We re-evaluate existing data that demonstrate a large amount of variability in the content of categories considering the fact that these data have been obtained in a specific task: the production of features of single isolated categories. We present new data that reveal a large consensus when participants have to judge whether or not a given feature is characteristic of a category and we show that classification tasks produce an intermediate level of consensus. We argue that the differences observed between (...) tasks are due to the extent of implied context and we propose a reinterpretation of typicality effects, demonstrating that they are compatible with the existence of a stable conceptual core. In order to explain how the existence of a conceptual core is consistent with variability due to context, we present a theory of categorisation based on a property tree organisation. Within a domain of description, we distinguish between semantic implications (flying → moving) and empirical implications (flying → having wings) as well as between properties used to describe objects. Semantic implications serve to build property lines and Galois lattices are used to reveal category structures according to empirical implications. We show that variability in the category content may be explained by the fact that some properties are emphasised while others are masked according to the context. (shrink)

A general model of problem‐solving processes based on misconception elimination is presented to simulate both impasses and solving processes. The model operates on goal‐related rules and a set of constraint rules in the form of “if (state or goal), do not (Action)” for the explicit constraints in the instructions and the implicit constraints that come from misconceptions of legal moves. When impasses occur, a constraint elimination mechanism is applied. Because successive eliminations of implicit constraints enlarge the problem space and have (...) an effect on planning, the model integrates “plan‐based” and “constraint‐based” approaches to problem‐solving behavior.Simulating individual protocols of Tower of Hanoi situations shows that the model, which has a proper set of constraints, predicts a single move with no alternative on about 61% of the movements and that protocols are quite successfully simulated movement by movement. Finally, it is shown that many features of previous models are embedded in the constraint elimination model. (shrink)

The triangle in general or the man as such are general objects. These are objects that possess the properties common to all the individual objects in their range. Stanisław Leśniewski and Tadeusz Kotarbiński, two Polish philosophers and logicians belonging to the Lvov-Warsaw School, produced several proofs aiming to show that such objects are impossible because the principles that govern them lead to a contradiction. In this paper I first clarify the structure of their proofs. Then I suggest a way to (...) elude their conclusion. In order to do that I use two Meinongian distinctions: the distinction between complete and incomplete objects, on the one hand, and the distinction between nuclear and extranuclear properties, on the other hand. I claim first that general objects are incomplete objects, i.e. they do not satisfy the ontological principle of the excluded middle, and second that the principle that governs the relations between the properties of general objects and the properties of the individual objects in their range should be restricted to nuclear properties. (shrink)

Les ontologies catégoriales tentent de répartir la totalité des objets en différentes catégories ontologiques entretenant certaines relations déterminées entre elles. Ces ontologies ont connu un regain d’intérêt dans la métaphysique analytique contemporaine, regain d’intérêt qui trouve son origine dans les travaux de Brentano. Dans cet article, nous examinons dans quelle mesure la théorie de l’objet développée par un élève de Brentano, Meinong, peut être comptée au nombre des ontologies catégoriales. Pour ce faire, nous analysons en premier lieu les différents sortes (...) d’objets meinongiens selon les types de vécus élémentaires auxquels ils se rapportent. Nous étudions ensuite les modes d’être (réel et idéal) qui échoient éventuellement à ces objets. Qu’un objet soit réel ou idéal, il est complet, mais il y a aussi des objets qui, comme la montagne d’or ou le cercle-carré, sont incomplets. Analysant cette dernière classe d’objets, nous montrons comment les objets de ce type se voient attribuer un statut extraontologique, un mode d’objectualité qui ne se réduit pas à un mode d’être. Si Meinong semble de la sorte subsumer tous les objets sous une seule et même catégorie, nous expliquons qu’il n’en est en fait rien, la notion d’objet (en général) n’étant en aucun cas un summum genus. Dans la conclusion, nous défendons l’idée que la théorie de l’objet de Meinong n’est pas une ontologie catégoriale au sens strict. S’il y a bien des catégories, celles-ci sont des catégories objectuelles, des catégories dont les catégories ontologiques sont au mieux une sous-classe. (shrink)

Leśniewski’s metalogic is often considered to be difficult to understand because it differs greatly from its standard formulation. In this paper I try to explain the reasons of these idiosyncrasies. I claim that they have mainly two sources. First of all there is Leśniewski’s conviction that a formal system should be conceived as a set of concrete marks that can always physically and syntactically be expanded by the addition of new theses. Secondly there is Leśniewski’s conviction that definitions should neither (...) be formulas belonging to the metalanguage, nor deduction rules, but formulas belonging to the object-language and expressed with the help of the biconditional functor. The realisation of the first point is linked to the second one in so far as the metalinguistic rule for the writing out of definitions has to be formulated in a way that makes it possible to build the formal system in agreement with Leśniewski’s conception. While explaining these points I give an overview of the main peculiarities of Leśniewski’s metalogic. (shrink)

English summary: Jan Lukasiewicz (1878-1956) was one of the most important members of the Lwow-Warsaw school of logic. The thirteen translated articles in this volume demonstrate the protean form of Lukasiewiczs work, from his texts on Aristotle and the principle of non-contradiction and syllogistics to modal logic, intuitionism, and multivalent logics. The articles show in particular his preoccupations with logical precision and the problem of human liberty. French description: Avec Kazimierz Twardowski, Stanislaw Lesniewski et Alfred Tarski, le logicien et philosophe (...) polonais Jan Lukasiewicz (1878-1956) est l'un des membres les plus importants de l'Ecole de Lvov-Varsovie. Celebre pour ses ouvrages consacres a Aristote, notamment sur le principe de non-contradiction et sur la syllogistique, il a egalement publie des articles majeurs sur la logique propositionnelle, la logique modale, l'intuitionnisme et les logiques multivalentes, dont il fut l'un des fondateurs. Enfin, il a contribue a faire reconnaitre l'importance des travaux en logique de l'ecole megarico-stoicienne, trop longtemps eclipses par ceux d'Aristote sur la syllogistique. Mais Lukasiewicz ne fut pas seulement un logicien et un historien brillant, il s'engagea aussi dans les polemiques philosophiques de son temps. Il defendit ainsi la methode logique en philosophie. Proche sur ce point des membres du Cercle de Vienne, il ne rejetait pas pour autant les questions metaphysiques, commecelle du determinisme qui l'occupa toute sa vie. Les treize articles de ce recueil, fruit d'un travail collectif de traduction, ont pour ambition de montrer le caractere proteiforme de l'oeuvre de Lukasiewicz, preoccupe autant par la precision logique que par le probleme de la liberte humaine. (shrink)

This collection of fourteen original essays addresses the seminal contribution of Franz Brentano and his heirs, to philosophy of language. Despite the great interest provoked by the Brentanian tradition and its multiple connections with early analytic philosophy, precious little is known about the Brentanian contribution to philosophy of language. The aim of this new collection is to fill this gap by providing the reader with a more thorough understanding of the legacy of Brentano and his school, in their pursuit of (...) a unique research programme according to which the analysis of meaning is inseparable from philosophical inquiries into what goes on in the mind and what there is in the world. In three parts, the volume first reconstructs Brentano’s pathbreaking thoughts on meaning and grammatical illusions, exploring their strong connections with the Austro-German tradition and analytic philosophy. It then addresses the multifaceted debates on the objectivity of meaning in the Brentano School and its aftermath. Finally, part three explores Brentano’s wider legacy, namely: Husserl’s theory of modification and typicality, Bühler’s theory of linguistic and non-linguistic expressions, and Wittgenstein’s thoughts on guidance and rule-following. The result is a unique collection of essays which shows the significance, originality and timely character of the Brentanian philosophy of language. (shrink)

Dialectica, Volume 73, Issue 4, Page 591-597, December 2019.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Return of Scepticism: From Hobbes and Descartes to BayleSébastien CharlesGianni Paganini, editor. The Return of Scepticism: From Hobbes and Descartes to Bayle. Dordrecht: Kluwer, 2003. Pp. xxviii + 486. Cloth, $180.00.Cette édition des actes du congrès international « The Return of Scepticism », organisé par Gianni Paganini à l'Université du Piémont-Oriental de Vercelli en mai 2000, a pour ambition de faire le point sur l'état de la (...) recherche actuelle en cherchant à cerner au mieux les implications épistémologiques et les répercussions européennes du scepticisme à la période moderne. Placés sous le patronage de Richard H. Popkin, dont un essai ouvre l'ouvrage et pave la voie à de futures recherches sur la question, les textes rassemblés par Gianni Paganini ont pour trait commun d'insister sur la prégnance du scepticisme à l'époque moderne, tout en prenant garde au fait de bien replacer chaque stratégie sceptique dans l'environnement culturel et philosophique qui fut le sien. Divisé en sept sections, l'ouvrage fournit une vue d'ensemble de la question sceptique qui s'étale sur deux siècles, le XVIIe et le XVIIIe.Dans la première section, l'accent est mis sur un aspect délaissé de l'histoire du scepticisme moderne, à savoir le traitement particulier qui lui fut réservé dans la pensée anglaise des XVIIe et XVIIIe siècles. Sont abordés ici les cas de Hobbes, dont le traitement du scepticisme est pensé en relation inversée avec celui de Descartes (G. Paganini), Locke, qui tend à faire sien le principe sceptique de la limitation du savoir (G. A. J. Rogers), et les Platoniciens de Cambridge, qui s'inspirent de la méthode sceptique pour compartimenter le champ du savoir (F. Tomasoni).Dans la deuxième section, c'est la pensée continentale qui est à l'honneur, avec des textes consacrés à Descartes spécifiquement ou à La Mothe le Vayer et Descartes, avec pour objectif commun de questionner l'originalité du travail cartésien en insistant notamment sur le rôle de l'epoché chez Charron comme source possible du cogito (J. R. Maia Neto) et sur une tradition sceptique non fidéiste présente dans les œuvres de La Mothe le Vayer comme de Descartes (J.-P. Cavaillé).La troisième section évoque la prise de conscience des enjeux sceptiques chez les sectateurs et les adversaires de Descartes, qui s'accordent tous à reconnaître l'insuffisance de la réfutation du scepticisme proposée par ce dernier. Ce point fait l'unanimité tant chez les opposants à Descartes—Martin Schoock (A. Del Prete), Pierre Villemandy (C. Borghero), Pierre-Daniel Huet (T. M. Lennon), et les philosophes italiens Fardella et Doria (M. T. Marcialis)—que chez ceux qui se sont inspirés de sa philosophie—Arnauld (G. Belgioioso), Malebranche, Foucher et Desgabets (E. Scribano).La prise en compte des enjeux sceptiques aux plans politique et religieux est intégrée dans la quatrième partie au sein de laquelle sont évoquées des thématiques plurielles comme la présence du probabilisme néo-académique chez Pascal (A. McKenna), l'interprétation sceptique, voire libertine, du pouvoir et de la liberté rattachée à la théorie hobbesienne de l'état de nature chez Samuel Sorbière (L. Bianchi), ou le rapport existant entre scepticisme et tolérance (L. Simonutti).La section suivante délaisse politique et religion pour aborder le cas de la science, et de l'effet du scepticisme au niveau épistémologique. Le cas de Martín Martínez témoigne du fait que le scepticisme peut être conciliable avec une vision empiriste de la science et qu'une physique sceptique reste possible (J. C. Laursen). De même, le rapport des savants italiens comme Redi, Magalotti ou Dati à l'égard du scepticisme est évocateur de la prise de conscience des dangers que le scepticisme pose pour le domaine du démontrable (M. Torrini), ce qui vaut également pour toute théorie de la signification, dont les implications sceptiques sont patentes (G. Hassler), ou pour toute approche historique minée par des considérations pyrrhoniennes (C. Grell... (shrink)

Gottfried Leibniz is well known for his claim to have “rehabilitated” the substantial forms of scholastic philosophy, forging a reconciliation of the New Philosophy of Descartes, Mersenne and Gassendi with Aristotelian metaphysics (in his so-called Discourse on Metaphysics, 1686). Much less celebrated is the fact that fifty years earlier (in his Hypomnemata Physica, 1636) the Bratislavan physician and natural philosopher Daniel Sennert had already argued for the indispensability to atomism of (suitably re-interpreted) Aristotelian forms, in explicit opposition to the rejection (...) of substantial forms by his fellow atomist Sébastien Basson.1.. (shrink)

Sébastien Richard se propose dans ce quinzième volume des Cahiers du Centre de logique de présenter ces résultats, à la fois du point de vue des concepts philosophiques et du point de vue de la technique logique mis en jeu dans la ...

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

This study reconstructs the relationship between philosophy and politics in the way in which Heidegger's failure as a politician influenced the redevelopment of philosophy in the 1930s. The author also explains how Heidegger's failure influenced the content and direction of his later work.

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Whether unconscious stimuli can modulate the preparation of a cognitive task is still controversial. Using a backward masking paradigm, we investigated whether the modulation could be observed even if the prime was made unconscious in 100% of the trials. In two behavioral experiments, subjects were instructed to initiate a phonological or semantic task on an upcoming word, following an explicit instruction and an unconscious prime. When the SOA between prime and instruction was sufficiently long , primes congruent with the task (...) set instruction led to speedier responses than incongruent primes. In the other condition , no task set priming was observed. Repetition priming had the opposite tendency, suggesting the observed task set facilitation cannot be ascribed solely to perceptual repetition priming. Our results therefore confirm that unconscious information can modulate cognitive control for currently active task sets, providing sufficient time is available before the conscious decision. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Studies the politics of Heidegger in terms of "thrownness" or "existential contingency". Attempts to think through Heidegger's philosophy in a manner that parallels his own dialogue with other key western thinkers.

Psychopathy is a personality disorder frequently associated with immoral behaviors. Previous behavioral studies on the influence of psychopathy on moral decision have yielded contradictory results, possibly because they focused either on judgment (abstract evaluation) or on choice of hypothetical action, two processes that may rely on different mechanisms. In this study, we explored the influence of the level of psychopathic traits on judgment and choice of hypothetical action during moral dilemma evaluation. A population of 102 students completed a questionnaire with (...) ten moral dilemmas and nine non-moral dilemmas. The task included questions targeting both judgment (“Is it acceptable to … in order to …?”) and choice of hypothetical action (“Would you … in order to …?”). The level of psychopathic traits of each participant was evaluated with the Levenson Self-Report Psychopathy (LSRP) scale. Logistic regression fitted with the generalized estimating equations method analyses were conducted using responses to the judgment and choice tasks as the dependent variables and psychopathy scores as predictor. Results show that a high level of psychopathic traits, and more specifically those related to affective deficit, predicted a greater proportion of utilitarian responses for the choice but not for the judgment question. There was no first-order interaction between the level of psychopathic traits and other potential predictors. The relation between a high level of psychopathic traits and increased utilitarianism in choice of action but not in moral judgment may explain the contradictory results of previous studies where these two processes were not contrasted. It also gives further support to the hypothesis that choice of action endorsement and abstract judgment during moral dilemma evaluation are partially distinct neural and psychological processes. We propose that this distinction should be better taken into account in the evaluation of psychopathic behaviors. (shrink)

The ancient Taoist text that forms the central part of this book was discovered by Wilhelm, who recognized it as essentially a practical guide to the integration of personality. Foreword and Appendix by Carl Jung; illustrations. Translated by Cary F. Baynes.A Helen and Kurt Wolff Book.

In a globalizing world, governments are not always able or willing to regulate the social and environmental externalities of global business activities. Multi-stakeholder initiatives (MSI), defined as global institutions involving mainly corporations and civil society organizations, are one type of regulatory mechanism that tries to fill this gap by issuing soft law regulation. This conceptual paper examines the conditions of a legitimate transfer of regulatory power from traditional democratic nation-state processes to private regulatory schemes, such as MSIs. Democratic legitimacy is (...) typically concerned with input legitimacy (rule credibility, or the extent to which the regulations are perceived as justified) and output legitimacy (rule effectiveness, or the extent to which the rules effectively solve the issues). In this study, we identify MSI input legitimacy criteria (inclusion, procedural fairness, consensual orientation, and transparency) and those of MSI output legitimacy (rule coverage, efficacy, and enforcement), and discuss their implications for MSI democratic legitimacy. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

"This is an excellent textbook on Neoplatonism which gives the reader a very concise and lucid overview of the basic doctrines and leading thinkers of the last great philosophy to emerge before the Christianization of the Roman Empire. I’ve no doubt that my students next semester will benefit from the analyses contained in the book. The contents of the chapters are very informative and adequately place developments in their socio-cultural context." --Michael B. Simmons, Auburn University at Montgomery.

In a globalizing world, governments are not always able or willing to regulate the social and environmental externalities of global business activities. Multi-stakeholder initiatives (MSI), defined as global institutions involving mainly corporations and civil society organizations, are one type of regulatory mechanism that tries to fill this gap by issuing soft law regulation. This conceptual paper examines the conditions of a legitimate transfer of regulatory power from traditional democratic nation-state processes to private regulatory schemes, such as MSIs. Democratic legitimacy is (...) typically concerned with input legitimacy (rule credibility, or the extent to which the regulations are perceived as justified) and output legitimacy (rule effectiveness, or the extent to which the rules effectively solve the issues). In this study, we identify MSI input legitimacy criteria (inclusion, procedural fairness, consensual orientation, and transparency) and those of MSI output legitimacy (rule coverage, efficacy, and enforcement), and discuss their implications for MSI democratic legitimacy. (shrink)

Here we question the mechanisms underlying the emergence of the feeling of control that can be modulated even when the feeling of being the author of one’s own action is intact. With a haptic robot, participants made series of vertical pointing actions on a virtual surface, which was sometimes postponed by a small temporal delay (15 or 65 ms). Subjects then evaluated their subjective feeling of control. Results showed that after temporal distortions, the hand-trajectories were adapted effectively but that the (...) feeling of control decreased significantly. This was observed even in the case of subliminal distortions for which subjects did not consciously detect the presence of a distortion. Our findings suggest that both supraliminal and subliminal temporal distortions that occur within a healthy perceptual–motor system impact the conscious experience of the feeling of control of self-initiated motor actions. (shrink)

Having visited Ireland regularly during the 1930s, Ludwig Wittgenstein resigned his Cambridge philosophy professorship in 1947 and moved there, living in a fishing village on the Atlantic coast and hotels in Dublin and the Wicklow Mountains. Although Wittgenstein spent some time out of the country, Ireland was effectively his base for three very productive years during which he worked on what would become one of his key books, the posthumously published Philosophical Investigations. Wittgenstein in Ireland represents the first sustained account (...) of Wittgenstein's time in Ireland, placing it in its historical context. Wall pays a good deal of attention to the representation of the Irish landscape in which the Austrian philosopher found himself able to work; a large part of his writings were produced in the bleak landscapes of Ireland and Norway. (shrink)

Despite their differences in origin, the three influential schools of twentieth-century continental cultural criticism--the Frankfurt School, existentialism, and poststructuralism--have long been treated as an ensemble and with critical hesitancy. Examining these schools as responses to the apparent collapse of Western civilization in the twentieth-century and as formidable intellectual challenges to the cultural legacies of the Enlightenment, this book provides a productive base for criticism and broadens our understanding of their histories and reception.

We present an empirical case study that connects psycholinguistics with the field of cultural evolution, in order to test for the existence of cultural attractors in the evolution of quotations. Such attractors have been proposed as a useful concept for understanding cultural evolution in relation with individual cognition, but their existence has been hard to test. We focus on the transformation of quotations when they are copied from blog to blog or media website: by coding words with a number of (...) well-studied lexical features, we show that the way words are substituted in quotations is consistent with the hypothesis of cultural attractors and with known effects of the word features. In particular, words known to be harder to recall in lists have a higher tendency to be substituted, and words easier to recall are produced instead. Our results support the hypothesis that cultural attractors can result from the combination of individual cognitive biases in the interpretation and reproduction of representations. (shrink)

A problem is a situation in which an agent seeks to attain a given goal without knowing how to achieve it. Human problem solving is typically studied as a search in a problem space composed of states (information about the environment) and operators (to move between states). A problem such as playing a game of chess has possible states, and a traveling salesperson problem with as little as 82 cities already has more than different tours (similar to chess). Biological neurons (...) are slower than the digital switches in computers. An exhaustive search of the problem space exceeds the capacity of current computers for most interesting problems, and it is fairly clear that humans cannot in their lifetime exhaustively search even small fractions of these problem spaces. Yet, humans play chess and solve logistical problems of similar complexity on a daily basis. Even for simple problems humans do not typically engage in exploring even a small fraction of the problem space. This begs the question: How do humans solve problems on a daily basis in a fast and efficient way? Recent work suggests that humans build a problem representation and solve the represented problem—not the problem that is out there. The problem representation that is built and the process used to solve it are constrained by limits of cognitive capacity and a cost–benefit analysis discounting effort and reward. In this article, we argue that better understanding the way humans represent and solve problems using heuristics can help inform how simpler algorithms and representations can be used in artificial intelligence to lower computational complexity, reduce computation time, and facilitate real-time computation in complex problem solving. (shrink)

This article aims first at showing that Russell's general doctrine according to which all mathematics is deducible ‘by logical principles from logical principles’ does not require a preliminary reduction of all mathematics to arithmetic. In the Principles, mechanics (part VII), geometry (part VI), analysis (part IV–V) and magnitude theory (part III) are to be all directly derived from the theory of relations, without being first reduced to arithmetic (part II). The epistemological importance of this point cannot be overestimated: Russell's logicism (...) does not only contain the claim that mathematics is no more than logic, it also contains the claim that the differences between the various mathematical sciences can be logically justified—and thus, that, contrary to the arithmetization stance, analysis, geometry and mechanics are not merely outgrowths of arithmetic. The second aim of this article is to set out the neglected Russellian theory of quantity. The topic is obviously linked with the first, since the mere existence of a doctrine of magnitude, in a work dated from 1903, is a sign of a distrust vis-à-vis the arithmetization programme. After having shown that, despite the works of Cantor, Dedekind and Weierstrass, many mathematicians at the end of the 19th Century elaborated various axiomatic theories of the magnitude, I will try to define the peculiarity of the Russellian approach. I will lay stress on the continuity of the logicist's thought on this point: Whitehead, in the Principia, deepens and generalizes the first Russellian 1903 theory. (shrink)