Isaac Newton

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.

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 -/- DOI: 10.13140/RG.2.2.25823.92320. (shrink)

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)

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)

Dans une note intitulée « Un état vrai de l'affaire et la controverse entre Sr Isaak Newton et le Dr Robert Hooke comme priorité de cette noble hypothèse du mouvement des planètes autour du Soleil en tant que leurs centres » non publié au cours de sa vie, Hooke a décrit sa théorie de la gravité. Pour soutenir sa « priorité », Hooke cite ses conférences sur les mouvements planétaires du 23 mai 1666, « Une tentative de prouver le mouvement (...) de la Terre à partir d'observations » publiées en 1674 et la correspondance avec Isaac Newton en 1679. DOI: 10.13140/RG.2.2.26375.24485. (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. Le but de cet article est d'argumenter que Newton a catégoriquement rejeté les types d'action directe en tant que propriété intrinsèque des corps et l'action à distance médiée par un éther matériel. En ce qui concerne les deux autres types d’actions, directe par intervention divine et médiatisée par un environnement immatériel, Newton a répété à plusieurs reprises qu’il ne connaissait pas la cause exacte de la gravité, mais dans les deux cas, il avait directement impliqué Dieu, directement dans le premier cas. et comme cause principale (l'environnement/éther étant la cause secondaire) dans l'action médiatisée immatérielle. Mais comme la reconnaissance de l'action directe à distance aurait pu donner quelque crédit à ceux qui pensaient que la gravité pouvait être essentielle à la matière, et donc à l'athéisme, Newton n'a jamais ouvertement reconnu la possibilité d'une telle idée. Vers la fin de sa vie, Newton s'est penché davantage vers une action à distance médiée par un éther immatériel. -/- SOMMAIRE: -/- Abstract Introduction Principia Correspondance avec Richard Bentley Questions de l'Opticks Conclusions Bibliographie -/- DOI: 10.13140/RG.2.2.31322.70080 . (shrink)

Teoreticienii au formulat un set de criterii fundamentale pe care orice teorie a gravitației ar trebui să le satisfacă, două pur teoretice și două care se bazează pe dovezi experimentale. Astfel, o teorie trebuie să fie: 1. completă (capabilă să analizeze din "primele principii" rezultatul oricărui experiment de interes); 2. auto-consistentă (predicția sa pentru rezultatul fiecărui experiment trebuie să fie unică); 3. relativistă (la limită când se neglijează gravitația în comparație cu alte interacțiuni fizice, legile non-gravitaționale ale fizicii trebuie să (...) se reducă la legile relativității speciale); 4. cu limita newtoniană corectă (în limitele câmpurilor gravitaționale slabe și ale mișcărilor lente, trebuie să reproducă legile lui Newton). DOI: 10.13140/RG.2.2.22012.90244. (shrink)

Exemplul clasic al unui program de cercetare de succes este teoria gravitațională a lui Newton, probabil cel mai de succes program de cercetare lakatosian. Inițial, teoria gravitațională a lui Newton s-a confruntat cu o mulțime de "anomalii" ("contraexemple"), și a contrazis teoriile observaționale care susțineau aceste anomalii. Dar suporterii programului de cercetare a gravitației newtoniene au transformat fiecare anomalie în cazuri coroborante. Mai mult, au evidențiat ei înșiși contraexemple pe care le-au explicat apoi prin teoria newtoniană. DOI: 10.13140/RG.2.2.25794.32969.

L'une des controverses les disputées sur la priorité des découvertes scientifiques est celle de la loi de la gravitation universelle, entre Isaac Newton et Robert Hooke. Hooke a accusé Newton de plagiat, de reprendre ses idées exprimées dans des travaux antérieurs. J'essaie de montrer, sur la base d'une analyse précédente, que tous les deux scientifiques avaient tort: Robert Hooke parce que sa théorie n'était fondamentalement que des idées qui ne se seraient jamais matérialisées sans l'appui mathématique d'Isaac Newton; et ce (...) dernier avait tort de ne pas reconnaître les idées de Hooke dans l'élaboration de la théorie de la gravité. En outre, après la mort de Hooke et son accession à la présidence de la Royal Society, Newton a retiré de l'institution toute trace de l'ancien président Robert Hooke. Pour cela, je détaille les accusations et les arguments de chacune des parties, et comment ce différend a été perçu par les contemporains des deux scientifiques. Je termine le papier avec les conclusions tirées du contenu. -/- TABLE: -/- Abstract Introduction La contribution de Robert Hooke à la loi de la gravitation universelle La contribution d'Isaac Newton à la loi de la gravitation universelle La revendication de priorité de Robert Hooke sur la loi de la gravitation universelle La défense de Newton La controverse dans l'opinion des scientifiques contemporains Ce que disent les supporters d'Isaac Newton Ce que disent les supporters de Robert Hooke Conclusions Bibliographie Notes -/- DOI: 10.13140/RG.2.2.20313.06245. (shrink)

În mod obișnuit, "laboratorul" testelor gravitaționale a fost corpurile cerești, sistemele astrofizice. Dar astfel de teste sunt perturbate de efecte non-gravitaționale. Cel mai utilizat astfel de "laborator" a fost sistemul solar. De curând, oamenii de știință s-au concentrat pe observarea pulsarilor binari pentru verificarea teoriilor gravitaționale, prin observațiile privind variațiile perioadei orbitale, furnizând astfel dovezi indirecte pentru emisia de radiație gravitațională. Dar experimentatorul nu poate ”aranja laboratorul” după nevoile sale, și nici declanșa anumite evenimente atunci când are nevoie de ele. (...) Însă actuala dezvoltare tehnologică începe să permită experimente pure de laborator. DOI: 10.13140/RG.2.2.31987.48169 . (shrink)

The first edition of Newton's Principia contains only two additional comments on the methodology: the notification that the purpose of the paper is to explain "how to determine the true motions from their causes, effects, and apparent differences, and, conversely, how to determine from motions, whether true or apparent, their causes and effects"; and, in the Scholium at the end of Book 1, Section 11, Newton asserts that his distinctive approach makes possible a safer argumentation in natural philosophy. DOI: 10.13140/RG.2.2.35946.88003 (...) . (shrink)

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).

Une présentation de la monographie de 1674 de Hooke présentant l'idée de la gravitation universelle est apparue dans Philosophical Transactions de 1674, et puis plusieurs lettres contenant des observations, dont celle de Huygens. Mais évidemment, après la publication du Principia en 1687, la priorité de Hooke dans la proposition de la gravitation universelle a été oubliée. Après avoir entendu parler de la demande de Hooke de reconnaître sa priorité, Newton a supprimé les nombreuses références à Hooke dans Principia. DOI: 10.13140/RG.2.2.27734.40009.

Newton a sugerat, în timp, mai multe tipuri de eter care ar putea media acțiunea la distanță. Dar, consecvent ideii sale că nu va născoci ipoteze care nu se bazează pe dovezi experimentale, nu a promovat niciodată aceste sugestii la nivelul unor ipoteze științifice. Trebuia să împace mecaniciștii, astfel încât a mers pe ideea unui eter din particule atât de fine încât masa e neglijabilă (practic, un eter imaterial). Mediul pe care Newton l-a introdus în Interogarea 21 constă din corpuri (...) materiale extrem de mici care sunt separate spațial, pe de o parte, și din principiul activ non-mecanic care produce și mediază forțele repulsive dintre aceste corpuri, pe de altă parte. DOI: 10.13140/RG.2.2.30606.72002. (shrink)

A presentation of Hooke’s 1674 monograph introducing the idea of universal gravity was included in the Philosophical Transactions (Royal Society 1775) and subsequently several letters containing observations, including one of Huygens. But obviously, after the publication of Principia in 1687, Hooke’s priority in proposing universal gravitation was forgotten. Hooke, considered as a “mechanical genius” rather than a scientist, was often at a social disadvantage to Newton, the noble theorist, or Huygens. Hooke’s inferior social status did not allow him to identify (...) with “free and unconfin’d” gentlemen such as Boyle, for example. DOI: 10.13140/RG.2.2.13746.45763. (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)

Dans sa correspondance avec Richard Bentley, Newton a rejeté la possibilité d'une action à distance, bien qu'il l'ait acceptée en Principia. L’environnement introduit par Newton à la question 21 d'Opticks se compose d’une part de corps matériels extrêmement petits, séparés dans l’espace, et d’un principe actif non mécanique produisant et médiatisant les forces de répulsion entre ces corps. À la question 28, il a clairement fait valoir qu'un environnement mécanique devrait être rejeté. L'éther traverse les corps, il est donc sans (...) importance. DOI: 10.13140/RG.2.2.23101.41446. (shrink)

Based on Galileo's experiments, Newton develops the theory of gravity in his first book Philosophiæ Naturalis Principia Mathematica ("Principia") of 1686. Immediately after, Robert Hooke accused Newton of plagiarism, claiming that he unduly assumed his "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". But, according to Edmond Halley, Hooke agreed that "the demonstration of the curves generated by it" belongs entirely to Newton.

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)

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)

L'exemple classique d'un programme de recherche réussi est la théorie gravitationnelle de Newton, probablement le programme de recherche lakatosien le plus réussi. Initialement, la théorie gravitationnelle de Newton était confrontée à de nombreuses « anomalies » (« contre-exemples ») et contredisait les théories observationnelles qui soutenaient ces anomalies. Mais les partisans du programme de recherche sur la gravité newtonienne ont transformé chaque anomalie en cas corroborants. De plus, ils ont eux-mêmes indiqué des contre-exemples qu'ils ont ensuite expliqués à travers la (...) théorie newtonienne. DOI: 10.13140/RG.2.2.16540.44165. (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)

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)

Practic, Newton vrea pur și simplu să reafirme adevărul omniprezenței lui Dumnezeu, fără să-l implice direct în fizica sistemului mondial. Newton dorește pur și simplu să se distanțeze de un concept cartezian al lui Dumnezeu și să-i convingă pe atei că Dumnezeu este o prezență reală extinsă în lume. Dumnezeu trebuie să existe în spațiu, pentru a exista, dar Dumnezeu nu acționează numai prin contact. Newton a presupus întotdeauna că Dumnezeu a acționat prin cauze secundare. DOI: 10.13140/RG.2.2.22468.78720.

Paper presented to the Twenty-seventh Hume Society Conference, 26 July 2000, Williamsburg, Virginia. -/- At the time I thought there was a stronger link between Maclaurin and Hume, but in discussions at and after the meeting, decided Hume was not taking his mechanics out of Maclaurin’s Account. Although I still have found Maclaurin useful in interpreting Hume -- see Sapadin 1997 for a discussion of popular Newtonianism in Hume's day -- I suspect my draft suffers somewhat from ambivalence. There are (...) still similarities, and possible avenues of influence, arguing that Hume was not ignorant of the new mechanics, but it also becomes clear that he did not understand it: although he adopts the Newtonian measure of force, he misapplies it. (shrink)

Newton described his Principia as a work of ‘experimental philosophy’, where theories were deduced from phenomena. He introduced six ‘phenomena’: propositions describing patterns of motion, generalised from astronomical observations. However, these don’t fit Newton’s contemporaries’ definitions of ‘phenomenon’. Drawing on Bogen and Woodward’s distinction between data, phenomena and theories, I argue that Newton’s ‘phenomena’ were explanatory targets drawn from raw data. Viewed in this way, the phenomena of the Principia and the experiments from the Opticks were different routes to the (...) same end: isolating explananda. (shrink)

It is common wisdom in intellectual history that eighteenth-century science of man evolved under the aegis of Newton. It is also frequently suggested that David Hume, one of the most influential practitioners of this kind of inquiry, aspired to be the Newton of the moral sciences. Usually this goes hand in hand with a more or less explicit reading of Hume’s theory of human nature as written in an idiom of particulate inert matter and active forces acting on it, i.e. (...) essentially that of Newton’s Principia. Hume’s outlook on the mental world is thus frequently described in terms of conceptual atoms whose association is compared to interparticulate attractions analogous with Newtonian forces in general, and gravity in particular. In the present paper I argue that Hume’s theory can indeed be understood in Newton’s wake, but not in the context of the Principa’s reception but that of the Opticks, which exerted a more significant influence on natural inquiry in eighteenth-century Scotland. I intend to show that Hume speaks a language and represents an outlook on human matters convergent with “philosophical chemistry” in Scotland at that time, and particularly to his later friend and physician William Cullen. (shrink)

To illustrate the view that a speaker can have a partial understanding of a concept, Burge uses the example of Leibniz’s and Newton’s understanding of the concept of derivative. In a recent article, Sheldon Smith criticizes this example and maintains that Newton’s and Leibniz’s use of their derivative symbols does not univocally determine their references. The present article aims at challenging Smith’s analysis. It first shows that Smith misconstrues Burge’s position. It second suggests that the philosophical lessons one should draw (...) from the practice of the historians of philosophy are more ambivalent than what Smith thinks. (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)

Elvira Mayordomo and Wolfgang Merkle The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 135-136, March 2013.

Early modern foundations for mechanics came in two kinds, nomic and material. I examine here the dynamical laws and pictures of matter given respectively by Newton, Leibniz, and Kant. I argue that they fall short of their foundational task, viz. to represent enough kinematic behavior; or at least to explain it. In effect, for the true foundations of classical mechanics we must look beyond Newton, Leibniz, and Kant.

This book argues that the Enlightenment was a golden age for the philosophy of body, and for efforts to integrate coherently a philosophical concept of body with a mathematized theory of mechanics. Thereby, it articulates a new framing for the history of 18th-century philosophy and science. It explains why, more than a century after Newton, physics broke away from philosophy to become an autonomous domain. And, it casts fresh light on the structure and foundations of classical mechanics. Among the figures (...) studied are Malebranche, Leibniz, Du Châtelet, Boscovich, and Kant, alongside d’Alembert, Euler, Lagrange, Laplace and Cauchy. (shrink)

Starting with Gottfried Leibniz, Isaac Newton's theology has often been caricatured as putting forward a “God of the gaps” argument for God's existence and continued involvement in the world. Peter Harrison has pointed out that this characterization of Newton's theology is “not entirely clear.” A closer look at Newton's letters and the drafts to the Opticks reveals that, rather than arguing God's providential ordering and care over the world, he takes these for granted and is reluctant to specify instances of (...) this order and care based on his physical research. He certainly believes in gaps in mechanical causes but is more eager to fill those gaps with nonmechanical natural causes than with God. Further, his system does not exhibit the two most prevalent weaknesses attributed to “God of the gaps” theologies: (1) that by describing God as intervening in natural causes his skill as a designer is maligned and (2) that by describing the physical details of God's involvement in the world one puts too much weight on theories likely to be replaced as science advances. Newton avoids the former weakness because it is only God's masterfulness as designer that he ties in any way to his theories of the physical world. He avoids the latter because he never points to God as the direct cause of any specific physical processes. Newton hoped that his system would cause his readers to marvel not only at God's providence but also at humankind's inability to sufficiently understand it. (shrink)

Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of real things. After situating Du Châtelet in this debate, this chapter (...) argues, first, that her account of the origins of mathematical objects is less subjectivist than it might seem. Mathematical objects are non-arbitrary, public entities. While mathematical objects are partly mind-dependent, so too are material things. Mathematical objects can approximate the material. Second, it is argued that this moderate metaphysical position underlies Du Châtelet’s persistent claims that mathematics is required for certain kinds of general knowledge, including in natural science. The chapter concludes with an illustrative example: an analysis of Du Châtelet’s argument that matter is continuous. A key but overlooked premise in the argument is that mathematical representations and material nature correspond. (shrink)

Much scholarship has claimed the physics of Emilie du Châtelet’s treatise, Institutions de physique, is Newtonian. I argue against that idea. To do so, I distinguish three strands of meaning for the category ‘Newtonian science,’ and I examine her book against them. I conclude that her physics is not Newtonian in any useful or informative sense. To capture what is specific about it, we need better interpretive categories.

The causes of tidal motions were widely debated from antiquity up to the eighteenth century. These discussions got a second wind in the early modern period, in the wake of a growing number of cosmological alternatives that challenged the dominant Aristotelian-Ptolemaic stance. The 1687 publication of Isaac Newton’s Principia Mathematica was a defining moment in the discussions and consequently made universal gravitation the most credible and generally accepted explanation. This paper investigates the aftermath of Newton’s discovery and demonstrates how his (...) understanding of tidal motion crowded out competing theories within a broader European context. My main point of reference is Roger Boscovich’s De aestu maris (1747). In his work, the leading Jesuit scholar of the time contrasted Newton’s interpretation to those of other major authorities, namely Johannes Kepler, Galileo Galilei, and René Descartes, and went on to claim the superiority of the British scientist’s achievements over anything written prior to the Principia. As this essay argues, alongside a significant body of literature produced under the umbrella of the Jesuit order, Boscovich’s De aestu maris subsequently contributed to the formation of the popular image of Newton as a “scientific hero.”. (shrink)

This paper has three aims: first, to present in a clear way Newton da Costa’s argument against the necessity of logical laws. In order to do so, we need to clearly advance his views on the idea that logic is context-relative, and not known a priori. Doing so, however, requires that we present his methodology for the development of counter-examples to logical laws: the use of hypothetical models in logic. Given that this method has been overlooked in most discussions on (...) the epistemology of logic, our second goal is to present da Costa’s views on it carefully. The discussion of some tensions resulting from the relation of a system of logic and the context it governs, in da Costa’s approach, is our third goal. Basically, da Costa seems to swing between two incompatible views on such relation, requiring sometimes that a logic is dependent on a context, and in other cases, that the nature of the context is dependent on a logic. Bringing this to light may also benefit current discussions on logical relativism. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical analogies (...) and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

In 1500, speculative philosophy lay at the heart of European intellectual life; by 1700, its role was drastically diminished. The Kingdom of Darkness tells the story of this momentous transformation. Dmitri Levitin explores the structural factors behind this change: the emancipation of natural philosophy from metaphysics; theologians' growing preference for philology over philosophy; and a new conception of the limits of the human mind derived from historical and oriental scholarship, not least concerning China and Japan. In turn, he shows that (...) the ideas of two of Europe's most famous thinkers, Pierre Bayle and Isaac Newton, were both the products of this transformation and catalysts for its success. Drawing on hundreds of sources in many languages, Levitin traces in unprecedented detail Bayle and Newton's conceptions of what Thomas Hobbes called The Kingdom of Darkness: a genealogical vision of how philosophy had corrupted the human mind. Both men sought to remedy this corruption, and their ideas helped lay the foundation for the system of knowledge that emerged in the eighteenth century. (shrink)