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.     

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.     

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.     

Explanation,understanding, and unrealistic models

How can false models be explanatory? And how can they help us to understand the way the world works? Sometimes scientists have little hope of building models that approximate the world they observe. Even in such cases, I argue, the models they build can have explanatory import. The basic idea is that scientists provide causal explanations of why the regularity entailed by an abstract and idealized model fails to obtain. They do so by relaxing some of its unrealistic assumptions. This method of ‘explanation by relaxation’ captures the explanatory import of some important models in economics. I contrast this method with the accounts that Daniel Hausman and Nancy Cartwright have provided of explanation in economics. Their accounts are unsatisfactory because they require that the economic model regularities obtain, which is rarely the case. I go on to argue that counterfactual regularities play a central role in achieving ‘understanding by relaxation.’ This has a surprising implication for the relation between explanation and understanding: Achieving scientific understanding does not require the ability to explain observed regularities.     

Signs, toy models, and the a priori: from Helmholtz to Wittgenstein

The Marburg neo-Kantians argue that Hermann von Helmholtz’s empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz’s account raises the ‘problem of validity’ (Gültigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz’s and Ludwig Wittgenstein’s Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz’s original account.     

Understanding,explanation, and unification

In this article I argue that there are two different types of understanding: the understanding we get from explanations, and the understanding we get from unification. This claim is defended by first showing that explanation and unification are not as closely related as has sometimes been thought. A critical appraisal of recent proposals for understanding without explanation leads us to discuss the example of a purely classificatory biology: it turns out that such a science can give us understanding of the world through unification of the phenomena, even though it does not give us any explanations. The two types of understanding identified in this paper, while strictly separate, do have in common that both consist in seeing how the individual phenomena of the universe hang together. Explanations give us connections between the phenomena through the asymmetric, ‘vertical’ relation of determination; unifications give us connections through the symmetric, ‘horizontal’ relation of kinship. We then arrive at a general definition of understanding as knowledge of connections between the phenomena, and indicate that there might be more than two types of understanding.     

‘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.     

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.     

Playing with molecules

Recent philosophy of science has seen a number of attempts to understand scientific models by looking to theories of fiction. In previous work, I have offered an account of models that draws on Kendall Walton’s ‘make-believe’ theory of art. According to this account, models function as ‘props’ in games of make-believe, like children’s dolls or toy trucks. In this paper, I assess the make-believe view through an empirical study of molecular models. I suggest that the view gains support when we look at the way that these models are used and the attitude that users take towards them. Users’ interaction with molecular models suggests that they do imagine the models to be molecules, in much the same way that children imagine a doll to be a baby. Furthermore, I argue, users of molecular models imagine themselves viewing and manipulating molecules, just as children playing with a doll might imagine themselves looking at a baby or feeding it. Recognising this ‘participation’ in modelling, I suggest, points towards a new account of how models are used to learn about the world, and helps us to understand the value that scientists sometimes place on three-dimensional, physical models over other forms of representation.     

The birth of modern science: culture, mentalities and scientific innovation

In a recent paper, Luc Faucher and others have argued for the existence of deep cultural differences between ‘Chinese’ and ‘East Asian’ ways of understanding the world and those of ‘ancient Greeks’ and ‘Americans’. Rejecting Alison Gopnik’s speculation that the development of modern science was driven by the increasing availability of leisure and information in the late Renaissance, they claim instead—following Richard Nisbett—that the birth of mathematical science was aided by ‘Greek’, or ‘Western’, cultural norms that encouraged analytic, abstract and rational theorizing. They argue that ‘Chinese’ and ‘East Asian’ cultural norms favoured, by contrast, holistic, concrete and dialectical modes of thinking. After clarifying some of the things that can be meant by ‘culture’ and ‘mentality’, the present paper shows that Faucher and his colleagues make a number of appeals—to the authority of comparative studies and history of science, to the psychological studies of Nisbett and his colleagues, and to a hidden assumption of strong cultural continuity in the West. It is argued that every one of these appeals is misguided, and, further, that the psychological findings of Nisbett and others have little bearing on questions concerning the origins of modern science. Finally, it is suggested that the ‘Needham question’ about why the birth of modern science occurred in Europe rather than anywhere else is itself multiply confused to the extent that it may express no significant query.     

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.     

The bootstrapped artefact: a collectivist account of technological ontology, functions, and normativity

In 2006, this journal addressed the problem of technological artefacts, and through a series of articles aimed at tackling the ‘dual nature of technical artefacts’, posited an understanding of these as constituted by both a structural (physical) and a functional (intentional) component. This attempt to conceptualise artefacts established a series of important questions, concerning such aspects of material technologies as mechanisms, functions, human intentionality, and normativity. However, I believe that in establishing the ‘dual nature’ thesis, the authors within this issue focused too strongly on technological function. By positing function as the analytic axis of the ‘dual nature’ framework, the theorists did not sufficiently problematise what is ultimately a social phenomenon. Here I posit a complementary analytic approach to this problem; namely, I argue that by using the Strong Programme’s performative theory of social institutions, we can better understand the nature of material technologies. Drawing particularly from Martin Kusch’s work, I here argue that by conceptualising artefacts as artificial kinds, we can better examine technological ontology, functions, and normativity. Ultimately, a Strong Programme approach, constructivist and collectivist in nature, offers a useful elaboration upon the important question raised by the ‘dual nature’ theorists.     

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.     

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.     

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

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

‘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.     

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’.