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This paper investigates the question of, and the degree to which, Newton’s theory of space constitutes a thirdway between the traditional substantivalist and relationist ontologies, i.e., that Newton judged that space is neither a type of substance/entity nor purely a relation among such substances. A nonsubstantivalist reading of Newton has been famously defended by Howard Stein, among others; but, as will be demonstrated, these claims are problematic on various grounds, especially as regards Newton’s alleged rejection of the traditional substance/accident dichotomy (...) 

This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neoPlatonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A nonsubstantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neoPlatonism on various aspects of Newton’s own spatial (...) 

Newton rested his theory of mechanics on distinct metaphysical and epistemological foundations. After Leibniz's death in 1716, the Principia ran into sharp philosophical opposition from Christian Wolff and his disciples, who sought to subvert Newton's foundations or replace them with Leibnizian ideas. In what follows, I chronicle some of the Wolffians' reactions to Newton's notion of absolute space, his dynamical laws of motion, and his general theory of gravitation. I also touch on arguments advanced by Newton's Continental followers, such as (...) 

This article investigates the problem of the identity of the parts of space in Newton’s natural philosophy, as well as the holistic or structuralist nature of Newton’s ontology of space. Additionally, this article relates the lessons reached in this historical and philosophical investigation to analogous debates in contemporary spacetime ontology. While previous contributions, by Nerlich, Huggett, and others, have proven to be informative in evaluating Newton’s claims, it will be argued that the underlying goals of Newton’s views have largely eluded (...) 





This paper proposes a parallel in the forms of Aristotle’s and Einstein’s physics. It’s an exercise on conceptual analysis rather than history. The possible similarity between Aristotle’s world and the form of Einstein’s universe is discussed. The correlation between kinematics, dynamics and gravity in their respective theories is also studied. Finally, Aristotle’s ontology of space is compared to the relativistic ontology spacetime. 

The determination of inertia by matter is looked at in general relativity, where inertia can be represented by affine or projective structure. The matter tensor T seems to underdetermine affine structure by ten degrees of freedom, eight of which can be eliminated by gauge choices, leaving two. Their physical meaningwhich is bound up with that of gravitational waves and the pseudotensor t, and with the conservation of energymomentumis considered, along with the dependence of reality on invariance and of causal explanation (...) 

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) 

On one popular view, the general covariance of gravity implies that change is relational in a strong sense, such that all it is for a physical degree of freedom to change is for it to vary with regard to a second physical degree of freedom. At a quantum level, this view of change as relative variation leads to a fundamentally timeless formalism for quantum gravity. Here, we will show how one may avoid this acute ‘problem of time’. Under our view, (...) 



Einstein regarded as one of the triumphs of his 1915 theory of gravity  the general theory of relativity  that it vindicated the actionreaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both (...) 

I discuss the three distinctions “absolute and relative”, “true and apparent”, and “mathematical and common”, for the specific case of time in Newton’s Principia. I argue that all three distinctions are needed for the project of the Principia and can be understood within the context of that project without appeal to Newton’s wider metaphysical and theological commitments. I argue that, within the context of the Principia, the three claims that time is absolute rather than relative, true rather than apparent, and (...) 

Sklar ([1974]) claimed that relationalism about ontologythe doctrine that space and time do not existis compatible with Newtonian mechanics. To defend this claim he sketched a relationalist interpretation of Newtonian mechanics. In his interpretation, absolute acceleration is a fundamental, intrinsic property of material bodies; that a body undergoes absolute acceleration does not entail that space and time exist. But Sklar left his proposal as just a sketch; his defense of relationalism succeeds only if the sketch can be filled in. I (...) 

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the puttingtogether in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. I (...) 

This paper reexamines the historical debate between Leibniz and Newton on the nature of space. According to the traditional reading, Leibniz (in his correspondence with Clarke) produced metaphysical arguments (relying on the Principle of Sufficient Reason and the Principle of Identity of Indiscernibles) in favor of a relational account of space. Newton, according to the traditional account, refuted the metaphysical arguments with the help of an empirical argument based on the bucket experiment. The paper claims that Leibniz’s and Newton’s arguments (...) 

Galileo’s dictum that the book of nature “is written in the language of mathematics” is emblematic of the accepted view that the scientific revolution hinged on the conceptual and methodological integration of mathematics and natural philosophy. Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and contextdependent phenomenon than the received historiography has indicated, and that philosophical controversies (...) 

In the Scholium to the Definitions at the beginning of the {\em Principia\/} Newton distinguishes absolute time, space, place and motion from their relative counterparts and attempts to justify they are indeed ontologically distinct in that the absolute quantity cannot be reduced to some particular category of the relative, as Descartes had attempted by defining absolute motion to be relative motion with respect to immediately ambient bodies. Newton's bucket experiment, rather than attempting to show that absolute motion exists, is one (...) 

