Different shades of Newton: Herman Boerhaave on Newton mathematicus,philosophus, and optico-chemicus

In this paper I will probe into Herman Boerhaave's (1668–1738) appropriation of Isaac Newton's natural philosophy. It will be shown that Newton's work served multiple purposes in Boerhaave's oeuvre, for he appropriated Newton's work differently in different contexts and in different episodes in his career. Three important episodes in, and contexts of, Boerhaave's appropriation of Newton's natural philosophical ideas and methods will be considered: 1710–11, the time of his often neglected lectures on the place of physics in medicine; 1715, when he delivered his most famous rectorial address; and, finally, 1731/2, in publishing his Elementa chemiae. Along the way, I will spell out the implications of Boerhaave's case for our understanding of the reception, or use, of Newton's ideas more generally.     

Science,self improvement and the first industrial revolution

This study considers Newton's views on space and time with respect to some important ontologies of substance in his period. Specifically, it deals in a philosophico-historical manner with his conception of substance, attribute, existence, to actuality and necessity. I show how Newton links these “features” of things to his conception of God's existence with respect of infinite space and time. Moreover, I argue that his ontology of space and time cannot be understood without fully appreciating how it relates to the nature of Divine existence. In order to establish this, the ontology embodied in Newton's theory of predication is analysed, and shown to be different from the presuppositions of the ontological argument. From the historical point of view Gassendi's influence is stressed, via the mediation of Walter Charleton. Furthermore, Newton's thought on these matters is contrasted with Descartes's and Spinoza's. In point of fact, in his earliest notebook Newton recorded observations on Descartes's version of the ontological argument. Soon, however, he was to oppose the Cartesian conception of the actuality of Divine existence by means of arguments similar to those of Gassendi. Lastly, I suggest that the nature and extent of Henry More's influence on Newton's conception of how God relates to absolute space and time bears further examination.     

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.     

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.     

Leonhard Euler's ‘anti-Newtonian’ theory of light

Leonhard Euler was the leading eighteenth-century critic of Isaac Newton's projectile theory of light. Euler's main criticisms of Newton's views are surveyed, and also his alternative account according to which light is a wave motion propagated through the aether. Important changes are identified as having occurred between 1744 and 1746 in Euler's thinking about the way in which a wave such as he supposed light to be is propagated through a medium. Paradoxically, in view of Euler's overtly anti-Newtonian stand, these amount to Euler abandoning his early, Malebranchian notions about the physical basis of wave propagation, in favour of the ideas set out by Newton in Book II of his Principia.     

Charles de Bovelles's treatise on the regular polyhedra (Paris, 1511)

The mathematical works of the French philosopher Charles de Bovelles (c. 1479–1566) have received little attention from historians of scientific thought. At the University of Paris, Bovelles studied under Jacques Lefèvre d'Étaples, sharing with him a high regard for the Christian Neoplatonic philosophy of Nicholas of Cusa. One aspect of Cusanus's philosophy (described in his major work, On Learned Ignorance) was particularly favoured by Lefèvre and Bovelles: the use of geometrical symbolism to provide mathematical guidance to the divine. While Lefèvre was preparing an edition of Cusanus's works (Paris, 1514), Bovelles wrote a treatise of his own, in which the geometry of the five polyhedra was used to provide an approach to the mystery of the Trinity. Seen in the context of Renaissance syncretism of Platonism and Christianity, Bovelles's treatise adds a theological layer of interpretation to the literal meaning of the polyhedral physics described by Plato in the Timaeus. In so doing, it contributes to the discussion of a problem that was later to concern several Renaissance philosophers and cosmologists, including, at the end of the century, Johannes Kepler.     

The Jalālī Calendar: the enigma of its radix date

The Jalālī (or Malikī) Calendar is well known to Iranian and Western researchers. It was established by the order of Sulṭān Jalāl al-Dīn Malikshāh-i Saljūqī in the 5th c. A.H. (The dates which are designated with A.H. indicate the Hijrī Calendar.)/11th c. A.D. in Isfahan. After the death of Yazdigird III (the last king of the Sassanid dynasty), the Yazdigirdī Calendar, as a solar one, gradually lost its position, and the Hijrī Calendar replaced it. After the rise of Islam, nonetheless, Iranians preferred various solar calendars to the Hijrī one. The Jalālī Calendar must be considered the culmination of such efforts. The present article deals with the riddle of the radix date (epoch) of the Jalālī Calendar. The author examines the problem through a historical approach and provides a novel solution to the question.

     

Between Viète and Descartes: Adriaan van Roomen and the <Emphasis Type="Italic">Mathesis Universalis</Emphasis>

Adriaan van Roomen published an outline of what he called a Mathesis Universalis in 1597. This earned him a well-deserved place in the history of early modern ideas about a universal mathematics which was intended to encompass both geometry and arithmetic and to provide general rules valid for operations involving numbers, geometrical magnitudes, and all other quantities amenable to measurement and calculation. ‘Mathesis Universalis’ (MU) became the most common (though not the only) term for mathematical theories developed with that aim. At some time around 1600 van Roomen composed a new version of his MU, considerably different from the earlier one. This second version was never effectively published and it has not been discussed in detail in the secondary literature before. The text has, however, survived and the two versions are presented and compared in the present article. Sections 1–6 are about the first version of van Roomen’s MU the occasion of its publication (a controversy about Archimedes’ treatise on the circle, Sect. 2), its conceptual context (Sect. 3), its structure (with an overview of its definitions, axioms, and theorems) and its dependence on Clavius’ use of numbers in dealing with both rational and irrational ratios (Sect. 4), the geometrical interpretation of arithmetical operations multiplication and division (Sect. 5), and an analysis of its content in modern terms. In his second version of a MU van Roomen took algebra into account, inspired by Viète’s early treatises; he planned to publish it as part of a new edition of Al-Khwarizmi’s treatise on algebra (Sect. 7). Section 8 describes the conceptual background and the difficulties involved in the merging of algebra and geometry; Sect. 9 summarizes and analyzes the definitions, axioms and theorems of the second version, noting the differences with the first version and tracing the influence of Viète. Section 10 deals with the influence of van Roomen on later discussions of MU, and briefly sketches Descartes’ ideas about MU as expressed in the latter’s Regulae.     

From Helmholtz to Schlick: The evolution of the sign-theory of perception

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zur?ck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his ‘method of coincidences’, similar to the ‘point-coincidences’ featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism.     

Kant and the scope of the analytic method

The paper investigates Kant's pre-critical views on the use of analytic and synthetic methods in Newtonian science and in philosophical reasoning. In his 1755/56 writings, Kant made use of two variants of the analytic method, i.e., conceptual analysis in a Cartesian (or Leibnizean) sense, and analysis of the phenomena in a Newtonian sense. His Prize Essay (1764) defends Newton's analytic method of physics as appropriate for philosophy, in contradistinction to the synthetic method of mathematics. A closer look, however, shows that Kant does not identify Newton's method with conceptual analysis, but just suggests a methodological analogy between both methods. Kant’s 1768 paper on incongruent counterparts also fits in with his pre-critical use of conceptual analysis. Here, Kant criticizes Leibniz’ relational concept of space, arguing that it is incompatible with the phenomenon of chiral objects. Since this result was in conflict with his pre-critical views about space, Kant abandoned the analytic method of philosophy in favour of his critical method. The paper closes by comparing Kant's pre-critical analytic method and the way in which he once again took up the methodological analogy between Newtonian science and metaphysics, in the preface B to the Critique of Pure Reason, in the context of his thought experiment of pure reason.     

Jean-François Pilˆatre de Rozier

A translation of Kant's early paper, ‘Die Frage, ob die Erde veralte, physikalisch erwogen’ (‘The question, whether the Earth is ageing, considered physically’) is presented, and the main features of his position on this question in 1754 are summarized. In that year, Kant believed that the Earth was ageing, and that it was about 6000 years old. The paper allows us to understand the approximate outline of Kant's general ‘theory of the Earth’, and the relation of this theory to the cosmogony that he propounded in 1755. His ideas on the processes of erosion, and the formation of rivers, deltas and sandbanks, are noteworthy, and provide a contribution to the eighteenth-century literature on the denudation dilemma. Kant's general theory of erosion and deposition was, it seems, based to a significant extent on his knowledge of the geographical features of the Königsberg district. The general teleological position underpinning his philosophy may be discerned in this early paper, and he may be thought of as having been trying to orientate himself in space and time, so to speak, before undertaking his major reconstructions in philosophy.     

Realism,functions, and the a priori: Ernst Cassirer's philosophy of science

This paper presents the main ideas of Cassirer's general philosophy of science, focusing on the two aspects of his thought that—in addition to being the most central ideas in his philosophy of science—have received the most attention from contemporary philosophers of science: his theory of the a priori aspects of physical theory, and his relation to scientific realism.     

Visiting Newton's atelier before the Principia, 1679–1684

The worksheets that presumably contained Newton's early development of the fundamental concepts in his Principia have been lost. A plausible reconstruction of this development is presented based on Newton's exchange of letters with Robert Hooke in 1679, with Edmund Halley in 1686, and on some clues in the diagram associated with Proposition 1 in Book 1 of the Principia that have been ignored in the past. A graphical construction associated with this proposition leads to a rapidly convergent method to obtain orbits for central forces, which elucidates how Newton may have have been led to formulate some of his most fundamental propositions in the Principia.     

Physical,Human and Divine attraction in the life and thought of George Cheyne

This paper is a study of the mental environment of the Newtonian conception of attraction in the case of George Cheyne, M.D. (1671–1743), physician of the early 18th century and author of a number of popular medical works. It traces the growth of his notions of a spiritual attraction between God and his creatures and between the creatures themselves, and the relation of these ideas both to his use of the Newtonian model of short-range attraction, and to his conception of the creatures as reflections of the divine essence. The paper contends that the development of these aspects of Cheyne's thought harmonizes with the changing pattern of his life, and that this harmony is expressed by his general technique of reasoning by analogy between the various spheres of experience.     

Zweideutigkeit about “Zweideutigkeit”: Sommerfeld,Pauli, and the methodological origins of quantum mechanics

In early 1925, Wolfgang Pauli (1900–1958) published the paper for which he is now most famous and for which he received the Nobel Prize in 1945. The paper detailed what we now know as his “exclusion principle.” This essay situates the work leading up to Pauli's principle within the traditions of the “Sommerfeld School,” led by Munich University's renowned theorist and teacher, Arnold Sommerfeld (1868–1951). Offering a substantial corrective to previous accounts of the birth of quantum mechanics, which have tended to sideline Sommerfeld's work, it is suggested here that both the method and the content of Pauli's paper drew substantially on the work of the Sommerfeld School in the early 1920s. Part One describes Sommerfeld's turn away from a faith in the power of model-based (modellmässig) methods in his early career towards the use of a more phenomenological emphasis on empirical regularities (Gesetzmässigkeiten) during precisely the period that both Pauli and Werner Heisenberg (1901–1976), among others, were his students. Part two delineates the importance of Sommerfeld's phenomenology to Pauli's methods in the exclusion principle paper, a paper that also eschewed modellmässig approaches in favour of a stress on Gesetzmässigkeiten. In terms of content, a focus on Sommerfeld's work reveals the roots of Pauli's understanding of the fundamental Zweideutigkeit (ambiguity) involving the quantum number of electrons within the atom. The conclusion points to the significance of these results to an improved historical understanding of the origin of aspects of Heisenberg's 1925 paper on the “Quantum-theoretical Reformulation (Umdeutung) of Kinematical and Mechanical Relations.”     

Poinsinet's Edition of the Naturalis historia (1771–1782) and the Revival of Pliny in the Sciences of the Enlightenment

This paper analyses the revival of Pliny's Naturalis historia within the scientific culture of the late eighteenth and early nineteenth centuries, focusing on a French effort to produce an edition with annotations by scientists and scholars. Between the Renaissance and the early eighteenth century, the Naturalis historia had declined in scientific importance. Increasingly, it was relegated to the humanities, as we demonstrate with a review of editions. For a variety of reasons, however, scientific interest in the Naturalis historia grew in the second half of the eighteenth century. Epitomizing this interest was a plan for a scientifically annotated, Latin-French edition of the Naturalis historia. Initially coordinated by the French governmental minister Malesherbes in the 1750s, the edition was imperfectly realized by Poinsinet a few decades later. It was intended to rival two of the period's other distinguished multi-volume books of knowledge, Diderot and D'Alembert's Encyclopédie and Buffon's Histoire naturelle, to which we compare it. Besides narrating the scientific revival of the Historia naturalis during this period, we examine its causes and the factors contributing to its end in the first half of the nineteenth century.     

Social Darwinism and constitutional law with special reference to Lochner v. New York

American historians have generally accepted Richard Hofstadter's thesis that the scientism of Social Darwinism, or more appropriately, Spencerianism, dominated American thought in the late nineteenth and early twentieth century, and nowhere more enthusiastically or more purposively than within the conservative business community, which used Herbert Spencer's scientism to justify corporate business practices and to rewrite American Constitutional law to protect property interests against governmental regulations. Following Sharlin's general exposition of Herbert Spencer's scientism, this paper examines in detail the validity of the Hofstadter thesis as applied to the notorious Lochner v. New York Supreme Court opinion of 1905. The conclusions drawn from this analysis are offered as a repudiation of the generally accepted belief that it was the conservative activists on the Court who were guilty of Spencerian scientism. On the contrary, the argument is presented that it was Justice Holmes and the liberal reformers who found the evolutionary doctrines of Spencer congenial to their efforts of identifying needed reinterpretations of the American Constitution with biological evolution.