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.     

Thomas Reid’s Newtonian Theism: his differences with the classical arguments of Richard Bentley and William Whiston

Reid was a Newtonian and a Theist, but did he found his Theism on Newton’s physics? In opposition to commonplace assumptions about the role of Theism in Reid’s philosophy, my answer is no. Reid prefers to found his Theism on a priori reasons, rather than on physics. Reid’s understanding of physics as an empirical science stops it from contributing in any clear and efficient way to issues of natural theology. In addition, Reid is highly sceptical of our ability to discover the efficient and final causes of natural phenomena, knowledge of which is essential for natural theology. To bring out Reid’s differences with classical Newtonian Theists Richard Bentley and William Whiston, I examine their use of the law and force of general gravitation, and reconstruct what would be Reidian objections.     

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.     

‘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.     

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.     

Incredulity towards Lyotard: a critique of a postmodernist account of science and knowledge

Philosophers of science have paid little attention, positive or negative, to Lyotard’s book The postmodern condition, even though it has been popular in other fields. We set out some of the reasons for this neglect. Lyotard thought that sciences could be justified by non-scientific narratives (a position he later abandoned). We show why this is unacceptable, and why many of Lyotard’s characterisations of science are either implausible or are narrowly positivist. One of Lyotard’s themes is that the nature of knowledge has changed and thereby so has society itself. However much of what Lyotard says muddles epistemological matters about the definition of ‘knowledge’ with sociological claims about how information circulates in modern society. We distinguish two kinds of legitimation of science: epistemic and socio-political. In proclaiming ‘incredulity towards metanarratives’ Lyotard has nothing to say about how epistemic and methodological principles are to be justified (legitimated). He also gives a bad argument as to why there can be no epistemic legitimation, which is based on an act/content confusion, and a confusion between making an agreement and the content of what is agreed to. As for socio-political legitimation, Lyotard’s discussion remains at the abstract level of science as a whole rather than at the level of the particular applications of sciences. Moreover his positive points can be accepted without taking on board any of his postmodernist account of science. Finally we argue that Lyotard’s account of paralogy, which is meant to provide a ‘postmodern’ style of justification, is a failure.     

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.     

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.     

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.     

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.     

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.     

Reception and discovery: the nature of Johann Wilhelm Ritter’s invisible rays

Ultraviolet radiation is generally considered to have been discovered by Johann Wilhelm Ritter in 1801. In this article, we study the reception of Ritter’s experiment during the first decade after the event—Ritter’s remaining lifetime. Drawing on the attributional model of discovery, we are interested in whether the German physicists and chemists granted Ritter’s observation the status of a discovery and, if so, of what. Two things are remarkable concerning the early reception, and both have to do more with neglect than with (positive) reception. Firstly, Ritter’s observation was sometimes accepted as a fact but, with the exception of C. J. B. Karsten’s theory of invisible light, it played almost no role in the lively debate about the nature of heat and light. We argue that it was the prevalent discourse based on the metaphysics of Stoffe that prevented a broader reception of Ritter’s invisible rays, not the fact that Ritter himself made his findings a part of his Naturphilosophie. Secondly, with the exception of C. E. Wünsch’s experiments on the visual spectrum, there was no experimental examination of the experiment. We argue that theorizing about ontological systems was more common than experimenting, because, given its social and institutional situation, this was the appropriate way of contributing to physics. Consequently, it was less clear in 1810 than in 1801 what, if anything, had been discovered by Ritter.     

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.     

Leibniz on Hobbes’s materialism

This paper discusses Leibniz’s interpretation and criticism of Hobbesian materialism in the period 1698-1705. Leibniz had continued to be interested in Hobbes’s work, despite not engaging with it as intensively as he did earlier (around 1670). Leibniz offers an interpretation of Hobbes that explains Hobbes’s materialism as derived from his imagistic theory of ideas. Leibniz then criticizes Hobbes’s view as being based on a faulty theory of ideas, and as having problematic consequences, particularly with regard to what one says about God. Some of this criticism is found in the New essays, but equally significant is Leibniz’s correspondence with Damaris Masham, who proposed an argument for materialism very much like that which Leibniz attributed to Hobbes. The paper concludes by discussing the suggestion that Leibniz at this time, particularly in the New essays, himself adopted Hobbesian ideas. Though Leibniz did use some of Hobbes’s examples, and did think at this time that all souls were associated with bodies, the resulting position is still rather distant from Hobbesian materialism.     

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.     

Kant and Newton on the a priori necessity of geometry

In the Transcendental Aesthetic, Kant explicitly rejects Newton’s absolutist position that space is an actually existing thing; however, Kant also concedes that the absolutist successfully preserves the a priori necessity that characterizes our geometrical knowledge of space. My goal in this paper is to explore why the absolutist can explain the a priori necessity of geometry by turning to Newton’s De Gravitatione, an unpublished text in which Newton addresses the essential features associated with our representation of space and the relationship between our geometrical investigation of space and our knowledge of the form of space that is a part of the natural order. Attention to Newton’s account of space in De Gravitatione offers insight into the sense in which absolutist space is a priori and reveals why, in the Aesthetic, Kant could concede a priori geometrical knowledge to his absolutist opponent. What I highlight in particular is that, by Kant’s standards, Newton employs the very constructive method of mathematics that secures the a priori necessity of geometry, even though, as an absolutist, and as emphasized in the arguments of the Aesthetic, Newton fails to provide a metaphysics of space that explains the success of his mathematical method.     

The Passions of the soul and Descartes’s machine psychology

Descartes developed an elaborate theory of animal physiology that he used to explain functionally organized, situationally adapted behavior in both human and nonhuman animals. Although he restricted true mentality to the human soul, I argue that he developed a purely mechanistic (or material) ‘psychology’ of sensory, motor, and low-level cognitive functions. In effect, he sought to mechanize the offices of the Aristotelian sensitive soul. He described the basic mechanisms in the Treatise on man, which he summarized in the Discourse. However, the Passions of the soul contains his most ambitious claims for purely material brain processes. These claims arise in abstract discussions of the functions of the passions and in illustrations of those functions. Accordingly, after providing an intellectual context for Descartes’s theory of the passions, especially by comparison with that of Thomas Aquinas, I examine its ‘machine psychology’, including the role of habituation and association. I contend that Descartes put forth what may reasonably be called a ‘psychology’ of the unensouled animal body and, correspondingly, of the human body when the soul does not intervene. He thus conceptually distinguished a mechanistically explicable sensory and motor psychology, common to nonhuman and human animals, from true mentality involving higher cognition and volition and requiring (in his view) an immaterial mind.