This paper examines Descartes' problematic relational theory of motion, especially when viewed within the context of his dynamics, the Cartesian natural laws. The work of various commentators on Cartesian motion is also surveyed, with particular emphasis placed upon the recent important texts of Garber and Des Chene. In contrast to the methodology of most previous interpretations, however, this essay employs a modern "spacetime" approach to the problem. By this means, the role of dynamics in Descartes' theory, which has often been (...) neglected in favor of kinematic factors, is shown to be central to finding a solution to the puzzle of Cartesian motion. (shrink)

This is about the tension between Epicurean and Galilean accounts of motion in Gassendi. For my more recent thoughts on this, see http://philpapers.org/rec/LOLCEG.

: In this paper I address the vexed question of secondary causation in René Descartes' physics, and examine several influential interpretations, especially the one recently proposed by Dennis Des Chene. I argue that interpreters who regard Cartesian bodies as real secondary causes, on the grounds that the modes of body include real forces, contradict Descartes' account of modes. On the other hand, those who deny that Descartes affirms secondary causation, on the grounds that forces cannot be modes of extension, commit (...) Descartes to the problematic view that the undetermined and immutable will of God is the sole cause of determinate and variable motions. Des Chene's contextualist approach to Descartes' texts leads him to an intermediate position that combines elements of both interpretations. However, in my view, Des Chene's interpretation likewise fails to resolve apparent tensions in Descartes' claims. I thus propose to separate the issue of secondary causation from what Des Chene dubs 'the problem of force'. On the basis of this approach, and a study of Jesuit commentaries familiar to Descartes, I develop a new interpretation which takes seriously Descartes' claim that the laws of nature are the secondary and particular causes of particular motions and changes in motion. (shrink)

As a practicing life scientist, Descartes must have a theory of what it means to be a living being. In this paper, I provide an account of what his theoretical conception of living bodies must be. I then show that this conception might well run afoul of his rejection of final causal explanations in natural philosophy. Nonetheless, I show how Descartes might have made use of such explanations as merely hypothetical, even though he explicitly blocks this move. I conclude by (...) suggesting that there is no reason for him to have blocked the use of hypothetical final causes in this way. (shrink)

Descartes notoriously characterizes substance in two ways: first, as an ultimate subject of properties ; second, as an independent entity. The characterizations have appeared to many to diverge on the definition as well as the scope of the notion of substance. For it is often thought that the ultimate subject of properties need not—and, in some cases, cannot—be independent. Drawing on a suite of historical, textual, and philosophical considerations, this essay argues for an interpretation that reconciles Descartes's two characterizations. It (...) proposes that both characterizations invoke a type of independence that obtains just in case there is no relation to another entity that holds by the nature of the entity in question. Even though the ultimate subject of properties is sometimes not independent in other respects, it satisfies this independence-by-nature condition. (shrink)

I explain and assess here Huygens’ concept of relative motion. I show that it allows him to ground most of the Law of Inertia, and also to explain rotation. Thereby his concept obviates the need for Newton’s absolute space. Thus his account is a powerful foundation for mechanics, though not without some tension.

This chapter contains section titled: The Rejection of Teleology and Its Limits Reconciling God's Goodness with Misjudgment and Misperception The Clock Analogy and Engineering the Body The Special Place of the Passions The Structure of the Passions of the Soul The Need for a General Remedy Notes References and Further Reading.

I critically examine the view that Descartes’s independence conception (IC) of substance plays a crucial role in his “separability argument” for substance dualism. I argue that IC is a poisoned chalice. I do so by considering how an IC-based separability argument fares on two different ways of thinking about principal attributes. On the one hand, if we take principal attributes to be universals, then a separability argument that deploys IC establishes a version of dualism that is unacceptably strong. On the (...) other hand, if we take principal attributes to be tropes, then IC introduces challenges which undermine the argument. This is partly because the assumption of tropes makes it possible to distinguish several versions of substance dualism, versions which differ with respect to their degree of generality. I argue that taking principal attributes to be tropes makes it challenging to establish any of these versions by way of an IC-based separability argument. I conclude the paper by suggesting a way forward for the proponent of the separability argument. (shrink)

Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...) show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes' mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes' physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity. In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable. La filosofía de Descartes contiene una noción intrigante de lo infinito, un concepto nombrado por el filósofo como indefinido. Aunque en varias ocasiones Descartes definió claramente este término en su correspondencia con sus contemporáneos y en sus Principios de filosofía, han surgido muchos problemas acerca de su significado a lo largo de los años. La mayoría de comentaristas rechaza la idea de que indefinido podría significar una cosa real y, en cambio, la identifica con un infinito potencial aristotélico. En la primera parte de este artículo muestro por qué no hay infinito numérico en las matemáticas cartesianas, en la medida en que tal concepto sería inconsistente con el principal atributo fundamental de los números: ser comparables entre sí. En la segunda parte analizo lo indefinido en el contexto de la física matemática de Descartes. Mi argumento es que, aunque no hay rastro de infinito en sus matemáticas, Descartes se refiere a un indefinido real a causa de sus aplicaciones al mundo material dentro del sistema de su física. Este hecho subraya una discrepancia entre sus matemáticas y su física de lo infinito, pero no implica ninguna dificultad en su física matemática. Así pues, en la física de Descartes, lo indefinido se refiere a una dimensión real del mundo más que a una infinitud potencial matemática aristotélica. De hecho, Descartes establece la realidad e infinitud de la extensión del cosmos y, por extensión, la naturaleza real de su mundo indefinido. Esta indefinición tiene una dimensión física aunque no sea medible. (shrink)

Although Newton carefully eschews questions about gravity’s causal basis in the published Principia, the original version of his masterwork’s third book contains some intriguing causal language. “These forces,” he writes, “arise from the universal nature of matter.” Such remarks seem to assert knowledge of gravity’s cause, even that matter is capable of robust and distant action. Some commentators defend that interpretation of the text—a text whose proper interpretation is important since Newton’s reasons for suppressing it strongly suggest that he continued (...) to endorse its ideas. This article argues that the surface appearance of Newton’s causal language is deceptive. What does New- ton intend with his causal language if not a full causal hypothesis? His remarks actually indicate a way of considering the force mathematically, something he contrasts to the structure of the force as it really is in nature. In explaining that, he identifies a significant disjunction between the physical force itself and mathematical ways of considering it, and the text’s significance lies in its view of the force’s structure and in the questions raised about the relationship between mathematical representations and the physical world. (shrink)

Scholars have long recognized that Newton regarded Descartes as his principal philosophical interlocutor when composing the first edition of Philosophiae Naturalis Principia Mathematica in 1687. The arguments in the Scholium on space and time, for instance, can profitably be interpreted as focusing on the conception of space and motion in part two of Descartes's Principles of Philosophy (1644). What is less well known, however, is that this Cartesian conception, along with Descartes's attempt to avoid Galileo's fate in 1633, serves as (...) an essential background to understanding Newton's own (poorly understood) view of the theological implications of his theory of space and motion. In particular, after withdrawing Le Monde from publication in 1633 because of its Copernican leanings, Descartes later introduced what some regard as a “fudge factor” into the theory of motion in the Principles: from an ordinary perspective the earth does move; but from a philosophical one, it does not. This background indicates the novelty and originality of Newton's own attempt to explicate how scriptural passages concerning the motions of the heavenly bodies can be reconciled with the philosophical views he developed during the 1680s. New evidence from archival sources and correspondence supports this argument, shedding light on the Scholium and on Newton's conception of philosophy's relation to theology. (shrink)

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

From the topics discussed by Hattab and Menn, I examine two of special importance. The first is that of active powers: does the Cartesian natural world contain any, or is the apparent efficacy of natural agents always to be referred to God? In arguing that it is, I consider, following Hattab, Descartes' characterization of natural laws as "secondary causes." The second topic is that of ends. Menn argues, and I agree, that in late Aristotelianism Aristotle's own conception of an "art (...) in things" has been abandoned. The point is reinforced when one considers the general divine ends which must be invoked in cases of aborted action. In them no individual agent attains its end. Yet Nature as a whole continues to act toward ends. I suggest that those general ends, to which Suárez, for example, refers, may have served later philosophers, especially Malebranche, in combining the Cartesian notion of law with a teleological interpretation of nature that Descartes, for his part, rejected. (shrink)

The chapter begins with an initial survey of ups and downs of contextualist history of philosophy during the twentieth century in Britain and America, which finds that historically serious history of philosophy has been on the rise. It then considers ways in which the study of past philosophy has been used and is used in philosophy, and makes a case for the philosophical value and necessity of a contextually oriented approach. It examines some uses of past texts and of history (...) that reveal limits to noncontextual history, including Strawson's Kant, Rorty's grand diagnosis of the Western tradition, and Friedman on Kant's philosophy of mathematics. It then considers ways in which the history of philosophy may become philosophically deeper by becoming more historical, and instances in which history of philosophy of various stripes has or may deliver a philosophical payoff. Along the way, it urges historians of philosophy to attend not only to individual philosophers and their problems and projects, but also to the larger shape of the history of philosophy and its narrative themes. (shrink)

This paper explores the possibility of constructing a Cartesian space-time that can resolve the dilemma posed by a famous argument from Newton's early essay, De gravitatione. In particular, Huygens' concept of a center-of-mass reference frame is utilized in an attempt to reconcile Descartes' relationalist theory of space and motion with both the Cartesian analysis of bodily impact and conservation law for quantity of motion. After presenting a modern formulation of a Cartesian space-time employing Huygens' frames, a series of Newtonian counter-replies (...) are developed in order to estimate the viability of this relationalist project. (shrink)

In De gravitatione, Newton contends that Descartes' physics is fundamentally untenable since the "fixed" spatial landmarks required to ground the concept of inertial motion cannot be secured in the constantly changing Cartesian plenum. Likewise, it is has often been alleged that the collision rules in Descartes' Principles of Philosophy undermine the "relational" view of space and motion advanced in this text. This paper attempts to meet these challenges by investigating the theory of connected gears (or "kinematics of mechanisms") for a (...) potential Cartesian method of positing the permanent reference frames necessary to uphold Descartes' conservation law for the quantity of motion. In particular, the insights gained from an examination of the kinematics of mechanisms will provide the Cartesian with much needed resources to counter the two threats posed above. (shrink)

: This paper presents a detailed account of Descartes' derivation of his second law of nature—the law of rectilinear motion—from a priori metaphysical principles. Unlike the other laws the proof of the second depends essentially on a metaphysical assumption about the temporal immediacy of God's operation. Recent commentators (e.g., Des Chene and Garber) have not adequately explained the precise role of this assumption in the proof and Descartes' reasoning has continued to seem somewhat arbitrary as a result. My account better (...) reveals the dependence of the second law on fundamental principles about time and causality. (shrink)

: Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace (...) him by a new philosophy. In this essay, I would like to examine Mersenne's changing attitude toward Galileo. In the early 1620s, Mersenne lists Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne has become one of Galileo's most ardent supporters. How, then, did Mersenne learn to love Galileo? (shrink)

Despite holding to the essential distinction between mind and body, Descartes did not adopt a life-body dualism. Though humans are the only creatures which can reason, as they are the only creatures whose body is in an intimate union with a soul, they are not the only finite beings who are alive. In the present note, I attempt to determine Descartes'' criteria for something to be ''living.'' Though certain passages associate such a principle with the presence of a properly functioning (...) heart, I show that there are important reasons for also understanding life in terms of a degree of complexity of design. (shrink)

The significance or vacuity of the statement, “Everything has just doubled in size,” attracted considerable attention last century from scientists and philosophers. Presenting his conventionalism in geometry, Poincaré insisted on the emptiness of a hypothesis that all objects have doubled in size overnight. Such expansion could have meaning, he argued, “only for those who reason as if space were absolute … it would be better to say that space being relative, nothing at all has happened.” The logical empiricists concurred, viewing (...) the universal doubling hypothesis as illustrating the intrinsic metrical amorphousness of continuous manifolds. It is striking, therefore, to find Kant invoking a universal contraction in space and time to support his famous doctrine of transcendental idealism. In one of several completely neglected passages, he writes: “The proof that the things in space and time are mere appearances can also be grounded on the fact that the whole world could be contained in a nutshell and the entirety of elapsed time in a second without the least difference being met with.” Kant's “also” may suggest an idealist argument distinct from any proposed in published works. Here I ask: What is the meaning of Kant's Nutshell Argument for Idealism? (shrink)

That Descartes’ God is not a deceiver is amongst the canonical claims of early modern philosophy. The significance of this (purported) fact to the coherence of Descartes’ system is likewise canonical, infused in how we teach and think about the _Meditations_. Though prevalent, both ends of this narrative are suspect. We argue that Descartes’ color eliminativism, when coupled with his analysis of the cognitive structure of our sensory systems, entails that God is a deceiver. It’s doubtful that Descartes recognized this, (...) given his insistence that God is not a deceiver, and the role this plays in his system. But this is a concession Descartes can grant if we are careful about the kind of deception at play—a kind Descartes _does_ recognize, albeit not without some ambiguity. On our story, Descartes’ metaphysics and epistemology are not driven by concerns about deception _per se_, but by concerns about God’s _benevolence_. (shrink)

This paper explicates Descartes’ theory of intuition (intuitus). Departing from certain commentators, I argue that intuition, for Descartes, is a form of clear and distinct intellectual perception. Because it is clear and distinct, it is indubitable, infallible, and provides a grade of certain knowledge he calls ‘cognitio’. I pay special attention to why he treats intuition as a form of perception, and what he means when he says it is ‘clear and distinct’. Finally, I situate his view in relation to (...) those of his Scholastic predecessors on one hand and current theories on the other. His view anticipates the contemporary ‘perceptual model of intuition’, though it is much bolder with its promise of certainty. (shrink)

This paper is on Descartes’ account of modality and, in particular, his account of the necessity of the laws of nature. He famously argues that the necessity of the “eternal truths” of logic and mathematics depends on God’s will. Here I suggest he has the same view about the necessity of the laws of nature. Further, I argue, this is a plausible theory of laws. For philosophers often talk about something being nomologically or physically necessary because of the laws of (...) nature, but this necessity is thought to be metaphysically contingent. However, they struggle to explain how the laws could be genuinely necessary while being metaphysically contingent. The chief advantage of Descartes view, I argue, is that God’s will can plausibly explain both the necessity of the laws and the contingency of the laws. So, Descartes’ theistic account of laws provides a plausible explanation, perhaps the best explanation, of the contingent-necessity of laws of nature. (shrink)

This essay proposes a new interpretation of a central, and yet overlooked, argument Leibniz offers against Descartes’s power-free ontology of the corporeal world. Appealing to considerations about the successiveness of motion, Leibniz attempts to show that the reality of motion requires force. It is often assumed that the argument is driven by concerns inspired by Zeno. Against such a reading, this essay contends that Leibniz’s argument is instead best understood against the background of an Aristotelian view of the priority of (...) real being over time. The essay also shows how this alternative interpretation can help to shed new light on the difference between Leibnizian forces and Aristotelian powers, as well as on Leibniz’s famous claim that accounting for force leads us beyond the mechanistic corporeal realm. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such a metaphysics (...) can help us make progress on the problem of induction. (shrink)

This article addresses a debate in Descartes scholarship over the mind-dependence or -independence of time by turning to Merleau-Ponty’s "Nature" and "The Visible and the Invisible." In doing so, it shows that both sides of the debate ignore that time for Descartes is a measure of duration in general. The consequences to remembering what time is are that the future is shown to be the invisible of an intertwining of past and future, and that historicity is the invisible of God.

In the _Meditations_ and related texts from the early 1640s, Descartes argues that the self can be correctly considered as either a mind or a human being, and that the self’s properties vary accordingly. For example, the self is simple considered as a mind, whereas the self is composite considered as a human being. Someone might object that it is unclear how merely considering the self in different ways blocks the conclusion that a single subject of predication—the self—is both simple (...) and composite, which is contradictory. In response to this objection, this paper develops a reading of Descartes’s various ways of considering the self. I argue that the best reading of Descartes’s qualified claims about the self, i.e., about the self _qua_ mind or the self qua human being, presupposes an account of the unqualified self, that is, of the self _simpliciter_. I argue that the self _simpliciter_ is not a mind, and that it is not a human being either. This result might suggest the pessimistic conclusion that Descartes’s view of the self is incoherent. To avoid this result, I introduce a new metaphysical account of the Cartesian self. On my view, the self is individuated by a unified mental life. The self is constituted by the beings that jointly produce this mental life, and derives its unity from it. (shrink)

My thesis in this paper is: the modern concept of laws of motion—qua dynamical laws—emerges in 18th-century mechanics. The driving factor for it was the need to extend mechanics beyond the centroid theories of the late-1600s. The enabling result behind it was the rise of differential equations. -/- In consequence, by the mid-1700s we see a deep shift in the form and status of laws of motion. The shift is among the critical inflection points where early modern mechanics turns into (...) classical mechanics as we know it. Previously, laws of motion had been channels for truth and reference into mechanics. By 1750, the laws lose these features. Instead, now they just assert equalities between functions; and serve just to entail (differential) equations of motion for particular mechanical setups. This creates two philosophical problems. First, it’s unclear what counts as evidence for the laws of motion in the Enlightenment. Second, it’s a mystery whether these laws retain any notion of causality. That subverts the early-modern dictum that physics is a science of causes. (shrink)

In the period of emergence of early modern science, ‘monsters’ or individuals with physical congenital anomalies were considered as rare events which required special explanations entailing assumptions about the laws of nature. This concern with monsters was shared by representatives of the new science and Late Scholastic authors of university textbooks. This paper will reconstruct the main theses of the treatment of monsters in Late Scholastic textbooks, by focusing on the question as to how their accounts conceived nature’s regularity and (...) teleology. It shows that they developed a naturalistic teratology in which, in contrast to the naturalistic explanations usually offered by the new science, finality was at central stage. This general point does not impede our noticing that some authors were closer to the views emerging in the Scientific Revolution insofar as they conceived nature as relatively autonomous from God and gave a relevant place to efficient secondary causation. In this connection, this paper suggests that the concept of the laws of nature developed by the new science –as exception-less regularities—transferred to nature’s regularity the ‘strong’ character that Late Scholasticism attributed to finality and that the decline of the Late Scholastic view of finality played as an important concomitant factor permitting the transformation of the concept of laws of nature. (shrink)

RESUMEN La interpretación habitual de Descartes sostiene que la nueva ciencia cartesiana es resultado del remplazo, en las explicaciones científicas, de las causas finales y formales por las causas eficientes. Si bien dicha afirmación en líneas generales es correcta, se ha tendido a asumir que las causas eficientes no entrañan problema alguno. Este artículo desea cuestionar dicha asunción, poniendo de manifiesto una serie de problemáticas concernientes a la cognoscibilidad de las causas eficientes. ABSTRACT The common interpretation of Descartes argues that (...) the new science is a result of Cartesian replacement, in scientific explanations, of the final and formal causes by the efficient causes. While this statement is broadly correct, it has tended to assume that efficient causes do not imply any problem. This paper wishes to question this assumption, showing a number of problems concerning the knowability of efficient causes. (shrink)

The history of the Parallelogram Rule for composing physical quantities, such as motions and forces, is marked by conceptual difficulties leading to false starts and halting progress. In particular, authors resisted the required assumption that the magnitude and the direction of a quantity can interact and are jointly necessary to represent the quantity. Consequently, the origins of the Rule cannot be traced to Pseudo-Aristotle or Stevin, as commonly held, but to Fermat, Hobbes, and subsequent developments in the latter part of (...) the seventeenth century. (shrink)

The best way to understand the Meditations is through the lens of Descartes's theistic metaphysics rather than via his programme for physical science. This applies to his use of the concept of ‘nature’ in the Sixth Meditation, which serves Descartes's goal of theodicy. In working this out, Descartes reaches a conclusion about the functional role of sensory perception that is, paradoxically, not far from that offered by Darwinian naturalism. So far from being inherently geared to tracking the truth, the role (...) of sensation is linked to its survival value for the organism. In virtue of his theistic metaphysics however, Descartes is able to set this conclusion against the background of other cognitive faculties that are in principle accurate detectors of the truth; the absence of such a resource for modern Darwinian naturalists creates difficulties for the presumption that humans are cognitively equipped to search for the truth. (shrink)

The aim of this paper is to revisit the major arguments of the seventeenth century debate concerning laws and powers. Its primary points are two. First, though the dominant conception of nature was such that there was no room for power in bodies, the very idea that laws govern the behaviour of matter in motion brought with it the following issue, which came under sharp focus in the work of Leibniz: how possibly can passive matter, devoid of power, obey laws? (...) Though Leibniz’s answer was to re-introduce powers, two radically different conceptualisations of the relation between laws and powers became available after him. Hume denied powers altogether, whereas Newton thought that to introduce a power is to introduce a law. The second main point will be that though laws were meant to replace powers, the real dilemma ended up being not laws vs powers, but rather necessity vs non-necessity in nature. To exploit, an expression used by Newton, the question was: what is the place of necessity in the frame of nature? (shrink)

The distinction between the mental operations of abstraction and exclusion is recognized as playing an important role in many of Descartes’ metaphysical arguments, at least after 1640. In this paper I first show that Descartes describes the distinction between abstraction and exclusion in the early Rules for the Direction of the Mind, in substantially the same way he does in the 1640s. Second, I show that Descartes makes the test for exclusion a major component of the method proposed in the (...) Rules. Third, I argue that in Rule 14 the exclusion-abstraction distinction is connected to a theory of distinctions, which includes a notion of real distinction as essentially tied to the imagination. This sheds light on Descartes’ development in and after the Rules. (shrink)

This essay offers an interpretation of Descartes’ treatment of the concepts of place and space in the Principles of Philosophy. On the basis of that interpretation, I argue that his understanding and application of the concept of space supports a pluralist interpretation of Descartes on extended substance. I survey the Scholastic evolution of issues in the Aristotelian theory of place and clarify elements of Descartes’ appropriation and transformation thereof: the relationship between internal and external place, the precise content of the (...) claim that space and body are really identical, and the way we conceptually distinguish space from body. Descartes applies his concept of space in ways that illuminate the metaphysical structure of extension. In particular, he uses the concept to specify the degree to which finite parts of matter are independent of each other. I argue that for Descartes, conceiving extension as indivisible is an artifact of conceiving it as a space. That is, pace the monistic reading of Cartesian extended substance, regarding extension as indivisible is an artifact of conceiving it in a way more removed from its real nature. (shrink)

Algebraic equations in the tradition of Descartes and Frans Van Schooten accompany Christiaan Huygens’s early work on collision, which later would be reorganized and presented as De motu corporum ex percussione. Huygens produced the equations at the same time as his announcement of his rejection of Descartes’s rules of collision. Never intended for publication, the equations appear to have been used as preliminary scaffolding on which to build his critiques of Descartes’s physics. Additionally, Huygens used algebraic equations of this form (...) to accurately predict the speeds of bodies after collision in experiments carried out at the Royal Society. Despite their deceptive simplicity, Huygens’s algebraic equations pose significant conceptual problems both mathematically and for their physical interpretation especially for negative speeds; they may very well have been the source of a new principle, the conservation of quantity of motion with direction. (shrink)

This paper presents a praxiological analysis of three everyday educational practices or strategies that can be considered as being directed at the moral formation of the emotions. The first consists in requests to imagine other's emotional reactions. The second comprises requests to imitate normative emotional reactions and the third to re-appraise the features of a situation that are relevant to an emotional response. The interest of these categories is not just that they help to organize and recognize the significance of (...) what might otherwise appear to be a disparate set of ordinary moral-educational interactions between children and educators. We suggest, further, that this analysis provides some new insight into what distinguishes the broad and recurrent conceptions of moral education from one another. Rather than being straightforwardly reducible to intractable differences over core normative or meta-ethical questions they can also be seen as correlating with different suppositions about the central role of the emotions in moral life and, correspondingly, different but to a large degree compatible interpretations of what the. (shrink)

The employment by seventeenth-century natural philosophers of stock theological notions like creation, immensity, and eternity in the articulation and justification of emerging physical programs disrupted a delicate but longstanding balance between transcendent and immanent conceptions of God. By playing a prominent (if not always leading) role in many of the major scientific developments of the period, God became more intimately involved with natural processes than at any time since antiquity. In this discussion, I am particularly concerned with the causal and (...) spatio-temporal relations between God and nature in the seventeenth century as recent scholarship has revealed how dramatically traditional conceptions of these relations were transformed by philosophers and scientists like Descartes, Malebranche, More, and Newton. (shrink)

(2005). Learning From Descartes, Via Bennett. British Journal for the History of Philosophy: Vol. 13, No. 1, pp. 139-147. doi: 10.1080/0960878042000317636.

: This paper offers my current view of a joint research project, with Bernard R. Goldstein, that examines Kepler's unification of physics and astronomy. As an organizing theme, I describe the extent to which the work of Kepler led to the appearance of the form of Copernicanism that we accept today. In the half century before Kepler's career began, the understanding of Copernicus and his work was significantly different from the modern one. In successive sections I consider the modern conception (...) of Kepler's contribution to Copernicanism, the most influential sixteenth century view of Copernicus's work and its sequel, Kepler's work from the viewpoint of this tradition, and finally the historical origins of the modern view of Copernicanism. (shrink)

I survey the debate over rationalism and empiricism in science. This chapter contains sections titled: The New Experimental Science as a Challenge to Intuition, Geometry and Intuition, The Mathematical Tradition and Theoretical Science.

Descartes’s most extensive discussion of the law of refraction and the shape of the anaclastic lens is contained in Rule 8 of "Rules for the Direction of the Mind". Few reconstructions of Descartes’s discovery of the law of refraction take Rule 8 as their basis. In Rule 8, Descartes denies that the law of refraction can be discovered by purely mathematical means, and he requires that the law of refraction be deduced from physical principles about natural power or force, the (...) nature of the action of light, and the behavior of light rays in a variety of transparent media. For over a century, however, there has been broad agreement that Descartes discovered the law of refraction by purely mathematical means, and that he only later provided the relevant physical rationale (via comparisons or analogies) in Dioptrics II. I execute each step in Descartes’s proposed deduction of the law of refraction and the shape of the anaclastic lens in Rule 8 and concretely show how Descartes could have discovered the law of refraction and the shape of the anaclastic by its means. Rule 8, I argue, reflects Descartes’s actual path to the discovery of the law of refraction and the shape of the anaclastic lens. (shrink)

This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical (...) theory presented in Tractatus Opticus I constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in Tractatus Opticus II and First Draught, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in De Corpore Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in De Corpore does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of Tractatus Opticus I. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics. (shrink)

In Spinoza’s substance monism, radically different attributes constitute the essence of one and the same substance qua a strongly unified whole. Showing how this is possible poses a formidable Cartesian challenge to Spinoza’s metaphysics. In this paper I suggest a reconstruction of Spinoza’s notion of substance that meets this challenge and explains a major feature of this notion. I then show how this reconstruction can be used to resolve two fundamental problems of the Cartesian framework that pertain to Spinoza’s metaphysics. (...) On this basis, I then explain two further major features of Spinoza’s notion of substance. While my suggested reconstruction has all these advantages and accords well with Spinoza’s conceptual framework, it goes beyond what he explicitly says concerning substance monism. It is in the spirit of his metaphysical framework rather than in its letter. Thus, all I intend to show is that Spinoza has the conceptual resources for coming to terms with some of the deep problems that beset his metaphysics. (shrink)