Newton's Argument Research Articles

Disregarding evidence: Reasonable options for Newton and Rutherford?

To determine whether, and to what extent, you are justified in believing a proposition you need to consider all the relevant evidence available to you, not just some part of it. So says the “Requirement of Total Evidence” (RTE). If you violate this you are unreasonable. Are you? Two scientific cases will be presented to defend the answer: Not necessarily. The first involves Newton's argument for universal gravity, the second, Rutherford's argument for his model of the atom. These cases, it will be argued, show something important about the limitations of RTE and about reasonable belief. At the end a way of rethinking RTE will be proposed.

Clarifying some misconceptions in interpreting Ernst Mach's views on thought experiments

Proponents of a recent interpretation of Ernst Mach's views on thought experiments argue that for Mach thought experiments must be continuous with and return to cached experiences. These criteria, the proponents hold, explain the tension which has been noted in Mach's views on thought experiments: on the one hand, Mach reprimands Newton in “extending principles beyond the boundaries of experience” when critiquing Newton's bucket argument, while on the other, Mach himself engages in speculative reasoning when presenting ‘Mach's principle’. Against this interpretation, I argue that Mach's critique of Newton's argument does not turn on Newton’s illegitimate use of thought experiments, but instead turns on Newton's illegitimate use of thoughts in thought experiments. Recognizing this leads to a simple and more compelling interpretation of Mach's views. I close the paper by gesturing towards such an interpretation and noting that taking Mach's views on thought experiments seriously implies that Mach is much less of a strict empiricist than he is usually understood to be.

Introduction to the Special Issue: Time

If you were to list the perennial issues in philosophy, the nature of time would no doubt be on that list. The essays in the present volume all touch upon the problem of time. The volume includes four contributions from different perspectives within the history of philosophy of time.Jani Hakkarainen and Todd Ryan delve into David Hume's account of time. Hume thinks there can be no time without succession. Consequently, unchanging, steadfast objects do not have a duration. They are stationary, not subject to any change. Although they lack a duration, they coexist with a temporal succession. This introduces a problem: What is the relation between unchanging objects and time? Hakkarainen and Ryan draw on what they call Hume's Principle of Quantitative Comparison. Each indivisible temporal extent is equal to any other temporal extent; differences in duration are due to the different number of temporal parts. Steadfast objects may be thought to undergo a certain number of calculable changes when they are compared to ordinary successions we experience. This experience is provided, for example, by the ticking of a clock. We have the capacity to think that steadfast objects have precise durations. We humans nevertheless cannot give any deep explanation as how we come to this conclusion.Emily Thomas focuses on the graphic representation of time. Whereas the visual representation of time has typically been done with matrices or grids, Joseph Priestley represented time in a line in 1765. Priestley's line divides time “by an equal scale” into centuries. Many have interpreted this as being evidence of a Newtonian influence, as if there is an absolute time flowing equably. Thomas situates Priestley's position in the modern debates on the nature of our ideas. She argues that the absolutist reading does not have merit. Thomas thinks rather that Priestley sides with David Hartley, who explained how we acquire the ideas of duration and time from sensation. Thomas's essay advances our understanding of the history of space-time parallelism. With timelines, the analogy between time and space becomes a possibility.In my essay I assess Ernst Mach's criticism of Isaac Newton's substantivalist account of time. Newton's argument for absolute time relates to his mathematical-empirical physics and theology. In his Science of Mechanics, Mach largely neglects the laws of motion, calculus and the omnipresence theology that is at the background of Newton's concept of time. Mach did however criticize Newton's absolutist argument on the basis that the self-existing flow cannot be observed, measured, or experimented with, and he provided an alternative relational account of time. I point out that this was not only extreme positivism or phenomenalism, but an epistemology and ontology suited for the subsequent physical theories of relativity. Finally, I argue that Mach's denial of the independent atomic structure of matter should not be entirely assimilated to his denial of substantivalism about time. The two phenomena are different, so we should evaluate Mach's reasoning concerning them accordingly.Matyáš Moravec and Peter West go through Susan Stebbing's criticism of Arthur Eddington's popular account of the passage of time. Stebbing's target, Moravec and West argue, is Eddington's largely Bergsonian view on time. She objects to the view that our minds have “a private door” to the physical reality which no measurements can disclose. Stebbing believes that our experience of the passage of time belongs to our ordinary, every-day experience, and she thinks Eddington mystifies the whole idea by leaning on a peculiar form of introspection. Moravec and West build a case for Bergson's influence on Eddington, arguing that Bergson probably did contribute to Eddington's idea of “the intuition of becoming.” Both seem to think that we may access the dynamic temporal reality in ways not captured by scientific investigation, by means of an introspective internal experience of duration.As a final remark, I think I should note, with regret, that out of the six authors in this volume only one is a woman. Let the reader know that as an editor I tried to strike a better balance. I still trust that the quality of the articles is high, and most importantly, worthwhile for readers interested in the history of philosophy of time.

Mach's Denial of Absolute Time

AbstractMach repudiated Newton's argument for absolute time. He denied there is such a thing as time itself that exists independently of any external change. In doing so, Mach failed to appreciate Newton's scientific practice. Absolute time is intrinsically related to Newton's laws of motion and the method of fluxions. Commentators have noted similarities between Mach's rejection of Newtonian time and his rejection of the independent existence of atoms. In this article, it shall be argued that the juxtaposition of absolute time and the atomic theory is unsound. Mach had good reasons to question the existence of substantial time, and he went on to provide an alternative, ontologically relational account. Whereas his dismissal of atoms can be seen as a questionable form of “phenomenalism” or “positivism,” this is not the case regarding his position on time.

Newton on active and passive quantities of matter

Newton published his deduction of universal gravity in Principia (first ed., 1687). To establish the universality (the particle-to-particle nature) of gravity, Newton must establish the additivity of mass. I call ‘additivity’ the property a body's quantity of matter has just in case, if gravitational force is proportional to that quantity, the force can be taken to be the sum of forces proportional to each particle's quantity of matter. Newton's argument for additivity is obscure. I analyze and assess manuscript versions of Newton's initial argument within his initial deduction, dating from early 1685. Newton's strategy depends on distinguishing two quantities of matter, which I call ‘active’ and ‘passive’, by how they are measured. These measurement procedures frame conditions on the additivity of each quantity so measured. While Newton has direct evidence for the additivity of passive quantity of matter, he does not for that of the active quantity. Instead, he tries to infer the latter from the former via conceptual analyses of the third law of motion grounded largely on analogies to magnetic attractions. The conditions needed to establish passive additivity frustrate Newton's attempted inference to active additivity.

Chunk and Permeate: The Infinitesimals of Isaac Newton

In the paper of Brown and Priest 2004, the authors developed the chunk and permeate method, which they described as a ‘paraconsistent reasoning strategy’. There it is suggested that the method of chunk and permeate could apply to the historical infinitesimal calculus. However, no attempt was made to look at actual historical examples. In this paper, I show that the method of chunk and permeate can indeed apply, as a rational reconstruction, to certain of Isaac Newton's arguments that use infinitesimals. This rational reconstruction maintains and uses, rather than sidesteps, the apparent contradictions in Newton's arguments. The applicability of chunk and permeate to other historical arguments, e.g. of Leibniz/L'Hospital and Fermat, has also been investigated and will be communicated in future publications.

Hannah Newton, The Sick Child in Early Modern England, 1580-1720

The myth of neglected sick children in the past was deconstructed during the last few decades by diverse authors of both medical and social history. Families saw children as worthwhile members, and assisted them in sickness and misery. Hannah Newton's book The Sick Child in Early Modern England stands in this tradition. But she achieves more than to affirm the results of earlier research. The author is a social historian of the early modern period, specialising in the history of medicine, childhood and emotions. The book, started as her PhD thesis, comprises three parts, each with two chapters. The first part deals with medical perceptions, the second with the family's perspective and the third with the child's experience. The bibliography contains an impressive amount of unpublished and published sources, sadly excluding the secondary literature listed only in the footnotes. Instead, there is a carefully compiled and helpful index. Newton attests a broad empathy to sick children during the long seventeenth century by their families and medical therapists. Furthermore, she describes a child specific medicine with particular, carefully modified therapies, its own anatomy and physiology of children, and special diagnoses. Newton's arguments about the positive perception of children and the application of specific children's medicine are not absolutely new arguments in the history of medicine, but Newton extends the results of former studies, based on the eighteenth century and more recent periods, to the seventeenth and the late sixteenth centuries.

NEWTON AND HAMILTON: IN DEFENSE OF TRUTH IN ALGEBRA

abstractAlthough it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of algebra. Namely, Hamilton's defense of algebra, like Newton's defense of geometry, is driven by the claim that a mathematical science must have a proper object and thus a basis in truth. In particular, Hamilton aims to show that algebra is not a mere language, or tool, or a mere “art”; instead, he argues, algebra is a bona fide mathematical science, like geometry, because its methods also provide true and accurate insight into a genuine subject matter, namely, the pure form of temporal intuition.

NEWTON AND PROCLUS: GEOMETRY, IMAGINATION, AND KNOWING SPACE

abstractI aim to clarify the argument for space that Newton presents in De Gravitatione (composed prior to 1687) by putting Newton's remarks into conversation with the account of geometrical knowledge found in Proclus's Commentary on the First Book of Euclid's Elements (ca. 450). What I highlight is that both Newton and Proclus adopt an epistemic progression (or “order of knowing”) according to which geometrical knowledge necessarily precedes our knowledge of metaphysical truths concerning the ontological state of affairs. As I argue, Newton's commitment to this order of knowing clarifies the interplay of the imagination and understanding in geometrical inquiry and illuminates how geometrical knowledge of space can lead to knowledge that space depends on and is related to God. In general, appreciating the Proclean elements of Newton's argument brings added light to the significance of geometrical inquiry for his general natural philosophical program and grants us insight into the philosophical grounding for the notion of absolute space that is presented in the Principia mathematica (1687).

The Curse of Ham in the Early Modern Era: The Bible and the Justifications for Slavery (review)

The Curse of Ham in the Early Modern Era: The Bible and the Justifications for Slavery. By David M. Whitford. [St. Andrews Studies in Reformation History] (Burlington, VT: Ashgate Publishing. 2009. Pp. xviii, 217. $119.95. ISBN 978-0-754-66625-7.) Among the followers of the Abrahamic religions, the Curse of Ham has arguably been the most wide spread justification for condemning darkskinned peoples to slavery. Its purported proof-text is Genesis 9:18-27, the story of the responses of the sons of Noah to their father's nakedness. Whatever Ham did - mockery, voyeurism, rape, castration? - and Shem and Japheth did not, it provoked a paternal curse, targeting Ham's son Canaan with enslavement. On this as well as almost everything else, the twists of the text as well as its subsequent interpretations are endlessly confusing. Over recent decades, exactly when, where, how, and among whom these disturbing verses became the Curse have provoked studies by numerous scholars, notably David Aaron, John Bergsma, David Goldenberg, Scott Hahn, Steven Haynes, Ephraim Isaac, Sylvester Johnson, Abraham Melamed, Thomas Peterson, Jonathan Shorsch, and the present reviewer. To a degree, David Whitford engages this growing research. Displaying much erudition, the author has exhaustively revealed new details from the sixteenth to the eighteenth centuries about the emergence and diffusion of the Curse. His painstaking examination of how Ham supplants Canaan as its target during the sixteenth century (pp. 77-104) is his most significant contribution. Unfortunately, he fails to explore the relationship of the medieval Latin manuscript confusion of Ham, Canaan, and Cain (which he acknowledges, p. 35n57) to this later transformation. By adding persuasive new details (pp. 105-22), his argument about the motive instigating the sixteenth-century George Best to introduce the blackened Ham to England reinforces the emerging consensus that it arose from the advocacy of expansion, not racism. Whitford attempts to sort out the degree of influence of two eighteenth-century divines in firmly establishing the Curse. He argues that Thomas Newton, the Anglican bishop of Bristol, played a greater role than the learned Benedictine Augustin Calmet (pp. 141-69). Since the earlier Calmet did play a part in the later Newton's argument - albeit in misleading fashion, as revealed by Whitford - the question is still unresolved, but Whitford does present evidence that Newton was favored by Anglophones. …

Newton's Radii, Maupertuis’ Arc Length, and Voltaire's Giant

SummaryGiven two arc length measurements along the perimeter of an ellipse—one taken near the long diameter, the other taken anywhere else—how do you find the lengths of major and minor axes? This was a problem of great interest from the time of Newton's Principia until the mid-eighteenth century when France launched twin geodesic expeditions—one to the equator near Quito, the other to the Finnish arctic led by Maupertuis—so as to determine whether the earth was lemon-shaped, as the French Academy long contended, or like a mandarin orange as Newton promised. We give a simplified version of Newton's argument, and show how an elliptical profile model for the earth's shape together with an arc length measurement determines the amount of flattening of the earth at the poles. We conclude by speculating why Voltaire made his giant Micromégas exactly 23 miles tall.

Qualities, Properties, and Laws in Newton's Induction

Newton's argument for universal gravitation in the Principia eventually rested on the third “Rule of Philosophizing,” which warrants the generalization of “qualities of bodies.” An analysis of the rule and the history of its development indicate that the term ‘quality’ should be taken to include both inherent properties of bodies and relations among systems of bodies, generalized into ‘laws'. By incorporating law-induction into the rule, Newton could legitimately rebuff objections to his theory by claiming that universal gravitation was justified by his method even if he could not specify the cause of gravity.

Force, deflection, and time: Proposition VI of Newton's Principia

In this extended study of Proposition VI, and its first corollary, in Book I of Newton's Principia, we clarify both the statements and the demonstrations of these fundamental results. We begin by tracing the evolution of this proposition and its corollary, to see how their texts may have changed from their initial versions. To prepare ourselves for some of the difficulties our study confronts, we then examine certain confusions which arise in two recent commentaries on Proposition VI. We go on to note other confusions, not in any particular commentary, but in Newton's demonstration and, especially, in his statement of the proposition. What, exactly, does Newton mean by a “body [that] revolves … about an immobile center”? By a “just-nascent arc”? By the “sagitta of the arc”? By the “centripetal force”? By “will be as”? We search for the mathematical meanings that Newton has in mind for these fragments of the Proposition VI statement, a search that takes us to earlier sections of the Principia and to discussions of the “method of first and last ratios,” centripetal force, and the second law of motion. The intended meaning of Proposition VI then emerges from the combined meanings of these fragments. Next we turn to the demonstration of Proposition VI, noting first that Newton's own argument could be more persuasive, before we construct a modern, more rigorous proof. This proof, however, is not as simple as one might expect, and the blame for this lies with the “sagitta of the arc,” Newton's measure of deflection in Proposition VI. Replacing the sagitta with a more natural measure of deflection, we obtain what we call Platonic Proposition VI, whose demonstration has a Platonic simplicity. Before ending our study, we examine the fundamental first corollary of Proposition VI. In his statement of this Corollary 1, Newton replaces the sagitta of Proposition VI by a not quite equal deflection from the tangent and the area swept out (which represents the time by Proposition I) by a not quite equal area of a triangle. These two approximations create small errors, but are these errors small enough? Do the errors introduced by these approximations tend to zero fast enough to justify these replacements? Newton must believe so, but he leaves this question unasked and unanswered, as have subsequent commentators on this crucial corollary. We end our study by asking and answering this basic question, which then allows us to give Corollary 1 a convincing demonstration.

Newton's Argument for Proposition 1 of the Principia

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center'' – we describe two serious flaws in the Principia's argument for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given'' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.''

Model Selection, Simplicity, and Scientific Inference

The Akaike Information Criterion can be a valuable tool of scientific inference. This statistic, or any other statistical method for that matter, cannot, however, be the whole of scientific methodology. In this paper some of the limitations of Akaikean statistical methods are discussed. It is argued that the full import of empirical evidence is realized only by adopting a richer ideal of empirical success than predictive accuracy, and that the ability of a theory to turn phenomena into accurate, agreeing measurements of causally relevant parameters contributes to the evidential support of the theory. This is illustrated by Newton's argument from orbital phenomena to the inverse-square law of gravitation.

Newton's aerodynamic problem in the presence of friction

This paper delivers an extension to a celebrated solution of Newton on the shape of the profile of an axisymmetric rigid body which, under prescribed length and caliber, has the least aerodynamic resistance. Newton assumed that the drag exerted by the surrounding gas on the body is exclusively due to the smooth impact of small gaseous particles against its surface. However, a more realistic description of the phenomenon must account for the friction between particles and body. This problem can be solved explicitly by essentially repeating Newton's argument and its subsequent improvements. The result is that the presence of friction has a noticeable effect both on the shape and resistance of the optimal body, even when the friction factor is small.

The Integrability of Ovals: Newton's Lemma 28 and Its Counterexamples

(Book 1, Sect. 6), Newton's Lemma 28 on the algebraic nonintegrability of ovals has had an unusually mixed reception. Beginning in 1691 with Jakob Bernoulli (who accepted the lemma) and Huygens and Leibniz (who rejected it and offered counterexamples), Lemma 28 has a history of eliciting seemingly contradictory reactions. In more recent times, D.T. Whiteside in 1974 gave an “unchallengeable counterexample,” while the mathematician V.I. Arnol'd in 1987 sided with Bernoulli and called Newton's argument an “astonishingly modern topological proof.” This disagreement mostly stems, we argue, from Newton's vague statement of the lemma. Indeed, we identify several different interpretations of Lemma 28, any one of which Newton may have been intending to assert, and we then test a number of proposed counterexamples to see which, if any, are true counterexamples to one or more of these versions of the lemma. Following this, we study Newton's argument for the lemma to see whether and where it fails to be convincing. In the end, our study of Newton's Lemma 28 provides an answer to the question, Who is right: Huygens, Leibniz, Whiteside and the others who reject the lemma, or Bernoulli, Arnol'd, and the others who accept it?

Reflections on Parity Nonconservation

This paper considers the implications for the relational-substantival debate of observations of parity nonconservation in weak interactions, a much neglected topic. It is argued that ‘geometric proofs’ of absolute space, first proposed by Kant (1768), fail, but that parity violating laws allow ‘mechanical proofs’, like Newton's laws. Parity violating laws are explained and arguments analogous to those of Newton's Scholium are constructed to show that they require absolute spacetime structure—namely, an orientation—as Newtonian mechanics requires affine structure. Finally, it is considered how standard relationist responses to Newton's argument might respond to the new challenge of parity nonconservation.

“ Conatus recedenti ab axe motus ” ou a parábola do balde de Newton

An analysis of Newton's argument on absolute space is provided. The equation of the parable is given by describing the water surface from a rotating bucket related to the Earth. This rotation generates a trend by which the water recedes from the axis of its motion, or in the classic Latin allusion: conatus recedenti ab axe motus . The theme and its implications will be discussed from the point of view of the teaching of Physics

John Hutchinson's Critique of Newtonian Heterodoxy

“Nature and Nature's laws lay hid in night: God said, Let Newton be!—and all was light,” according to Alexander Pope. Other British subjects were not so sure. In recent years, historians have begun to take more seriously the persons who opposed Newton on either philosophical, scientific or theological grounds. Rival systems of natural philosophy were already in the field, including the scholastic, the alchemical, and especially the Cartesian. Newton had learned a great deal from Descartes, but he also set out to correct the errors in his system. Many Cartesians, at least in the period shortly after 1687, were not convinced by Newton's arguments. His methodology was suspect as well. The mathematics that Newton had invented was hard to follow and the role that it played in his system was unfamiliar. Political antipathies sometimes led to the rejection of Newtonianism. But the crux of the problem was theological. Newton's natural philosophy, as stated in hisPrincipia Mathematica, seemed to undermine the traditional doctrines of the Christian religion.