Gravity and Newton’s Substance Counting Problem

A striking feature of Newton’s thought is the very broad reach of his empiricism, potentially extending even to immaterial substances, including God, minds, and should one exist, a non-perceiving immaterial medium. Yet Newton is also drawn to certain metaphysical principles—most notably the principle that matter cannot act where it is not—and this second, rationalist feature of his thought is most pronounced in his struggle to discover ‘gravity’s cause’. The causal problem remains vexing, for he neither invokes primary causation, nor accepts action at a distance by locating active powers in matter. To the extent that he is drawn to metaphysical principles, then, the causal problem is that of discovering some non-perceiving immaterial medium. Yet Newton’s thought has a third striking feature, one with roots in the other two: he allows that substances of different kinds might simultaneously occupy the very same region of space. I elicit the implications of these three features. For Newton to insist upon all three would transform the causal question about gravity into an insoluble problem about apportioning active powers. More seriously, it would undermine his means of individuating substances, provoking what I call ‘Newton’s Substance Counting Problem’.     

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.     

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.     

Newton’s “satis est”: A new explanatory role for laws

In this paper I argue that Newton’s stance on explanation in physics was enabled by his overall methodology and that it neither committed him to embrace action at a distance nor to set aside philosophical and metaphysical questions. Rather his methodology allowed him to embrace a non-causal, yet non-inferior, kind of explanation. I suggest that Newton holds that the theory developed in the Principia provides a genuine explanation, namely a law-based one, but that we also lack something explanatory, namely a causal account of the explanandum. Finally, I argue that examining what it takes to have law-based explanation in the face of agnosticism about the causal process makes it possible to recast the debate over action at a distance between Leibniz and Newton as empirically and methodologically motivated on both sides.     

Newtonianism in early Enlightenment Germany, c. 1720 to 1750: metaphysics and the critique of dogmatic philosophy

The acceptance of Newton’s ideas and Newtonianism in the early German Enlightenment is usually described as hesitant and slow. Two reasons help to explain this phenomenon. One is that those who might have adopted Newtonian arguments were critics of Wolffianism. These critics, however, drew on indigenous currents of thought, pre-dating the reception of Newton in Germany and independent of Newtonian science. The other reason is that the controversies between Wolffians and their critics focused on metaphysics. Newton’s reputation, however, was that of a mathematician, and one point, on which Wolffians and their opponents agreed, was that mathematics was of no use in the solution of metaphysical questions. The appeal to Newton as an authority in metaphysics, it was argued, was the fault of Newton’s over-zealous disciples in Britain, who tried to transform him from a mathematician into the author of a general philosophical system. It is often argued that the Berlin Academy after 1743 included a Newtonian group, but even there the reception of Newtonianism was selective. Philosophers such as Leonhard Euler were also reluctant to be labelled ‘Newtonians’, because this implied a dogmatic belief in Newton’s ideas. Only after the mid-eighteenth century is ‘Newtonianism’ increasingly accepted in the sense of a philosophical system.     

The methodological origins of Newton’s queries

This paper analyses the different ways in which Isaac Newton employed queries in his writings on natural philosophy. It is argued that queries were used in three different ways by Newton and that each of these uses is best understood against the background of the role that queries played in the Baconian method that was adopted by the leading experimenters of the early Royal Society. After a discussion of the role of queries in Francis Bacon’s natural historical method, Newton’s queries in his Trinity Notebook are shown to reveal the influence of his early reading in the new experimental philosophy. Then after a discussion of Robert Hooke’s view of the role of queries, the paper turns to an assessment of Newton’s correspondence and Opticks. It is argued that the queries in his correspondence with Oldenburg on his early optical experiments are closely tied to an experimental program, whereas the queries in the Opticks are more discursive and speculative, but that each of these uses of queries represents a significant Baconian legacy in his natural philosophical methodology.     

Is Newton a ‘radical empiricist’ about method?

Recently, some Newton scholars have argued that Newton is an empiricist about metaphysics—that ideally, he wants to let advances in physical theory resolve either some or all metaphysical issues. But while proponents of this interpretation are using ‘metaphysics’ in a very broad sense, to include the ‘principles that enable our knowledge of natural phenomena’, attention has thus far been focused on Newton’s approach to ontological, not epistemological or methodological, issues. In this essay, I therefore consider whether Newton wants to let physical theory bear on the very ‘principles that enable our knowledge’. By examining two kinds of argument in the Principia, I contend that Newton can be considered a methodological empiricist in a substantial respect. I also argue, however, that he cannot be a ‘radical empiricist’—that he does not and cannot convert all methodological issues into empirical issues.     

Kant’s third law of mechanics: The long shadow of Leibniz

This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter.     

Newton’s substance monism, distant action, and the nature of Newton’s empiricism: discussion of H. Kochiras “Gravity and Newton’s substance counting problem”

This paper is a critical response to Hylarie Kochiras’ “Gravity and Newton’s substance counting problem,” Studies in History and Philosophy of Science 40 (2009) 267-280. First, the paper argues that Kochiras conflates substances and beings; it proceeds to show that Newton is a substance monist. The paper argues that on methodological grounds Newton has adequate resources to respond to the metaphysical problems diagnosed by Kochiras. Second, the paper argues against the claim that Newton is committed to two speculative doctrines attributed to him by Kochiras and earlier Andrew Janiak: i) the passivity of matter and ii) the principle of local causation. Third, the paper argues that while Kochiras’ (and Janiak’s) arguments about Newton’s metaphysical commitments are mistaken, it qualifies the characterization of Newton as an extreme empiricist as defended by Howard Stein and Rob DiSalle. In particular, the paper shows that Newton’s empiricism was an intellectual and developmental achievement that built on non trivial speculative commitments about the nature of matter and space.     

Newton on action at a distance and the cause of gravity

In this discussion paper, I seek to challenge Hylarie Kochiras’ recent claims on Newton’s attitude towards action at a distance, which will be presented in Section 1. In doing so, I shall include the positions of Andrew Janiak and John Henry in my discussion and present my own tackle on the matter (Section 2). Additionally, I seek to strengthen Kochiras’ argument that Newton sought to explain the cause of gravity in terms of secondary causation (Section 3). I also provide some specification on what Kochiras calls ‘Newton’s substance counting problem’ (Section 4). In conclusion, I suggest a historical correction (Section 5).     

Gravity’s cause and substance counting: contextualizing the problems

This paper considers Newton’s position on gravity’s cause, both conceptually and historically. With respect to the historical question, I argue that while Newton entertained various hypotheses about gravity’s cause, he never endorsed any of them, and in particular, his lack of confidence in the hypothesis of robust and unmediated distant action by matter is explained by an inclination toward certain metaphysical principles. The conceptual problem about gravity’s cause, which I identified earlier along with a deeper problem about individuating substances, is that a decisive conclusion is impossible unless certain speculative aspects of his empiricism are abandoned. In this paper, I situate those conceptual problems in Newton’s natural philosophy. They arise from ideas that push empiricism to potentially self-defeating limits, revealing the danger of allowing immaterial spirits any place in natural philosophy, especially spatially extended spirits supposed capable of co-occupying place with material bodies. Yet because their source ideas are speculative, Newton’s method ensures that these problems pose no threat to his rational mechanics or the profitable core of his empiricism. They are easily avoided by avoiding their source ideas, and when science emerges from natural philosophy, it does so with an ontology unencumbered by immaterial spirits.     

Three concepts of causation in Newton

In this paper, I argue that recent debates about Newton’s attitude toward action at a distance have been hampered by a lack of conceptual clarity. To clarify the metaphysical background of the debates, I distinguish three kinds of causes within Newton’s work: mechanical, dynamical, and substantial causes. This threefold distinction enables us to recognize that although Newton clearly regards gravity as an impressed force that operates across vast distances, he denies that this commitment requires him to think that some substance acts at a distance on another substance. (Dynamical causation is distinct from substantial causation.) Newton’s denial of substantial action at a distance may strike his interpreters as questionable, so I provide an argument to show that it is in fact acceptable.     

Emilie du Châtelet’s Institutions de physique as a document in the history of French Newtonianism

This paper discusses the contribution of Madame Du Châtelet to the reception of Newtonianism in France prior to her translation of Newton’s Principia. It focuses on her Institutions de physique, a work normally considered for its contribution to the reception of Leibniz in France. By comparing the different editions of the Institutions, I argue that her interest in Newton antedated her interest in Leibniz, and that she did not see Leibniz’s metaphysics as incompatible with Newtonian science. Her Newtonianism can be seen to be in the course of development between 1738 and 1742 and it was shaped by contemporary French debates (for example the vis viva controversy) and the achievement of French Newtonians like Maupertuis in confirming his theories. Her Institutions therefore is linked to the same drive to disseminate Newtonianism undertaken by popularisations such as Voltaire’s Elements de la philosophie de Newton and Algarotti’s Newtonianismo per le dame.     

Newton’s notion and practice of unification

In this paper I deal with a neglected topic with respect to unification in Newton’s Principia. I will clarify Newton’s notion (as can be found in Newton’s utterances on unification) and practice of unification (its actual occurrence in his scientific work). In order to do so, I will use the recent theories on unification as tools of analysis (Kitcher, Salmon and Schurz). I will argue, after showing that neither Kitcher’s nor Schurz’s account aptly capture Newton’s notion and practice of unification, that Salmon’s later work is a good starting point for analysing this notion and its practice in the Principia. Finally, I will supplement Salmon’s account in order to answer the question at stake.     

The influence of Spinoza’s concept of infinity on Cantor’s set theory

Georg Cantor, the founder of set theory, cared much about a philosophical foundation for his theory of infinite numbers. To that end, he studied intensively the works of Baruch de Spinoza. In the paper, we survey the influence of Spinozean thoughts onto Cantor’s; we discuss Spinoza’s philosophy of infinity, as it is contained in his Ethics; and we attempt to draw a parallel between Spinoza’s and Cantor’s ontologies. Our conclusion is that the study of Spinoza provides deepening insights into Cantor’s philosophical theory, whilst Cantor can not be called a ‘Spinozist’ in any stricter sense of that word.     

‘Good Sense’ in context: A response to Kidd

In his response to my (2010), Ian Kidd claims that my argument against Stump’s interpretation of Duhem’s concept of ‘good sense’ is unsound because it ignores an important distinction within virtue epistemology. In light of the distinction between reliabilist and responsibilist virtue epistemology, Kidd argues that Duhem can be seen as supporting the latter, which he further illustrates with a discussion of Duhem’s argument against ‘perfect theory’. I argue that no substantive argument is offered to show that the distinction is relevant and can establish that Duhem’s ‘good sense’ can be understood within responsibilist virtue epistemology. I furthermore demonstrate that Kidd’s attempt to support his contention relies on a crucial misreading of Duhem’s general philosophy of science, and in doing so highlight the importance of understanding ‘good sense’ in its original context, that of theory choice.     

The early Kant’s (anti-) Newtonianism

It is well known that during his pre-Critical period, Kant was a major proponent of Newtonian physics, for the project of the Universal Natural History explicitly uses “Newtonian principles” to explain the formation of the various bodies that constitute our solar system as well as those that lie beyond. What has not been widely noted, however, is that the early Kant also developed a major criticism of Newton, one that is based on subtle metaphysical issues pertaining to God, which are most at home in philosophical theology. Interestingly, this criticism is neither an inchoate precursor of his later criticisms of Newton’s account of absolute space, nor isolated to the abstract realm of metaphysics, but has a wide range of implications for the way in which a scientific account of the formation and constitution of the heavenly bodies ought to be developed, that is, for the kind of argument Newton offered in the Principia. That Kant remained interested in this set of issues later in his Critical period suggests that, alongside the revolutionary changes that comprise transcendental idealism, there are deep continuities not only in his Newtonian commitments, but in his anti-Newtonian tendencies as well.     

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.