 cm, are arranged parallel to form a capillary net system.Four elements, each consisting of 2000 narrow channels, are needed in order to obtain a clearance of 80 ml/min. The quantity of blood needed to fill the elements is about 5 cm³ for each element.

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Vorgetragen am Kongress der «3^o riunioni medico chirurgiche internazionali», Turin 1957.     

Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Änderungen der Zellzyklusparameter chinesischer Hamsterfibroblasten unter chronischer Hypoxie,gemessen am Impulszytophotometer

Summary By means of a pulse cytophotometer, changes in the distribution of chronically hypoxic Chinese hamster cells in vitro in the different phases of the cell cycle, were measured. Within a few hours, the fraction of cells in G₂ phase and late S phase decreases to a value which is no longer measurable, indicating a partial synchronization in G₁ and early S phase.

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Wir danken Herrn Dr.W. Göhde, Münster, für wertvolle Hinweise zur Interpretation der impulszytophotometrischen Histogramme.     

Epstein-barr virus and inflammatory bowel disease

Zusammenfassung Die Häufigkeit und der Antikörpertiter gegen Epstein-Barr-Virus (EBV) wurde in Patienten mit Ulkus-Colitis und Crohn's Krankheit, eine granulomatische Abnormalität ähnlich zur Sarkoidose untersucht und normale Häufigkeit und Antikörpertiter gegen EBV bei ihnen gefunden.

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Supported by Research Contract No. NIH-69-2078 within the Special Virus Cancer Program of the National Cancer Institute, National Institutes of Health, USPHS, National Institutes of Health Grant No. AM 05126 and the National Foundation for Ileitis and Colitis, Inc., New York, New York.

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Dr.Grotsky is a recipient of a National Institutes of Health Graduate Training Grant in Gastroenterology, No. Am 05126.

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Dr.Hirshaut is a recipient of a National Cancer Institute Grant No. CA 08748 an a grant from the New York Cancer Research Institute.

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Dr.Glade is a recipient of a Research Career Development Award No. A1-46371 of the USPHS.     

The extracellular protease fromPseudomonas fluorescens

Summary An extracellular protease has been purified from cultures ofPseudomonas fluorescens. It is a metalloenzyme with a molecular weight of 37,000±3,700, able to digest casein, hemoglobin and gelatine.This work was supported by grants from the Consejo Nacional de Investig ciones Científicas y Técnicas de la República Argentina, and the Consejo de Investigaciones de la Universidad Nacional de Rosario. JJC is a member of the Carrera del Investigador Científico, and SMJ the recipient, of a schollarship, of the former institution.