Cartesian analysis and synthesis

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

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.     

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.     

Descartes’s changing mind

Descartes is always concerned about knowledge. However, the Galileo affair in 1633, the reactions to his Discourse on method, and later his need to reply to objections to his Meditations provoked crises in Descartes’s intellectual development the import of which has not been sufficiently recognized. These events are the major reasons why Descartes’s philosophical position concerning how we know and what we may know is radically different at the end of his life from what it was when he began. We call this later position Descartes’s epistemic stance and contrast it with his earlier methodological, metaphysical realism. Yet Descartes’s epistemic views cannot be separated from other aspects of his work, for example, his views concerning God, causality, metaphysics, and the nature of science. A further meta-implication is that serious errors await any scholar who cites early Cartesian texts in support of late Cartesian positions, or who uses later texts in conjunction with early ones to support a reading of Descartes’s philosophy.     

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.     

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

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

Cartesian causation: body–body interaction, motion, and eternal truths

There is considerable debate among scholars over whether Descartes allowed for genuine body–body interaction. I begin by considering Michael Della Rocca’s recent claim that Descartes accepted such interaction, and that his doctrine of the creation of the eternal truths indicates how this interaction could be acceptable to him. Though I agree that Descartes was inclined to accept real bodily causes of motion, I differ from Della Rocca in emphasizing that his ontology ultimately does not allow for them. This is not the end of the story however, since two of Descartes’s successors offered incompatible ways of developing his conflicted account of motion. I contrast the occasionalist view of Nicolas Malebranche that changes in motion derive directly from divine volitions with the non-occasionalist claim of Pierre-Sylvain Regis that such changes derive from a nature distinct from God. In light of Della Rocca’s interpretation, it is noteworthy that the issue of eternal truths is relevant to both alternative accounts. Indeed, Regis took the doctrine that such truths are created to provide crucial support for his alternative to an occasionalist account of body–body interaction. What does not help Della Rocca, however, is that Regis’s view of motion requires a fundamental revision of Descartes’s ontology.     

Computational models: a modest role for content

The computational theory of mind construes the mind as an information-processor and cognitive capacities as essentially representational capacities. Proponents of the view (hereafter, ‘computationalists’) claim a central role for representational content in computational models of these capacities. In this paper I argue that the standard view of the role of representational content in computational models is mistaken; I argue that representational content is to be understood as a gloss on the computational characterization of a cognitive process.     

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.     

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.     

‘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.     

‘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.     

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.     

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

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

Computation, individuation, and the received view on representation

The ‘received view’ about computation is that all computations must involve representational content. Egan and Piccinini argue against the received view. In this paper, I focus on Egan’s arguments, claiming that they fall short of establishing that computations do not involve representational content. I provide positive arguments explaining why computation has to involve representational content, and how that representational content may be of any type (distal, broad, etc.). I also argue (contra Egan and Fodor) that there is no need for computational psychology to be individualistic. Finally, I draw out a number of consequences for computational individuation, proposing necessary conditions on computational identity and necessary and sufficient conditions on computational I/O equivalence of physical systems.     

Stance relativism: empiricism versus metaphysics: The Empirical Stance Bas C. Van Fraassen; Yale University Press, London & New Haven, 2002, pp. xix+282, Price £22.50 hardback, ISBN 0300088744.

In The empirical stance, Bas van Fraassen argues for a reconceptualization of empiricism, and a rejection of its traditional rival, speculative metaphysics, as part of a larger and provocative study in epistemology. Central to his account is the notion of voluntarism in epistemology, and a concomitant understanding of the nature of rationality. In this paper I give a critical assessment of these ideas, with the ultimate goal of clarifying the nature of debate between metaphysicians and empiricists, and more specifically, between scientific realists and empiricist antirealists. Despite van Fraassen’s assertion to the contrary, voluntarism leads to a form of epistemic relativism. Rather than stifling debate, however, this ‘stance’ relativism places precise constraints on possibilities for constructive engagement between metaphysicians and empiricists, and thus distinguishes, in broad terms, paths along which this debate may usefully proceed from routes which offer no hope of progress.     

Quelques conceptions de la théorie des proportions dans des traités de la seconde moitié du dix septième siècle

This article examines how the theory of proportions was explained during the second half of the seventeenth century in the works of Andreas Tacquet, Antoine Arnauld, Ignace Gaston Pardies, Bernard Lamy, and Jacques Rohault. These five authors had very different conceptions of this subject, and on one hand, they show that this question was not forgotten, even after the Geometry of Descartes, and on the other hand, their work displays the progressive transformation of mathematical objects. While Tacquet deepened Euclidean thought, the others stopped taking the Euclidean model as paradigmatic and tried to change the order of the Elements and to establish book V of Euclid in new ways. We shall see that this multiplicity of the approaches highlights both the vitality of the reflections and the difficulty in developing a new ontology of mathematics. Some of them nevertheless opened new perspectives that were to bloom only much later. We shall also see the increasingly important place of the algebra as time went by.     

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.     

On the sources and implications of Carnap’s Der Raum

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