Abstract considerations: disciplines and the incoherence of Newton’s natural philosophy

Historians have long sought putative connections between different areas of Newton’s scientific work, while recently scholars have argued that there were causal links between even more disparate fields of his intellectual activity. In this paper I take an opposite approach, and attempt to account for certain tensions in Newton’s ‘scientific’ work by examining his great sensitivity to the disciplinary divisions that both conditioned and facilitated his early investigations in science and mathematics. These momentous undertakings, exemplified by research that he wrote up in two separate notebooks, obey strict distinctions between approaches appropriate to both new and old ‘natural philosophy’ and those appropriate to the mixed mathematical sciences. He retained a fairly rigid demarcation between them until the early eighteenth century. At the same time as Newton presented the ‘mathematical principles’ of natural philosophy in his magnum opus of 1687, he remained equally committed to a separate and more private world or ontology that he publicly denigrated as hypothetical or conjectural. This is to say nothing of the worlds implicit in his work on mathematics and alchemy. He did not lurch from one overarching ontological commitment to the next (for example, moving tout court from radical aetherial explanations to strictly vacuist accounts) but instead simultaneously—and often radically—developed generically distinct concepts and ontologies that were appropriate to specific settings and locations (for example, private, qualitative, causal natural philosophy versus public quantitative mixed mathematics) as well as to relevant styles of argument. Accordingly I argue that the concepts used by Newton throughout his career were intimately bound up with these appropriate generic or quasi-disciplinary ‘structures’. His later efforts to bring together active principles, aethers and voids in various works were not failures that resulted from his ‘confusion’ but were bold attempts to meld together concepts or ontologies that belonged to distinct enquiries. His analysis could not be ‘coherent’ because the structures in which they appeared were fundamentally incompatible.     

The intelligibility of motion and construction: Descartes’ early mathematics and metaphysics, 1619-1637

I argue for an interpretation of the connection between Descartes’ early mathematics and metaphysics that centers on the standard of geometrical intelligibility that characterizes Descartes’ mathematical work during the period 1619 to 1637. This approach remains sensitive to the innovations of Descartes’ system of geometry and, I claim, sheds important light on the relationship between his landmark Geometry (1637) and his first metaphysics of nature, which is presented in Le monde (1633). In particular, I argue that the same standard of clear and distinct motions for construction that allows Descartes to distinguish ‘geometric’ from ‘imaginary’ curves in the domain of mathematics is adopted in Le monde as Descartes details God’s construction of nature. I also show how, on this interpretation, the metaphysics of Le monde can fruitfully be brought to bear on Descartes’ attempted solution to the Pappus problem, which he presents in Book I of the Geometry. My general goal is to show that attention to the standard of intelligibility Descartes invokes in these different areas of inquiry grants us a richer view of the connection between his early mathematics and philosophy than an approach that assumes a common method is what binds his work in these domains together.     

Francesco Patrizi’s two books on space: geometry, mathematics, and dialectic beyond Aristotelian science

Francesco Patrizi was a competent Greek scholar, a mathematician, and a Neoplatonic thinker, well known for his sharp critique of Aristotle and the Aristotelian tradition. In this article I shall present, in the first part, the importance of the concept of a three-dimensional space which is regarded as a body, as opposed to the Aristotelian two-dimensional space or interval, in Patrizi’s discussion of physical space. This point, I shall argue, is an essential part of Patrizi’s overall critique of Aristotelian science, in which Epicurean, Stoic, and mainly Neoplatonic elements were brought together, in what seems like an original theory of space and a radical revision of Aristotelian physics. Moreover, I shall try to show Patrizi’s dialectical method of definition, his geometrical argumentation, and trace some of the ideas and terms used by him back to Proclus’ Commentary on Euclid. This text of Proclus, as will be shown in the second part of the article, was also important for Patrizi’s discussion of mathematical space, where Patrizi deals with the status of mathematics and redefines some mathematical concepts such as the point and the line according to his new theory of space.     

Grasping the spirit in nature: Anschauung in Ørsted's epistemology of science and beauty

The intersection between art, poetry, philosophy and science was the leitmotif which guided the lives and careers of romantic natural philosophers including that of the Danish natural philosopher, H. C. Ørsted. A simple model of Ørsted’s career would be one in which it was framed by two periods of philosophical speculation: the youth’s curious and idealistic interest in new attractive thoughts and the experienced man’s mature reflections at the end of his life. We suggest that a closer look at the epistemological aspects of his works on the theory of beauty reveals a connection between this late work and his early philosophical work including experimental philosophy, but also with the work in teaching and textbook writing, that lies in between. The latter includes Ørsted’s view on the application of mathematics in natural philosophy as well as his failed attempt at a genetic presentation of elementary geometry.     

‘The long-lost truth’: Sir Isaac Newton and the Newtonian pursuit of ancient knowledge

In the 1720s the antiquary and Newtonian scholar Dr. William Stukeley (1687-1765) described his friend Isaac Newton as ‘the Great Restorer of True Philosophy’. Newton himself in his posthumously published Observations upon the prophecies of Daniel, and the Apocalypse of St. John (1733) predicted that the imminent fulfilment of Scripture prophecy would see ‘a recovery and re-establishment of the long-lost truth’. In this paper I examine the background to Newton’s interest in ancient philosophy and theology, and how it related to modern natural philosophical discovery. I look at the way in which the idea of a ‘long-lost truth’ interested others within Newton’s immediate circle, and in particular how it was carried forward by Stukeley’s researches into ancient British antiquities. I show how an interest in and respect for ancient philosophical knowledge remained strong within the first half of the eighteenth century.     

William Whiston, Isaac Newton and the crisis of publicity

William Whiston was one of the first British converts to Newtonian physics and his 1696 New theory of the earth is the first full-length popularization of the natural philosophy of the Principia. Impressed with his young protégé, Newton paved the way for Whiston to succeed him as Lucasian Professor of Mathematics in 1702. Already a leading Newtonian natural philosopher, Whiston also came to espouse Newton’s heretical antitrinitarianism in the middle of the first decade of the eighteenth century. In all, Whiston enjoyed twenty years of contact with Newton dating from 1694. Although they shared so much ideologically, the two men fell out when Whiston began to proclaim openly the heresy that Newton strove to conceal from the prying eyes of the public. This paper provides a full account of this crisis of publicity by outlining Whiston’s efforts to make both Newton’s natural philosophy and heterodox theology public through popular texts, broadsheets and coffee house lectures. Whiston’s attempts to draw Newton out through published hints and innuendos, combined with his very public religious crusade, rendered the erstwhile disciple a dangerous liability to the great man and helps explain Newton’s eventual break with him, along with his refusal to support Whiston’s nomination to the Royal Society. This study not only traces Whiston’s successes in preaching the gospel of Newton’s physics and theology, but demonstrates the ways in which Whiston, who resolutely refused to accept Newton’s epistemic distinction between ‘open’ and ‘closed’ forms of knowledge, transformed Newton’s grand programme into a singularly exoteric system and drove it into the public sphere.     

On the sources and implications of Carnap’s Der Raum

Der Raum, Carnap’s earliest published work, finds him largely a follower of Husserl. In particular, he holds a distinctively Husserlian conception of the synthetic a priori—a view, I will suggest, paradigmatic of what he would later reject as ‘metaphysics’. His main purpose is to reconcile that Husserlian view with the theory of general relativity. On the other hand, he has already broken with Husserl, and in ways which foreshadow later developments in his thought. Especially important in this respect is his use of Hans Driesch’s Ordnungslehre.     

Intensions, belief and science: Kuhn’s early philosophical outlook (1940-1945)

Between 1940 and 1945, while still a student of theoretical physics and without any contact with the history of science, Thomas S. Kuhn developed a general outline of a theory of the role of belief in science. This theory was well rooted in the philosophical tradition of Emerson Hall, Harvard, and particularly in H. M. Sheffer’s and C. I. Lewis’s logico-philosophical works—Kuhn was, actually, a graduate student of the former in 1945. In this paper I reconstruct the development of that general outline after Kuhn’s first years at Harvard. I examine his works on moral and aesthetic issues—where he displayed an already ‘anti-Whig’ stance concerning historiography—as well as his first ‘Humean’ approach to science and realism, where his earliest concern with belief is evident. Then I scrutinise his graduate work to show how his first account of the role of belief was developed. The main aim of this paper is to show that the history of science illustrated for Kuhn the epistemic role and effects of belief he had already been theorising about since around 1941.     

Hermeneutic strategies in Gerd Buchdahl’s Kantian philosophy of science

Gerd Buchdahl’s international reputation rests on his masterly writings on Kant. In them he showed how Kant transformed the philosophical problems of his predecessors and he minutely investigated the ways in which Kant related his critical philosophy to the contents and methods of natural science. Less well known, if only because in large part unpublished, are the writings in which Buchdahl elaborated his own views on the methods and status of the sciences. In this paper I examine the roles of hermeneutics in Buchdahl’s reconstruction of Kant’s philosophical system and in his own ‘transcendental methodological’ approach to the philosophy of science. The first section looks at Buchdahl’s views on the theory and practice of historical interpretation and at the Husserlian hermeneutic scheme of reduction and realisation that he used in his later accounts of the philosophies of science of Kant and himself. The second section concentrates on Buchdahl’s treatment of the grounds of science in Kant; and the third on the hermeneutic strategies Buchdahl employed in articulating and justifying his own views. The paper closes with reflections on the impact and importance of Buchdahl’s interpretation of Kant’s critical philosophy in relation to the sciences and of his own hermeneutically based philosophy of science.     

The transcendental method from Newton to Kant

Kant’s transcendental method, as applied to natural philosophy, considers the laws of physics as conditions of the possibility of experience. A more modest transcendental project is to show how the laws of motion explicate the concepts of motion, force, and causal interaction, as conditions of the possibility of an objective account of nature. This paper argues that such a project is central to the natural philosophy of Newton, and explains some central aspects of the development of his thinking as he wrote the Principia. One guiding scientific aim was the dynamical analysis of any system of interacting bodies, and in particular our solar system; the transcendental question was, what are the conceptual prerequisites for such an analysis? More specifically, what are the conditions for determining “true motions” within such a system—for posing the question of “the frame of the system of the world” as an empirical question? A study of the development of Newton’s approach to these questions reveals surprising connections with his developing conceptions of force, causality, and the relativity of motion. It also illuminates the comparison between his use of the transcendental method and that of Euler and Kant.     

The functional bias of the dual nature of technical artefacts program

In 2006, in a special issue of this journal, several authors explored what they called the dual nature of artefacts. The core idea is simple, but attractive: to make sense of an artefact, one needs to consider both its physical nature—its being a material object—and its intentional nature—its being an entity designed to further human ends and needs. The authors construe the intentional component quite narrowly, though: it just refers to the artefact’s function, its being a means to realize a certain practical end. Although such strong focus on functions is quite natural (and quite common in the analytic literature on artefacts), I argue in this paper that an artefact’s intentional nature is not exhausted by functional considerations. Many non-functional properties of artefacts—such as their marketability and ease of manufacture—testify to the intentions of their users/designers; and I show that if these sorts of considerations are included, one gets much more satisfactory explanations of artefacts, their design, and normativity.     

Cartesian analysis and synthesis

This paper aims to provide an explication of the meaning of ‘analysis’ and ‘synthesis’ in Descartes’ writings. In the first part I claim that Descartes’ method is entirely captured by the term ‘analysis’, and that it is a method of theory elaboration that fuses the modern methods of discovery and confirmation in one enterprise. I discuss Descartes’ methodological writings, assess their continuity and coherence, and I address the major shortcoming of previous interpretations of Cartesian methodology. I also discuss the Cartesian method in the context of other conceptions of scientific method of that era and argue that Descartes’ method significantly transforms these conceptions. In the second part I argue that mathematical and natural-philosophical writings exhibit this kind of analysis. To that effect I examine in Descartes’ writings on the method as used in mathematics, and Descartes’ account of the discovery of the nature of the rainbow in the Meteors. Finally, I briefly assess Descartes’ claim regarding the universality of his method.     

How not to integrate the history and philosophy of science: a reply to Chalmers

Alan Chalmers uses Robert Boyle’s mechanical philosophy as an example of the irrelevance of ‘philosophy’ to ‘science’ and criticizes my 2006 book Atoms and alchemy for overemphasizing Boyle’s successes. The present paper responds as follows: first, it argues that Chalmers employs an overly simplistic methodology insensitive to the distinction between historical and philosophical claims; second, it shows that the central theses of Atoms and alchemy are untouched by Chalmers’s criticisms; and third, it uses Boyle’s analysis of subordinate causes and his debate with Henry More in the 1670s to demonstrate the inadequacy of Chalmers’s construal of the mechanical philosophy.     

Transcendental philosophy and mathematical physics

This paper explores the relationship between Kant’s views on the metaphysical foundations of Newtonian mathematical physics and his more general transcendental philosophy articulated in the Critique of pure reason. I argue that the relationship between the two positions is very close indeed and, in particular, that taking this relationship seriously can shed new light on the structure of the transcendental deduction of the categories as expounded in the second edition of the Critique.     

Putting pragmatism to work in the Cold War: Science, technology, and politics in the writings of James B. Conant

This paper examines James Conant’s pragmatic theory of science—a theory that has been neglected by most commentators on the history of 20^th-century philosophy of science—and it argues that this theory occupied an important place in Conant’s strategic thinking about the Cold War. Conant drew upon his wartime science policy work, the history of science, and Quine’s epistemological holism to argue that there is no strict distinction between science and technology, that there is no such thing as “the scientific method,” and that theories are better interpreted as policies rather than creeds. An important consequence that he drew from these arguments is that science is both a thoroughly value-laden, and an intrinsically social, enterprise. These results led him to develop novel proposals for reorganizing scientific and technological research—proposals that he believed could help to win the Cold War. Interestingly, the Cold War had a different impact upon Conant’s thinking than it did upon many other theorists of science in postwar America. Instead of leading him to “the icy slopes of logic,” it led him to develop a socially- and politically-engaged theory that was explicitly in the service of the American Cold War effort.     

Leibniz and the post-Copernican universe. Koyré revisited

This paper employs the revised conception of Leibniz emerging from recent research to reassess critically the ‘radical spiritual revolution’ which, according to Alexandre Koyré’s landmark book, From the closed world to the infinite universe (1957) was precipitated in the seventeenth century by the revolutions in physics, astronomy, and cosmology. While conceding that the cosmological revolution necessitated a reassessment of the place of value-concepts within cosmology, it argues that this reassessment did not entail a spiritual revolution of the kind assumed by Koyré, in which ‘value-concepts, such as perfection, harmony, meaning and aim’ were shed from the conception of the structure of the universe altogether. On the contrary, thanks to his pioneering intuition of the distinction between physical and metaphysical levels of explanation, Leibniz saw with great clarity that a scientific explanation of the universe which rejected the ‘closed world’ typical of Aristotelian cosmology did not necessarily require the abandonment of key metaphysical doctrines underlying the Aristotelian conception of the universe. Indeed the canon of value-concepts mentioned by Koyré—meaning, aim, perfection and harmony—reads like a list of the most important concepts underlying the Leibnizian conception of the metaphysical structure of the universe. Moreover, Leibniz’s universe, far from being a universe without God—because, as Clarke insinuated, it does not need intervention from God—is a universe which in its deepest ontological fabric is interwoven with the presence of God.     

Mathematical method and Newtonian science in the philosophy of Christian Wolff

This paper aims to illuminate Christian Wolff’s view of mathematical reasoning, and its use in metaphysics, by comparing his and Leibniz’s responses to Newton’s work. Both Wolff and Leibniz object that Newton’s metaphysics is based on ideas of sense and imagination that are suitable only for mathematics. Yet Wolff expresses more regard (than Leibniz) for Newton’s scientific achievement. Wolff’s approval of the use of imaginative ideas in Newtonian mathematical science seems to commit him to an inconsistent triad. For he rejects their use in metaphysics, and also holds that every scientific discipline must follow mathematics’ method. A facile resolution would be to suppose Wolff identifies the method of mathematics with the order in which propositions are deduced, or with “analysis” that reveals the structure of concepts. This would be to assimilate Wolff’s view to Leibniz’s (on which all mathematical propositions are ultimately derived from definitions, and definitions are justified by conceptual analysis). On this construal, mathematical reasoning involves only the understanding. But Wolff conceives mathematics’ method more broadly, to include processes of concept-formation which involve perception and imagination. Thus my way of resolving the tension is to find roles for perception and imagination in the formation of metaphysical concepts.     

John Dalton’s puzzles: from meteorology to chemistry

Historical research on John Dalton has been dominated by an attempt to reconstruct the origins of his so-called “chemical atomic theory”. I show that Dalton’s theory is difficult to define in any concise manner, and that there has been no consensus as to its unique content among his contemporaries, later chemists, and modern historians. I propose an approach which, instead of attempting to work backward from Dalton’s theory, works forward, by identifying the research questions that Dalton posed to himself and attempting to understand how his hypotheses served as answers to these questions. I describe Dalton’s scientific work as an evolving set of puzzles about natural phenomena. I show how an early interest in meteorology led Dalton to see the constitution of the atmosphere as a puzzle. In working on this great puzzle, he gradually turned his interest to specifically chemical questions. In the end, the web of puzzles that he worked on required him to create his own novel philosophy of chemistry for which he is known today.     

Athanasius Kircher’s magical instruments: an essay on ‘science’, ‘religion’ and applied metaphysics

In this paper I endeavour to bridge the gap between the history of material culture and the history of ideas. I do this by focussing on the intersection between metaphysics and technology—what I call ‘applied metaphysics’—in the oeuvre of the Jesuit scholar Athanasius Kircher. By scrutinising the interplay between texts, objects and images in Kircher’s work, it becomes possible to describe the multiplicity of meanings related to his artefacts. I unearth as yet overlooked metaphysical and religious meanings of the camera obscura, for instance, as well as of various other optical and magnetic devices. Today, instruments and artefacts are almost exclusively seen in the light of a narrow economic and technical concept. Historically, the ‘use’ of artefacts is much more diverse, however, and I argue that it is time to historicize the concept of ‘utility’.