Do Newton’s rules of reasoning guarantee truth … must they?

Newton’s Principia introduces four rules of reasoning for natural philosophy. Although useful, there is a concern about whether Newton’s rules guarantee truth. After redirecting the discussion from truth to validity, I show that these rules are valid insofar as they fulfill Goodman’s criteria for inductive rules and Newton’s own methodological program of experimental philosophy; provided that cross-checks are used prior to applications of rule 4 and immediately after applications of rule 2 the following activities are pursued: (1) research addressing observations that systematically deviate from theoretical idealizations and (2) applications of theory that safeguard ongoing research from proceeding down a garden path.     

The Newtonian Myth

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.     

Kepler’s theory of the soul: a study on epistemology

Kepler is mainly known among historians of science for his astronomical theories and his approaches to problems having to do with philosophy of science and ontology. This paper attempts to contribute to Kepler studies by providing a discussion of a topic not frequently considered, namely Kepler’s theory of the soul, a general theory of knowledge whose central problem is what makes knowledge possible, rather than what makes knowledge true, as happens in the case of Descartes’s and Bacon’s epistemologies. Kepler’s theory consists of four issues: the theory of the different sorts of soul—that is, the human soul, the animal soul, the vegetable soul, and the Earth soul—concerning their faculties, the differences and the resemblances emerging among them, the relation they maintain with their own bodies and the world, and the distinction soul–world. The paper discusses these issues from a historical perspective, that is, it reconstructs the way they appear in three periods of Kepler’s career: the period prior to the publication of the Mysterium cosmographicum, the period from 1596 to 1611, and the period of the Harmonices mundi libri V. Finally, Kepler’s epistemology is briefly contrasted with Descartes’s and Bacon’s in order to suggest that Kepler’s could be seen as a third way to understand the philosophical origins of Modernity.     

Thomas Reid’s Newtonian Theism: his differences with the classical arguments of Richard Bentley and William Whiston

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.     

Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Hidden depths: Halley, hell and other people

During the long eighteenth century, boundaries between theology and natural philosophy, between imaginary and factual travel narratives, between fiction and social commentary, were far more fluid than they are today. To explore these relationships, this paper links Mary Shelley’s Frankenstein—a book often hailed as the first science fiction novel—to two earlier works which are now less well known: Edmond Halley’s article about terrestrial magnetism, in which he suggested that God had created inhabited illuminated cavities inside the earth; and a satirical fantasy voyage written by the Danish author Ludvig Holberg, but published anonymously as Niels Klim’s journey to the underground and immediately translated into many languages. Attention is focussed on how the ambiguous presentation of these and other texts blurs any straightforward classification of genres. The aim of examining these writers together is not to search for direct mappings from one project to another, but instead to introduce Holberg’s unfamiliar yet important book and also to cast new light on Frankenstein, one of England’s most famous works of literature.     

Response to one point in Gingras’s review of Gravity’s shadow

Yves Gingras says of my book Gravity’s shadow that it is too long, the style is poor, and in its 870 pages there is nothing new that is not to be regretted. Gingras’s purity of vision would be a cause for congratulation were it not for the appalling implications of one of his claims. For the sake of the future of social science—indeed for the sake of the future of civilisation—it is impossible to leave unchallenged the idea that respondents, who don’t like to see their use of data questioned, are to be commended when they withhold those data from public scrutiny.     

Newton’s notion and practice of unification

In this paper I deal with a neglected topic with respect to unification in Newton’s Principia. I will clarify Newton’s notion (as can be found in Newton’s utterances on unification) and practice of unification (its actual occurrence in his scientific work). In order to do so, I will use the recent theories on unification as tools of analysis (Kitcher, Salmon and Schurz). I will argue, after showing that neither Kitcher’s nor Schurz’s account aptly capture Newton’s notion and practice of unification, that Salmon’s later work is a good starting point for analysing this notion and its practice in the Principia. Finally, I will supplement Salmon’s account in order to answer the question at stake.     

Causally productive activities

This paper suggests and discusses an answer to the following question: What distinguishes causal from non-causal or coincidental co-occurrences? The answer derives from Elizabeth Anscombe’s idea that causality is a highly abstract concept whose meaning derives from our understanding of specific causally productive activities (e.g., pulling, scraping, burning), and from her rejection of the assumption that causality can be informatively understood in terms of actual or counterfactual regularities.     

Descartes’s changing mind

Descartes is always concerned about knowledge. However, the Galileo affair in 1633, the reactions to his Discourse on method, and later his need to reply to objections to his Meditations provoked crises in Descartes’s intellectual development the import of which has not been sufficiently recognized. These events are the major reasons why Descartes’s philosophical position concerning how we know and what we may know is radically different at the end of his life from what it was when he began. We call this later position Descartes’s epistemic stance and contrast it with his earlier methodological, metaphysical realism. Yet Descartes’s epistemic views cannot be separated from other aspects of his work, for example, his views concerning God, causality, metaphysics, and the nature of science. A further meta-implication is that serious errors await any scholar who cites early Cartesian texts in support of late Cartesian positions, or who uses later texts in conjunction with early ones to support a reading of Descartes’s philosophy.     

The early application of the calculus to the inverse square force problem

The translation of Newton’s geometrical Propositions in the Principia into the language of the differential calculus in the form developed by Leibniz and his followers has been the subject of many scholarly articles and books. One of the most vexing problems in this translation concerns the transition from the discrete polygonal orbits and force impulses in Prop. 1 to the continuous orbits and forces in Prop. 6. Newton justified this transition by lemma 1 on prime and ultimate ratios which was a concrete formulation of a limit, but it took another century before this concept was established on a rigorous mathematical basis. This difficulty was mirrored in the newly developed calculus which dealt with differentials that vanish in this limit, and therefore were considered to be fictional quantities by some mathematicians. Despite these problems, early practitioners of the differential calculus like Jacob Hermann, Pierre Varignon, and Johann Bernoulli succeeded without apparent difficulties in applying the differential calculus to the solution of the fundamental problem of orbital motion under the action of inverse square central forces. By following their calculations and describing some essential details that have been ignored in the past, I clarify the reason why the lack of rigor in establishing the continuum limit was not a practical problem.     

Incommensurabilities in the work of Thomas Kuhn

I distinguish between two ways in which Kuhn employs the concept of incommensurability based on for whom it presents a problem. First, I argue that Kuhn’s early work focuses on the comparison and underdetermination problems scientists encounter during revolutionary periods (actors’ incommensurability) whilst his later work focuses on the translation and interpretation problems analysts face when they engage in the representation of science from earlier periods (analysts’ incommensurability). Secondly, I offer a new interpretation of actors’ incommensurability. I challenge Kuhn’s account of incommensurability which is based on the compartmentalisation of the problems of both underdetermination and non-additivity to revolutionary periods. Through employing a finitist perspective, I demonstrate that in principle these are also problems scientists face during normal science. I argue that the reason why in certain circumstances scientists have little difficulty in concurring over their judgements of scientific findings and claims while in others they disagree needs to be explained sociologically rather than by reference to underdetermination or non-additivity. Thirdly, I claim that disagreements between scientists should not be couched in terms of translation or linguistic problems (aspects of analysts’ incommensurability), but should be understood as arising out of scientists’ differing judgments about how to take scientific inquiry further.     

Proposition II (Book I) of Newton’s <Emphasis Type="Italic">Principia</Emphasis>

After preparing the way with comments on evanescent quantities and then Newton’s interpretation of his second law, this study of Proposition II (Book I)— Proposition II Every body that moves in some curved line described in a plane and, by a radius drawn to a point, either unmoving or moving uniformly forward with a rectilinear motion, describes areas around that point proportional to the times, is urged by a centripetal force tending toward that same point. —asks and answers the following questions: When does a version of Proposition II first appear in Newton’s work? What revisions bring that initial version to the final form in the 1726 Principia? What, exactly, does this proposition assert? In particular, what does Newton mean by the motion of a body “urged by a centripetal force”? Does it assert a true mathematical claim? If not, what revision makes it true? Does the demonstration of Proposition II persuade? Is it as convincing, for example, as the most convincing arguments of the Principia? If not, what revisions would make the demonstration more persuasive? What is the importance of Proposition II, to the physics of Book III and the mathematics of Book I?     

Between autobiography and reality: Popper's inductive years

On the basis of his unpublished thesis ‘Gewohnheit und Gesetzerlebnis in der Erziehung’ (1926–7) a historical reconstruction is given of the genesis of Popper's ideas on induction and demarcation which differs radically from his own account in Unended quest. It is shown not only that he wholeheartedly endorses inductive epistemology and psychology but also that his ‘demarcation’ criterion is inductivistic. Moreover it is shown that his later demarcation thesis arises not from his worries about, on the one hand, Marxism and psychoanalysis and, on the other hand, Einstein's physics, but rather from his urgent preoccupation with providing pedagogy with a psychological foundation, which has its sources in Karl Bühler's cognitive psychology as well as, surprisingly, Adler's Characterology. Aside from Adler some lesser known psychologists, such as Karl Groos, will also be seen to have played a formative role on Popper's early thinking.     

Collecting airs and ideas: Priestley’s style of experimental reasoning

It has often been claimed that Priestley was a skilful experimenter who lacked the capacities to analyze his own experiments and bring them to a theoretical closure. In attempts to revise this view some scholars have alluded to Priestley’s ‘synoptic’ powers while others stressed the contextual role of British Enlightenment in understanding his chemical research. A careful analysis of his pneumatic reports, privileging the dynamics of his experimental practice, uncovers significant yet neglected aspects of Priestley’s science. By focusing on his early experimental conduct and writing on nitrous air, I demonstrate how his methodological and rhetorical devices, far from being consequences of compulsive writing or theoretical naïveté, were deeply entwined with his chemical research. I employ the notion of ‘style of experimental reasoning’ (SER)—derived from A. C. Crombie and I. Hacking—to shed light on the intersection at which Priestley’s unique method, literary style, and epistemology converged to generate scientific knowledge. Establishing Priestley’s SER advances a finer understanding of the interactive character of his pneumatic experimentalism, peculiar dimensions of which have evaded both traditional as well as revisionist scholarship, thus infusing the longstanding historiographic debate over his scientific merits.     

Written in the flesh: Isaac Newton on the mind–body relation

Isaac Newton’s views on the mind–body relation are of interest not only because of their somewhat unique departure from popular early modern conceptions of mind and its relation to body, but also because of their connections with other aspects of Newton’s thought. In this paper I argue that (1) Newton accepted an interesting sort of mind–body monism, one which defies neat categorization, but which clearly departs from Cartesian substance dualism, and (2) Newton took the power by which we move our bodies by thought alone to be a member of the family of forces that includes gravity and electricity. Time and again, Newton draws an analogy between the ultimate cause and nature of the volitional powers of mind and the ultimate cause and nature of these other forces.     

Primary source knowledge and technical decision-making: Mbeki and the AZT debate

Demands for public participation in technical decision-making are currently high on the agenda of Science & Technology Studies. It is assumed that the democratisation of technical decision-making processes generally leads to more socially desirable and acceptable outcomes. While this may be true in certain cases, this assumption cannot be generalised. I will discuss the case of the so-called ‘South African AZT debate’. The controversy started when President Thabo Mbeki, after reading some scientific papers on the toxicity of AZT, decided to bar the use of the drug in the public health sector as a means to reduce the transmission of HIV from mothers to children. While the scientific mainstream accepts the effectiveness of AZT in reducing the risk of vertical HIV transmission, a few maverick scientists reject the clinical evidence and argue that the risks of using AZT by far outweigh its benefits. Based on various textual sources and using the ‘Periodic Table of Expertises’ developed by Collins and Evans, Mbeki’s expertise at the time of his intervention into the technical question whether AZT is a medicine or a poison can be classified as primary source knowledge. It is shown that this type of expertise is insufficient for technical decision-making. Mbeki’s primary source knowledge legitimated his presentation of the claims of maverick scientists as a serious contribution to the debate—with tragic consequences for tens of thousands of babies.     

Newton’s De gravitatione: a review and reassessment

The widely accepted supposition that Newton’s De gravitatione was written in 1684/5 just before composing the Principia is examined. The basis for this determination has serious difficulties starting with the failure to examine the numerical estimates for the resistance of aether. The estimated range is not nearly nil as claimed but comparable with air at or near the earth’s surface. Moreover, the evidence provided most likely stems from experiments by Boyle, Hooke, and others in the 1660s and does not use evidence available in the late 1684. The document supports Newton’s contention that the aether medium incorporates very large voids thereby proving that body and space differ but does by no means completely reject its corporeal nature or eliminate its resistance. Newton’s use of the term inertia provides no conclusive evidence for a late date as often claimed and his definition of gravitas is difficult to reconcile with a late one.     

Looking for structure in all the wrong places: Ramsey sentences, multiple realisability, and structure

‘Epistemic structural realism’ (ESR) insists that all that we know of the world is its structure, and that the ‘nature’ of the underlying elements remains hidden. With structure represented via Ramsey sentences, the question arises as to how ‘hidden natures’ might also be represented. If the Ramsey sentence describes a class of realisers for the relevant theory, one way of answering this question is through the notion of multiple realisability. We explore this answer in the context of the work of Carnap, Hintikka and Lewis. Both Carnap and Hintikka offer clear structuralist perspectives which, crucially, accommodate the openness inherent in theory change. Unfortunately there is little purchase for a viable form of realism in either case. Lewis’s approach, on the other hand, offers more scope for realism but, as we shall see, concerns arise as to whether a relevant form of structuralism can be maintained. In particular his thesis of Ramseyan humility undermines certain conceptions of scientific laws that the structural realist might naturally cleave to. Our overall conclusion is that the representational device of Ramsey sentence plus multiple realisability can accommodate either the structuralist or realist aspects of ESR but has difficulties capturing both.