Zvi Biener

Newton's Regulae philosophandi — the rules for reasoning in natural philosophy — are maxims of causal reasoning and induction. This chapter reviews their significance for Newton's method of inquiry, as well as their application to particular propositions within the Principia. Two main claims emerge. First, the rules are not only interrelated, they defend various facets of the same core idea: that nature is simple and orderly by divine decree, and that, consequently, human beings can be justified in inferring universal causes from limited phenomena, if only fallibly. Second, the rules make substantive ontological assumptions on which Newton's argument in the Principia relies. Along the way, some standard interpretations of the rules are challenged.

I argue that Isaac Newton's _De Gravitatione_ should not be considered an authoritative expression of his thought about the metaphysics of space and its relation to physical inquiry. I establish the following narrative: In _De Gravitatione_ (circa 1668--1684), Newton claimed he had direct experimental evidence for the work's central thesis: that space had ``its own manner of existing'' as an affection or emanative effect. In the 1710s, however, through the prodding of both Roger Cotes and G. W. Leibniz, he came to see that this evidence relied on assumptions that his own _Principia_ rendered unjustifiable. Consequently, he (i) revised the conclusions he explicitly drew from the experimental evidence, (ii) rejected the idea that his spatial metaphysics was grounded in experimental evidence, and (iii) reassessed the epistemic status of key concepts in his metaphysics and natural philosophy. The narrative I explore shows not only that _De Gravitatione_ did not constitute the metaphysical backdrop of the _Principia_ as Newton ultimately understood it, but that it was the _Principia_ itself that ultimately lead to the demise of key elements of _De Gravitatione_. I explore the implications of this narrative for Andrew Janiak's and Howards Stein's interpretations of Newton's metaphysics.

Accounts of Hobbes’s ‘system’ of sciences oscillate between two extremes. On one extreme, the system is portrayed as wholly axiomatic-deductive, with state- craft being deduced in an unbroken chain from the principles of logic and  rst philosophy. On the other, it is portrayed as rife with conceptual cracks and  ssures, with Hobbes’s statements about its deductive structure amounting to mere window- dressing. This paper argues that a middle way is found by conceiving of Hobbes’s Elements of Philosophy on the model of a mixed-mathematical science, not the model provided by Euclid’s Elements of Geometry. I suggest that Hobbes is a test case for understanding early-modern system-construction more generally, as inspired by the structure of the applied mathematical sciences. This approach has the additional virtue of bolstering, in a novel way, the thesis that the transformation of philosophy in the long seventeenth century was heavily indebted to mathematics, a thesis that has increasingly come under attack in recent years.

Teaching Newtonian physics involves the replacementof students' ideas about physical situations with precise conceptsappropriate for mathematical applications. This paper focuses on theconcepts of `matter' and `mass'. We suggest that students, likesome pre-Newtonian scientists we examine, use these terms in a waythat conflicts with their Newtonian meaning. Specifically, `matter'and `mass' indicate to them the sorts of things that are tangible,bulky, and take up space. In Newtonian mechanics, however, the termsare defined by Newton's Second Law: `mass' is simply a measure ofthe acceleration generated by an impressed force. We examine therelationship between these conceptions as it was discussed by Newtonand his editor, Roger Cotes, when analyzing a series of pendulumexperiments. We suggest that these experiments, as well as moresophisticated computer simulations, can be used in the classroom tosufficiently differentiate the colloquial and precise meaning of theseterms.