Galileo’s quanti: understanding infinitesimal magnitudes

In On Local Motion in the Two New Sciences, Galileo distinguishes between ‘time’ and ‘quanto time’ to justify why a variation in speed has the same properties as an interval of time. In this essay, I trace the occurrences of the word quanto to define its role and specific meaning. The analysis shows that quanto is essential to Galileo’s mathematical study of infinitesimal quantities and that it is technically defined. In the light of this interpretation of the word quanto, Evangelista Torricelli’s theory of indivisibles can be regarded as a natural development of Galileo’s insights about infinitesimal magnitudes, transformed into a geometrical method for calculating the area of unlimited plane figures.     

Reconstructing Thomist astrology: Robert Bellarmine and the papal bull Coeli et terrae*

ABSTRACT

Historians have portrayed the papal bull Coeli et terrae (1586) as a significant turning point in the history of the Catholic Church’s censorship of astrology. They argue that this bull was intended to prohibit the idea that the stars could naturally incline humans towards future actions, but also had the effect of preventing the discussion of other forms of natural astrology including those useful to medicine, agriculture, and navigation. The bull, therefore, threatened to overturn principles established by Thomas Aquinas, which not only justified long-standing astrological practices, but also informed the Roman Inquisition’s attitude towards this art. The promulgation of the bull has been attributed to the ‘rigour’ of the incumbent pope, Sixtus V. In this article I revise our understanding of this bull in two ways. First, I reconsider the Inquisition’s attitude towards astrology in the mid-sixteenth century, arguing that its members promoted a limited form of Thomist astrology that did not permit the doctrine of inclination. Second, using Robert Bellarmine’s unpublished lectures discussing Aquinas’s views of astrology, I suggest that this attitude was common during the sixteenth century, and may have been caused by the crisis of Renaissance astrology precipitated by the work of Giovanni Pico.     

Knowing what would happen: The epistemic strategies in Galileo's thought experiments

While philosophers have subjected Galileo's classic thought experiments to critical analysis, they have tended to largely ignored the historical and intellectual context in which they were deployed, and the specific role they played in Galileo's overall vision of science. In this paper I investigate Galileo's use of thought experiments, by focusing on the epistemic and rhetorical strategies that he employed in attempting to answer the question of how one can know what would happen in an imaginary scenario. Here I argue we can find three different answers to this question in Galileo later dialogues, which reflect the changing meanings of ‘experience’ and ‘knowledge’ (scientia) in the early modern period. Once we recognise that Galileo's thought experiments sometimes drew on the power of memory and the explicit appeal to ‘common experience’, while at other times, they took the form of demonstrative arguments intended to have the status of necessary truths; and on still other occasions, they were extrapolations, or probable guesses, drawn from a carefully planned series of controlled experiments, it becomes evident that no single account of the epistemological relationship between thought experiment, experience and experiment can adequately capture the epistemic variety we find Galileo's use of imaginary scenarios. To this extent, we cannot neatly classify Galileo's use of thought experiments as either ‘medieval’ or ‘early modern’, but we should see them as indicative of the complex epistemological transformations of the early seventeenth century.     

Chemist,entomologist, Darwinian,and man of affairs: Raphael Meldola and the making of a scientific career

In 1925 a debate erupted in the correspondence columns of the British Medical Journal concerning the effectiveness of eating raw pancreas as a treatment for diabetes. Enthusiasts were predominantly general practitioners (GPs), who claimed success for the therapy on the basis of their clinical impressions. Their detractors were laboratory‐oriented ‘biochemist‐physicians,’ who considered that their own experiments demonstrated that raw pancreas therapy was ineffective. The biochemist‐physicians consistently dismissed the GPs' observations as inadequately ‘controlled’. They did not define the meaning of ‘control’ in this context, although it clearly did not have the term's present‐day meaning of a trial employing an untreated comparison group of patients. Rather, the physician‐biochemists' ‘properly controlled’ experiments involved careful regulation of their patients' diet and other environmental factors, and evaluation of the therapy's success through biochemical, rather than just clinical, criteria. However, my analysis suggests that these factors alone are inadequate to account for the biochemist‐physicians' dismissal of the GPs' work as ‘uncontrolled’. I suggest that the biochemist‐physicians were deliberately exploiting the powerful rhetorical connotations of the term ‘control’. Ultimately, they implied that only a trial which they themselves had conducted could be deemed ‘adequately controlled’.     

Aristotle, Copernicus, Bruno: centrality, the principle of movement and the extension of the Universe

This paper¹ studies the different conceptions of both centrality and the principle or starting point of motion in the Universe held by Aristotle and later on by Copernicanism until Kepler and Bruno. According to Aristotle, the true centre of the Universe is the sphere of the fixed stars. This is also the starting point of motion. From this point of view, the diurnal motion is the fundamental one. Our analysis gives pride of place to De caelo II, 10, a chapter of Aristotle’s text which curiously allows an ‘Alpetragian’ reading of the transmission of motion.In Copernicus and the Copernicans, natural centrality is identified with the geometrical centre and, therefore, the Sun is acknowledged as the body through which the Deity acts on the world and it also plays the role of the principle and starting point of cosmic motion. This motion, however, is no longer diurnal motion, but the annual periodical motion of the planets. Within this context, we pose the question of to what extent it is possible to think that, before Kepler, there is a tacit attribution of a dynamic or motive role to the Sun by Copernicus, Rheticus, and Digges.For Bruno, since the Universe is infinite and homogeneous and the relationship of the Deity with it is one of indifferent presence everywhere, the Universe has no absolute centre, for any point is a centre. By the same token, there is no place that enjoys the prerogative of being—as being the seat of God—the motionless principle and starting point of motion.     

Rome and Theistic Evolutionism: The Hidden Strategies behind the ‘Dorlodot Affair’, 1920–1926

In 1918, Henry de Dorlodot—priest, theologian, and professor of geology at the University of Louvain (Belgium)—published Le Darwinisme au point de vue de l'Orthodoxie Catholique (translated as Darwinism and Catholic Thought) in which he defended a reconciliation between evolutionary theory and Catholicism with his own particular kind of theistic evolutionism. He subsequently announced a second volume in which he would extend his conclusions to the origin of Man. Traditionalist circles in Rome reacted vehemently. Operating through the Pontifical Biblical Commission, they tried to force Dorlodot to withdraw his book and to publicly disown his ideas by threatening him with an official condemnation, a strategy that had been used against Catholic evolutionists since the late nineteenth century. The archival material on the ‘Dorlodot affair’ shows how this policy ‘worked’ in the early stages of the twentieth century but also how it would eventually reach the end of its logic. The growing popularity of theistic evolutionism among Catholic intellectuals, combined with Dorlodot's refusal to pull back amidst threats, made certain that the traditionalists did not get their way completely, and the affair ended in an uncomfortable status quo. Dorlodot did not receive the official condemnation that had been threatened, nor did he withdraw his theories, although he stopped short on publishing on the subject. With the decline of the traditionalists’ power and authority, the policy of denunciation towards evolutionists made way for a growing tolerance. The ‘Dorlodot affair’—which occurred in a pivotal era in the history of the Church—can be seen as exemplary with regards to the changing attitude of the Roman authorities towards evolutionism in the first half of the twentieth century.     

Editing Newton in Geneva and Rome: The Annotated Edition of the Principia by Calandrini,Le Seur and Jacquier

This contribution examines the circumstances of composition of the annotated edition of Newton's Principia that was printed in Geneva in 1739–1742, which ran to several editions and was still in print in Britain in the mid-nineteenth century. This edition was the work of the Genevan Professor of Mathematics, Jean Louis Calandrini, and of two Minim friars based in Rome, Thomas Le Seur and François Jacquier. The study of the context in which this edition was conceived sheds light on the early reception of Newtonianism in Geneva and Rome. By taking into consideration the careers of Calandrini, Le Seur and Jacquier, as authors, lecturers and leading characters of Genevan and Roman cultural life, I will show that their involvement in the enterprise of annotating Newton's Principia answered specific needs of Genevan and Roman culture. The publication and reception of the Genevan annotated edition has also a broader European dimension. Both Calandrini and Jacquier were in touch with the French république des lettres, most notably with Clairaut and Du Châtelet, and with the Bernoulli family in Basel. Therefore, this study is also relevant for the understanding of the dissemination of Newton's ideas in Europe.     

Jewish theologies of space in the scientific revolution: Henry More,Joseph Raphson,Isaac Newton and their predecessors

Theological speculations on God's relation to place and space were introduced into the Jewish tradition by the early rabbis, initially in response to the previous appearance of words like māqôm (place) in Biblical literature. In the Middle Ages, Jewish philosophers modified these rabbinical ideas in the context of Aristotelian, Neoplatonic, and anti-Aristotelian currents within Jewish thought. One development in medieval Jewish thought of special interest for the development of ideas of space was the rise of Cabala, which Christian thinkers of the Renaissance and early modern periods saw as a sacred and primeval deposit of wisdom akin to prisca theologia. Both Henry More and, under More's influence, Joseph Raphson made use of Cabalist ideas in developing their own theologies of space. Isaac Newton was aware of these Jewish ideas but for the most part repudiated them, while making some use of māqôm as an expression of God's omnipresence.     

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.     

The Replication of Hertz's Cathode Ray Experiments

I reappraise in detail Hertz's cathode ray experiments. I show that, contrary to Buchwald's (1995) evaluation, the core experiment establishing the electrostatic properties of the rays was successfully replicated by Perrin (probably) and Thomson (certainly). Buchwald's discussion of ‘current purification’ is shown to be a red herring. My investigation of the origin of Buchwald's misinterpretation of this episode reveals that he was led astray by a focus on what Hertz ‘could do’—his experimental resources. I argue that one should focus instead on what Hertz wanted to achieve—his experimental goals. Focusing on these goals, I find that his explicit and implicit requirements for a successful investigation of the rays’ properties are met by Perrin and Thomson. Thus, even by Hertz's standards, they did indeed replicate his experiment.     

Giordano Bruno and the heresy of many worlds

This paper analyses the importance of Giordano Bruno's belief in many worlds, including the Moon, the planets and the stars, in the context of his trial by the Inquisitions in Venice and Rome. Historians have claimed that this belief was not heretical and therefore was not a major factor in Bruno's trial or execution. On the contrary, by examining neglected treatises on theology, heresies and Catholic canon law, I show that the belief in many worlds was formally heretical. Multiple Christian authorities denounced it. A systematic analysis of the extant primary sources shows that Bruno's belief in many worlds was, surprisingly, of primary importance in his trial and execution. The evidence includes recent and newly discovered primary sources.     

Alexis Fontaine's ‘Fluxio-differential method’ and the origins of the calculus of several variables

Alexis Fontaine des Bertins (1704–1771) was the first French mathematician to introduce what we would now regard as results in the calculus of several variables. One example is Fontaine's theorem nF = (?F/?x)x + (?F/?y)y of 1737 for homogeneous expressions F of degree n in x and y. Many years later Fontaine indicated this particular result to have been ‘a continuation of the method of solution’ introduced by him in 1734 to solve the problem of the tautochrones. It is tempting to disregard this announcement, since the method applied to the tautochrones was a method of variations and not manifestly an exercise in the calculus of several variables. Do we have just another case of a mathematician's confusion about the origins of his earlier work? In this paper I describe Fontaine's possible intentions in his remarks.     

Henry Dresser and Victorian Ornithology: Birds,Books and Business

The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. Part I of this paper contains a discussion of how, for Kepler, the circle also functions in geometry to select the basic polygons, in music to select the basic harmonies, and in astrology to select the basic aspects. In Part II, the discussion centres on the question of how the replacement of circular planetary orbits by elliptical orbits in the Astronomia Nova of 1609 affected Kepler's metaphysical commitment to celestial circularity that was made manifest in the derivation of planetary radii in the Mysterium Cosmographicum of 1596. The answer is found in the new and much more accurate derivation of both the planetary radii and their eccentricities in the Harmonice Mundi of 1619. It is the relationship of the diurnal movements of single planets at aphelion and perihelion to specific musical consonances that provides the first step. Then, in the second step, these ratios are ‘tempered’ so that all six planets can provide a heavenly choir. The third and final step employs the ‘mean period’, which is obtained directly from the tempered ratios given by musical theory and diurnal (not annual) motion, in the 3/2 power law to calculate the planetary radii and eccentricities with amazing accuracy. Thus the ellipse is necessary to supply the variation in angular velocities that contain the Creator's archetypal celestial circularity.     

The rise of western rationalism: Paul Feyerabend's story

I summarize certain aspects of Paul Feyerabend's account of the development of Western rationalism, show the ways in which that account is supposed to run up against an alternative, that of Karl Popper, and then try to give a preliminary comparison of the two. My interest is primarily in whether what Feyerabend called his ‘story’ constitutes a possible history of our epistemic concepts and their trajectory. I express some grave reservations about that story, and about Feyerabend's framework, finding Popper's views less problematic here. However, I also suggest that one important aspect of Feyerabend's material, his treatment of religious belief, can be given an interpretation which makes it tenable, and perhaps preferable to a Popperian approach.     

Hobbes on natural philosophy as “True Physics” and mixed mathematics

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the ‘why’ in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience.     

Galilean argumentation and the inauthenticity of the Cigoli letter on painting vs. sculpture

This essay is partly a case study of the role of logic in historiography. It is also partly a test case for the thesis of a Galilean correspondence between aesthetic attitude and scientific thought, advanced by Panofsky, Koyré, and Heilbron. Intrinsically, it is a discussion of the authenticity of the letter to Cigoli dated 26 June 1612, widely attributed to Galileo, containing argumentation about the relative aesthetic merits of painting and sculpture. I undertake a systematic analysis of the letter’s method of argument, comparing and contrasting it with Galileo’s. I argue that the letter does have some Galilean characteristics: critical reasoning; ad hominem argumentation, in the seventeenth-century sense; and appeal to experimentation. However, the letter falls short of the typical Galilean open-mindedness, fair-mindedness, and clarity; crucially, it uses several illative terms which Galileo never uses, and does not use the one he uses most often. The latter features outweigh the former. Moreover, I discuss some aspects of the letter’s substantive content, primarily a theory of vision that disregards the dynamics of perspective and the faculty of binocularity, which Galileo understood and exploited very well. My novel argument vindicates an old judgment of Favaro, who doubted the letter’s authenticity.     

Savant Officials in the Prussian Mining Administration

Summary

In the second half of the eighteenth century, the Prussian State supported savants who combined learned inquiry into nature with technical work. Members of the physical and mathematical classes of the Royal Prussian Academy of Sciences were involved in State projects such as surveying for the construction of canals, chemical analysis of Silesian iron, production of porcelain and of beet sugar. Some of these men were truly ‘hybrid’ experts living both in the worlds of State-directed manufacture and academic natural inquiry. Among these savant experts there was a particular sub-group that is at the centre of this paper: mining officials who were also recognized as mineralogists, geologists and chemists. The paper describes and analyses the training and the varied technical and scientific activities of these ‘savant officials’. At the centre of attention are the travels of inspection of the mineralogist and mining official Carl Abraham Gerhard (1738–1821) in the late 1760s. I argue that Gerhard's travels of inspection were at the same time geological travels and that savant officials like Gerhard made a significant contribution to the fledgling science of geology.     

James geikie,james croll,and the eventful ice age

James Geikie's Great Ice Age (1874) first presented to the geological public the Pleistocene. modern interpretation of alternating mild and cold periods during the Though it was supported by geological evidence, Geikie's view of the Ice Age was based on a theoretical framework supplied by the climatic physics of James Croll. Mid-nineteenth-century British geologists had encountered great difficulty in making sense out of the varied and complicated glacial deposits, or ‘drift’, and had formulated the ‘iceberg’ theory to account for the apparent chaos of the drift, an explanation which discouraged its stratigraphic study. The reaffirmation of faith in continental glaciation by several Scottish geologists in the 1850s brought with it a belief in an eventful Pleistocene, but it remained difficult to discover the events of Ice Age history from study of the glacial deposits. In 1864 Croll presented a detailed climatic history of the Ice Age deduced from astronomy and physical geography. By 1871 James Geikie was using Croll's scheme of Ice Age history as the basis for his impressive synthesis of Pleistocene data from throughout the world.     

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.