I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to ``explain'' inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of ``explain'' is rather different from what one might have expected. This (...) sense of explanation is connected with a view of theories---I call it the ``puzzleball view''---on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions. (shrink)

The history of mechanics has been extensively investigated in a number of historical works. The full story from the Greeks and medievals through the Scientific Revolution to the modern era is long and complex. But it is also incomplete. Studies to date have been admirably thorough in putting empirical discoveries into proper perspective and in making clear the great importance of mathematical innovations. But there has been surprisingly little regard for the role of thought experiments in the development of mechanics. (...) We attempt to rectify this, at least in part. After a brief account of Greek ideas of space and motion, we focus on late medieval and early modern physics, especially the development of inertial motion. In particular, we examine the thought experiments of Buridan, Oresme, and Galileo, which did so much to undermine Aristotle’s account of motion and lead the way to the modern concept of inertia. (shrink)

This paper enquires into a paradigmatic change concerning the concept of motion: from a phenomenological conception of motion understood as a continuous and finite process of translation, to a physical conception of motion as rectilinear, uniform and continuous, that is, as an inertial state that if unhindered, can extend infinitely – the former held by Aristotle, the latter by Koyré, a shift that is evidenced by their contrasting treatment of Zeno’s paradoxes. I argue that both ontologies (...) of motion can be understood in phenomenological terms: Motion is accomplished by the real itself. However, while Aristotle’s continuous motion as actualization of the form of a given body involves its formal determination and constitution of sense, Koyré’s conceives of motion and rest as kinds of being and motion itself as exemplifcation of the mathematization of nature that Husserl described in the Crisis. Taken together, these changes presuppose a transformation of metaphysical and epistemic frameworks. (shrink)

We present an approach to understanding the origin of inertia involving the electromagnetic component of the quantum vacuum and propose this as a step toward an alternative to Mach's principle. Preliminary analysis of the momentum flux of the classical electromagnetic zero-point radiation impinging on accelerated objects as viewed by an inertial observer suggests that the resistance to acceleration attributed to inertia may be at least in part a force of opposition originating in the vacuum. This analysis avoids the ad (...) hoc modeling of particle-field interaction dynamics used previously by Haisch, Rueda, and Puthoff (Phys. Rev. A 49, 678, (1994)) to derive a similar result. This present approach is not dependent upon what happens at the particle point, but on how an external observer assesses the kinematical characteristics of the zero-point radiation impinging on the accelerated object. A relativistic form of the equation of motion results from the present analysis. Its manifestly covariant form yields a simple result that may be interpreted as a contribution to inertial mass. We note that our approach is related by the principle of equivalence to Sakharov's conjecture (Sov. Phys. Dokl. 12, 1040, (1968)) of a connection between Einstein action and the vacuum. The argument presented may thus be construed as a descendant of Sakharov's conjecture by which we attempt to attribute a mass-giving property to the electromagnetic component—and possibly other components—of the vacuum. In this view the physical momentum of an object is related to the radiative momentum flux of the vacuum instantaneously contained in the characteristic proper volume of the object. The interaction process between the accelerated object and the vacuum (akin to absorption or scattering of electromagnetic radiation) appears to generate a physical resistance (reaction force) to acceleration suggestive of what has been historically known as inertia. (shrink)

A theorem due to Bob Geroch and Pong Soo Jang [“Motion of a Body in General Relativity.” Journal of Mathematical Physics 16, ] provides the sense in which the geodesic principle has the status of a theorem in General Relativity. Here we show that a similar theorem holds in the context of geometrized Newtonian gravitation. It follows that in Newtonian gravitation, as in GR, inertial motion can be derived from other central principles of the theory.

It is no inconsiderable endeavor to undertake a philosophical analysis of the notions of inertia and absolute space from Newton to Einstein. This is all the more so insofar as Ghins' approach is far from the orthodoxy of the logical empiricists: his claim is that the scientists themselves were seeking to attribute the effects of inertia to real causes, or, in other words, "to specify adequately the system or systems of reference relative to which motions, whether accelerated or not, would (...) give rise or not to such effects". In terms of this causal point of view, he then defines the fundamental question as that of the determination of the inertial or noninertial character of a motion or of a reference system. (shrink)

A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies. A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. A dynamical account of motion leads to the idea of an “inertial (...) frame,” or a reference frame relative to which motions have distinguished dynamical properties. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions. It follows that, in an inertial frame, the center of mass of a system of bodies is always at rest or in uniform motion. It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame. For example, in Newtonian celestial mechanics, taking the “fixed stars” as a frame of reference, we can determine an inertial frame whose center is the center of mass of the solar system; relative to this frame, every acceleration of every planet can be accounted for as a gravitational interaction with some other planet in accord with Newton 's laws of motion. (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.

Le présent essai se propose d'appréhender la doctrine cartésienne selon laquelle ce qui existe ne saurait subsister sans que Dieu le soutienne dans l'être par une activité créatrice continuée. Comment Dieu soutient-il l'existence et pourquoi lui est-il nécessaire de le faire ? L'auteur analyse l'apparente contradiction, qui fait problème, entre la doctrine de la création continuée et l'affirmation par Descartes que le mouvement se poursuit à moins que n'intervienne quelque force extérieure. Il examine ensuite, pour la récuser, la thèse (défendue (...) par Gilson et par Gueroult) selon laquelle la doctrine de la création continuée impliquerait la discontinuité du temps. This essay seeks to understand Descartes's doctrine that what exists cannot continue to exist unless God sustains it by continuous creative activity. How does God sustain existence and why is it necessary for Him to do this ? The essay explores a puzzling apparent contrast between the doctrine of continuous creation and Descartes's claim that motion continues unless an external force interferes. Further, it considers and rejects the thesis (maintained by Gilson and Gueroult) that the doctrine of continuous creation entails that time is discontinuous. (shrink)

Le présent essai se propose d'appréhender la doctrine cartésienne selon laquelle ce qui existe ne saurait subsister sans que Dieu le soutienne dans l'être par une activité créatrice continuée. Comment Dieu soutient-il l'existence et pourquoi lui est-il nécessaire de le faire ? L'auteur analyse l'apparente contradiction, qui fait problème, entre la doctrine de la création continuée et l'affirmation par Descartes que le mouvement se poursuit à moins que n'intervienne quelque force extérieure. Il examine ensuite, pour la récuser, la thèse selon (...) laquelle la doctrine de la création continuée impliquerait la discontinuité du temps. This essay seeks to understand Descartes's doctrine that what exists cannot continue to exist unless God sustains it by continuous creative activity. How does God sustain existence and why is it necessary for Him to do this ? The essay explores a puzzling apparent contrast between the doctrine of continuous creation and Descartes's claim that motion continues unless an external force interferes. Further, it considers and rejects the thesis that the doctrine of continuous creation entails that time is discontinuous. (shrink)

In Book 1 of the Principia, Newton presented two different descriptions of orbital motion under the action of a central force. In Prop. 1, he described this motion as a limit of the action of a sequence of periodic force impulses, while in Prop. 6, he described it by the deviation from inertial motion due to a continuous force. From the start, however, the equivalence of these two descriptions has been the subject of controversies. Perhaps the (...) earliest one was the famous discussion from December 1704 to 1706 between Leibniz and the French mathematician Pierre Varignon. But confusion about this subject has remained up to the present time. Recently, Pourciau has rekindled these controversies in an article in this journal, by arguing that “Newton never tested the validity of the equivalency of his two descriptions because he does not see that his assumption could be questioned. And yet the validity of this unseen and untested equivalence assumption is crucial to Newton’s most basic conclusions concerning one-body motion” (Pourciau in Arch Hist Exact Sci 58:283–321, 2004, 295). But several revisions of Props. 1 and 6 that Newton made after the publication in 1687 of the first edition of the Principia reveal that he did become concerned to provide mathematical proof for the equivalence of his seemingly different descriptions of orbital motion in these two propositions. In this article, we present the evidence that in the second and third edition of the Principia, Newton gave valid demonstrations of this equivalence that are encapsulated in a novel diagram discussed in Sect. 4. (shrink)

Galileo proposed what has been called a proto-inertial principle, according to which a body un horizontal motion will conserve its motion. This statement is only true in counterfactual circumstances where no impediments are present. This paper analyzes how Galileo could have been justified in ascribing definite properties to this idealized motion. This analysis is then used to better understand the relation of Galileo’s proto-inertial principle to the classical inertial principle.

The physical origin of inertial forces is shown to be a consequence of the local interaction of Dirac's real covariant ether model(1) with accelerated microobjects, considered as real extended particlelike solitons, piloted by surrounding subluminal real wave fields packets.(2) Their explicit form results from the application of local inertial Lorentz transformations to the particles submitted to noninertial velocitydependent accelerations, i.e., constitute a natural extension of Lorentz's interpretation of restricted relativity.(3) Indeed Dirac's real physical covariant ether model implies (...) class='Hi'>inertial forces if one considers the real accelerated noninertial motions of general relativity, defined within the absolute local inertial frames associated with the observed local isotropy of the 2.7° K background microwave radiation.(4) Inertia thus appears as a necessary consequence of the real particle motions described by the E.d.B.B. formalism of quantum mechanics. (shrink)

The concept of forcefree motion is primitive, i.e., unexplained, in special relativity. The paper demonstrates a way to characterize it by “more primitive,” directly operationally interpreted notions. These are the worldlines of (more or less) pointlike, but non-quantum bodies and of light signals, clock parametrizations of the former kind of worldlines and the direction, in which an observer sees a light signal go out. Already at this general level one can define the “radar distance” and the “radar (initial) velocity” (...) of one body with respect to another, and can define in a reasonable manner that two bodies move in “opposite directions” with respect to an observer. These concepts are then used to formulate a certain criterion for path structures which can experimentally be tested without presupposing inertial frames, atomic clocks, etc. It is demonstrated that the path structure of free motion in gravity-free regions of space-time, i.e., in the domain of validity of special relativity, satisfies that criterion. (shrink)

_ Source: _Volume 29, Issue 1, pp 9 - 38 Hobbes tried to develop a strict version of the mechanical philosophy, in which all physical phenomena were explained only in terms of bodies in motion, and the only forces allowed were forces of collision or impact. This ambition puts Hobbes into a select group of original thinkers, alongside Galileo, Isaac Beeckman, and Descartes. No other early modern thinkers developed a strict version of the mechanical philosophy. Natural philosophies relying solely (...) on bodies in motion require a concept of inertial motion. Beeckman and Descartes assumed rectilinear motions were rectilinear, but Galileo adopted a theory which has been referred to as circular inertia. Hobbes’s natural philosophy depended to a large extent on what he called “simple circular motions.” In this paper, I argue that Hobbes’s simple circular motions derived from Galileo’s belief in circular inertia. The paper opens with a section outlining Galileo’s concept, the following section shows how Hobbes’s physics depended upon circular motions, which are held to continue indefinitely. A third section shows the difficulty Hobbes had in maintaining a strictly mechanistic philosophy, and the conclusion offers some speculations as to why Galileo’s circular inertia was never entertained as a serious rival to rectilinear inertia, except by Hobbes. (shrink)

Previous studies have shown that the motion intention recognition for lower limb prosthesis mainly focused on the identification of performed gait. However, the bionic prosthesis needs to know the next movement at the beginning of a new gait, especially in complex operation environments. In this paper, an upcoming locomotion prediction scheme via multilevel classifier fusion was proposed for the complex operation. At first, two motion states, including steady state and transient state, were defined. Steady-state recognition was backtracking of (...) a completed gait, which would be used as prior knowledge of motion prediction. In steady-state recognition, surface electromyographic and inertial sensors were fused to improve recognition accuracy; five typical locomotion modes were recognized by random forest classifier with over 97.8% accuracy. The transient state was defined as an observation period at the initial stage of upcoming movement, in which only the sEMG signal was recorded due to the limitation of sliding window length. LightGBM classifier was validated to outperform other methods in the accuracy and prediction time of transient-state recognition. Finally, a simplified HMM model based on prior knowledge and observation result was constructed to predict upcoming locomotion. The results indicated that the locomotion prediction was over 91% accuracy. The proposed scheme implements the locomotion prediction at the initial stage of each gait and provides critical information for the gait control of lower limb prosthesis. (shrink)

Contrary to popular belief, I argue that Leibniz is not hopelessly confused about motion: Leibniz is indeed both a relativist and an absolutist about motion, as suggested by the textual evidence, but, appearances to the contrary, this is not a problem; Leibniz’s infamous doctrine of the equivalence of hypotheses is well-supported and well-integrated within Leibniz’s physical theory; Leibniz’s assertion that the simplest hypothesis of several equivalent hypotheses can be held to be true can be explicated in such a (...) way that it makes good sense; the mere Galilean invariance of Leibniz’s conservation law does not compromise Leibniz’s relativism about motion; and Leibniz has a straightforward response to Newton’s challenge that the observable effects of the inertial forces of rotational motions empirically distinguish absolute from relative motions. (shrink)

In a way similar to classical mechanics where we have the concept of inertial time as expressed in the motions of bodies, in the theory of relativity we can regard the inertial time as the only notion of time at play. The inertial time is expressed also in the propagation of light. This gives rise to a notion of clock—the light clock, which we can regard as a notion derived from the inertial time. The light clock (...) can be seen as a solution of the theory, which complies with the requirement that a clock to be so must have a rate that is independent from its past history. Contrary to Einstein’s view, we do not need the concept of “clock” as an independent concept. This implies, in particular, that we do not need to rely on the notions of atomic clock or atomic time in the theory of relativity. (shrink)

The principle of relativity, that there is no preferred state of uniform motion, has recently come into conflict with certain cosmological observations. In an attempt to overcome this difficulty, an alternative formulation is explored in which this principle is replaced by the principle of universal time, while retaining the invariance of the speed of light. These two postulates lead to a well-defined world model in which one inertial frame has a preferred status. But the invariance properties of the (...) laws of physics are unaffected, and the model may be regarded as a modified form of special relativity which is in accordance with the new cosmological evidence. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity in some sense relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in (...) a space-time coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

Mach's principle is discussed as a fundamental statement on kinematics, and an apparent contradiction is identified in the Lorentz-Minkowski form of the inertial metric. To resolve the incompatibility, length is redefined so that the speed of light is a field-dependent variable, although still constant for all inertial observers at a point in space-time. Gravitational theories with variableG are considered, and it is shown that a redefinition of length and time results in constantG and variablec.

The obvious metaphysical differences between Newton and Leibniz concerning space, time, and motion reflect less obvious differences concerning the relation between geometry and physics, expressed in the questions: what are the invariant quantities of classical mechanics, and what sort of geometrical frame of reference is required to represent those quantities? Leibniz thought that the fundamental physical quantity was “living force” (mv2), of which every body was supposed to have a definite amount; this notion violates the classical principle of relativity, (...) since it makes a physical distinction between uniform velocity and absolute rest. But Leibniz did not try to represent this physical quantity in a spatio-temporal reference frame, assuming, instead, that all such frames are equivalent so long as they agree on the relative motions (changes in the mutual Euclidean distances) among bodies. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time (...) coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

Head stabilization is fundamental for balance during locomotion but can be impaired in elderly or diseased populations. Previous studies have identified several parameters of head stability with possible diagnostic value in a laboratory setting. Recently, the ecological validity of measures obtained in such controlled contexts has been called into question. The aim of this study was to investigate the ecological validity of previously described parameters of head stabilization in a real-world setting. Ten healthy subjects participated in the study. Head and (...) trunk movements of each subject were recorded with inertial measurement units (IMUs) for a period of at least ten hours. Periods of locomotion were extracted from the measurements and predominant frequencies, root mean squares (RMSs) and bout lengths were estimated. As parameters of head stabilization, attenuation coefficients (ACs), harmonic ratios (HRs), coherences and phase differences were computed. Predominant frequencies were distributed tightly around 2 Hz and ACs, HRs and coherences exhibited the highest values in this frequency range. All head stability parameters exhibited characteristics consistent with previous reports, although higher variances were observed. These results suggest that head stabilization is tuned to the 2 Hz fundamental frequency of locomotion and that previously described measures of head stability could generalize to a real-world setting. This is the first study to address the ecological validity of these measures, highlighting the potential use of head stability parameters as diagnostic tools or outcome measures for clinical trials. The low cost and ease of use of the IMU technology used in this study could additionally be of benefit for a clinical application. (shrink)

In a recent article in this journal, Barbara Lariviere offers a very useful distinction between two ways of understanding the claims that Leibniz, or relational theorists in general, might wish to make about the nature of motion and the structure of space and time; viz., There is no real inertial structure to space-time.and There is a real inertial structure to space-time, but it is dynamical rather than absolute.Citing the authority of Weyl, the author argues that L1 is (...) untenable; indeed, the argument purports to show that if L1 were true, then there would be no coherent basis for a theory of motion, not even a relational theory. My main goal in this note is to point out why this argument is mistaken while at the same time sketching the real reason why the relational conception of motion is untenable. In addition I will offer a few remarks about the relevance of L2 to the absolute-relational controvery. (shrink)

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to (...) figure in a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

This paper explores the Cartesian physics of circular motion, in particular, the long-standing puzzle concerning the possible role of a circular inertial concept in Descartes' theories. Although some commentators have claimed that Descartes' famous "rotating sling" examples favor a rotational component of "striving" towards motion, and that this aspect of his project constitutes a form of inertial thinking, it will be argued that a much stronger case for a Cartesian brand of rotational inertial motion (...) can be constructed from a little-known correspondence, the letter to Ciermans, dated 1638. (shrink)

James A. Diefenbeck, Wayward Reflections on the History ofPhilosophyThomas R. Flynn Sartre, Foucault and Historical Reason. Volume 1:Toward an Existential Theory of HistoryMark Golden and Peter Toohey Inventing Ancient Culture:Historicism, Periodization and the Ancient WorldZenonas Norkus Istorika: Istorinis IvadasEverett Zimmerman The Boundaries of Fiction: History and theEighteenth‐Century British Novel.

The status of the geodesic principle in General Relativity has been a topic of some interest in the recent literature on the foundations of spacetime theories. Part of this discussion has focused on the role that a certain energy condition plays in the proof of a theorem due to Bob Geroch and Pong-Soo Jang [“Motion of a Body in General Relativity.” Journal of Mathematical Physics16(1) (1975)] that can be taken to make precise the claim that the geodesic principle is (...) a theorem, rather than a postulate, of General Relativity. In this brief note, I show, by explicit counterexample, that not only is a weaker energy condition than the one Geroch and Jang state insufficient to prove the theorem, but in fact a condition still stronger than the one that they assume is necessary. (shrink)

Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues to defend (...) apriorism in the physical world. This edition features two new chapters, one on “counter thought experiments” and another on the development of inertial motion. With plenty of illustrations and updated coverage of the debate between Platonic rationalism and classic empiricism, this is a lively and engaging contribution to the field of philosophy of science. (shrink)

We argue that the fundamental assertion underlying Mach's critique of Newton's first law is that inertial motion is not motion in the absence of causes; rather, it is motion whose cause lies in some homogeneous aspect of the environment. We distinguish this formal requirement (Mach's principle) from two hypotheses which Mach considers concerning the origin of inertia: that the distant stars play (1) a merely “collateral” or (2) a “fundamental” role in the causal determination of (...) class='Hi'>inertial motion. -/- In his later writings, Mach deliberately avoids referring to the concept of causation, and indeed, this has made the interpretation of Mach's principle a subject of widespread controversy. However, in his earlier writings, the substance of Mach's critique is less ambiguously expressed. Therefore, close attention is given to Mach's early writings and the evolution of his thought. Various accounts in the secondary literature on Mach's principle, in particular those of Norton and DiSalle, are assessed on this basis. We end with a defence of the Machian status and legitimacy of the early Einstein's research program. (shrink)

As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. (...) I conclude by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter. (shrink)

The idea at the core of the New Mechanical account of explanation can be summarized in the claim that explaining means showing ‘how things work’. This simple motto hints at three basic features of Mechanistic Explanation (ME): ME is an explanation-how, that implies the description of the processes underlying the phenomenon to be explained and of the entities that engage in such processes. These three elements trace a fundamental contrast with the view inherited from Hume and later from strict logical (...) empiricism (see Creath 2017), focused on epistemic and formal features of science and according to which issues concerning the kind of entities and processes that lie within a theory’s domain are extraneous to science and belong instead to ontology or metaphysics. Philosophers belonging to the new mechanical philosophy believe that the received view of scientific explanation (Hempel 2001), pivoting on the notion of law of nature, overshadows this insight. Since its origin in the 17th century, mechanical philosophy aimed to explain natural phenomena by reducing them to mechanisms. Traditional attempts to define the concept of mechanism involved the identification of a limited set of fundamental elements as, for instance, contact action, action at a distance, inertial motion (see e.g. Hesse 2005), and, more recently, transmission of a mark, or of a conserved quantity (see Frisch, this volume). The new mechanical philosophy rejects this austere characterization of mechanisms and mechanistic explanation and aim at providing a novel, philosophically rigorous explication of the concept of mechanism and of its role in scientific explanation and practice. ME has been adopted with profit in philosophy of special sciences (for instance in biomedical sciences, e.g. in the explanation of chemical transmission at synapses ((Machamer, Darden and Craver 2000), MDC henceforth); but also in social sciences, e.g. the three kinds of social mechanisms in Coleman’s analysis of Max Weber’s account of the role of the Protestant ethic in the growth of capitalism (Hedström and Swedberg 1998)), where exceptionless regularities are rarely ever found. In physics, it is generally possible to formulate explanations in law-based form, with the result that the plurality of explanatory forms might be overlooked. This should not come as a surprise, given that physics was the main inspiration for logical empiricists, and, in particular, Newtonian physics was a template for Hempel’s formulation of the covering law model. However, this situation is unfortunate, since, we will argue, knowing how things work is often part of the explanation of physical phenomena. In this chapter, we provide an introduction to the basic features of ME, with specific focus on its application to physics (section 1). The main part of the chapter is devoted to the defence of two theses: on the one hand, some domains of physics are not compatible with mechanistic reasoning and explanation (section 2); on the other hand, a comprehensive account of explanation in physics can’t dispense with ME (section 3). (shrink)

The rich connections between metaphysics and natural philosophy in the early modern period have been widely acknowledged and productively mined, thanks in no small part to the work of Margaret Wilson, whose book, Descartes, served as an inspirational example for a generation of scholars. The task of this paper is to investigate one particular such connection, namely, the relation between occasionalist metaphysics and strict mechanism. My focus will be on the work of Nicholas Malebranche, the most influential Cartesian philosopher after (...) Descartes himself. I begin with two crucial facts about Malebranche’s philosophy: (1) Malebranche was an occasionalist, that is, he held that God was the only true cause, that all modifications of bodies and of minds can be produced by God alone. (2) Malebranche adhered firmly to strict mechanism. By strict mechanism, I mean the view, found most prominently in Descartes and in Boyle’s more ideological writings, that the qualities of bodies are exhausted by a very short list (size, shape, motion, and perhaps solidity) and that, most importantly, bodies interact only at contact by impact. Another way of describing this “contact action” requirement is as the thesis that the only fundamental laws of physics are laws of inertial motion and laws of the communication of motion at impact. In.. (shrink)

In a crucial passage of the second-edition Transcendental Deduction, Kant claims that the concept of motion is central to our understanding of change and temporal order. I show that this seemingly idle claim is really integral to the Deduction, understood as a replacement for Locke’s “physiological” epistemology (cf. A86-7/B119). Béatrice Longuenesse has shown that Kant’s notion of distinctively inner receptivity derives from Locke. To explain the a priori application of concepts such as succession to this mode of sensibility, Kant (...) construes the mind as receptive to its own activity. As Longuenesse understands Kant’s response to Locke, “motion” becomes little more than a metaphor for the action of understanding on inner sense. For Michael Friedman, in contrast, this passage evidences Kant’s deep concern with the foundations of Newtonian science. He reads it as a reference to inertial motion, the standard by which temporal intervals are measured. I show that Longuenesse’s and Friedman’s interpretations are in fact complementary. Both Locke and Kant are deeply concerned with the quantification of time. So Longuenesse is right that §24 is meant to supplant Locke’s account, and Friedman correctly takes it as the foundation of Kant’s account of the application of quantitative concepts to time. Kant aims, specifically, to explain cognition of time as continuous magnitude. However, Longuenesse leaves Kant without an answer to Locke’s challenge that continuous magnitude cannot be understood on the basis of discrete magnitude. And on Friedman’s view Kant’s account of the understanding’s activity presupposes, and thus cannot explain, the achievements of the mathematical sciences (such as the representation of temporal continuity). On my reading, Kant’s key contention is that we must regard the segregation of temporally ordered representation into units as the work of the understanding, rather than (as Locke views it) of sensibility. By giving the understanding this role, Kant succeeds where he takes Locke to fail. I show how the power to unify temporal representation can be ascribed to the understanding on the basis, not of assumed mathematical or scientific knowledge, but of its characterization as the power of judgment. (shrink)

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic (...) properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. (shrink)

In the Principles of Philosophy, Descartes attempts to explicate the well-known phenomena of varying bodily size through an appeal to the concept of "solidity," a notion that roughly corresponds to our present-day concept of density. Descartes' interest in these issues can be partially traced to the need to define clearly the role of matter in his natural laws, a problem particularly acute for the application of his conservation principle. Specifically, since Descartes insists that a body's "quantity of motion," defined (...) as the product of its "size" and speed, is conserved in all material interactions, it is imperative that he explain how solidity influences the magnitude of this force. As a means of resolving this problem, Descartes postulated an idealized condition of "perfect solidity" which correlates a body's "agitation" force (a forerunner of Newton's concept of non-accelerating, or "inertial" motion) with the interplay of its volume, surface area, and composition of minute particles. This essay explores this often misunderstood aspect of Descartes' physics, as well as the special function of idealized conditions in his collision rules. Contrary to those commentators who regard "perfect solidity" as a stipulation on bodily impact, this notion, it will be argued, is primarily concerned with the internal composition of macroscopic bodies, and only indirectly with their collision characteristics. Along the way, many of Descartes' hypotheses will be shown to display a level of sophistication and intricacy that, despite their essential incompatibility, belie several of the common misconceptions of Cartesian science. (shrink)

This paper argues against a standard view that all deterministic and conservative classical mechanical systems are time-reversible, by asking how the temporal evolution of a system modulates parametric imprecision (either ontological or epistemic). It notes that well-behaved systems (e.g. inertial motion) can possess a dynamics which is unstable enough to fail at reversing uncertainties—even though exact values are reliably reversed. A limited (but significant) source of irreversibility is thus displayed in classical mechanics, closely analogous the lack of predictability (...) revealed by unstable chaotic systems. (shrink)

This work is an argument for the notion of knowledge production. It is an attempt at an epistemological and historiographic position which treats all facets and modes of knowledge as products of human practices, a position developed and demonstrated through a reconstruction of two defining episodes in the scientific career of Robert Hooke : the composition of his Programme for explaining planetary orbits as inertial motion bent by centripetal force, and his development of the spring law in relation (...) to his invention of the spring watch. ;The revival of interest in the history of experimental and technological knowledge has accorded Hooke much more attention than before. However, dependent on the conception of knowledge as a representation of reality, this scholarship is bound to the categories of influence and competition, and concentrates mainly on Hooke's numerous passionate exchanges with Isaac Newton and Christiaan Huygens. I favourably explore the neo-pragmatist criticism of representation epistemology in the writing of Richard Rorty and Ian Hacking. This criticism exposes the conventional portrayal of Hooke as "a mechanic of genius, rather than a scientist" as a reification of the social hierarchy between Hooke's Royal Society employers and his artisan-experimenters employees. ;However, Rorty and Hacking's efforts to do away with the image of the human knower as an enclosed realm of 'ideas' have not been completed. Undertaking this unfinished philosophical task, my main strategy is to erase the false gap between knowledge which is clearly produced--practical, technological and experimental, 'know how', and knowledge which we still think of as representation--theoretical 'knowing that'. I present Hooke, Newton and Huygens as craftsmen, who, employing various resources, labor to manufacture material and theoretical artifacts. Eschewing the category of independent facts awaiting discovery, I attempt to compare practices and techniques rather than to adjudicate priority claims, replacing ideas which 'develop', 'inspire', and 'influence', with tools and skills which are borrowed, appropriated and modified for new uses. ;This approach enables tracing Hooke's creation of his Programme from his microscopy, and reconstructing his use of springs to structure a theory of matter. With his unique combination of technical and speculative talents Hooke comes to personify the relations between the theoretical-linguistic and the experimental-technological in their full complexity. (shrink)

Leibniz coined the word “dynamics,” but his own dynamics has never been completed. However, there are many illuminating ideas scattered in his writings on dynamics and metaphysics. In this paper, I will present my own interpretation of Leibniz’s dynamics and metaphysics. To my own surprise, Leibniz’s dynamics and metaphysics are incredibly flexible and modern. In particular, the metaphysical part, namely Monadology, can be interpreted as a theory of information in terms of monads, which generate both physical phenomena and mental phenomena. (...) The phenomena, i.e., how the world of monads appears to each monad must be distinguished from its internal states, which Leibniz calls perceptions, and the phenomena must be understood as the results of these states and God’s coding. My distinctive claim is that most interpreters ignored this coding. His dynamics and metaphysics can provide a framework good enough for enabling Einstein’s special relativity. And finally, his dynamics and metaphysics can provide a very interesting theory of space and time. In Part 1, we will focus on the relationship between metaphysics and dynamics. Leibniz often says that dynamics is subordinated to metaphysics. We have to take this statement seriously, and we have to investigate how dynamics and metaphysics are related. To this question, I will give my own answer, based on my informational interpretation. On my view, Leibniz’s metaphysics tries, among others, to clarify the following three: How each monad is programmed. How monads are organized into many groups, each of which is governed by a dominant monad ; this can be regarded as a precursor of von Neumann’s idea of cellular automata. And how the same structure is repeated in sub-layers of the organization. This structure is best understood in terms of the hierarchy of programs, a nested structure going down from the single dominant program to subprograms, which again controls respective subprograms, and ad infinitum. If we may use a modern term, this is a sort of recursion, although Leibniz himself did not know this word. And one of my major discoveries is that the same recursive structure is repeated in the phenomenal world, the domain of dynamical investigations. Recursion of what, you may ask. I will argue that it is elastic collision. For Leibniz, aside from inertial motions, dynamical changes of motion are brought about by elastic collisions, at any level of the infinite divisibility of matter. This nicely corresponds to the recursive structure of the program of a monad, or of the program of an organized group of monads. This is the crux of his claim that dynamics is subordinated to metaphysics. Moreover, the program of any monad is teleological, whereas the phenomenal world is governed by efficient cause of dynamics. And it is natural that the pre-established harmony is there, since God is the ultimate programmer, as well as the creator. (shrink)

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s paper, and J. A. Cover’s (...) improvement. Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum, I arrived at the following interpretation. Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. What Leibniz calls “simultaneity” should be understood as a unique 1- to-1 correspondence of the states of different monads. With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, we can introduce a metric of time based on congruence of duration. Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path of a moving point; thus the congruence of duration can be reduced to congruence of distance. Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. (shrink)

I offer support for the view that physicalist theories of cognition don't reduce to neurophysiological theories. On my view, the mind-brain relationship is to be explained in terms of evolutionary forces, some of which tug in the direction of a reductionistic mind-brain relationship, and some of which which tug in the opposite direction. This theory of forces makes possible an anti-reductionist account of the cognitive mind-brain relationship which avoids psychophysical anomalism. This theory thus also responds to the complaint which arguably (...) lies behind the Churchlands' strongest criticisms of anti-reductionism — namely the complaint that anti-reductionists fail to supply principled explanations for the character of the mind-brain relationship. While lending support to anti-reductionism, the view defended here also insures a permanent place for mind-brain reduction as an explanatory ideal analogous to Newtonian inertial motion or Aristotelian natural motion. (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)