Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices, in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the axiom was replaced by the deontic axiom. In this paper, we propose even weaker systems, by eliminating (...) both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

The Logics of Deontic (In)Consistency (LDI's) can be considered as the deontic counterpart of the paraconsistent logics known as Logics of Formal (In)Consistency. This paper introduces and studies new LDI's and other paraconsistent deontic logics with different properties: systems tolerant to contradictory obligations; systems in which contradictory obligations trivialize; and a bimodal paraconsistent deontic logic combining the features of previous systems. These logics are used to analyze the well-known Chisholm's paradox, taking profit of the fact that, besides contradictory obligations do (...) not trivialize in LDI's, several logical dependencies of classical logic are blocked in the context of LDI's, allowing to dissolve the paradox. (shrink)

In the first part of this paper we analyzed finite non-deterministic matrix semantics for propositional non-normal modal logics as an alternative to the standard Kripke possible world semantics. This kind of modal system characterized by finite non-deterministic matrices was originally proposed by Ju. Ivlev in the 70s. The aim of this second paper is to introduce a formal non-deterministic semantical framework for the quantified versions of some Ivlev-like non-normal modal logics. It will be shown that several well-known controversial issues of (...) quantified modal logics, relative to the identity predicate, Barcan’s formulas and de re and de dicto modalities, can be tackled from a new angle within the present framework. (shrink)

In view of the limitations of classical, free, and modal logics to deal with fictional names, we develop in this paper a four-valued logical framework that we see as a promising strategy for modeling contexts of reasoning in which those names occur. Specifically, we propose to evaluate statements in terms of factual and fictional truth values in such a way that, say, declaring ‘Socrates is a man’ to be true does not come down to the same thing as declaring ‘Sherlock (...) Holmes is a man’ to be so. As a result, our framework is capable of representing reasoning involving fictional characters that avoids evaluating statements according to the same semantic standards. The framework encompasses two logics that differ according to alternative ways one may interpret the relationships among the factual and fictional truth values. (shrink)

In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness showed that not every modal logic (...) can be characterized by Kripke frames. Besides, the creation of non-classical modal logics puts the problem of characterization of finite matrices very far away from the original scope of Dugundji’s result. In this sense, we will show how to update Dugundji’s result in order to make precise the scope and the limits of many-valued matrices as semantic of modal systems. A brief comparison with the useful Chagrov and Zakharyaschev’s criterion of tabularity for modal logics is provided. (shrink)

In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to (...) recover the theorems of propositional classical logic within three sub-classical modal systems. (shrink)

Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part of the paper (...) is devoted to four-valued Nmatrices, including Kearns’s and Ivlev’s. Besides proving with full details Kearns’s results for T, S4 and S5, we also obtain a characterisation of the system B by four-valued Nmatrices with level valuations. Concerning Ivlev’s results, two new modal systems are introduced and char.. (shrink)

In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...) in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed. (shrink)

L'œuvre de Cassirer nous offre une vision pluraliste du XVIIIe siècle. Sous cet éclairage, Rousseau redevient citoyen de Genève et Bayle le banni de Rotterdam, le cartésianisme se fait principalement hollandais et Voltaire l'interprète de Newton. Pour Cassirer, le XVIIIe siècle est ce foisonnement convergent qui rompt les frontières nationales comme les frontières de langues, de classes ou de disciplines. Dans cette brillante synthèse, Cassirer s'emploie à balayer les poncifs. Certes, le XVIIIe siècle politique, mais il est aussi un (...) grand siècle religieux : celui de la lutte contre l'intolérance et la superstition, celui, surtout, de l'élaboration des fondements de la foi. Siècle qui marque la naissance de l'esprit historique, le XVIIIe siècle a le sens de la relativité des valeurs. Enfin, il est le siècle de l'esthétique : toute théorie de l'art en viendra. (shrink)

C’est à Maurolic, et non à Dominis, comme l’ont dit certains auteurs, que, selon nous, Descartes doit quelques éléments de son explication de l’arc- en-ciel, en particulier l’idée du rôle fondamental et de la position relative générale du soleil et des gouttes d’eau.Mais cette théorie, magistrale application de la Méthode, porte surtout la marque du génie cartésien par la forme mathématique que prennent les résultats des expériences.Lies physiciens cartésiens la reproduisirent. Malebranche l’élargit sous l’influence de Huygens et de Newton, (...) et l’exprima en termes d’optique ondulatoire. (shrink)

En contrepoint à son œuvre mathématique et physique — et en relation avec elle — d'Alembert a développé une théorie de la connaissance influencée par Locke et le sensualisme de Condillac, mais centrée avant tout sur une épistémologie de la physique newtonienne. Réaliste, prônant le recours à l'expérience, il est en même temps profondément rationaliste, et même précisément, quoiqu'il s'en défende plutôt, dans la lignée de Descartes, Mais, bien que la Raison soit sa référence fondamentale, à tel point qu'il voudrait (...) fonder sur ses principes les plus évidents toute la science physico-mathématique — c'est-à-dire par excellence la Mécanique —, son programme ne peut être dit cartésien : non seulement il rejette les idées innées, mais il accepte la critique d'une rationalité apparente requise par la considération de faits irréductibles (l'attraction par exemple). Son épistémologie est un réalisme rationnel référé à l'être même de la Nature (la Raison et la Nature se rejoignent en profondeur). C'est en fonction de ces conceptions qu'il accepte ou rejette certaines notions physiques soit ambiguës, soit incertaines. Son rejet du concept de force comme celui de la considération d'une texture intime des corps semblent en faire, par le refus de ce qui ne serait pas directement mesurable, l'annonciateur du positivisme de Laplace et de Comte : une telle interprétation serait inexacte, et d'Alembert considère que la pensée peut parvenir à la connaissance du réel. Si ses conceptions s'élaborent en contrepoint de son activité scientifique, c'est en même temps en lutte et polémique contre la métaphysique, au sein de son engagement philosophique — il est tête de file, avec Voltaire, du « parti philosophique » — et notamment dans l'Encyclopédie. Bien qu'il se réfère, comme Newton, à une Intelligence suprême à l'œuvre dans l'Univers, il n'est pas déiste et affiche bientôt une position sceptique. Sa recherche et son affirmation de l'autonomie des lois de la Nature sont a-thées au sens privatif qui annonce Laplace. Il s'oppose au matérialisme de d'Holbach ou Helvétius, mais il se rapproche peu à peu — et notamment vers 1765, sans doute sous l'influence de Diderot qui rédigea vers cette époque Le rêve de d'Alembert et avec qui il venait de renouer — d'un matérialisme dynamique : mais, ce matérialisme, il ne le professe qu'en privé (essentiellement dans sa correspondance avec Frédéric de Prusse). L'âme est matérielle, et si « le plus simple raisonnement prouve qu'il y a un être éternel » , ce Dieu est matériel, il « n'est que la matière en tant qu'intelligente » , ce qui rejoint la définition du matérialisme donnée par Diderot dans l'Encyclopédie. Toutefois, refusant de se prononcer sur l'en-soi des choses, et sur la nature de la matière elle-même, comme de se définir métaphysiquement, son matérialisme tardif est encore marqué de scepticisme. (shrink)

Aside from the Principia and occasional appearances of the Opticks , Newton' writings have remained largely inaccessible to students of philosophy, science, and literature as well as to other readers. This book provides a remedy with wide representation of the interests, problems, and diverse philosophic issues that preoccupied the greatest scientific mind of the seventeenth century. Grouped in sections corresponding to methods, principles, and theological considerations, these selections feature explanatory notes and cross-references to related essays.

Concepts stand at the centre of human cognition. We use concepts in categorizing objects and events in the world, in reasoning and action, and in social interaction. It is therefore not surprising that the study of concepts constitutes a central area of research in philosophy and psychology, yet only recently have the two disciplines developed greater interaction. Recent experiments in psychology that test the role of concepts in categorizing and reasoning have found a great deal of variation, across individuals and (...) cultures, in categorization behaviour. Meanwhile, philosophers of language and mind have investigated the semantic properties of concepts, and how concepts are related to linguistic meaning and linguistic communication. A key motivation behind this was the idea that concepts must be shared across individuals and cultures. With the dawn of experimental philosophy, the proposal that the experimental data from psychology lacks relevance to semantics is increasingly difficult to defend. -/- This volume brings together leading psychologists and philosophers to advance the interdisciplinary debate on the role of concepts in categorizing and reasoning, the relationship between concepts and linguistic meaning and communication, the challenges conceptual variation poses to communication, and the social and political effects of conceptual change. (shrink)

: Newton's critics argued that his treatment of gravity in the Principia saddles him with a substantial dilemma. If he insists that gravity is a real force, he must invoke action at a distance because of his explicit failure to characterize the mechanism underlying gravity. To avoid distant action, however, he must admit that gravity is not a real force, and that he has therefore failed to discover the actual cause of the phenomena associated with it. A reinterpretation of (...) Newton's distinction between the "mathematical" and the "physical" treatment of force indicates how he can reject each horn of this dilemma. (shrink)

A review of Matthew Karush and Oscar Chamosa, The New Cultural History of Peronism: Power and Identity in Mid-Twentieth Century Argentina.

Newton's philosophical views are unique and uniquely difficult to categorise. In the course of a long career from the early 1670s until his death in 1727, he articulated profound responses to Cartesian natural philosophy and to the prevailing mechanical philosophy of his day. Newton as Philosopher presents Newton as an original and sophisticated contributor to natural philosophy, one who engaged with the principal ideas of his most important predecessor, René Descartes, and of his most influential critic, G. (...) W. Leibniz. Unlike Descartes and Leibniz, Newton was systematic and philosophical without presenting a philosophical system, but over the course of his life, he developed a novel picture of nature, our place within it, and its relation to the creator. This rich treatment of his philosophical ideas will be of wide interest to historians of philosophy, science, and ideas. (shrink)

We all think that science is special. Its products—its technological spin-off—dominate our lives which are thereby sometimes enriched and sometimes impoverished but always affected. Even the most outlandish critics of science such as Feyerabend implicitly recognize its success. Feyerabend told us that science was a congame. Scientists had so successfully hood-winked us into adopting its ideology that other equally legitimate forms of activity—alchemy, witchcraft and magic—lost out. He conjured up a vision of much enriched lives if only we could free (...) ourselves from the domination of the ‘one true ideology’ of science just as our ancestors freed us from the domination of the Church. But he told us these things in Switzerland and in California happily commuting between them in that most ubiquitous product of science—the aeroplane. (shrink)

Isaac Newton's Scientific Method examines Newton's argument for universal gravity and his application of it to resolve the problem of deciding between geocentric and heliocentric world systems by measuring masses of the sun and planets. William L. Harper suggests that Newton's inferences from phenomena realize an ideal of empirical success that is richer than prediction. Any theory that can achieve this rich sort of empirical success must not only be able to predict the phenomena it purports to (...) explain, but also have those phenomena accurately measure the parameters which explain them. Harper explores the ways in which Newton's method aims to turn theoretical questions into ones which can be answered empirically by measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally accepted as guides to further research. This methodology, guided by its rich ideal of empirical success, supports a conception of scientific progress that does not require construing it as progress toward Laplace's ideal limit of a final theory of everything, and is not threatened by the classic argument against convergent realism. Newton's method endorses the radical theoretical transformation from his theory to Einstein's. Harper argues that it is strikingly realized in the development and application of testing frameworks for relativistic theories of gravity, and very much at work in cosmology today. (shrink)

Newton’s Regulae philosophandi—the rules for reasoning in natural philosophy—are maxims of causal reasoning and induction. This essay reviews their significance for Newton’s method of inquiry, as well as their application to particular propositions within the Principia. Two main claims emerge. First, the rules are not only interrelated, they defend various facets of the same core idea: that nature is simple and orderly by divine decree, and that, consequently, human beings can be justified in inferring universal causes from limited (...) phenomena, if only fallibly. Second, the rules make substantive ontological assumptions on which Newton’s argument in the Principia relies. (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)

The article examines the philosophical works of Ugo Perone. It explores the different aspects of temporality and spatiality inherent in Perone's understanding of time in the figure of threshold, and analyzes the notion of the so-called political present. Also investigated are the claims of Perone about the significance of politics and the public space on the human life.

This is the first volume of original commissioned papers on the subject of Newton and empiricism. The chapters, contributed by a leading team of both established and younger international scholars, explore the nature and extent of Newton's relationship to a variety of empiricisms and empiricists.

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this (...) framework, never absolute ones. (shrink)

This paper is a critical response to Hylarie Kochiras’ “Gravity and Newton’s substance counting problem,” Studies in History and Philosophy of Science 40 267–280. First, the paper argues that Kochiras conflates substances and beings; it proceeds to show that Newton is a substance monist. The paper argues that on methodological grounds Newton has adequate resources to respond to the metaphysical problems diagnosed by Kochiras. Second, the paper argues against the claim that Newton is committed to two (...) speculative doctrines attributed to him by Kochiras and earlier Andrew Janiak: i) the passivity of matter and ii) the principle of local causation. Third, the paper argues that while Kochiras’ arguments about Newton’s metaphysical commitments are mistaken, it qualifies the characterization of Newton as an extreme empiricist as defended by Howard Stein and Rob DiSalle. In particular, the paper shows that Newton’s empiricism was an intellectual and developmental achievement that built on non trivial speculative commitments about the nature of matter and space.Keywords: Newton; Substance; Action at a distance; Space; Matter; Empiricism. (shrink)

This paper has the aim to provide a general view of the so called Jesuit Edition (hereafter JE) of Newton’s Philosophiae Naturalis Principia Mathematica (1739–1742). This edition was conceived to explain all Newton’s methods through an apparatus of notes and commentaries. Every Newton’s proposition is annotated. Because of this, the text – in four volumes – is one of the most important documents to understand Newton’s way of reasoning. This edition is well known, but systematic works (...) on it are still missing. We are going to fill this gap by means of a project exposed in the final remarks of this paper. In this paper we will: A) expound the way in which the notes and the additions to the JE were conceived by the commentators; B) provide some pieces of information about the commentators; C) summarize the most important of their notes; D) examine closely their notes as to a particularly important question: the so called "inverse problem of the central forces". (shrink)

I identify a set of interlocking views that became (and still are) very influential within philosophy in the wake of Newton’s success. These views use the authority of natural philosophy/mechanics to settle debates within philosophy. I label these “Newton’s Challenge.”.