The power of images: mathematics and metaphysics in Hobbes's optics

This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, ‘A Minute or First Draught of the Optiques’ (1646), and published in abridged version in De homine (1658). The paper suggests that Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbes's philosophy. The paper points to some difficulties in the thesis of Shapin and Schaffer, who presented geometry as a ‘paradigm’ for Hobbes's natural philosophy. It will be argued here that Hobbes's application of geometry to optics was dictated by his metaphysical and epistemological principles, not by a blind belief in the power of geometry. Geometry supported causal explanation, and assisted reason in making sense of appearances by helping the philosopher understand the relationships between the world outside us and the images it produces in us. Finally the paper broadly suggests how Hobbes's theory of images may have triggered, by negative example, the flourishing of geometrical optics in Restoration England.     

A remark on Fuchs’ Bayesian interpretation of quantum mechanics

Quantum mechanics is a theory whose foundations spark controversy to this day. Although many attempts to explain the underpinnings of the theory have been made, none has been unanimously accepted as satisfactory. Fuchs has recently claimed that the foundational issues can be resolved by interpreting quantum mechanics in the light of quantum information. The view proposed is that quantum mechanics should be interpreted along the lines of the subjective Bayesian approach to probability theory. The quantum state is not the physical state of a microscopic object. It is an epistemic state of an observer; it represents subjective degrees of belief about outcomes of measurements. The interpretation gives an elegant solution to the infamous measurement problem: measurement is nothing but Bayesian belief updating in a analogy to belief updating in a classical setting. In this paper, we analyze an argument that Fuchs gives in support of this latter claim. We suggest that the argument is not convincing since it rests on an ad hoc construction. We close with some remarks on the options left for Fuchs’ quantum Bayesian project.     

Incommensurabilities in the work of Thomas Kuhn

I distinguish between two ways in which Kuhn employs the concept of incommensurability based on for whom it presents a problem. First, I argue that Kuhn’s early work focuses on the comparison and underdetermination problems scientists encounter during revolutionary periods (actors’ incommensurability) whilst his later work focuses on the translation and interpretation problems analysts face when they engage in the representation of science from earlier periods (analysts’ incommensurability). Secondly, I offer a new interpretation of actors’ incommensurability. I challenge Kuhn’s account of incommensurability which is based on the compartmentalisation of the problems of both underdetermination and non-additivity to revolutionary periods. Through employing a finitist perspective, I demonstrate that in principle these are also problems scientists face during normal science. I argue that the reason why in certain circumstances scientists have little difficulty in concurring over their judgements of scientific findings and claims while in others they disagree needs to be explained sociologically rather than by reference to underdetermination or non-additivity. Thirdly, I claim that disagreements between scientists should not be couched in terms of translation or linguistic problems (aspects of analysts’ incommensurability), but should be understood as arising out of scientists’ differing judgments about how to take scientific inquiry further.     

Science, truth and history, part II. Metaphysical bolt-holes for the Sociology of Scientific Knowledge?

Historians of science have frequently sought to exclude modern scientific knowledge from their narratives. Part I of this paper, published in the previous issue, cautioned against seeing more than a literary preference at work here. In particular, it was argued—contra advocates of the Sociology of Scientific Knowledge (SSK)—that a commitment to epistemological relativism should not be seen as having straightforward historiographical consequences. Part II considers further SSK-inspired attempts to entangle the currently fashionable historiography with particular positions in the philosophy of science. None, I argue, is promising. David Bloor’s proposed alliance with scientific realism relies upon a mistaken view of contrastive explanation; Andrew Pickering’s appeal to instrumentalism is persuasive for particle physics but much less so for science as a whole; and Bruno Latour’s home-grown metaphysics is so bizarre that its compatibility with SSK is, if anything, a further blow to the latter’s plausibility.     

Reconsidering the Fresnel–Maxwell theory shift: how the realist can have her cake and EAT it too

This paper takes another look at a case study which has featured prominently in a variety of arguments for rival realist positions. After critically reviewing the previous commentaries of the theory shift that took place in the transition from Fresnel’s ether to Maxwell’s electromagnetic theory of optics, it will defend a slightly different reading of this historical case study. Central to this task is the notion of explanatory approximate truth, a concept which must be carefully analysed to begin with. With this notion properly understood, it will be finally argued, the popular Fresnel–Maxwell case study points towards a novel formulation of scientific realism.     

Scientific realism bit by bit: part I. Kitcher on reference

In this paper, I consider Kitcher’s (1993) account of reference for the expressions of past science. Kitcher’s case study is of Joseph Priestley and his expression ‘dephlogisticated air’. There is a strong intuitive case that ‘dephlogisticated air’ referred to oxygen, but it was underpinned by very mistaken phlogiston theory, so concluding either that dephlogisticated air referred straightforwardly or that it failed to refer both have unpalatable consequences. Kitcher argues that the reference of such terms is best considered relative to each token—some tokens refer, and others do not. His account thus relies crucially on how this distinction between tokens can be made good—a puzzle I call the discrimination problem. I argue that the discrimination problem cannot be solved. On any reading of Kitcher’s defence of the distinction, the grounds provided are either insufficient or illegitimate. On the first reading, Kitcher violates the principle of humanity by making Priestley’s referential success a matter of the mental contents of modern speakers. The second reading sidesteps the problem of beliefs by appealing to mind-independent facts, but I argue that these are insufficient to achieve reference because of the indeterminacy introduced by the qua problem. On the third and final reading, Priestley’s success is given by what he would say in counterfactual circumstances. I argue that even if there are facts about what Priestley would say, and there is reason for doubt, there is no motivation to think that such facts determine how Priestley referred in the actual world.     

Malaria prophylaxis in travellers: The current position

Summary Malaria prevention is a main challenge for physicians, nurses, health officers and tour operators. The attack rate of malaria in travellers is 1–10/10,000 departures, and the case fatality rate of imported malaria is around 0.5/100. Travellers should be informed about the risk they are going to take, how to protect against mosquito bites, about the antimalarials they will have to take and about what to do when a malaria breakthrough should occur.The 4-aminoquinolines (chloroquine, amodiaquine) remain the drug of choice for the prevention ofPlasmodium vivax and of sensitiveP. falciparum infections. The problem is to find an effective and safe drug combination for travellers to areas whereP. falciparum is either resistant to chloroquine, to Fansidar (the combination of pyrimethamine plus sulfadoxine) or to both. These travellers will probably best be protected by an individually tailored drug combination, which includes amodiaquine or mefloquine as baseline drugs, and a supplementation with Fansidar, Maloprim (the combination of pyrimethamine with dapsone), paludrine or an antibiotic.     

Kepler’s theory of the soul: a study on epistemology

Kepler is mainly known among historians of science for his astronomical theories and his approaches to problems having to do with philosophy of science and ontology. This paper attempts to contribute to Kepler studies by providing a discussion of a topic not frequently considered, namely Kepler’s theory of the soul, a general theory of knowledge whose central problem is what makes knowledge possible, rather than what makes knowledge true, as happens in the case of Descartes’s and Bacon’s epistemologies. Kepler’s theory consists of four issues: the theory of the different sorts of soul—that is, the human soul, the animal soul, the vegetable soul, and the Earth soul—concerning their faculties, the differences and the resemblances emerging among them, the relation they maintain with their own bodies and the world, and the distinction soul–world. The paper discusses these issues from a historical perspective, that is, it reconstructs the way they appear in three periods of Kepler’s career: the period prior to the publication of the Mysterium cosmographicum, the period from 1596 to 1611, and the period of the Harmonices mundi libri V. Finally, Kepler’s epistemology is briefly contrasted with Descartes’s and Bacon’s in order to suggest that Kepler’s could be seen as a third way to understand the philosophical origins of Modernity.     

Les manifestations électriques consensuelles de l'activité rétinienne chez l'homme (Electrorétinographie binoculaire)

Summary Binocular Electroretinography in man shows that the elective light-stimulation of one retina produces a normal Electroretinogramm at the stimulated, ipsilateral eye, furthermore a bioelectric consensual response at the contralateral eye. This latter response consists in a positive deflection, corresponding to increased electropositivity under the corneal electrode. A close synchronism exists between the consensual response and the secondary rise (c-potential) of the ipsilateral Electroretinogramm. The consensual response does not appear to be of pupillary or oculomotor origin, but can probably be identified with thec-potential, the significance of which will have to bee reexamined, as well as the problem of the efferent innervation of the retina.     

Insolubility of the quantum measurement problem for unsharp observables

The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this problem by eliminating idealizations from the characterization of measurement. We state and prove two ‘insolubility theorems’ that disappoint this hope. In both the initial state of the apparatus is taken to be mixed rather than pure, and the correlation of the object observable and the pointer observable is allowed to be imperfect. In the insolubility theorem for sharp observables, which is only a modest extension of previous results, the object observable is taken to be an arbitrary projection valued measure. In the insolubility theorem for unsharp observables, which is essentially new, the object observable is taken to be a positive operator valued measure. Both theorems show that the measurement problem is not the consequence of neglecting the ever-present imperfections of actual measurements.     

The theory theory thrice over: the child as scientist, Superscientist or social institution?

Alison Gopnik and Andrew Meltzoff have argued for a view they call the ‘theory theory’: theory change in science and children are similar. While their version of the theory theory has been criticized for depending on a number of disputed claims, we argue that there is a fundamental problem which is much more basic: the theory theory is multiply ambiguous. We show that it might be claiming that a similarity holds between theory change in children and (i) individual scientists, (ii) a rational reconstruction of a Superscientist, or (iii) the scientific community. We argue that (i) is false, (ii) is non-empirical (which is problematic since the theory theory is supposed to be a bold empirical hypothesis), and (iii) is either false or doesn't make enough sense to have a truth-value. We conclude that the theory theory is an interesting failure. Its failure points the way to a full, empirical picture of scientific development, one that marries a concern with the social dynamics of science to a psychological theory of scientific cognition.     

Das Parallelenproblem im Corpus Aristotelicum

Summary In the Corpus Aristotelicum are numerous items suggesting that the assertion of the fifth postulate in Euclid's Elements had been preceded by attempts to demonstrate this postulate itself, or some equivalent fundamental proposition, within the rigorous frame of Absolute Geometry in Bolyai's sense. Thus geometers contemporary with Aristotle tried to solve the problem which became known commonly in later centuries as the Problem of Parallels.Probably these geometers first attempted a direct solution. Only one text at our disposal supports this hypothesis: (1) Anal. Prior. 65 a 4–7. My analysis below in Chapter I shows that a mathematical meaning can be read from this somewhat obscure text only if it is interpreted as an allusion by Aristotle to those geometers who believe they are demonstrating, obviously in an absolute way, the proposition Elem. I 29, equivalent to the fifth postulate, but do not realize that in the process they are using lemmas which result themselves from the proposition to be demonstrated. Such a lemma would assert the uniqueness of the parallels, existence of which was shown in an absolute way in Elem. I 27. My conjecture and reconstruction afford a natural explanation for an inconsequence singular for Book I of the Elements, namely, the presence of the proposition Elem. I 31 in the purely Euclidean part of the book, in spite of the fact that the assertion merely repeats the absolute proposition Elem. I 27 without explicitly containing any Euclidean element.It is probable that the failure of these direct attempts led to an indirect approach to the problem through reductio ad absurdum of some hypothesis contrary to what was to become Postulate V or to some equivalent proposition. Numerous texts survive from which it is clear that geometers contemporary with Aristotle followed fairly far the consequences of an hypothesis contrary to the fifth postulate, obtaining important results which are partly identical with some theorems of Saccheri. Some of these texts attest first of all that what Saccheri called the Hypothesis of the Obtuse Angle had been stated in an independent and explicit way and that the fundamental result, identical with Prop. 14 of Saccheri's Euclides ab omni naevo vindicatus (1733), had been obtained, namely, that within Bolyai's Absolute Geometry this hypothesis leads to the remarkable formal contradiction that parallels intersect. This conclusion followed from two different formulations of the Obtuse Angle Hypothesis: (2) Anal. Prior. 66a 11–14, if the exterior angle (formed by a secant which intersects two parallel straight lines) is smaller than the interior angle (opposite and situated on the same side of the secant), and (3) 66a 14–15, if the sum of the angles in a triangle is greater than 2R. Finally, an item in (4) Ethica ad Eudemum 1222b 35–36 shows us that by investigating the Obtuse Angle Hypothesis, the Greek geometers also discovered the quadrilateral in which the sum of the angles is equal to 8R; this quadrilateral, which does not appear even in Saccheri's book, is the maximal quadrilateral of the Riemann geometry, a quadrilateral degenerated into a straight line closed upon itself (Chapter IV 20).Nowhere in the Corpus does the Hypothesis of the Acute Angle appear in an independent formulation. Nevertheless in (5) Anal. Poster. 90a 33–34 this Hypothesis is mentioned along with the other two: namely, Aristotle states that the essence of the triangle consists in the sum of its angles' being equal to, greater than or less than 2R (Chapter V 27). The formulation of the fifth postulate in the Elements allows greater probability to the conjecture of independent existence of the Acute Angle Hypothesis as well. Indeed, in its original formulation the fifth postulate is redundant, since it unnecessarily specifies in which of the half-planes (bounded by the secant) the intersection of the two straight lines occurs; this specification is itself a theorem. The Acute Angle Hypothesis must have been formulated not only symmetrically to (3) Anal. Prior. 66 a 14–15, that is, the sum of the angles of the triangle is less than 2R, as results from (5) Anal. Poster. 90 a 33–34, but also symmetrically to (2) Anal. Prior. 66 a 11–14. In the latter case the following final conclusion should have been reached in order to reduce to absurdity the Acute Angle Hypothesis: Two straight lines cut by a secant are incident if the sum of the interior angles (on the same side of the secant) is smaller than 2R, and the incidence occurs on that side of the secant where the sum of the angles is less than 2R. In the frame of the Acute Angle Hypothesis, this end conclusion is relevant only if this final specification (concerning the half-plane where the incidence occurs) is explicitly emphasised. According to my conjecture, it was precisely the practical impossibility of reaching this conclusion as a theorem of Absolute Geometry that later determined Euclid to transpose this decisive end conclusion from the Acute Angle Hypothesis, without changing its wording, and to include it among the postulates (Chapter II 13).A queer passage of Proklos (In primum Euclidis Elementorum, ed. Friedlein p. 368, 26–369, 1) in which the Acute Angle Hypothesis is presented in the form of a Zenonian paradox reinforces the conjecture that this hypothesis was studied independently by the ancient geometers (Chapter VI 33). Thus failure to solve the Problem of Parallels preceded not only the later Non-Euclidean geometry but also Euclidean geometry itself.The general undifferentiated Contra-Euclidean Hypothesis appears in the following form in all the other texts examined: The sum of the angles in the triangle is not equal to 2R. This hypothesis is nowhere qualified by Aristotle as being absurd or impossible: On the contrary, he takes it always as being just as much justified a priori as is the Euclidean theorem Elem. I 32 which contradicts it. For instance in (6) Anal. Poster. 93 a 33–35 Aristotle puts the problematical alternative: Which of the two propositions is right (or, which of the two constitutes the Logos, the raison d'être of the triangle), the one that states that the sum of the angles in the triangle is equal to 2R, or on the contrary, the one that states that the sum of the angles in the triangle is not equal to 2R (Chapter V 28)?In a number of texts the theorem Elem. I 32 itself and the general Contra-Euclidean Hypothesis are treated as being a sort of principle, and stress is laid on the idea that the logical consequences of each of these items invariantly preserve its specific (Euclidean or non-Euclidean) geometrical content [(7) 1187 a 35–38 (Chapter IV 18); (8) 1222 b 23–26 (Chapter IV 19); (9) 1187 b 1–2 (Chapter IV 18); (10) 1222 b 41–42 Chapter IV 21); (11) 1187 b 2–4 (Chapter IV 18)]; (12) Physica 200 a 29–30: If the sum of the angles in the triangle is not equal to 2R, then the principles of geometry cannot remain the same (Chapter V 25); (13) Metaph. 1052 a 6–7: It is impossible that the sum of the angles in the triangle be sometimes equal to 2R and sometimes not equal to 2R (Chapter V 24). Finally, the most important item of this sort is to be found in (14) De Caelo 281 b 5–7: If we accept as a starting hypothesis that it is impossible for the sum of the angles in the triangle to be equal to 2R, then the diagonal of the square is commensurable with its side (Chapter III).Another group of texts reveal Aristotle's attitude as regard these Contra-Euclidean theorems: (15) 1222 b 38–39 (Chapter IV 20); (16) 200 a 16–19 (Chapter VI 30); (17) 402 b 18–21 (Chapter VI 31); (18) 171 a 12–16 (Chapter VI 32); (19) 77 b 22–26 (Chapter V 26); (20) 101 a 15–17 (Chapter VI 31); (21) 76 b 39–77 a 3 (Chapter VI 31). These passages reveal Aristotle's conviction that these paradoxical Contra-Euclidean propositions (which cannot be annihilated by reductio ad absurdum) are nevertheless inacceptable as bad, probably because their graphical construction requires curved lines for representing the concept of straight lines.Finally, another group of texts show that Aristotle sensed in a way the necessity of adding to the foundations of Geometry a new postulate, from which the proposition Elem. I 32 should follow rigorously.

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Aram Frenkian zum Gedächtnis

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Vorgelegt von J. E. Hofmann     

They give you the keys and say ‘drive it!’ Managers, referred expertise, and other expertises

On the face of it, the directors of new large scientific projects have an impossible task. They have to make technical decisions about sciences in which they have never made a research contribution—sciences in which they have no contributory expertise. Furthermore, these decisions must be accepted and respected by the scientists who are making research contributions. The problem is discussed in two interviews conducted with two directors of large scientific projects. The paradox is resolved for the managers by their use of interactional and referred expertise. The same analysis might be applicable to management in general. An Appendix, co-authored with Jeff Shrager, compares the notion of referred expertise with contributory expertise.     

Between autobiography and reality: Popper's inductive years

On the basis of his unpublished thesis ‘Gewohnheit und Gesetzerlebnis in der Erziehung’ (1926–7) a historical reconstruction is given of the genesis of Popper's ideas on induction and demarcation which differs radically from his own account in Unended quest. It is shown not only that he wholeheartedly endorses inductive epistemology and psychology but also that his ‘demarcation’ criterion is inductivistic. Moreover it is shown that his later demarcation thesis arises not from his worries about, on the one hand, Marxism and psychoanalysis and, on the other hand, Einstein's physics, but rather from his urgent preoccupation with providing pedagogy with a psychological foundation, which has its sources in Karl Bühler's cognitive psychology as well as, surprisingly, Adler's Characterology. Aside from Adler some lesser known psychologists, such as Karl Groos, will also be seen to have played a formative role on Popper's early thinking.     

Geometry of Light and Shadow: Francesco Maurolyco (1494–1575) and the Pinhole Camera

In his Theoremata de lumine, et umbre (1521), Francesco Maurolyco (1494–1575) discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a framework based on Euclidean geometry in which he applied the rectilinear propagation of light to the casting of shadow on a screen behind a pinhole. We limit our discussion to the problem of how the image behind an aperture is formed, and follow the way Maurolyco combined theory with instrument to solve the problem of the projection of light through small apertures. We show that Maurolyco not only reformed the classical sources which, he thought, were no longer the authoritative code of textual knowledge, but also established with the dioptra a novel linkage of method, theory, and instrument. He thereby demonstrated the importance of optics to the science of astronomy.     

A Companion to the History of Science

Snell's law of refraction did not affect the study of optics until twenty‐five years after its publication in 1637 and by then its universality threatened to break down already. Two optical phenomena—colour dispersion and strange refraction—were discovered that did not conform to the sine law. In the early 1670s, Isaac Newton and Christiaan Huygens respectively investigated these phenomena. They tried to describe the irregular behaviour of light rays mathematically and to reconcile it with ordinary refraction. This paper discusses their investigations and aims at throwing new light on the history of seventeenth‐century optics. Both initially approached the problem in a mathematical way in which they built on Descartes' analysis of refraction. This is surprising because it contradicts their earlier dismissal of Descartes' account and it does not fit our picture of them as mathematical physicists. By looking more closely at their early investigations it becomes clear that Newton and Huygens first had to develop the approach to optics of their later writings. After Descartes placed the issue of the physical nature of light rays on the scientific agenda in 1637, they recognized its purport in their struggles with colour dispersion and strange refraction. It was at this point that their physical optics evolved from the traditional geometrical optics with which they had started.     

Rotationssinn nach dem Bogengangsprinzip bei Crustaceen

Summary Blinded crabs (Carcinus maenas andMaja verrucosa) show compensatory eye stalk movements on rotation about a vertical axis, in water and in air. On a sudden arrest of the turntable typical after-effects are observed, which show a striking resemblance to those known from vertebrates. All these reactions are abolished after bilateral elimination of the so-called thread hairs within the statocysts (experiments onMaja). In fresh preparations these hairs can be seen to follow the slightest movements of the surrounding fluid, swaying around their point of attachment.Elimination of the thread hairs does not diminish, but does markedly delay the compensatory eye stalk movements of a blinded crab on rotation about horizontal axes. The latter reactions are abolished if in addition the hook hairs (i.e. the sense hairs of the statolith-bearing type) are destroyed.It is concluded that the statocyst of crabs is a staticdynamic sense organ: the hook hairs are position receptors, the thread hairs react to angular displacements about all three main body axes; the group hairs may have no sensory function at all.Rotation sense may be expected to occur in other Crustacea possessing thread hairs or similar receptors in their statocysts as well.     

The development of the Neurath principle: unearthing the Romantic link

Otto Neurath’s thoroughgoing anti-foundationalism is connected to the recognition that protocol sentences are not inviolable, that is they are fallible and their choice cannot be determined: ‘Poincaré, Duhem and others have adequately shown that even if we have agreed on the protocol statements, there is a not limited number of equally applicable, possible systems of hypotheses. We have extended this tenet of the uncertainty of systems of hypotheses to all statements, including protocol statements that are alterable in principle’ (Neurath, 1983, p. 105). Later historiography has called Neurath’s extension of Duhemian holism the Neurath principle. Based on a study of Neurath’s early works on the history of optics, the paper investigates a previously unnoticed influence on the development of this principle, Neurath’s reading of Goethe’s Theory of colours. The historical and polemical parts of Goethe’s tripartite book provided Neurath with ideal examples for the vertical extension of Duhem’s thesis to observation statements. Moreover, Goethe’s critique of the language of science and his views on the theory-ladenness of observation, as well as on the history of science show strong parallels to many of Neurath’s ideas. These demonstrate the existence of surprisingly direct textual links between Romantic views on science and the development of twentieth-century philosophy of science. Neurath’s usage of Goethe’s examples also indicates that the birth of the Neurath principle is more tightly connected to actual scientific practice than to theory-testing, and that by admitting the theory-ladenness of observation reports and fallibility of protocol statements Neurath does not throw empiricism overboard.     

Galileo as a ‘bad theologian’: a formative myth about Galileo’s trial

For 150 years after Galileo’s condemnation in 1633, there were many references to the trial, but no sustained, heated or polarized discussions. Then came the thesis that Galileo was condemned not for being a good astronomer but for being a bad theologian (using Scripture to support astronomical hypotheses); it began in 1784–1785 with an apology of the Inquisition by Mallet du Pan in the Mercure de France and the printing in Tiraboschi’s Storia della letteratura italiana of an apocryphal letter attributed to Galileo but forged by Onorato Gaetani. This thesis is not only untenable and false but inverts and subverts the truth; it proved to be long-lasting and widely accepted; so it may be labeled a myth. It was held by such writers as Bergier; Bergier; B; Feller; Cooper; Purcell; Marini; Reumont; Madden and Duhem. Afterwards, it was generally abandoned, its death knell being pope John Paul II’s speeches in 1979–1992. The myth seems to have acted as a catalyst insofar as its creation encouraged the proliferation of pro-clerical accounts and the articulation of pro-Galilean ones, thus making the discussion of Galileo’s trial the cause célèbre it is today.