One of the questions that any future history of British moral philosophy in the twentieth century should investigate and document is how it came about that Moore's Principia Ethica was appropriated by what we can call the Humean tradition of moral philosophy. I shall not trace that development now but only argue that there was no excuse or justification for it.

Newton veut simplement réaffirmer la vérité sur l'omniprésence de Dieu sans l'impliquer directement dans la physique du système du monde. Newton veut se distancer d'un concept cartésien de Dieu et convaincre les athées que Dieu est une présence réelle dans le monde. Dieu doit exister dans l'espace pour exister l'espace, mais Dieu n'agit pas seulement par contact. Newton a toujours supposé que Dieu agît par le biais de causes secondaires. Dans l'édition de 1687 des Principes mathématiques de la philosophie naturelle, (...) Newton déclare clairement qu'il n'attribue pas de cause particulière à l'attraction gravitationnelle. DOI: 10.13140/RG.2.2.27735.42402 . (shrink)

The Oxford Handbook of the History of Physics brings together cutting-edge writing by more than twenty leading authorities on the history of physics from the seventeenth century to the present day. By presenting a wide diversity of studies in a single volume, it provides authoritative introductions to scholarly contributions that have tended to be dispersed in journals and books not easily accessible to the general reader. While the core thread remains the theories and experimental practices of physics, the Handbook contains (...) chapters on other dimensions that have their place in any rounded history. These include the role of lecturing and textbooks in the communication of knowledge, the contribution of instrument-makers and instrument-making companies in providing for the needs of both research and lecture demonstrations, and the growing importance of the many interfaces between academic physics, industry, and the military. (shrink)

A New Italian translation of Principia Ethica coming almost 60 years after the 1964 translation by Gianni Vattimo with Nicola Abbagnano’s preface. The new edition makes room for the English text alongside the Italian translation; it includes the 1922 Preface, a bibliography of Moore’s ethical writings with critical literature, a chronology of Moore’s life and works, and an Index. The Introduction by Sergio Cremaschi reconstructs the background of ideas, concerns and intentions from which Moore’s Principia Ethica originated. It (...) stresses the role of religious concerns, as well as that of the Idealist legacy. I argue that PE is more a patchwork of incompatible lines of argument than a consistent work. It compares PE with Rashdall’s almost contemporary ethical work, suggesting that the latter defends the same general claims in a different and more plausible way, which manages to answer decisive objections. It ends with the suggestion that the emergence of Analytic Ethics was a more multi-faceted phenomenon than the received view would make us believe and the analytic tradition's wheat, that is, what logic can do for philosophy, has to be separated from the chaff, that is, the confused, and besides mutually incompatible, legacies of Utilitarianism and Idealism. (shrink)

Moore's moral programme is increasingly unpopular. Judith Jarvis Thomson's attack has been especially influential; she says the Moorean project fails because ‘there is no such thing as goodness’. I argue that her objection does not succeed: while Thomson is correct that the kind of generic goodness she targets is incoherent, it is not, I believe, the kind of goodness central to the Principia. Still, Moore's critics will resist. Some reply that we cannot understand Moorean goodness without generic goodness. Others (...) claim that even if Moore does not need Thomson's concept, he still requires the objectionable notion of absolute goodness. I undermine both these replies. I first show that we may dispense with generic goodness without losing Moorean intrinsic goodness. Then, I argue that though intrinsic goodness is indeed a kind of absolute goodness, the objections marshalled against the concept are unsound. (shrink)

This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and (...) class='Hi'>Principia Mathematica. (shrink)

In this paper, I discuss how Newton’s inductive argument of the Principia can be defended against criticisms levelled against it by Duhem, Popper and myself. I argue that Duhem’s and Popper’s criticisms can be countered, but mine cannot. It requires that we reconsider, not just Newton’s inductive argument in the Principia, but also the nature of science more generally. The methods of science, whether conceived along inductivist or hypothetico-deductivist lines, make implicit metaphysical presuppositions which rigour requires we make (...) explicit within science so that they can be critically assessed, alternatives being developed and assessed, in the hope that they can be improved. Despite claiming to derive his law of gravitation by induction from phenomena without resource to hypotheses, Newton does nevertheless acknowledge in the Principia that his rules of reasoning make metaphysical presuppositions. To this extent, Newton has a more enlightened view of scientific method than most 20th and 21st century scientists and historians and philosophers of science. (shrink)

Spinoza’s Principles of Cartesian Philosophy is often presented simply as an interpretation of Descartes’ Principia that does not reveal anything significant about Spinoza’s philosophy and its development. This paper, however, shows that Spinoza altered Descartes’ text in a way congruent with what he would later write in his Theological Political Treatise and the Ethics. More precisely, this paper concentrates not on what Spinoza added to Descartes’ texts but on how he presented them. The paper furthermore examines questions that were (...) obviously important for Descartes but absent in Spinoza’s interpretation. Finally, this paper examines two concrete examples to show that Spinoza’s adaptations function as an unmasking of Descartes’ physics. (shrink)

A core feature of Kant’s Critical account of moral motivation is that pure reason can be practical by itself. I argue that Kant developed this view in the 1770s concerning the principium diiudicationis and principium executionis. These principles indicate the normative and performative aspects of moral motivation. I demonstrate that cognition of the normative principle effects the moral incentive. So, the hallmark of Kant’s Critical account of motivation was contained in his pre-Critical view. This interpretation resolves a controversy about Kant’s (...) apparent eudaimonism in the first Critique and shows that he developed his account of moral autonomy in the 1770s. (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)

Mi objetivo es discutir las principales dificultades que Frank P. Ramsey encontró en Principia Mathematica y la solución que, vía el Tractatus Logico-Philosophicus, propuso al respecto. Sostengo que las principales dificultades que Ramsey encontró en Principia Mathematica están, todas, relacionadas con que Russell y Whitehead desatendieron la forma lógica de las proposiciones matemáticas, las cuales, según Ramsey, deben ser tautológicas.

In the Foundations of Mathematics, Ramsey attempted to amend Principia Mathematica’s logicism to meet serious objections raised against it. While Ramsey’s paper is well known, some questions concerning Ramsey’s motivations to write it and its reception still remain. This paper considers these questions afresh. First, an account is provided for why Ramsey decided to work on his paper instead of simply accepting Wittgenstein’s account of mathematics as presented in the Tractatus. Secondly, evidence is given supporting that Wittgenstein was not (...) moved by Ramsey’s objection against the Tractarian account of arithmetic, and a suggestion is made to explain why Wittgenstein reconsidered Ramsey’s account in the early thirties on several occasions. Finally, a reading is formulated to understand the basis on which Wittgenstein argues against Ramsey’s definition of identity in his 1927 letter to Ramsey. (shrink)

Bei den korpuskulartheoretischen Erklärungen von Naturphänomenen, wie sie Descartes in den Principia philosophiae vornimmt und im Discours de la methode anspricht, lassen sich zwei verschiedene und nur teilweise miteinander vereinbare Bedeutungsgruppen des Hypothesenbegriffs nachweisen. Sie verbinden sich mit unterschiedlichen Bewertungen des Status von Hypothesen im wissenschaftlichen Erkenntnisprozeß. Einerseits findet man eine Verwandtschaft zum heute wissenschaftstheoretisch verbreiteten Verständnis von Hypothesen als positivem und integralem Bestandteil der Naturerkenntnis. Typischer für Descartes' Naturphilosophie ist jedoch die andererseits von ihm vertretene Vorstellung, daß der (...) Umfang des bloß hypothetischen Wissens im Fortgang der Naturerkenntnis zu minimieren sei. Mit dieser Forderung erweist sich Descartes als Vertreter einer neuzeitlichen Wissenschaftsauffassung, die deutlich vom modernen Verzicht auf ein ausschließlich geltendes System der Naturerkenntnis abgehoben ist. (shrink)

Newton rested his theory of mechanics on distinct metaphysical and epistemological foundations. After Leibniz's death in 1716, the Principia ran into sharp philosophical opposition from Christian Wolff and his disciples, who sought to subvert Newton's foundations or replace them with Leibnizian ideas. In what follows, I chronicle some of the Wolffians' reactions to Newton's notion of absolute space, his dynamical laws of motion, and his general theory of gravitation. I also touch on arguments advanced by Newton's Continental followers, such (...) as Leonhard Euler, who made novel attempts to defend his mechanical foundations against the pro-Leibnizian attack. This examination grants us deeper insight into the fate of Newton's mechanics on the Continent during the early eighteenth century and, more specifically, sheds needed light on the conflicts and tensions that characterized the reception of Newton's philosophy of mechanics among the Leibnizians. (shrink)

I argue that The Metaethical Moral Relativism has been being used as a form of support in order to commit desire–belief actions against Human Biology Principia. The lacking of Moral Epistemology allows me illustrate and explain practical downsides in the Ontological part of Moral Knowledge. I recommend a departure from The Biological Basis of Morality in favor to avoid contemporary misuses in the Justification of The Metaethical Moral Relativism.

Conceptual engineers have made hay over the differences of their metaphilosophy from those of conceptual analysts. In this article, I argue that the differences are not as great as conceptual engineers have, perhaps rhetorically, made them seem. That is, conceptual analysts asking ‘What is X?’ questions can do much the same work that conceptual engineers can do with ‘What is X for?’ questions, at least if conceptual analysts self-understand their activity as a revisionary enterprise. I show this with a study (...) of Russell's metaphilosophy, which was just such a revisionary conception of conceptual analysis. (shrink)

Teaching Newtonian physics involves the replacement of students’ ideas about physical situations with precise concepts appropriate for mathematical applications. This paper focuses on the concepts of ‘matter’ and ‘mass’. We suggest that students, like some pre-Newtonian scientists we examine, use these terms in a way that conflicts with their Newtonian meaning. Specifically, ‘matter’ and ‘mass’ indicate to them the sorts of things that are tangible, bulky, and take up space. In Newtonian mechanics, however, the terms are defined by Newton’s Second (...) Law: ‘mass’ is simply a measure of the acceleration generated by an impressed force. We examine the relationship between these conceptions as it was discussed by Newton and his editor, Roger Cotes, when analyzing a series of pendulum experiments. We suggest that these experiments, as well as more sophisticated computer simulations, can be used in the classroom to sufficiently differentiate the colloquial and precise meaning of these terms. (shrink)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist (...) methodologies. Newton's thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)

When Newton articulated the concept of absolute time in his treatise, Philosophae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), along with its correlate, absolute space, he did not present it as anything controversial. Whereas his references to attraction are accompanied by the self- protective caveats that typically signal an expectation of censure, the Scholium following Principia’s definitions is free of such remarks, instead elaborating his ideas as clarifications of concepts that, in some manner, we already possess. This (...) is not surprising. The germ of the concept emerged naturally from astronomers’ findings, and variants of it had already been formulated by other seventeenth century thinkers. Thus the novelty of Newton’s absolute time lay mainly in the use to which he put it. (shrink)

According to Russell, the notation in Principia Mathematica has been designed to avoid the vagueness endemic to our natural language. But what does Russell think vagueness is? My argument is an attempt to show that his views on vagueness evolved and that the final conception he adopts is not coherent. Three phases of his conception of vagueness are identified, the most significant being the view that he articulates on vagueness in his 1923 address to the Jowett Society. My central (...) thesis is that the 1912 conception of vagueness -- what I characterize as "semantic egalitarianism" -- seriously conflicts with the later paradoxical account of vagueness. (shrink)

Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey to basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if- then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if-then” are used instead of being mentioned as the (...) premise and the conclusion of an implication relation. It was his opinion that the criticisms and alternatives to the material implication presented by C. I. Lewis and others would never be made in the first place if Russell simply called the Philonian construction “material conditional” instead of “material implication”. Quine’s interpretation of the topic became hugely influential if not universally accepted. This paper will present the following criticisms against this interpretation: (1) the notion of material implication does not involve a use-mention fallacy, since the components of “if-then” are mentioned and not used; (2) Quine’s belief that the components of “if-then” are used was motivated by a conditional-assertion view of conditionals that is widely controversial and faces numerous difficulties; (3) if anything, it was Quine who could be accused of fallacious reasoning: he ignored that in the assertion of a conditional is the whole proposition that is asserted and not its constituents; (4) the Philonian construction remains counter-intuitive even if it is called “material conditional”; (5) the Philonian construction is more plausible when it is interpreted as a material implication. (shrink)

Tamas Demeter presents a clear and compelling new perspective of Hume’s methodology and conceptual structure in David Hume and the Culture of Scottish Newtonianism. Hume, he argues, is a Newtonian of the Scottish tradition, but not the mechanical kind that is modeled after the Principia. Instead, Hume should be understood as a kind of European Enlightenment “vitalist.” As a result, his work reflects the more organic methodology that defines Newton’s Opticks.

In Principia philosophiae antiquissimae et recentissimae (1690) Anne Conway (1631-1679) develops her monistic metaphysics regarding creation, whose distinctive characteristic is transmutations for the individuals that compose it. In chapter VI of this posthumous work, Conway exemplifies this process of transmutation with the case of a horse, which changes, after death, into a human being. In this article I intend to analyze this example to show that it is not casual that the horse in question rises in the hierarchy of (...) beings. To do this I will develop my interpretation of Conway’s philosophy, her understanding of created substance and its characteristics. In this way, I want to point out that her philosophy opens up the possibility of another understanding of non-human animals by human beings, even when the latter continue to occupy a prominent place in her proposal. (shrink)

Newton began his Principia with three Axiomata sive Leges Motus. We offer an interpretation of Newton’s dual label and investigate two tensions inherent in his account of laws. The first arises from the juxtaposition of Newton’s confidence in the certainty of his laws and his commitment to their variability and contingency. The second arises because Newton ascribes fundamental status both to the laws and to the bodies and forces they govern. We argue the first is resolvable, but the second (...) is not. However, the second tension shows that Newton conceives laws as formal causes of bodies and forces. This neo-Aristotelian conception goes missing in Kantian accounts of laws, as well as accounts that stress laws’ grounding in powers and capacities. (shrink)

La première édition de Principia de Newton ne contient que deux remarques supplémentaires sur la méthodologie: la notification que le but de l'article est d'expliquer « comment déterminer les véritables mouvements de leurs causes, les effets et les différences apparents et, au contraire, comment déterminer à partir des hypothèses si elles sont vraies ou apparentes, leurs causes et leurs effets »; et, dans le Scholium à la fin du Livre 1, Section 11, Newton affirme que son approche distinctive permet (...) une argumentation plus sûre dans la philosophie naturelle. DOI: 10.13140/RG.2.2.19797.58082. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood (...) as a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the final analysis. The paper offers a pattern borrowed from the (...) theory of information and quantum information (therefore relating philosophy to both mathematics and physics) to formalize logically a few key concepts of Husserl’s phenomenology such as “epoché” “eidetic, phenomenological, and transcendental reductions” as well as the identification of “phenomenological, transcendental, and psychological reductions” in a way allowing for that identification to be continued to “eidetic reduction” (and thus to mathematics). The approach is tested by an independent and earlier idea of Husserl, “logical arithmetic” (parallelly implemented in mathematics by Whitehead and Russell’s Principia) as what “Hilbert arithmetic” generalizing Peano arithmetics is interpreted. A basic conclusion states for the unification of philosophy, mathematics, and physics in their foundations and fundamentals to be the Husserl tradition both tracked to its origin (in the being itself after Heidegger or after Husserl’s “zu Sache selbst”) and embodied in the development of human cognition in the third millennium. (shrink)

In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, but (...) if, for example, PM’s disjunction (∨) is a relation, what is it a relation between? There is no obvious answer to this given Russell’s other philosophical commitments at this time, although hints are left in some of the pre-PM manuscripts. In this paper, I explore this tension in Russell's philosophy and relate it to developments both before and after Problems. (shrink)

Prima ediție a Principia lui Newton conține doar două comentarii suplimentare despre metodologie: notificarea că scopul lucrării este de a explica "cum să determinăm mișcările adevărate din cauzele lor, efectele și diferențele aparente și, dimpotrivă, cum să determinăm din ipoteze dacă sunt adevărate sau aparente, cauzele și efectele lor"; și, în Scholiul de la sfârșitul Cărții 1, Secțiunea 11, Newton afirmă că abordarea sa distinctivă face posibilă argumentarea mai sigură în filosofia naturală. În a doua ediție (1713) Newton introduce (...) secțiuni separate pentru fenomene și reguli implicate în determinarea gravitației universale, iar la sfârșitul Scholiului General din cea de-a treia ediție, 1726, include cea mai faimoasă declarație metodologică. DOI: 10.13140/RG.2.2.34012.54403. (shrink)

Newton’s First Law of Motion is typically understood to govern only the motion of force-free bodies. This paper argues on textual and conceptual grounds that it is in fact a stronger, more general principle. The First Law limits the extent to which any body can change its state of motion –– even if that body is subject to impressed forces. The misunderstanding can be traced back to an error in the first English translation of Newton’s Principia, which was published (...) a few years after Newton’s death. (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)

This paper offers a reconstruction of the interpretations of Descartes's ideas of place and motion by Dutch Cartesians (Henricus Regius, Johannes de Raey, Johannes Clauberg, and Christoph Wittich). It does so by focusing on the reading of Descartes's Principia philosophiae (1644) offered, in particular, by the dictated commentaries on it. It is shown how such commentaries bring to the light new potential Aristotelian-Scholastic sources of Descartes, and the different ways Dutch Cartesians brought to the fore, also with the help (...) of such sources, the rationale of the Cartesian text: in doing so, they constituted a philosophical school. (shrink)

Bis vor kurzem wurden die Namen Alfred North Whitehead und Bertrand Russell zumeist in einem Atemzug genannt. Im Anschluss an die gemeinsam verfassten Principia Mathematica gingen beide jedoch dezidiert eigene philosophische Wege. Wahrend Russell maageblich zur Entstehung der analytischen Philosophie beitrug, markiert Whiteheads spate Philosophie den Beginn der bis heute virulenten prozessmetaphysischen Tradition. Stand Whitehead dabei lange im Schatten seines langjahrigen Freundes und Kollegen, zeichnet sich spatestens seit Beginn des 21. Jahrhunderts ein bemerkenswerter Umschwung ab. Der vorliegende Band nimmt (...) die Entwicklung zum Anlass, um Gemeinsamkeiten und Differenzen der beiden Klassiker der angelsachsischen Philosophie neu zu sondieren. (shrink)

Bertrand Russell’s conception of philosophy evolved dramatically in 1911 — the year he fell in love with Lady Ottoline Morrell. For many years Russell had been an ardent advocate of the view that philosophers ought to look for truths that are certain. The co-author of Principia Mathematica altered his commitment to certainty in philosophy in 1911. An analysis of his published views and correspondence from this time strongly suggests that the radical transformation was induced by an epiphany brought about (...) by his emotional entanglement with his lover. (shrink)

According to Descartes, physics rests on metaphysics. Various possible interpretations of this metaphor are considered. I will show that only a weak interpretation can be brought into accordance with other parts of Descartes' philosophy. According to the weak interpretation, physics has to presuppose metaphysics because the latter shows that contrary to widespread contemporary arguments the concepts of mathematical physics are adequate to describe nature. It is argued for this position by comparing the Regulae, where Descartes did not make use of (...) metaphysical arguments, with the Principia, where he did. (shrink)

Locke’s metaphysical commitments are a matter of some controversy. Further controversy attends the issue of whether and how Locke adapts his views in order to accommodate the success of Newton’s Principia. The chapter lays out an interpretation of Locke’s commitments according to which Locke’s response to Newton on gravity does not require the positing of brute powers and is consistent with his core essentialism. The chapter raises the question of how the hypothesis concerning the creation of matter, alluded to (...) at 4.10.18, fits with these commitments. The chapter concludes that the De grav hypothesis would represent a significant revision to the background metaphysical picture of the Essay, but that nevertheless its attractions to Locke are intelligible and illuminating. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as (...) value. Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

I argue that the key dynamical concepts and laws of Newton's Principia never gained a solid foothold in Germany before Kant in the 1750s. I explain this absence as due to Leibniz. Thus I make a case for a robust Leibnizian legacy for Enlightenment science, and I solve what Jonathan Israel called “a meaningful historical problem on its own,” viz. the slow and hesitant reception of Newton in pre-Kantian Germany.

Anne Finch Conway es una de las filósofas del siglo XVII que discutió con los filósofos destacados de su época. La única obra con la que contamos de esta autora es Principia Philosophiae Anticissimae et Recentissimae o The Principle of the Most Ancient and Modern Philosophy. En este artículo me propongo dar cuenta del rol que la naturaleza humana tiene en su metafísica, de modo de encontrar un lugar más específico para el dolor y el sufrimiento en un mundo (...) que parece ante todo gobernado por el amor recíproco y la simpatía. El concepto de hombre microcosmos y la relación de este con Cristo tiene una importancia poco destacada por la bibliografía sobre nuestra filósofa. Con esta meta, presentaré su metafísica prestando especial atención a la sustancia creada y su relación con la sustancia media, Cristo, y la sustancia primera, Dios. De este modo, además, daré cuenta de la responsabilidad que la naturaleza humana tiene con el mundo de la creación, por lo cual me permito mencionar también lo “ecológico” en el pensamiento de Conway, ya que el perfeccionamiento de la naturaleza humana es el perfeccionamiento de toda la naturaleza. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Newton's Metaphysics: Essays by Eric SchliesserMarius StanEric Schliesser. Newton's Metaphysics: Essays. Oxford: Oxford University Press, 2021. Pp. 328. Hardback, $99.90.Newton owes his high regard to the quantitative science he left us, but his overall picture of the world had some robustly metaphysical threads woven in as well. Posthumous judgment about the value of these threads has varied wildly. Christian Wolff thought him a metaphysical rustic, as did Hans (...) Reichenbach some two centuries later ("Die Bewegungslehre bei Newton, Leibniz und Huygens," Kant-Studien 29 [1924]: 416–38). In the 1960s, the tide would turn, as Howard Stein and James Edward McGuire separately began to show that Newton's metaphysics was not just sophisticated, but often more compelling than its early modern alternatives (see respectively "Newtonian Spacetime," Texas Quarterly 10 [1967]: 174–200; and Tradition and Innovation: Newton's Metaphysics of Nature [Dordrecht: Kluwer Academic Publishers, 1995]). Eric Schliesser's book unfolds in that same register of appreciative, high scholarship, and it attests to the enduring attraction of its subject.The book grew out of previous discrete papers, to which he added a few more for this occasion. Accordingly, it does not come with a master argument. Rather, it is an in-depth exploration of some key metaphysical themes in Newton. As such, it befits its subject figure, who reflected on themes and concepts while stopping short of working out systems.The first major theme is Newton and Spinozism. The latter does not denote Spinoza's metaphysics. In fact, Schliesser explains, Newton shared with Spinoza some weighty commitments, for example, to space being actually infinite, and to substance monism: "for Newton, there is strictly speaking only one genuine substance," namely, God (33). Rather, "Spinozism" is an interpreter's category for a bundle of three theses: identifying God and nature; denying final causation in the physical world; and the assumption of "blind" metaphysical necessity. Some counted Hobbes and John Toland as Spinozist in this sense, and even Epicurus, avant la lettre. Newton and his followers argued vehemently against this package, as Schliesser shows in chapters 4, 5, and 8. Their chief complaint was that Spinozism is unable to account for the "origin of motion," for a certain type of order, and for the stability of cosmological structure—and to do so in a way that "meets the standards of Newtonian mechanics" (122). This interpretive lens allows Schliesser to draw Kant in, by reading his youthful Theory of Heaven as a possible Spinozist reply to their objections (chapter 3). [End Page 157]A second theme is the metaphysics of mechanics, where Schliesser weaves together several strands. One is the ontology of gravity, for which he offers a novel construal: for Newton, gravity counts as real, but in a qualified sense. Namely, it is not essential and not intrinsic: "even after creation, a lonely partless particle of matter in the universe would not be said to gravitate." And gravity is relational: a "shared quality" of two or more bits of matter, which obtains in virtue of their sharing a nature (19). Another strand is Newton's ontology of time—really, a subtle, difficult topic long neglected. Famously, Newton in Principia defends absolute, true, and mathematical time. The question is what these three qualifiers denote, and whether Newton thought they were synonymous. Schliesser in chapter 7 argues for the provocative view that "absolute" and "true" time are not identical concepts; rather, they pick out different entities. These entities share a common structure, namely, metric and topological. That makes them species of "mathematical" time (179). But, Schliesser contends, Newton has unequal warrant for his two concepts of time.Yet another theme is formal causation. It comes to the fore in chapter 5, which grapples with Newton's opaque idea that space is an "emanative effect." Schliesser explains that here, "emanation picks out a species of formal causation" (147), but in a novel, early modern sense that comes from Bacon, not Aristotle. If space has a formal cause, then so has its twin brother, time, the topic of chapter 7. God is their common formal cause. Then in chapter 6 (coauthored with Zvi Biener) Schliesser adds that, for Newton, laws... (shrink)

Newton frequently characterized his methodology as distinctive and capable of achieving greater evidential support than that of his contemporaries, due to its mathematical character. Newton's pronouncements reflect a striking position regarding the role of mathematics in natural philosophy. We can give an initial characterization of his position by considering two questions central to seventeenth century debates about the applicability of mathematics. First, how are we to understand the distinctive universality and necessity of mathematical reasoning? One common way to preserve the (...) demonstrative character of mathematics was to restrict its domain, as far as possible, to pure abstractions. The subject matter of mathematics is then taken to be abstracted from the changeable natural world, consisting of quantity and magnitude themselves rather than the objects bearing quantifiable properties. Yet restricting the domain in this way leaves it difficult to see how mathematics relates to natural phenomena. How could the book of nature be written in a language of pure abstractions? Second, what is the proper role of mathematical reasoning in natural philosophy? Many followed Aristotle in consigning mathematics to a subordinate role. Mathematics could not fulfill the main aim of natural philosophy, namely to provide demonstrations reflecting the essences of things and nature's causal order. A related concern was also pressing for the mechanical philosophers: a merely mathematical demonstration fails to provide an intelligible mechanical explanation. The very title of Newton's masterpiece, Philosophiae Naturalis Principia Mathematica, would have been extremely perplexing: how could natural philosophy be based on mathematical principles? My aim is to articulate Newton's position regarding the mathematization of nature in response to these two concerns. (shrink)

Cover Philosophical Mechanics in the Age of Reason Katherine Brading and Marius Stan Description From pebbles to planets, tigers to tables, pine trees to people; animate and inanimate, natural and artificial; bodies are everywhere. Bodies populate the world, acting and interacting with one another, and they are the subject-matter of Newton's laws of motion. But what is a body? And how can we know how they behave? In Philosophical Mechanics in the Age of Reason, Katherine Brading and Marius Stan examine (...) the struggle for a theory of bodies. -/- At the beginning of the 18th century, physics was the branch of philosophy that studied bodies in general. Its primary task was to provide a qualitative account of the nature of bodies, including their essential properties, causal powers, and generic behaviors. Pursued by a variety of figures both canonical (from Leibniz to Kant) and less familiar (from Du Châtelet and Euler to d'Alembert and Lagrange), this proved a difficult task. At stake were the appropriate epistemologies and methods for theorizing about the natural world. Solutions demanded the combined resources of philosophy, physics, and mechanics: what Brading and Stan call a “philosophical mechanics.” -/- Brading and Stan analyze a century of widespread, concerted efforts to solve “the problem of bodies,” they examine the consequences of the many failures, both for the problem itself and for philosophy more generally. They reveal relationships among disparate themes of 18th century physics and philosophy, from the nature of matter to the motion of a vibrating string; causation to the principle of least action; and the role of subtle matter in collision theory to analytic mechanics. All of these, Brading and Stan argue, are related to the eventual emergence of physics as an independent discipline, autonomous from philosophy, more than a century after Newton's Principia. This book provides a new framing of natural philosophy and its transformations in the Enlightenment; and it proposes an account of how physics and philosophy evolved into distinct fields of inquiry. (shrink)

The so-called problem of arguing “from what is to what ought to be” was popularized by G.E. Moore in Principia Ethica (1903), and has received much attention from modern philosophers. I would like to argue that this apparent problem rests on a false dichotomy between our knowing and our doing.

Henry Sidgwick taught G.E. Moore as an undergraduate at the University of Cambridge. Moore found Sidgwick’s personality less than attractive and his lectures “rather dull”. Still, philosophically speaking, Moore absorbed a great deal from Sidgwick. In the Preface to the Trinity College Prize Fellowship dissertation that he submitted in 1898, just two years after graduation, he wrote “For my ethical views it will be obvious how much I owe to Prof. Sidgwick.” Later, in Principia Ethica, Moore credited Sidgwick with (...) having “first clearly exposed the [naturalistic] fallacy” – a fallacy putatively committed when one defines naturalistically or super-naturalistically “good” – which was one of the book’s main ambitions (PE 39; also 17, 59). It is therefore unsurprising that Moore remarks in the intellectual autobiography he wrote years later that “From…[Sidgwick’s] published works…I have gained a good deal, and his clarity and his belief in Common Sense were very sympathetic to me.” This influence did not, however, prevent Moore from registering disagreements with Sidgwick, the sharpest of which concern the viability of egoism and the nature of the good. The disagreements between Sidgwick and Moore speak to many important moral theoretical issues arising both within and without the utilitarian tradition in ethical thinking. Because the two share much in common, a critical comparison of them on a range of moral philosophical questions proves instructive. It will tell us in particular something about the general direction of ethical thinking in the utilitarian tradition at the dawn of the twentieth century. This chapter has four parts. Part I compares the versions of utilitarianism to which Sidgwick and Moore subscribed. Part II examines the arguments each provides for the view. Part III discusses their conflicting theories of value. Part IV sums things up. (shrink)

Bertrand Russell was one of the best-known proponents of logicism: the theory that mathematics reduces to, or is an extension of, logic. Russell argued for this thesis in his 1903 The Principles of Mathematics and attempted to demonstrate it formally in Principia Mathematica (PM 1910–1913; with A. N. Whitehead). Russell later described his work as a further “regressive” step in understanding the foundations of mathematics made possible by the late 19th century “arithmetization” of mathematics and Frege’s logical definitions of (...) arithmetical concepts. The logical system of PM sought to improve on earlier attempts by solving the contradictions found in, e.g., Frege’s system, by employing a theory of types. In this article, I also consider and critically evaluate the most common objections to Russell’s logicism, including the claim that it is undermined by Gödel’s incompleteness results, and Putnam's charge of “if-thenism”. I suggest that if we are willing to accept a slightly revisionist account of what counts as a mathematical truth, these criticisms do not obviously refute Russell’s claim to have established that mathematical truths generally are a species of logical truth. (shrink)

Isaac Newton, in popular imagination the Ur-scientist, was an outstanding humanist scholar. His researches on, among others, ancient philosophy, are thorough and appear to be connected to and fit within his larger philosophical and theological agenda. It is therefore relevant to take a closer look at Newton’s intellectual choices, at how and why precisely he would occupy himself with specific text-sources, and how this interest fits into the larger picture of his scientific and intellectual endeavours. In what follows, we shall (...) follow Newton into his study and look over his shoulder while reading compendia and original source-texts in his personal library at Cambridge, meticulously investigating and comparing fragments and commentaries, and carefully keeping track in private notes of how they support his own developing ideas. Indeed, Newton was convinced that precursors to his own insights and discoveries were present already in Antiquity, even before the Greeks, in ancient Egypt, and he puts a lot of time and effort into making the point, especially, and not incidentially, in the period between the first and the second edition of the Principia. A clear understanding of his reading of the classic sources therefore matters to our understanding of its content and gestation process. In what follows we will confine ourselves to the classical legacy, and investigate Newton’s intellectual intercourse with it. (shrink)