This thesis develops a hermeneutic philosophy of science to provide insights into physics education. -/- Modernity cloaks the authentic character of modern physics whenever discoveries entertain us or we judge theory by its use. Those who justify physics education through an appeal to its utility, or who reject truth as an aspect of physics, relativists and constructivists, misunderstand the nature of physics. Demonstrations, not experiments, reveal the essence of physics as two characteristic engagements with truth. First, truth in its guise (...) as correspondence enables a human being to prepare for the distinctive event of physics. -/- Second, the event of physics occurs in human perception when someone forces a hidden reality to disclose an aspect of itself. Thus, the ground of physics is our human involvement with reality achieved by way of truth. -/- To support this account of physics, the thesis reports phenomenological investigations into Isaac Newton’s involvement with optics and a secondary school physics laboratory. These involve interpretations of Heidegger’s theory of beings, schema and signification. The project draws upon, and contributes to, the hermeneutic phenomenology of modern physics, a tradition in continental philosophy that begins with Immanuel Kant, and advances particularly from Martin Heidegger to Patrick Heelan. -/- The thesis advocates an ontological pedagogy for modern physics which has as its purpose each individual student’s engagement with reality and truth. Students may achieve this through demonstrations of phenomena that will enable them to dwell with physics, an experience that contrasts with their embroilment in modernity, and which perpetuates nature’s own science. (shrink)

(2008). The Connection Between Postformal Thought and Major Scientific Innovations. World Futures: Vol. 64, Postformal Thought and Hierarchical Complexity, pp. 503-512.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Ecological Ethics: An IntroductionDavid Keller (bio)Patrick Curry, Ecological Ethics: An Introduction. Malden, Massachusetts: Polity Press, 2007, 173pages.Were I in Bath having drinks with Patrick Curry, we would have much to agree about. Explaining his choice of title of his book, Ecological Ethics, he rightly points out that the more common descriptor "environmental ethics" presupposes a dualism between human beings and the nonhuman environment—an assumption which is itself anthropocentric (...) (p. 4). For philosophers interested in studying the human/ nonhuman dynamic, the legitimacy of anthropocentrism is itself an open question. Because the word 'ecology' treats humans, as biota, as integral parts of ecological systems, the phrase "ecological ethics" is less presumptuous and hence more accurate. The word 'ecological' also has the benefit of conveying the message that the subject is notgoing to involve extending moral considerability from humans out into the "environment." Instead, ecological systems as the locus of value provide the starting point for the elaboration of ethics (p. 2). For Curry, as for Leopold (1960) and Callicott (1989), "ecological community" is coextensive with the ethical community.To correlate the ethical community with the biotic community within the rubric of "ecological ethics" is nothing novel. Curry's claim that "there is something ancient about an ecological ethic" (p. 7) got me thinking: [End Page 153]prior to Abrahamic monotheism and Greek rationalism, ancient peoples, particularly nomadic hunter-gatherers, probably considered themselves as integral parts of what encompassed them, moving with herds, in concert with meteorological and seasonal changes, seeing themselves as one amongst other living beings. They probably did not see themselves apart from the "environment" as we have learned to do. Then with the advent of agriculture, linear furrows and controlled inundations must have fostered an addictive sense of security from flood and famine. Later, the innovations of industrial civilization further distanced us from the caprice of nature's wild vicissitudes. Yet that comfort comes at the expense of lost awareness of our responsibilities as bioticcitizens. Therefore, Curry says, following Sylvan (1973), we need a new ecological ethic since traditional Western morality "is no longer up to the job" (ibid.).Curry remarks that ethics, cast in this light, is not something "optional," something to be addressed after one's belly is full, debts settled, and lodging secured. Rather, ethics cuts directly to the core of human action, of all human activity (p. 5)—a claim reminiscent of Socrates' exhortation to Thrasymachus that it is no small matter that they are discussing, nothing of less importance than the right way to live one's life (Plato 2005, p. 603).Over the first sips of ale, I would praise him for giving his book a simple and straightforward structure that makes a challenging subject accessible, especially to students. After laying down the groundwork of basic concepts in moral philosophy (chapter 3)—objectivism versus relativism, the problem of the is/ought gap, religious morality and environmental philosophy (domination, stewardship, and managerialism), and virtue and rule-based ethics (chapter 4)—Curry addresses axiology (chapter 5). Are humans the sole locus of value (anthropocentrism), or are there other entities worthy of some sort of moral consideration who themselves do not carry the burden of moral responsibility (zoocentrism, biocentrism, ecocentrism)? Curry answers the latter in the affirmative, arguing that ontological interconnectedness of humans with other living beings within ecological systems discloses that something greater than humanity is the locus of value (p. 46).The most useful part of the book for my students out in Utah would be the middle chapters (6–8) in which Curry casts degrees of nonanthropocentrism [End Page 154]in shades of green. These shades range from light green or "shallow" anthropocentric ethics such Bookchin's Social Ecology (p. 50), Hardin's Lifeboat Ethics (pp. 52–54), and mainstream environmentalism (p. 51), through medium green ethics based on the extension of traditional human-oriented moral philosophy to nonhumans such as Singer's Animal Liberation (pp. 56–59), Regan's Animal Rights (pp. 59–60), and Taylor's Biocentrism (pp. 60–62). Curry proceeds to the dark green ethics of ecocentrism, such as Land Ethics (pp. 65–68), the Gaia Hypothesis (pp. 68–71... (shrink)

Utilizing Einstein’s comparison of General Relativity and Descartes’ physics, this investigation explores the alleged conventionalism that pervades the ontology of substantival and relationist conceptions of spacetime. Although previously discussed, namely by Rynasiewicz and Hoefer, it will be argued that the close similarities between General Relativity and Cartesian physics have not been adequately treated in the literature—and that the disclosure of these similarities bolsters the case for a conventionalist interpretation of spacetime ontology.

Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous claim that any proper natural science must be mathematical should be understood on the basis of these conditions. In order to substantiate (...) this reading, I will show that only in this way it can be explained why Kant thought (1) that mathematics has a particular foundational function with respect to the natural sciences and (2) as such secures their scientific status. (shrink)

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. (shrink)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis (...) (SIA), as propounded by John Bell. Despite many parallels between SIA and Leibniz’s approach —the non-punctiform nature of infinitesimals, their acting as parts of the continuum, the dependence on variables (as opposed to the static quantities of both Standard and Non-standard Analysis), the resolution of curves into infinitesided polygons, and the finessing of a commitment to the existence of infinitesimals— I find some salient differences, especially with regard to higher-order infinitesimals. These differences are illustrated by a consideration of how each approach might be applied to Newton’s Proposition 6 of the Principia, and the derivation from it of the v2/r law for the centripetal force on a body orbiting around a centre of force. It is found that while Leibniz’s syncategorematic approach is adequate to ground a Leibnizian version of the v2/r law for the “solicitation” ddr experienced by the orbiting body, there is no corresponding possibility for a derivation of the law by nilsquare infinitesimals; and while SIA can allow for second order differentials if nilcube infinitesimals are assumed, difficulties remain concerning the compatibility of nilcube infinitesimals with the principles of SIA, and in any case render the type of infinitesimal analysis adopted dependent on its applicability to the problem at hand. (shrink)

In this essay I argue against I. Bernard Cohen's influential account of Newton's methodology in the Principia: the 'Newtonian Style'. The crux of Cohen's account is the successive adaptation of 'mental constructs' through comparisons with nature. In Cohen's view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive, which is at odds with Newton's rejection of the hypothetical-deductive method. An adequate account of Newton's methodology needs to show how Newton's (...) method proceeds differently from the hypothetical-deductive method. In the constructive part I argue for my own account, which is model based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton's models is a result of exploring increasingly complex force functions (intra-theoretical dynamics) rather than a successive comparison with nature (extra-theoretical dynamics). Nature did not enter the scene here. This intra-theoretical dynamics is related to the 'autonomy of the models'. (shrink)

In this paper, I give a brief overview of ideas from Reformed Epistemology, and the relationship between faith, evidence, and belief. I discuss what makes belief in God rationally warranted, and how reformed epistemology strikes a middle ground between fideism and evidentialism. In effect, reformed epistemology avoids the fideist idea that belief in God must be taken on "blind faith," but also avoids some of the epistemic issues present in evidentialism, such as its self-referential incoherence. The reformed epistemologist says belief (...) in God is rational, but not for the reasons demanded by evidentialists. (shrink)

We make physical efforts when we swim, carry shopping bags, push heavy doors, or cycle up hills. A growing concern among philosophers and scientists in related fields is the absence of a well-defined concept for physical efforts. This paper addresses this issue by presenting a force-based definition of physical efforts. In Sect. 1, we explore the shortcomings of existing definitions of effort. Section 2 introduces the force-based account of efforts according to which making an effort consists in exerting a force (...) so as to make an object move or stay at rest. Section 3 introduces three central distinctions stemming from the account: failed vs. successful efforts; resisted vs. unresisted efforts; and efforts vs. effortful actions. Section 4 presents a key objection, to the effect that the force-based theory cannot account for the difficulty of efforts: efforts usually feel difficult, but effort’s difficulty is not always a function of the magnitude of force(s) exerted. Section 5 argues that the most in-depth account of difficulty so far, that developed by Bradford ( 2015 ), cannot account for the difficulty of efforts. Sections 6 & 7 develop a novel account of effort’s difficulty. (shrink)

Timelines is an inquiry into the nature of time, both as an apparent feature of the external physical world and as a fundamental feature of our experience of ourselves in the world. The principal argument of Timelines is that our coventional ideas about time are largely mistaken and that what we think of as independent physical time is actually our calibration of a certain relation between events. Namely, the relation between time-keeping events and the causal sequential differences of physical processes (...) which are real and independent of us. (shrink)

I examine Du Châtelet’s methodology for physics and metaphysics through the lens of her engagement with Newton’s Rules for Reasoning in Natural Philosophy. I first show that her early manuscript writings discuss and endorse these Rules. Then, I argue that her famous published account of hypotheses continues to invoke close analogues of Rules 3 and 4, despite various developments in her position. Once relevant experimental evidence and some basic constraints are met, it is legitimate to inductively generalize from observations; general (...) hypotheses can thereafter be assumed as true until contrary experiments show otherwise. I conclude by arguing that this account of induction plays an essential role in her metaphysics, both in an argument for simple substances—which has an inductive premise—and in her attempt to distinguish acceptable and unacceptable metaphysical commitments. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

I show how Sir William Rowan Hamilton’s philosophical commitments led him to a causal interpretation of classical mechanics. I argue that Hamilton’s metaphysics of causation was injected into his dynamics by way of a causal interpretation of force. I then detail how forces are indispensable to both Hamilton’s formulation of classical mechanics and what we now call Hamiltonian mechanics (i.e., the modern formulation). On this point, my efforts primarily consist of showing that the contemporary orthodox interpretation of potential energy is (...) the interpretation found in Hamilton’s work. Hamilton called the potential energy function the “force-function” because he believed that it represents forces at work in the world. Various non-historical arguments for this orthodox interpretation of potential energy are provided, and matters are concluded by showing that in classical Hamiltonian mechanics, facts about the potential energies of systems are grounded in facts about forces. Thus, if one can tolerate the view that forces are causes of motion, then Hamilton provides one with a road map for transporting causation into one of the most mathematically sophisticated formulations of classical mechanics, viz., Hamiltonian mechanics. (shrink)

A volume of papers inspired by the work of George E. Smith on confirmation and evidence in advanced science—from Newton's gravitation theory to the physics of molecules.

In (Weaver 2021), I showed that Boltzmann’s H-theorem does not face a significant threat from the reversibility paradox. I argue that my defense of the H-theorem against that paradox can be used yet again for the purposes of resolving the recurrence paradox without having to endorse heavy-duty statistical assumptions outside of the hypothesis of molecular chaos. As in (Weaver 2021), lessons from the history and foundations of physics reveal precisely how such resolution is achieved.

In order to carry out “a great and important piece of work, and that in a complete and lasting way”, Kant claims that one must join one’s “effort with that of the author”. The reading of a work, therefore, must try to embrace “the articulation or structure of the system, which yet matters most when it comes to judging its unity and soundness”. This structure and articulation, however, may not be so easily accessible; it may, rather, be latent under “bright (...) colours [that] paint over and make unrecognizable” the argument’s essence, often confusing the reader, who “cannot quickly enough attain a survey of the whole”. Now, it would be expected, then, that Kant, condemning such “ornaments”, would not employ those resources I n his writings. However, it is curious that not infrequently he makes use of such “bright colours”. The present paper aims at pointing out some passages of Kant's theoretical and practical philosophy in which it is possible to identify such “colouring”. (shrink)

I examine the (mediated) correspondence between Spinoza and Robert Boyle concerning the latter’s account of fluidity and his experiments on reconstitution of niter in the light of the epistemology and doctrine of method contained in the Treatise on the Emendation of the Intellect. I argue that both the Treatise and the correspondence reveal that for Spinoza, the proper method of science is not experimental, and that he accepted a powerful under-determination thesis. I argue that, in contrast to modern versions, Spinoza’s (...) form of naturalism was a highly rationalist and anti-empirical one. I conclude with a brief account of the value of experience and experimentation for Spinoza’s scientific method. (shrink)

This book brings together papers from a conference that took place in the city of L'Aquila, 4–6 April 2019, to commemorate the 10th anniversary of the earthquake that struck on 6 April 2009. Philosophers and scientists from diverse fields of research debated the problem that, on 6 April 1922, divided Einstein and Bergson: the nature of time. For Einstein, scientific time is the only time that matters and the only time we can rely on. Bergson, however, believes that scientific time (...) is derived by abstraction, even in the sense of extraction, from a more fundamental time. The plurality of times envisaged by the theory of Relativity does not, for him, contradict the philosophical intuition of the existence of a single time. But how do things stand today? What can we say about the relationship between the quantitative and qualitative dimensions of time in the light of contemporary science? What do quantum mechanics, biology and neuroscience teach us about the nature of time? The essays collected here take up the question that pitted Einstein against Bergson, science against philosophy, in an attempt to reverse the outcome of their monologue in two voices, with a multilogue in several voices. (shrink)

El campo interpretativo sobre la obra de Newton ha sido ampliamente discutido y, particularmente, el tema de las hipótesis no ha sido la excepción. El objetivo de este texto es mostrar que la filosofía natural de Newton pareciera, en principio, rechazar la hipótesis, pero en realidad no es opuesta a la formulación de estas, si diferenciamos a qué tipo de hipótesis se hace referencia. Así pues, se muestra, en primer lugar, cómo desarrolla Newton su filosofía natural, y cómo es contrapuesta (...) a las hipótesis. Luego se muestra que bajo condiciones determinadas las hipótesis son aceptadas. Y, por consiguiente, se concluye que la filosofía de Newton no rechaza radicalmente las hipótesis, sino que, por el contrario, se puede valer de su formulación para el progreso de la investigación científica, dependiendo a qué tipo de hipótesis se haga referencia. (shrink)

I begin by outlining Du Châtelet’s ontology of mathematical objects: she is an idealist, and mathematical objects are fictions dependent on acts of abstraction. Next, I consider how this idealism can be reconciled with her endorsement of necessary truths in mathematics, which are grounded in essences that we do not create. Finally, I discuss how mathematics and physics relate within Du Châtelet’s idealism. Because the primary objects of physics are partly grounded in the same kinds of acts as yield mathematical (...) objects, she thinks we are sometimes licensed in drawing conclusions about physical things from mathematical premises. (shrink)

Virtually all philosophers of science have construed fundamental theories as descriptions of entities, properties, and/or structures. Call this the “descriptive-ontological” view. I argue that this view is incorrect, at least insofar as physical theories are concerned. I propose a novel construal of theories that I call the “prescriptive-dynamical” view. The central tenet of this view, roughly put, is that the _essential_ content of fundamental physical theories is a _prescription for interfacing with natural systems and translating local data into compact theoretical (...) language_. The descriptive-ontological aspects of theories, if any, are taken as _inessential_ content on this view: they do not contribute to the predictive success of the theory. Rather than describing _what is there_, the essence of a physical theory is to tell us _what to do_ when interfacing with a physical system. (shrink)

Given functionally equivalent minds, how does the expected quantity of their conscious experience differ across different substrates and how could we calculate this? We argue that a realistic digital brain emulation would be orders of magnitude less conscious than a real biological brain. On the other hand, a mind running on neuromorphic hardware or a quantum computer could in principle be more conscious than than a biological brain.

For Émilie Du Châtelet, I argue, a central role of the principle of sufficient reason is to discriminate between better and worse explanations. Her principle of sufficient reason does not play this role for just any conceivable intellect: it specifically enables understanding for minds like ours. She develops this idea in terms of two criteria for the success of our explanations: “understanding how” and “understanding why.” These criteria can respectively be connected to the determinateness and contrastivity of explanations. The crucial (...) role Du Châtelet’s principle of sufficient reason plays in identifying good explanations is often overlooked in the literature, or else run together with questions about the justification and likelihood of explanations. An auxiliary goal of the article is to situate Du Châtelet’s principle of sufficient reason with respect to some of the general epistemological and metaphysical commitments of her Institutions de Physique, clarifying how it fits into the broader project of that work. (shrink)

This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction.

Different authors have attempted to clarify the aspects of remote action and God's involvement on the basis of textual investigations, mainly from the Mathematical Principles of Natural Philosophy, (Newton, 1999b) Newton's correspondence with Richard Bentley (1692/93), (Bentley 1693) and Queries that Newton introduced at the end of the Opticks book in the first three editions (between 1704 and 1721). (Newton 1952) DOI: 10.13140/RG.2.2.12870.11844/1.

I will argue, pace a great many of my contemporaries, that there's something right about Boltzmann's attempt to ground the second law of thermodynamics in a suitably amended deterministic time-reversal invariant classical dynamics, and that in order to appreciate what's right about (what was at least at one time) Boltzmann's explanatory project, one has to fully apprehend the nature of microphysical causal structure, time-reversal invariance, and the relationship between Boltzmann entropy and the work of Rudolf Clausius.

The question of where the knowledge comes from when we conduct thought experiments has been one of the most fundamental issues discussed in the epistemological position of thought experiments. In this regard, Pierre Duhem shows a skeptical attitude on the subject by stating that thought experiments cannot be evaluated as real experiments or cannot be accepted as an alternative to real experiments. James R. Brown, on the other hand, states that thought experiments, which are not based on new experimental evidence (...) or logically derived from old data, called the Platonic thought experiment, provide intuitive access to a priori knowledge. Unlike Brown, John D. Norton strictly criticizes the idea that thought experiments provide mysterious access to the knowledge of the physical world, and states that thought experiments cannot provide knowledge that transcends empiricism. In the context of the NortonBrown debate, in this article, Brown's stance on thought experiments is supported by critically analyzing the thoughts put forward on the subject. -/- Düşünce deneylerini gerçekleştirdiğimizde sonucunda elde edilen bilginin nereden geldiği sorusu düşünce deneylerinin epistemolojik konumuna ilişkin tartışılan en temel konulardan bir tanesidir. Bu doğrultuda, Pierre Duhem düşünce deneylerinin gerçek deneyler ile aynı statüde değerlendirilemeyeceğini ve hatta düşünce deneylerinin gerçek deneylerin bir alternatifi olarak bile kabul edilemeyeceğini belirterek konuya ilişkin şüpheci bir tavır sergilemektedir. James R. Brown ise yeni deneysel kanıtlara dayanmayan ya da eski verilerden mantıksal olarak türetilmeyen, Platoncu düşünce deneyi olarak adlandırılan düşünce deneylerinin a priori bilgiye sezgisel erişim sağladığını ifade etmektedir. Brown’ın aksine, John D. Norton düşünce deneylerinin fiziksel dünyanın bilgisine gizemli bir erişim sağladığı yönündeki düşünceyi kesin bir dille eleştirmekte ve düşünce deneylerinin ampirizmi aşan bir bilgi sağlamasının mümkün olamayacağını ifade etmektedir. Norton-Brown tartışması çerçevesinde bu makalede, Brown'un düşünce deneylerine ilişkin tutumu, konuyla ilgili düşüncelerin eleştirel olarak analiz edilmesiyle desteklenmektedir. (shrink)

Eternalism is the view that all times are equally real. The relativity of simultaneity in special relativity backs this up. There is no cosmically extended, self-existing ‘now.’ This leads to a tricky problem. What makes statements about the present true? I shall approach the problem along the lines of perspectival realism and argue that the choice of the perspective does. To corroborate this point, the Lorentz transformations of special relativity are compared to the structurally similar equations of the Doppler effect. (...) The ‘now’ is perspectivally real in the same way as a particular electromagnetic spectrum frequency. I also argue that the ontology of time licensed by perspectival realism is more credible in this context than its current alternative, the fragmentalist interpretation of special relativity. (shrink)

There is a widely extended viewpoint about physical possibility, what we will call Standard Approach, which holds that the physically possible is delimited by the nomological structure of physical theories: to be physically possible is to be in accordance with the physical laws, to be physically impossible is to be prohibited by physical laws and to be physically necessary is to be demanded by the physical laws. However, it is possible to show that this approach is too relaxed and permissive (...) when it comes to collecting and systematizing many of the modal intuitions present in the physical community. In this work we will argue, on the one hand, that the notion of physical possibility is more complex and richer than suggested by the standard approach and, on the other hand, that it is necessary to add some extra elements to the characterization of physical possibility in order to that it is adequate in scientific contexts. (shrink)

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. (shrink)

Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that the Principia’s second (...) law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton’s own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the Principia’s second law fundamentally, unaware that they should be citing Neutonus, Prin., Phil. Nat. Math., Lex II. (shrink)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, (...) as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83). (shrink)

In the past, experts have disagreed about whether Samuel Clarke accepted the idea that gravity is a power superadded to matter by God. Most scholars now agree that Clarke did not support superaddition. But the argumentation employed by Clarke to reject superaddition has not been studied before in detail. In this paper, I explicate Clarke's argumentation by relating it to an important discussion about the possibility of superadded gravity in the Clarke-Collins correspondence. I examine Clarke's responses to Collins and draw (...) on his other works to reconstruct Clarke's reasons for rejecting superadded gravity. (shrink)

L'interprétation des textes d'Isaac Newton a suscité une controverse à ce jour. L'un des débats les plus animés a trait à l'action entre deux corps distants l'un de l'autre (l'attraction gravitationnelle), et à la mesure dans laquelle Newton a impliqué Dieu dans ce cas. Pratiquement, la plupart des articles traitent quatre types d’attractions gravitationnelles dans le cas des corps distants : l’action directe à la distance en tant que propriété intrinsèque des corps au sens épicurien du terme ; action directe (...) à distance divinement médiée par Dieu ; action à distance médiée par un éther matériel ; ou action à distance médiée par un éther immatériel. DOI: 10.13140/RG.2.2.17564.33926. (shrink)

In Newton’s correspondence with Richard Bentley, Newton rejected the possibility of remote action, even though he accepted it in the Principia. Practically, Newton’s natural philosophy is indissolubly linked to his conception of God. The knowledge of God seems to be essentially immutable, unlike the laws of nature that can be subjected to refining, revision and rejection procedures. As Newton later states in Opticks, the cause of gravity is an active principle in matter, but this active principle is not an essential (...) aspect of matter, but something that must have been added to matter by God, arguing in the same Query of Opticks even the need for divine intervention. DOI: 10.13140/RG.2.2.16732.44162 . (shrink)

Interpretarea textelor lui Isaac Newton a suscitat numeroase controverse, până în zilele noastre. Una din cele mai aprinse dezbateri este legată de acțiunea între două corpuri aflate la distanță unul de celălalt (atracția gravitațională), și în ce măsură Newton a implicat pe Dumnezeu în acest caz. Practic, majoritatea lucrărilor discută patru tipuri de atracții gravitaționale în cazul corpurilor aflate la distanță: acțiunea la distanță directă ca proprietate intrinsecă a corpurilor în sens epicurian; acțiunea la distanță directă mediată divin, de Dumnezeu; (...) acțiunea la distanță mediată printr-un eter material; sau acțiunea la distanță mediată printr-un eter imaterial. DOI: 10.13140/RG.2.2.33372.03203. (shrink)

As John Henry states, Newton simply wants to reaffirm the truth of God's omnipresence without directly involving him in the physics of the world system. Newton simply wants to distance himself from a Cartesian concept of God and convince the atheists that God is a real presence extended in the world. God must exist in space for the space to exist, but God does not only act through contact. Henry believes that Andrew Janiak and Hylarie Kochiras give us a wrong (...) picture of a Newton who believes in opportunism. Newton, Henry asserts, has always assumed that God acted through secondary causes: DOI: 10.13140/RG.2.2.35495.39846. (shrink)

The interpretation of Isaac Newton's texts has sparked controversy to this day. One of the most heated debates relates to the action between two bodies distant from each other (the gravitational attraction), and to what extent Newton involved God in this case. Practically, most of the papers discuss four types of gravitational attractions in the case of remote bodies: direct distance action as intrinsic property of bodies in epicurean sense; direct remote action divinely mediated by God; remote action mediated by (...) a material ether; or remote action mediated by an immaterial ether. The purpose of this paper is to argue that Newton categorically rejected the types of direct action as the intrinsic property of bodies, and remote action mediated by a material ether. Concerning the other two types of action, direct through divine intervention and mediated through an immaterial environment, Newton has repeatedly stated that he does not know the exact cause of gravity, but in both cases, he has directly involved God, directly in the first case and as the primary cause (the environment/ether being the secondary cause) in immaterial mediated action. But since recognition of direct distance action could have given some credit to those who thought gravity could be essential to matter, and hence to atheism, Newton never openly acknowledged the possibility of such an idea. -/- Keywords: Isaac Newton, action at a distance, God, gravity, gravity law, gravitation -/- CONTENTS -/- Abstract Introduction Principia Correspondence with Richard Bentley Queries in Opticks Conclusions Bibliography -/- ISBN 978-606-033-201-5, DOI: 10.58679/TW14959. (shrink)

In this article I argue for an empiricist view on laws. Some laws are fundamental in the sense that they are the result of inductive generalisations of observed regularities and at the same time in their formulation contain a new theoretical predicate. The inductive generalisations simul- taneously function as implicit definitions of these new predicates. Other laws are either explicit definitions or consequences of other previously established laws. I discuss the laws of classical mechanics, relativity theory and electromagnetism in detail. (...) Laws are necessary, whereas acciden- tal generalisations are not. But necessity here is not a modal concept, but rather interpreted as short for the semantic predicate “... is necessarily true”. Thus no modal logic is needed. The neces- sity attributed to law sentences is in turn interpreted as “necessary condition for the rest of the the- ory”, which is true since fundamental laws are implicit definitions of theoretical predicates use in the theory. (shrink)

Hume’s discussion of space in the Treatise addresses two main topics: divisibility and vacuum. It is widely recognized that his discussion of divisibility contains an answer to Bayle, whose Dictionary article “Zeno of Elea” presents arguments about divisibility as support for fideism. It is not so widely recognized that, elsewhere in the same article, Bayle presents arguments about vacuum as further support for fideism. This paper aims to show that Hume’s discussion of vacuum contains an answer to these vacuum-based fideistic (...) arguments. Key to this answer is a distinction between two ways in which vacuum was conceived in the early modern period: i) as a genuine thing that has spatial properties, and yet is immobile, indivisible, and penetrable ; ii) as a mere absence of spatial things. This paper also aims to provide a novel defense of Hume against the long-standing objection that he is inconsistent in denying that we can conceive of a vacuum, while allowing that we can conceive of “invisible and intangible distance.” As I interpret him, Hume consistently denies that we can conceive of a positive vacuum, while allowing that we can conceive of two or more objects’ being arranged so as to have privative vacuum between them. (shrink)

in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...) conceived by ancient Greek mathematicians. (shrink)

In this paper I will argue that what makes our ordinary judgements about token causation true can be explicated in terms of interferences into quasi-inertial processes. These interferences and quasi-inertial processes can in turn be fully explicated in scientific terms. In this sense the account presented here is reductive. I will furthermore argue that this version of a process-theory of causation can deal with the traditional problems that process theories have to face, such as the problem of misconnection and the (...) problem of disconnection as well as with a problem concerning the mis-classification of pre-emption cases. (shrink)

Although the main focus of Hume’s career was in the humanities, his work also has an observable role in the historical development of natural sciences after his time. To show this, I shall center on the relation between Hume and two major figures in the history of the natural sciences: Charles Darwin (1809–1882) and Albert Einstein (1879–1955). Both of these scientists read Hume. They also found parts of Hume’s work useful to their sciences. Inquiring into the relations between Hume and (...) the two scientists shows that his philosophical positions had a partial but constructive role in the formation of modern biology and physics. This is accordingly a clear indication of Hume’s impact on the scientific tradition. Before proceeding to analyze Hume’s contribution to the history of science, it is important to address his broader role in the history of philosophy of science. Hume’s discussions concerning the topics of causation, induction, the distinction between mathematical and empirical propositions, and laws of nature have been important for the philosophy of science of the nineteenth and twentieth centuries. (shrink)

In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes that we always (...) imagine an earlier time in which God might have created the world if he had wanted, but insists that this imaginary earlier existence of the world is not connected to its actual duration in the way that the indefinite extension of space is connected to the actual extension of the world. This paper considers whether Descartes’s metaphysics can sustain this asymmetrical attitude towards infinite space vs. time. I first consider Descartes’s relation to the ‘imaginary’ space/time tradition that extended from the late scholastics through Gassendi and More. I next examine carefully Descartes’s main argument for the indefinite extension of space and explain why it does not apply to time. Most crucially, since duration is merely conceptually distinct from enduring substance, the end or beginning of the world entails the end or beginning of real time. In contrast, extension does not depend on any enduring substance besides itself. (shrink)

Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)