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.     

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.     

Supervenience and (non-modal) reductionism in Leibniz’s philosophy of time

It has recently been suggested that, for Leibniz, temporal facts globally supervene on causal facts, with the result that worlds differing with respect to their causal facts can be indiscernible with respect to their temporal facts. Such an interpretation is at variance with more traditional readings of Leibniz’s causal theory of time, which hold that Leibniz reduces temporal facts to causal facts. In this article, I argue against the global supervenience construal of Leibniz’s philosophy of time. On the view of Leibniz defended here, he adopts a non-modal reduction of time to events, a form of reductionism that entails a strong covariation between a world’s temporal facts and its causal facts. Consequently, worlds discernible with respect to their temporal facts must be discernible with respect to their causal facts, and worlds discernible with respect to their causal facts must be discernible with respect to their temporal facts. This position strongly favors the standard identificatory reduction of time to causation often imputed to Leibniz.     

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.     

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.     

Leibniz’s syncategorematic infinitesimals

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83).      

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.     

Understanding as explanatory knowledge: The case of Bjorken scaling

In this paper, we develop and refine the idea that understanding is a species of explanatory knowledge. Specifically, we defend the idea that S understands why p if and only if S knows that p, and, for some q, S’s true belief that q correctly explains p is produced/maintained by reliable explanatory evaluation. We then show how this model explains the reception of James Bjorken’s explanation of scaling by the broader physics community in the late 1960s and early 1970s. The historical episode is interesting because Bjorken’s explanation initially did not provide understanding to other physicists, but was subsequently deemed intelligible when Feynman provided a physical interpretation that led to experimental tests that vindicated Bjorken’s model. Finally, we argue that other philosophical models of scientific understanding are best construed as limiting cases of our more general model.     

‘This inscrutable principle of an original organization’: epigenesis and ‘looseness of fit’ in Kant’s philosophy of science

Kant’s philosophy of science takes on sharp contour in terms of his interaction with the practicing life scientists of his day, particularly Johann Blumenbach and the latter’s student, Christoph Girtanner, who in 1796 attempted to synthesize the ideas of Kant and Blumenbach. Indeed, Kant’s engagement with the life sciences played a far more substantial role in his transcendental philosophy than has been recognized hitherto. The theory of epigenesis, especially in light of Kant’s famous analogy in the first Critique (B167), posed crucial questions regarding the ‘looseness of fit’ between the constitutive and the regulative in Kant’s theory of empirical law. A detailed examination of Kant’s struggle with epigenesis between 1784 and 1790 demonstrates his grave reservations about its hylozoist implications, leading to his even stronger insistence on the discrimination of constitutive from regulative uses of reason. The continuing relevance of these issues for Kant’s philosophy of science is clear from the work of Buchdahl and its contemporary reception.     

Poincaréan intuition revisited: what can we learn from Kant and Parsons?

This paper provides a comprehensive critique of Poincaré’s usage of the term intuition in his defence of the foundations of pure mathematics and science. Kant’s notions of sensibility and a priori form and Parsons’s theory of quasi-concrete objects are used to impute rigour into Poincaré’s interpretation of intuition. In turn, Poincaré’s portrayal of sensible intuition as a special kind of intuition that tolerates the senses and imagination is rejected. In its place, a more harmonized account of how we perceive concrete objects is offered whereby intuitive knowledge is consistently a priori whatever the domain of application.     

What’s right about Carnap, Neurath and the Left Vienna Circle thesis: a refutation

This paper rejects as unfounded a recent criticism of research on the so-called left wing of the Vienna Circle and the claim that it sported a political philosophy of science. The demand for ‘specific, local periodized claims’ is turned against the critic. It is shown (i) that certain criticisms of Red Vienna’s leading party cannot be transferred to the members of the Circle involved in popular education, nor can criticism of Carnap’s Aufbau be transferred to Neurath’s unified science project; (ii) that neither with regard to Carnap nor to Neurath does the criticism raise points that either engage with the thesis proposed or stand up to closer scrutiny; (iii) that the main thesis attacked is just what I had warned the claim that the Vienna Circle had a political philosophy of science should not be understood as. The question whether theirs is ‘political enough’ today can and should be discussed without distortion of the historical record.     

Relations between Karl Popper and Michael Polanyi

Karl Popper and Michael Polanyi grew up in central Europe and, having escaped from Nazism, went on to pursue academic careers in Britain where they wrote prolifically on science and politics. Popper and Polanyi corresponded with each other, and met for discussions in the late 1940s and early 50s, but they seldom referred to each other in their publications. This article examines their correspondence so as to produce a picture of their intellectual relations. The most important of the letters was one that Popper wrote in 1952, which we reproduce in its entirety, indicating his dissatisfaction with ideas that Polanyi had expressed in a paper of that year, ‘The Stability of Beliefs’. In this paper, Polanyi used the example of the framework of Zande witchcraft to shed analogical light on science and other systems of belief, arguing that ‘frameworks of belief’ equip their adherents with intellectual powers whose use reinforces commitment to the framework, inoculating adherents against criticism. Polanyi’s 1952 paper and his 1951 and 1952 Gifford Lectures (to which that paper is intimately tied) are the first articulation of Polanyi’s sharp rejection of the modern critical philosophical tradition that by implication included Popper’s philosophical ideas. The 1952 paper is also part of Polanyi’s constructive philosophical effort to set forth a fiduciary philosophy emphasizing commitment. Popper regarded Polanyi’s position as implying cognitive relativism and irrationalism, and from the time of Polanyi’s 1952 paper their personal relationship became strained. Discord between them became publicly manifest when Polanyi subtitled his book Personal Knowledge (1958), Towards a post-critical philosophy, and Popper lambasted the idea of a ‘post-critical’ philosophy in his Preface in The Logic of Scientific Discovery (1959).     

Kuhn and coherentist epistemology

The paper challenges a recent attempt by Jouni-Matti Kuukkanen to show that since Thomas Kuhn’s philosophical standpoint can be incorporated into coherentist epistemology, it does not necessarily lead to: (Thesis 1) an abandonment of rationality and rational interparadigm theory comparison, nor to (Thesis 2) an abandonment of convergent realism. Leaving aside the interpretation of Kuhn as a coherentist, we will show that Kuukkanen’s first thesis is not sufficiently explicated, while the second one entirely fails. With regard to Thesis 1, we argue that Kuhn’s view on inter-paradigm theory comparison allows only for (what we shall dub as) ‘the weak notion of rationality’, and that Kuukkanen’s argument is thus acceptable only in view of such a notion. With regard to Thesis 2, we show that even if we interpret Kuhn as a coherentist, his philosophical standpoint cannot be seen as compatible with convergent realism since Kuhn’s argument against it is not ‘ultimately empirical’, as Kuukkanen takes it to be.     

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.     

Locke’s construction of the idea of power

I explain Locke’s account of the origin of our idea of power, showing that it concerns the idea of the disposition to act or change, and that this idea is constructed out of the ideas of action or change. I also show how Locke could have modified his account to avoid Hume’s criticism and argue that his neglect to do so reflects a studied neglect of taxonomy, an ambiguity in the notion of capacity, and complications in Locke’s conception of simple ideas. A comparison of the two empiricists reveals that not only do they disagree about the role of reason in the origin of our idea of power, but they are also talking about different ideas. Within the framework of Locke’s account of the origin of the idea of power, I explain why he believes that bodies only provide us with an obscure idea of active power. I conclude by defending his insight that there is a deep connection between the ability to predict and the idea of power.     

Forces and causes in Kant’s early pre-Critical writings

This paper considers Kant’s conception of force and causality in his early pre-Critical writings, arguing that this conception is best understood by way of contrast with his immediate predecessors, such as Christian Wolff, Alexander Baumgarten, Georg Friedrich Meier, Martin Knutzen, and Christian August Crusius, and in terms of the scientific context of natural philosophy at the time. Accordingly, in the True estimation Kant conceives of force in terms of activity rather than in terms of specific effects, such as motion (as unnamed Wolffians had done). Kant’s explicit arguments in the Nova dilucidatio for physical influx (in the guise of the principle of succession) are directed primarily against the conception of grounds and existence held by Wolff, Baumgarten, and Meier, and only secondarily against Leibniz (by asserting the priority of bodies over mind rather than vice versa). Finally, Kant’s reconciliation of the infinite divisibility of space and the unity of monads in the Physical monadology is designed to respond to objections that could be raised naturally by Wolff and Baumgarten.     

Cartesian echoes in Kant’s philosophy of nature

In this paper, we take the cue from a recent observation of Dan Warren about pre-Newtonian elements in Kant’s philosophy of nature to argue that there are two puzzles concerning Kant’s claim that mechanical laws presuppose dynamical laws in Chapter Three of Metaphysical Foundations of Natural Science. We offer responses on Kant’s behalf to these puzzles. These responses take us through a journey via Kant’s first pre-Critical work, True Estimation of Living Forces, and the then lively debate between Cartesians and Leibnizians. We show how some important Cartesian echoes, clearly evident in True Estimation, have played a role in shaping some seminal ideas of Kant on dynamical forces.     

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.     

Making sense of Day 1 of the Two New Sciences: Galileo’s Aristotelian-inspired agenda and his Jesuit readers

This study proposes an explanation for the choice of topics Galileo addressed in Day 1 of his 1638 Two New Sciences, a section of the work which has long puzzled historians of science. I argue that Galileo’s agenda in Day 1, that is the topics he discusses and the questions he poses, was shaped by contemporary teaching commentaries on Books 3 through 8 of Aristotle’s Physics. Building on the insights and approach of theorists of reader reception, I confirm this interpretation by examining the response of professors of natural philosophy at the Jesuit Collegio Romano to Galileo’s text.