Understanding science through its history: a response to Newman

The paper is a response to William Newman’s rebuttal of a critique of his account of the origins of modern chemistry by Alan Chalmers. A way in which the nature of science can be illuminated by history of science is identified and an account of how this can be achieved in the context of a study of the work of Boyle defended in the face of Newman’s criticism. Texts from the writings of Boyle that are cited by Newman as posing problems for Chalmers’ thesis are interpreted as in fact supporting it.     

‘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.     

Radical mathematical Thomism: beings of reason and divine decrees in Torricelli’s philosophy of mathematics

Evangelista Torricelli (1608-1647) is perhaps best known for being the most gifted of Galileo’s pupils, and for his works based on indivisibles, especially his stunning cubature of an infinite hyperboloid. Scattered among Torricelli’s writings, we find numerous traces of the philosophy of mathematics underlying his mathematical practice. Though virtually neglected by historians and philosophers alike, these traces reveal that Torricelli’s mathematical practice was informed by an original philosophy of mathematics. The latter was dashed with strains of Thomistic metaphysics and theology. Torricelli’s philosophy of mathematics emphasized mathematical constructs as human-made beings of reason, yet mathematical truths as divine decrees, which upon being discovered by the mathematician ‘appropriate eternity’. In this paper, I reconstruct Torricelli’s philosophy of mathematics—which I label radical mathematical Thomism—placing it in the context of Thomistic patterns of thought.     

‘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.     

Conventionalism in Reid’s ‘geometry of visibles’

The subject of this investigation is the role of conventions in the formulation of Thomas Reid’s theory of the geometry of vision, which he calls the ‘geometry of visibles’. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid’s ‘geometry of visibles’ and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the construction and assignment of its various properties, especially metric properties, and this fact undermines the claim for a unique non-Euclidean status for the geometry of vision. Finally, a suggestion is offered for trying to reconcile Reid’s direct realist theory of perception with his geometry of visibles.While Thomas Reid is well-known as the leading exponent of the Scottish ‘common-sense’ school of philosophy, his role in the history of geometry has only recently been drawing the attention of the scholarly community. In particular, several influential works, by N. Daniels and R. B. Angell, have claimed Reid as the discoverer of non-Euclidean geometry; an achievement, moreover, that pre-dates the geometries of Lobachevsky, Bolyai, and Gauss by over a half century. Reid’s alleged discovery appears within the context of his analysis of the geometry of the visual field, which he dubs the ‘geometry of visibles’. In summarizing the importance of Reid’s philosophy in this area, Daniels is led to conclude that ‘there can remain little doubt that Reid intends the geometry of visibles to be an alternative to Euclidean geometry’;¹ while Angell, similarly inspired by Reid, draws a much stronger inference: ‘The geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764 ...’² The significance of these findings has not gone unnoticed in mathematical and scientific circles, moreover, for Reid’s name is beginning to appear more frequently in historical surveys of the development of geometry and the theories of space.³Implicit in the recent work on Reid’s ‘geometry of visibles’, or GOV, one can discern two closely related but distinct arguments: first, that Reid did in fact formulate a non-Euclidean geometry, and second, that the GOV is non-Euclidean. This essay will investigate mainly the latter claim, although a lengthy discussion will be accorded to the first. Overall, in contrast to the optimistic reports of a non-Euclidean GOV, it will be argued that there is a great deal of conceptual freedom in the construction of any geometry pertaining to the visual field. Rather than single out a non-Euclidean structure as the only geometry consistent with visual phenomena, an examination of Reid, Daniels, and Angell will reveal the crucial role of geometric ‘conventions’, especially of the metric sort, in the formulation of the GOV (where a ‘metric’ can be simply defined as a system for determining distances, the measures of angles, etc.). Consequently, while a non-Euclidean geometry is consistent with Reid’s GOV, it is only one of many different geometrical structures that a GOV can possess. Angell’s theory that the GOV can only be construed as non-Euclidean, is thus incorrect. After an exploration of Reid’s theory and the alleged non-Euclidean nature of the GOV, in 1 and 2 respectively, the focus will turn to the tacit role of conventionalism in Daniels’ reconstruction of Reid’s GOV argument, and in the contemporary treatment of a non-Euclidean visual geometry offered by Angell ( 3 and 4). Finally, in the conclusion, a suggestion will be offered for a possible reconstruction of Reid’s GOV that does not violate his avowed ‘direct realist’ theory of perception, since this epistemological thesis largely prompted his formulation of the GOV.     

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.     

Boyle on science and the mechanical philosophy: a reply to Chalmers

Robert Boyle thought that his scientific achievements in pneumatics and chemistry depended on, and thus provided support for, his mechanical philosophy. In a recent article in this journal, Alan Chalmers has challenged this view. This paper consists of a reply to Chalmers on two fronts. First it tries to specify precisely what ‘the mechanical philosophy’ meant for Boyle. Then it goes on to defend, against Chalmers, the view that Boyle's science does support his natural philosophy.     

‘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.     

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.     

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.     

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.     

Euler, vis viva, and equilibrium

Euler’s ‘On the force of percussion and its true measure’, published in 1746, shows that not only had the issue of vis viva not been settled, but that the concepts of inertia and even force were still very much up for grabs. This paper details Euler’s treatment of the vis viva problem. Within those details we find differences between his physics and that of Newton, in particular the rejection of empty space and reduction of all forces to the operation of inertia through contact. One can further see how Euler’s philosophy of science embraced explanation through mechanisms and equilibrium conditions.     

The rhetorical strategy of William Paley’s Natural theology (1802): Part 1, William Paley’s Natural theology in context

This article reconstructs the historical and philosophical contexts of William Paley’s Natural theology (1802). In the wake of the French Revolution, widely believed to be the embodiment of an atheistic political credo, the refutation of the transmutational biological theories of Buffon and Erasmus Darwin was naturally high on Paley’s agenda. But he was also responding to challenges arising from his own moral philosophy, principally the psychological quandary of how men were to be kept in mind of the Creator. It is argued here that Natural theology was the culmination of a complex rhetorical scheme for instilling religious impressions that would increase both the virtue and happiness of mankind. Philosophy formed an integral part of this strategy, but it did not comprise the whole of it. Equally vital were those purely rhetorical aspects of the discourse which, according to Paley, were more concerned with creating ‘impression’. This facet of his writing is explored in part one of this two-part article. Turning to the argumentative side of the scheme, part two examines Paley’s responses to David Hume and Erasmus Darwin in the light of the wider strategy of inculcation at work throughout all his writings.     

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.     

Boyle and the origins of modern chemistry: Newman tried in the fire

William Newman construes the Scientific Revolution as a change in matter theory, from a hylomorphic, Aristotelian to a corpuscular, mechanical one. He sees Robert Boyle as making a major contribution to that change by way of his corpuscular chemistry. In this article it is argued that it is seriously misleading to identify what was scientific about the Scientific Revolution in terms of a change in theories of the ultimate structure of matter. Boyle showed, especially in his pneumatics, how empirically accessible, intermediate causes, as opposed to ultimate, mechanical ones can be explored and identified by experiment. Newman is right to observe that Boyle constantly sought intimate links between chemistry and the mechanical philosophy. However, by doing so he did not thereby significantly aid the cause of attaining experimental knowledge of chemical phenomena and the support that Boyle’s chemistry provided for the mechanical philosophy was weaker than both Boyle and Newman imply. Boyle was intent on articulating and defending a strict, mechanical account of the ultimate structure of matter to be sure, but his contributions to the new experimental science in general, and chemistry in particular, are best seen as distinct from that endeavour.     

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).     

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.     

The dynamics of reason and its elusive object in Kant, Fichte and Schelling

Kant used transcendental reflection to distinguish in judgment what belongs to its form and what to its material. Regarding the form of judgment, Buchdahl’s work highlights the analogies between the different levels of judgment in Kant’s transcendental ontology. He uses the explicit contingency of judgments of the system of nature to illuminate the contingency of judgments of objects in general. In the Critique of pure reason, Kant had left much of the work of judgment to the unconscious imagination. Fichte and Schelling attempted to make conscious and determinate the work of the unconscious imagination, but found themselves unable to avoid a reflexive regress in trying to objectify and provide a foundation for the activity of the self in judgment. Buchdahl also clarifies the role Kant gave to the object in judgment, as the indeterminate ‘thinghood’ remaining once all forms of cognition are abstracted. Fichte represented this objective side of consciousness as the not-I, as the limit of the activity of the I, as an unconscious, alien element within consciousness. Schelling struggled to illuminate this unconscious object in judgment, to provide a construction of nature, without dissolving its positive presence into abstract formulations. In pursuing relentlessly Kant’s critique of judgment, Fichte and Schelling exposed its opaque points and problematized the ambition to build a complete system of philosophy.