Newton, along with a number of other seventeenth-century scientists, is frequently charged with having held an inconsistent view of nature and its operations, believing on the one hand in immutable laws of nature, and on the other in divine interventions into the natural order. In this paper I argue that Newton, William Whiston, and Samuel Clarke, came to understand miracles, not as violations of laws of nature, but rather as beneficent coincidences which were remarkable either because they were (...) unusual, or were beyond current understandings of nature. In this manner the Newtonians managed to reconcile their scientific pursuits with their religious convictions. (shrink)

The first two sections of this paper investigate what Newton could have meant in a now famous passage from “De Graviatione” (hereafter “DeGrav”) that “space is as it were an emanative effect of God.” First it offers a careful examination of the four key passages within DeGrav that bear on this. The paper shows that the internal logic of Newton’s argument permits several interpretations. In doing so, the paper calls attention to a Spinozistic strain in Newton’s thought. Second it sketches (...) four interpretive options: (i) one approach is generic neo-Platonic; (ii) another approach is associated with the Cambridge Platonist, Henry More; a variant on this (ii*) emphasizes that Newton mixes Platonist and Epicurean themes; (iii) a necessitarian approach; (iv) an approach connected with Bacon’s efforts to reformulate a useful notion of form and laws of nature. Hitherto only the second and third options have received scholarly attention in scholarship on DeGrav. The paper offers new arguments to treat Newtonian emanation as a species of Baconian formal causation as articulated, especially, in the first few aphorisms of part two of Bacon’s New Organon. If we treat Newtonian emanation as a species of formal causation then the necessitarian reading can be combined with most of the Platonist elements that others have discerned in DeGrav, especially Newton’s commitment to doctrines of different degrees of reality as well as the manner in which the first existing being ‘transfers’ its qualities to space (as a kind of causa-sui). This can clarify the conceptual relationship between space and its formal cause in Newton as well as Newton’s commitment to the spatial extended-ness of all existing beings. While the first two sections of this paper engage with existing scholarly controversies, in the final section the paper argues that the recent focus on emanation has obscured the importance of Newton’s very interesting claims about existence and measurement in “DeGrav”. The paper argues that according to Newton God and other entities have the same kind of quantities of existence; Newton is concerned with how measurement clarifies the way of being of entities. Newton is not claiming that measurement reveals all aspects of an entity. But if we measure something then it exists as a magnitude in space and as a magnitude in time. This is why in DeGrav Newton’s conception of existence really helps to “lay truer foundations of the mechanical sciences.”. (shrink)

Newtonian mechanics is more than just an empirically successful theory of matter in motion: it is an account of what knowledge of the physical world should look like. But what is this account? What is distinctive about it? To answer these questions, I begin by introducing the laws of motion, the relations among them, and the spatio-temporal framework that is implicit in them. Then I turn to the question of their methodological character. This has been the locus of (...) philosophical discussion from Newton’s time to the present, and I survey the views of some of the major contributors. I show that while Newtonian mechanics motivates a number of philosophical ideas about force, mass, motion, and causality – and through this, ideas about space and time – the laws are themselves the outcome of a philosophical or critical conceptual analysis. (shrink)

The laws of nature are central to our understanding of the world. And while there is often broad agreement about the technical formulations of the laws, there can be sharp disagreement about the metaphysical nature of the laws. For instance, the Newtonian laws of nature can be stated and analyzed by appealing to a set of possible worlds. Yet, some philosophers argue the worlds are mere notational devices, while others take them to be robust, concrete (...) entities in their own right. In this paper, I use a recent view of laws called the Mentaculus as a case study to illustrate the wide variety of metaphysical pictures that can accompany such a view. I conclude that the technical features of the laws -- typically (though not always) given to us by practicing scientists -- are compatible with many different metaphysical foundations. (shrink)

Newton’s impact on Enlightenment natural philosophy has been studied at great length, in its experimental, methodological and ideological ramifications. One aspect that has received fairly little attention is the role Newtonian “analogies” played in the formulation of new conceptual schemes in physiology, medicine, and life science as a whole. So-called ‘medical Newtonians’ like Pitcairne and Keill have been studied; but they were engaged in a more literal project of directly transposing, or seeking to transpose, Newtonian laws into (...) quantitative models of the body. I am interested here in something different: neither the metaphysical reading of Newton, nor direct empirical transpositions, but rather, a more heuristic, empiricist construction of Newtonian analogies. Figures such as Haller, Barthez, and Blumenbach constructed analogies between the method of celestial mechanics and the method of physiology. In celestial mechanics, they held, an unknown entity such as gravity is posited and used to mathematically link sets of determinate physical phenomena (e.g., the phases of the moon and tides). This process allows one to remain agnostic about the ontological status of the unknown entity, as long as the two linked sets of phenomena are represented adequately. Haller et. al. held that the Newtonian physician and physiologist can similarly posit an unknown called ‘life’ and use it to link various other phenomena, from digestion to sensation and the functioning of the glands. These phenomena consequently appear as interconnected, goal-oriented processes which do not exist either in an inanimate mechanism or in a corpse. In keeping with the empiricist roots of the analogy, however, no ontological claims are made about the nature of this vital principle, and no attempts are made to directly causally connect such a principle and observable phenomena. The role of the “Newtonian analogy” thus brings together diverse schools of thought, and cuts across a surprising variety of programs, models and practices in natural philosophy. (shrink)

This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as other fundamental classical laws are extended to a D-dimensional metric space, where D can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed properties of (...) galaxies and other astrophysical structures without requiring the dark matter hypothesis. The MOND acceleration constant $${a_{0}} \simeq 1.2 \times 10^{-10} \text {m}\, \text{s}^{-2}$$ can be related to a natural scale length $$l_{0}$$ in NFDG, i.e., $$a_{0} \approx GM/l_{0}^{2}$$, for astrophysical structures of mass M, and the deep-MOND regime is present in regions of space where the dimension is reduced to $$D \approx 2$$. For several fundamental spherically-symmetric structures, we compare MOND results, such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $$g_{obs}$$ vs. the baryonic radial acceleration $$g_{bar}$$, with NFDG results. We show that our model is capable of reproducing these results using a variable local dimension $$D\left( w\right)$$, where $$w =r/l_{0}$$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $$D\left( w\right)$$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFDG as a viable alternative model of gravity. (shrink)

Sir Isaac Newton, writing in Latin, defined his celebrated laws of motion verbally. When the laws of motion are read as relating to his arithmetic and his calculus, division by zero is undefined so his physics fails at mathematical singularities. The situation is unchanged in modern real arithmetic and real calculus: division by zero is undefined so both Newtonian Physics and its modern developments fail at mathematical singularities. However, when Newton’s text is read as relating to transreal (...) arithmetic and transreal calculus, division by zero is defined and we show that the resulting Transreal Newtonian Physics does operate at mathematical singularities. We hold out the hope that the whole of modern physics may be similarly extended. We use the new physics to predict a convection current at the singularity in a black hole and suggest experiments in astronomy and high energy physics that might confirm or rebut our predictions. Thus our exegesis of Newton’s text extends mathematical physics and may, in future, extend experimental physics. (shrink)

The proposal to add the behavioral momentum metaphor to Skinnerian psychology and the use of other borrowed physical explanatory concepts such as velocity and inertial mass has only superficial value. The basic problem is that, in contrast to Newtonian physics, the “laws” do not apply to a significant proportion of the phenomena to be explained, and these evidential discrepancies are ignored, rather than being used to modify the scientific explanations and improve technological applications that are based on those (...) explanations. (shrink)

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

The foundations of Statistical Mechanics can be recovered almost in their entirety from the principle of maximum entropy. In this work we show that its non-equilibrium generalization, the principle of maximum caliber (Jaynes, Phys Rev 106:620–630, 1957), when applied to the unknown trajectory followed by a particle, leads to Newton’s second law under two quite intuitive assumptions (both the expected square displacement in one step and the spatial probability distribution of the particle are known at all times). Our derivation explicitly (...) highlights the role of mass as an emergent measure of the fluctuations in velocity (inertia) and the origin of potential energy as a manifestation of spatial correlations. According to our findings, the application of Newton’s equations is not limited to mechanical systems, and therefore could be used in modelling ecological, financial and biological systems, among others. (shrink)

Is there any important distinction between a law and a theory? Some usages suggest that there is. Thus, everyone speaks of Boyle's Law and of the dynamical theory of gases. But the most summary inquiry will show that the distinction is not maintained consistently by individual authors, still less as between different authors; the terms “Newtonian law” and “theory of gravitation” seem to be used indifferently to denote the same proposition.

The challenge of this work is to connect physics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e., in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces (...) that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self-supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of the information force that represents a bridge to intelligent particle. As a follow-up of the proposed concept, the following question is addressed: can artificial intelligence system composed only of physical components compete with a human? The answer is proven to be negative if the AI system is based only on simulations, and positive if digital devices are included. It has been demonstrated that there exists such a quantum neural net that performs simulations combined with digital punctuations. The universality of this quantum-classical hybrid is in capability to violate the second law of thermodynamics by moving from disorder to order without external resources. This advanced capability is illustrated by examples. In conclusion, a mathematical machinery of the perception that is the fundamental part of a cognition process as well as intelligence is introduced and discussed. (shrink)

A closer examination of scientific practice has cast doubt recently on the thesis that observation necessarily fails to determine theory. In some cases scientists derive fundamental hypotheses from phenomena and general background knowledge by means of demonstrative induction. This note argues that it is wrong to interpret such an argument as providing inductive support for the conclusion, e.g. by eliminating rival hypotheses. The examination of the deduction of the inverse square law of gravitation due to J. Bertrand, and R. Fowler's (...) deduction of the quantization of the linear harmonic oscillator's energy spectrum from Planck's radiation law illustrates this point. It is suggested that demonstrative induction is a computational step in fitting a theoretical model and a set of phenomena, with little direct confirmational impact. The thesis of underdetermination, whatever one may think of it, is not threatened by demonstrative induction. (shrink)

The parametrized post-Newtonian (PPN) approximation is generalized to accommodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield (...) conserved energy-momentum and angularmomentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories. (shrink)

Comparativism—the view that mass ratios are not grounded in absolute masses—faces a challenge by Baker which suggests that absolute masses are empirically meaningful. Regularity comparativism uses a liberalized version of the Mill-Ramsey-Lewis Best Systems Account to have both the laws of Newtonian gravity and the absolute mass scale supervene on a comparativist Humean mosaic as a package deal. I discuss three objections to this view and conclude that it is untenable. The most severe problem is that once we (...) have reduced away the absolute masses, there is nothing that stops us from also reducing the mass ratios. (shrink)

I examine Popper’s claims about Newton’s use of induction in Principia with the actual contents of Principia and draw two conclusions. Firstly, in common with most other philosophers of his generation, it appears that Popper had very little acquaintance with the contents and methodological complexities of Principia beyond what was in the famous General Scholium. Secondly Popper’s ideas about induction were less sophisticated than those of Newton, who recognised that it did not provide logical proofs of the results obtained using (...) it, because of the possibilities of later, contrary evidence. I also trace the historical background to commonplace misconceptions about Newton’s method.Author Keywords: Newton; Popper; Induction; Principia; Kepler’s laws. (shrink)

This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter. I begin, in part I, by noting marked differences between Newton’s and Kant’s laws of action and (...) reaction. I argue that these are explainable by Kant’s allegiance to a Leibnizian mechanics. I show (in part II) that Leibniz too had a model of action and reaction, at odds with Newton’s. Then I reconstruct how Jakob Hermann and Christian Wolff received Leibniz’s model. I present (in Part III) Kant’s early law of action and reaction for mechanics. I show that he devised it so as to solve extant problems in the Hermann-Wolff account. I reconstruct Kant’s views on ‘mechanical’ action and reaction in the 1780s, and highlight strong continuities with his earlier, pre-Critical stance. I use these continuities, and Kant’s earlier engagement with post-Leibnizians, to explain the un-Newtonian features of his law of action and reaction. (shrink)

We investigate the evolution of linear density contrasts obtained with respect to a homogeneous spatially flat Friedman-Lemaître–Robertson–Walker background by solving the density contrast equations governed by Newtonian and MONDian force laws using symmetry-based approach. We find eight-parameter Lie group symmetries for the linear order density perturbation equation for the Newtonian case whereas the density contrast equation follows only one parameter Lie group symmetry in MONDian case. We use Lie symmetries to find the group invariant solutions from invariant (...) curve condition. The physical features of the evolution for various mode of density contrast with respect to the global cosmic background density in homogeneous isotropic cosmological models have been investigated using analytical group invariant solutions along with their numerical solutions. An account for cosmological density contrast and mass fluctuation also have been provided. We also have shown that the MONDian force law generates higher amplitudes in the density fluctuation, results in a more rapid structure formation that cannot be possible under the Newtonian force law. (shrink)

In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard method for assessing the (...) truth of certain counterfactuals. The truth of deterministic laws is `modally fragile' on the standard semantics for counterfactuals: if determinism is true and you were to do otherwise, the laws would be different. We provide two ways of avoiding this problem: 1) supplement the standard semantics for counterfactuals with impossible worlds, or 2) introduce rigid designators into the description of problematic decision situations. We argue that both of these approaches are well-motivated and can be readily incorporated into Lewisian Causal Decision Theory. (shrink)

The Newtonian universe is usually understood to contain two classes of causal factors: universal regularitiesand initial conditions. I demonstrate that,in fact, the Newtonian universe contains no causal factors other thanuniversal regularities: the initial conditions ofany physical system are merely theconsequence of universal regularities acting on previoussystems. It follows that aNewtonian universe lacks the degree of contingency that is usually attributed to it. This is a necessary precondition for maintaining that the Newtonian universe is a block universe that (...) exhibits no temporal development. It follows also that Newtonian physics is inconsistent, since a Newtonian universe as a whole exhibits some properties – such as the total mass of the universe – that are not determined by the laws of Newtonian physics, and that must therefore be considered contingent. (shrink)

A number of recent papers have criticized what they call the dynamical interpretation of evolutionary theory found in Elliott Sober’s The Nature of Selection. Sober argues that we can think of evolutionary theory as a theory of forces analogous to Newtonian mechanics. These critics argue that there are several important disanalogies between evolutionary and Newtonian forces: Unlike evolutionary forces, Newtonian forces can be considered in isolation, they have source laws, they compose causally in a straightforward way, (...) and they are intermediate causes in causal chains. Here we defend and extend the forces analogy by arguing that each of these criticisms is based on a misunderstanding of Newtonian forces. Our discussion also has the interesting consequence that natural selection turns out to be more similar to forces such as friction and elastic forces rather than the more canonical gravitation. (shrink)

Archibald Pitcairne’s medical writings are inspired by Newton’s Principia mathematica, as the Scottish physician assumed Newtonian physics as a model for scientific inquiry that should be applied to other branches of natural philosophy, including physiology and pathology. The ideal of a comprehensive mathematical science was very appealing to late seventeenth-century intellectuals, including physicians. This essay focuses on how Pitcairne tried to implement these ideas. In particular, I argue that Pitcairne’s medical thinking is based on three philosophical assumptions: first, a (...) methodological assumption, for which medical knowledge should be sought in the form of a deductive system; second, an epistemological assumption, that is, that our knowledge of physiological processes is sound only when we reduce them to a set of mathematical laws; and, third, an ontological assumption that identifies blood as the substance on which animal life most directly depends. I also suggest that such ideas should be studied against the backdrop of Pitcairne’s general mindset, including his personal sympathy for political conservativism. I further argue that his insistence on the reduction of natural processes to mathematical relations and his search for the universal order of nature also connect to his religious and political ideals. (shrink)

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be verified (...) with observation data. (shrink)

can prevent non-contact interactions in Newtonian collision mechanics. The proposal is weakened by the apparent arbitrariness of what will be shown as the requirement of only an odd number of sets of some ex nihilo-created self-exciting particles. There is, however, an initial condition such that, without the ex nihilo self-exciting particles, either there is a contradictory outcome, or there is a non-contact configuration law, or there are odds versus evens indeterminacies. With the various odds versus evens arbitrarinesses and other (...) such difficulties, there seems to be an ontological unsatisfactoriness in the speed-unbounded Newtonian collision system. Introduction Taking self-excitations very seriously A problematic initial condition Another alternative. (shrink)

This book presents a radical new picture of natural order. The Newtonian idea of a cosmos ruled by universal and exceptionless laws has been superseded; replaced by a conception of nature as a realm of diverse powers, potencies, and dispositions, a 'dappled world'. There is order in nature, but it is more local, diverse, piecemeal, open, and emergent than Newton imagined. In each chapter expert authors expound the historical context of the idea of laws of nature, and (...) explore the diverse sorts of order actually presupposed by work in physics, biology, and the social sciences. They consider how human freedom might be understood, and explore how Newton's idea of a 'universal designer' might be revised, in this new context. They argue that there is not one unified totalizing program of science, aiming at the completion of one closed causal system. We live in an ordered universe, but we need to rethink the classical idea of the 'laws of nature' in a more dynamic and creatively diverse way. (shrink)

Much has been written on Newton’s concept of matter, as well as Newton’s laws. Meanwhile, the metaphysical and epistemological relationships between these two principal features of Newtonian philosophy are relatively unexplored. Among the existing accounts of the relationship between bodies and laws, two are especially compelling: the “law-constitutive” approach from Katherine Brading and the “formal-cause” approach from Zvi Biener and Eric Schliesser. Both accounts argue that Newton’s bodies are (at least partially) metaphysically dependent on the laws. (...) That is, according to Brading, Biener, and Schliesser, Newtonian laws are ontologically prior to the bodies they govern. In this article, I reply to Brading, Biener, and Schliesser. I develop negative arguments against their approaches by closely examining three features of Newton’s ontology—forms, particles, and active principles—and their relationship to the laws. I also offer an explanation as to why “law-first” approaches have (understandably) dominated recent Newtonian exegesis. Finally, I present a positive argument for what I believe to be a superior alternative: Newton’s law-first approach is purely pragmatic. It is a feature of his experimental philosophy that we should begin our inquiry into the metaphysical constituents of the universe with the laws that arise from them. This does not entail, however, that Newton views laws as constituting or forming physical bodies. Newton’s metaphysics should be interpreted as “matter-first,” with bodies giving rise to laws, whereas his epistemology should be interpreted as “law-first,” with knowledge of laws giving rise to knowledge of bodies. (shrink)

This chapter investigates the prospects for an important position that falls under the "mere patterns" approach: what, for reasons that will emerge, the author calls"Humean reductionism" about laws of nature, a view championed perhaps most prominently by David Lewis. He reviews some of the most interesting arguments against this position from the literature, and adds some of his own that, he thinks, are more effective. The chapter considers how the best system account (BSA) would apply to the Newtonian (...) particle world. The BSA has been challenged in a wide variety of ways: it violates certain intuitions; It makes a hash out of the connection between laws on the one hand, and counterfactuals, explanation, and induction on the other. The author thinks that the problem he has raised‐challenging though he hopes it is, is really an occasion for the Humean reductionist to sharpen his position still further. (shrink)

Recently philosophers of biology have argued over whether or not Newtonian mechanics provides a useful analogy for thinking about evolutionary theory. For philosophers, the canonical presentation of this analogy is Sober's. Matthen and Ariew and Walsh, Lewins, and Ariew argue that this analogy is deeply wrong-headed. Here I argue that the analogy is indeed useful, however, not in the way it is usually interpreted. The Newtonian analogy depends on having the proper analogue of Newton's First Law. That analogue (...) is what McShea and Brandon call the Zero Force Evolutionary Law. According to the ZFEL, change, not stasis, is the default state of evolutionary systems. (shrink)

This book provides an introduction to Newtonian and relativistic mechanics. Unlike other books on the topic, which generally take a 'top-down' approach, it follows a novel system to show how the concepts of the 'science of motion' evolved through a veritable jungle of intermediate ideas and concepts. Starting with Aristotelian philosophy, the text gradually unravels how the human mind slowly progressed towards the fundamental ideas of inertia physics. The concepts that now appear so obvious to even a high school (...) student took great intellectuals more than a millennium to clarify. The book explores the evolution of these concepts through the history of science. After a comprehensive overview of the discovery of dynamics, it explores fundamental issues of the properties of space and time and their relation with the laws of motion. It also explores the concepts of spatio-temporal locality and fields, and offers a philosophical discussion of relative motion versus absolute motion, as well as the concept of an absolute space. Furthermore, it presents Galilean transformation and the principle of relativity, inadequacy of Galilean relativity and emergence of the spatial theory of relativity with an emphasis on physical understanding, as well as the debate over relative motion versus absolute motion and Mach's principle followed by the principle of equivalence. The natural follow-on to this section is the physical foundations of general theory of relativity. Lastly, the book ends with some new issues and possibilities regarding further modifications of the laws of motion leading to the solution of a number of fundamental issues closely connected with the characteristics of the cosmos. It is a valuable resource for undergraduate students of physics, engineering, mathematics, and related disciplines. It is also suitable for interdisciplinary coursework and introductory reading outside the classroom. (shrink)

This paper investigates Isaac Newton's rather unique account of God's relation to matter. According to this account, corpuscles depend on a substantially omnipresent God endowing quantities of objective space with the qualities of shape, solidity, the unfaltering tendency to move in accord with certain laws, and—significantly—the power to interact with created minds. I argue that there are important similarities and differences between Newton's account of matter and Berkeley's idealism. And while the role played by the divine will might at (...) first appear to be a species of occasionalism, I conclude that there are, for Newton, genuine causal relations between minds and bodies. Ultimately, to fully appreciate this account of the creation and persistence of matter, we must consider not only Newton's metaphysical writings, but also his sensorium theory of mind-body interaction, his heterodox theological commitments, and the influences of Descartes, More, and Locke. (shrink)

One of the most intuitive views about the metaphysics of laws of nature is Tim Maudlin's idea of a Fundamental Law of Temporal Evolution. So-called FLOTEs are primitive elements of the universe that produce later states from earlier states. While FLOTEs are at home in traditional Newtonian and non-relativistic quantum mechanical theories (not to mention our pre-theoretic conception of the world), I consider here whether they can be made to work with relativity. In particular, shifting to relativistic spacetimes (...) poses two threats to FLOTEs. First, the lack of a privileged spacelike hypersurface in relativistic spacetime makes it unclear how to understand what produces what. A survey of several conceptions of the nomic production relation compatible with relativity reveals all of them to be lacking. Second, relativity motivates a four-dimensional block universe conception of time, according to which all events that will ever occur already exist. On such a view, it's unclear what work there is to be done by FLOTEs. I consider how a proponent of FLOTEs might respond, but conclude that these combined threats seriously undermine the prospects of a productive conception of laws. In short, if spacetime is relativistic, laws are not productive. (shrink)

A supertask is a process in which an infinite number of individuated actions are performed in a finite time. A Newtonian supertask is one that obeys Newton''s laws of motion. Such supertasks can violate energy and momentum conservation and can exhibit indeterministic behavior. Perez Laraudogoitia, who proposed several Newtonian supertasks, uses a local, i.e., particle-by-particle, analysis to obtain these and other paradoxical properties of Newtonian supertasks. Alper and Bridger use a global analysis, embedding the system of (...) particles in a Banach space, to determine the origin of the strange behavior. This paper provides a common framework for the discussion of both the local and global methods of analysis. Using this single framework, the areas of disagreement and agreement are made explicit. Further examples of supertasks are proposed to illuminate various aspects of the discussion. (shrink)

Through an examination of the controversy between Clairaut and Buffon occasioned by Clairaut's proposed revision of Newton's inverse-square law, Clairaut's understanding of Newtonianism is revealed. The interplay in his thought between the possibility of falsification , and the necessity of seeking verification in terms of mathematically precise consequences, indicates a fruitful development of Newtonianism into probabilism. That Clairaut's principles stem from Newton rather than from the Cartesians is indicated by his retention of a delicate balance between the claims of mathematics (...) and those of observation, a balance in which the claims of metaphysics are weightless. (shrink)

This paper analyses the structure of evolutionary theory as a quasi-Newtonian theory and the need to establish a Zero-Cause Law. Several authors have postulated that the special character of drift is because it is the default behaviour or Zero-Cause Law of evolutionary systems, where change and not stasis is the normal state of them. For these authors, drift would be a Zero-Cause Law, the default behaviour and therefore a constituent assumption impossible to change without changing the system. I defend (...) that drift's causal and explanatory power prevents it from being considered as a Zero-Cause Law. Instead, I propose that the default behaviour of evolutionary systems is what I call the Principle of Stasis, which posits that an evolutionary system where there is no selection, drift, mutation, migration, etc., and therefore no difference-maker, will not undergo any change (it will remain in stasis). (shrink)

William Whewell’s philosophy of scientific discovery is applied to the problem of understanding the nature of unification and explanation by the composition of causes in Newtonian mechanics. The essay attempts to demonstrate: the sense in which ”approximate’ laws successfully refer to real physical systems rather than to idealizations of them; why good theoretical constructs are not badly underdetermined by observation; and why, in particular, Newtonian forces are not conventional and how empiricist arguments against the existence of component (...) causes, and against the veracity of the fundamental laws, are flawed. (shrink)

Laws in the special sciences are usually regarded to be non-universal. A theory of laws in the special sciences faces two challenges. (I) According to Lange's dilemma, laws in the special sciences are either false or trivially true. (II) They have to meet the ?requirement of relevance?, which is a way to require the non-accidentality of special science laws. I argue that both challenges can be met if one distinguishes four dimensions of (non-) universality. The upshot (...) is that I argue for the following explication of special science laws: L is a special science law just if (1) L is a system law, (2) L is quasi-Newtonian, and (3) L is minimally invariant. (shrink)

The seventh chapter focuses on the aftermath of the decline of Cartesianism as a leading force in the Dutch academic context. After De Volder and De Raey, indeed, only Ruardus Andala in Franeker carried on the teaching of Cartesian physics (which he taught by commenting upon Descartes’s Principia) and metaphysics, mainly for the sake of contrasting Spinozism and other forms of radical Cartesianism. Thus, Descartes’s philosophy came a dead end on the eve of the eighteenth century. Yet, Leiden Cartesianism and (...) the Leiden experimental tradition (which could include, after De Volder and Senguerd, the activities of Herman Boerhaave), favoured the introduction of Newtonianism as the standard in teaching natural philosophy. This was carried out by ’s Gravesande, who used logic and metaphysics (including rational theology), that is, the chief foundational disciplines in the Cartesian tradition, to introduce students to and justify the assumptions (methodological and ontological) of a Newtonian approach in natural philosophy. This had two outcomes. On the one hand, his arguments in metaphysics (i.e. ontology) have the function of clarifying which objects natural philosophy can investigate. These are natural laws, whose ultimate source in substances or modes cannot be ascertained by intellect alone, as they depend on the power of God. On the other, given the fact that experience is our only means of grasping such laws (which are then mathematically handled) he provides a rational-theological justification of experiential evidence, as capable of providing us with a degree of certainty equal to mathematical evidence. As for the Cartesians, this is still the paradigm of scientific knowledge. Accordingly, with the introduction of Newtonianism foundational disciplines such as logic and metaphysics (including rational theology) served as a justification for and a reflection on a given scientific methodology. Thus, philosophy started to be actually detached from the natural sciences, and to assume a subservient role with respect to them, as once it was the ancilla theologiae. (shrink)

It is often claimed (most recently by Michael Friedman) that Kant intended to justify Newton’s most fundamental claims expressed in the Principia, such as his laws of motion and the law of universal gravitation. In this article, I argue that the differences between Newton’s laws of motion and Kant’s laws of mechanics are not superficial or merely apparent. Rather, they reflect fundamental differences in their respective projects. This point can be seen especially clearly by considering the nature (...) of the various projects undertaken in Germany prior to Kant that discuss the laws of motion. Wolff and his followers qua metaphysicians were especially interested in providing nonempirical justifications of their laws of motion as well as an intelligible account of the fundamental properties of bodies in terms of substance, accident, and force. Maupertuis and Euler, despite often being seen as Newtonians, both drew on traditions other than Newton’s. Physics textbooks (by figures such as Erxleben, Karsten, ‘s Gravesande, and Musschenbroek) vary considerably in their aims, but in none of these cases is Newton’s main argument of the Principia presented. In light of the fact that these projects are distinct in significant ways from Newton’s project, the differences between Newton’s laws of motion and Kant’s laws of mechanics are most likely not merely apparent but reflect the fact that Kant, too, was pursuing a project fundamentally distinct from Newton’s. (shrink)

I describe a problem about the relations among symmetries, laws and measurable quantities. I explain why several ways of trying to solve it will not work, and I sketch a solution that might work. I discuss this problem in the context of Newtonian theories, but it also arises for many other physical theories. The problem is that there are two ways of defining the space-time symmetries of a physical theory: as its dynamical symmetries or as its empirical symmetries. (...) The two definitions are not equivalent, yet they pick out the same extension. This coincidence cries out for explanation, and it is not clear what the explanation could be. The Puzzle: Symmetries, Measurability and Invariance 1.1 The symmetries and the measurable quantities of Newtonian mechanics 1.2 The puzzle Two Easy Answers Another Unsuccessful Solution: Appeal to Geometrical Symmetries Locating the Puzzle The Relation between Laws and Measurability A Possible Solution CiteULike Connotea Del.icio.us What's this? (shrink)

In this article, we discuss the development of the concept of a ‘law’ (of nature) in the work of the Dutch natural philosopher and experimenter Petrus van Musschenbroek (1692–1761). Since Van Musschenbroek is commonly described as one of the first ‘Newtonians’ on the Continent in the secondary literature, we focus more specifically on its relation to Newton’s views on this issue. Although he was certainly indebted to Newton for his thinking on laws (of nature), Van Musschenbroek’s views can be (...) seen to diverge from Newton’s on crucial points. We show, moreover, how his thinking on laws of nature was shaped by both international and local factors. We start with a brief discussion of Newton’s concept of ‘laws of nature’ in order to set the stage for Van Musschenbroek’s. We then document the development of Van Musschenbroek’s views on laws of nature in chronological order. We demonstrate how his thinking on laws of nature was tied to institutional, theological and scientific factors. We conclude by pointing to the broader significance of this case study for our understanding of the development of the concept ‘law of nature’ during the eighteenth century. (shrink)

We give a precise and modern mathematical characterization of the Newtonian spacetime structure (ℕ). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are “timelike” vector fields on ℕ) plays a fundamental role in our approach, and the classification of all possible reference frames on ℕ is investigated in detail. We succeed in identifying a Lorentzian structure on ℕ and we study the classical electrodynamics of Maxwell and Lorentz (...) relative to this structure, obtaining the important result that there exists only one intrinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generalizations of the Lorentz force law appearing in the literature. We present also a formulation of Newtonian gravitational theory as a curve spacetime theory and discuss its meaning. (shrink)

Orthodoxy has it that only metaphysically elite properties can be invoked in scientifically elite laws. We argue that this claim does not fit scientific practice. An examination of candidate scientifically elite laws like Newton’s F = ma reveals properties invoked that are irreversibly defined and thus metaphysically non-elite by the lights of the surrounding theory: Newtonian acceleration is irreversibly defined as the second derivative of position, and Newtonian resultant force is irreversibly defined as the sum of (...) the component forces. We think that scientists are happy to invoke metaphysically non-elite properties in scientifically elite laws for reasons of convenience, such as to simplify the equations and to make them more modular. On this basis, we draw a deflationary moral about laws themselves, as being merely convenient summaries. 1 Introduction2 Orthodoxy2.1 Orthodoxy stated2.2 Orthodoxy explained2.3 A worrisome commitment: Term objectivism3 The Loose View3.1 The argument from practice3.2 Finding the scientifically elite equations3.3 Diagnosing the metaphysically non-elite properties3.4 Situating our challenge4 Newtonian Mechanics4.1 Newtonian acceleration4.2 Newtonian resultant force4.3 A metaphysical discovery?5 Objections5.1 Metaphysically elite after all?5.2 Scientifically non-elite after all?5.3 But our world is not Newtonian!6 Consequences6.1 Consequences for the motivations for link6.2 Consequences for metaphysically elite properties6.3 Consequences for lawhood. (shrink)

On the basis of evidence drawn from the Waste book, Westfall and Nicholas have argued that Newton arrived at his second law of motion by reflecting on the implications of the first law. I analyze another argument in the Waste book which reveals that Newton also arrived at the second law by another very different route. On this route, it is the consideration of the third law and the principle of conservation of motion—and not the first law—that prompts Newton to (...) formulate the second law. The existence of these two routes is significant because each employs a distinct kind of reasoning about forces. Whereas the Nicholas–Westfall route via the principle of inertia bears the mark of Descartes’s influence, the alternative route proceeds from the action–reaction principle, which is widely regarded as an original Newtonian contribution to mechanics. In the course of exploring this alternate route to the second law, the origins and justification of the third law are examined.Keywords: Issac Newton; Waste book; Third law of motion; Second law of motion; Richard Westfall; John Nicholas. (shrink)

If, as is universally acknowledged, the proper goal of the mathematical sciences is the discovery of the least possible number of principles from which the universal laws of empirically given facts emerge with mathematical necessity, and thus the discovery of principles equivalent to those empirical facts, then it must appear as a duty of indubitable importance to reflect carefully on the principles that have already surfaced with some certainty in one area of the natural sciences and present them in (...) a form that really fulfills the equivalence requirement. (shrink)

A four dimensional approach to Newtonian physics is used to distinguish between a number of different structures for Newtonian space-time and a number of different formulations of Newtonian gravitational theory. This in turn makes possible an in-depth study of the meaning and status of Newton's Law of Inertia and a detailed comparison of the Newtonian and Einsteinian versions of the Law of Inertia and the Newtonian and Einsteinian treatments of gravitational forces. Various claims about the (...) status of Newton's Law of Inertia are critically examined including these: the Law of Inertia is not an empirical law but a definition; it is not a law simpliciter but a family of schemata; it is a convention and gravitational forces exist only by convention; it is (or is not) redundant; the concepts it embodies can be dispensed with in favor of operationally defined entities; it is unique for a given theory. More generally, the paper demonstrates the importance of space-time structure for the philosophy of space and time and provides support for a realist interpretation of space-time theories. (shrink)

:This paper traces the early reflections of the pre-Critical Kant on laws of nature back to Newton’s governing conception of laws. Three problems with the Newtonian conception are identified. I argue that in the attempt to provide a solution to them, in 1763 Kant came to forge a novel governing conception of laws. Key to Kant’s novel view are the notions of ground and its determinations. The role of these two notions in delivering the nomological necessity, (...) explanatory power, and unity of the laws of nature is discussed and analysed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 351-383 [Access article in PDF] Hume's Pyrrhonian Skepticism and the Belief in Causal Laws Graciela De Pierris Hume endorses in no uncertain terms the normative use of causal reasoning. The most striking example of this commitment is Hume's argument in the Enquiry against the possibility of miracles. The argument sanctions, in particular, the use of scientific reflection on uniform experience (...) issuing in causal laws of nature (E 114): "A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined." 1 These words should give us pause; for how can Hume so confidently say, after his skeptical conclusions concerning our causal beliefs, that "a firm and unalterable experience has established" the laws of nature, and that we can therefore produce "proofs" against miracles? The Treatise gives rise to the same puzzle. In this text, too, Hume confidently prescribes methodical reflection based on causal reasoning. For example, in Book One, Part Three, Section Fifteen, Hume offers eight "Rules by which to judge of causes and effects." These rules are more than descriptions of our natural causal inferences. They are meant to guide us in making better causal inferences; in Hume's words they "ought to regulate" our probable reasoning since (T 149): "by them we learn to distinguish the accidental circumstances from the efficacious causes." 2Moreover, Hume consistently takes Newtonian science as a model for the proper employment of causal inferences in inquiries into matters of fact and, [End Page 351] in particular, as a model to be followed in his own science of human nature. 3 This paradigm of what the science of nature ought to be is understood by Hume as an inductive, experimental inquiry. 4 In the Enquiry, for example, Hume uses the label "sciences" for "politics, natural philosophy, physic, chemistry, &c." and in the preceding discussion argues that these sciences are not a priori but are based on causal reasoning (E 164-165). Thus, there are for Hume inquiries into matters of fact and existence that amount to more than blindly following natural propensities and habit. The sciences and many of our causal inferences in common life involve more than mere belief as a sentiment. They involve, in addition, careful reflection that results in improved causal inferences and thus provides normative standards. Yet, in thus upholding the normative use of causal reasoning in science and in everyday life, Hume appears to contradict his own radical skeptical conclusions concerning our knowledge of causation and induction. I here propose a novel way to resolve this puzzle.To acknowledge the existence of a puzzle, however, amounts to accepting the now controversial view that Hume provides, and takes at face value, a radical skeptical argument concerning our knowledge of causation and induction. 5 Moreover, the attempt to resolve this puzzle involves rejecting the suggestion [End Page 352] that Hume, without awareness or concern, happily holds flatly inconsistent views. 6 It also goes against the more sophisticated suggestion that Hume lightly alternates among different psychological moods, or perhaps different perspectives, which might eventually issue in results that contradict each other but are sufficiently localized so as to prevent serious conflict. Such a view might lead us to conceive Hume's texts as an unstructured and arbitrary patchwork of reflections, driven by different psychological moods or by the embellishments of a radiant literary style. This kind of reading is unacceptable as an interpretative tool, however, as H. J. Paton has acutely noted in his criticism of the patchwork interpretation of Kant's Critique of Pure Reason. 7 For such a reading would place no constraints at all on the task of establishing which parts of Hume's text belong to which moods or perspectives. The suggestion that Hume offers an unstructured patchwork of reflections masks the novel and systematic distinction Hume draws between his radical philosophical... (shrink)

Analogies between Newtonian mechanics and evolutionary processes are powerful but not infinitely versatile tools for generating explanations of particular biological phenomena. Their explanatory range is sensitive to a preliminary decision about which processes count as background conditions and which as special forces. Here I argue that the defenders of the zero-force evolutionary law are mistaken in defending their decision as the only appropriate one. The Hardy–Weinberg principle remains a viable option that is consistent with the epistemic role of Newton’s (...) own first law, and the strengths and weaknesses of each analogy are sufficiently distinct to justify their continued coexistence. (shrink)