Los Estados confederados proyectan la existencia de un doble sistema normativo: federal y local. Esto provoca el surgimiento de colisiones y contradicciones entre ambos sistemas, lo que se pensaría debería ser resuelto por el derecho internacional, atendiendo el principio de subsidiariedad, no obstante, esto no siempre es así, ya sea porque el derecho internacional no regule ese caso concreto o bien, porque el Estado en cuestión no haya otorgado su consentimiento y la respuesta no le sea vinculante. Estas reflexiones invitan (...) a contrastar la naturaleza de las normas del derecho local y del derecho internacional, pues mientras que las primeras son asociativas, dado que no necesariamente requieren ser consentidas para ser vinculantes, las segundas, aparentemente, sí requieren el consentimiento de los Estados para que tengan efectos vinculantes. En este artículo pretendemos postular una posible solución al problema del conflicto entre los distintos órdenes normativos, partiendo desde una postura cuasi-voluntarista. Las obligaciones cuasi-voluntarias son aquellas que no surgen del consentimiento, pero tampoco completamente de los roles que tienen los Estados en el sistema internacional. Estas obligaciones nacen en el núcleo de grupos dominantes, a los que llamaremos grupos autocontenidos en el ámbito internacional, que tienen como rol la creación y socialización de las normas y obligaciones de derecho internacional, logrando que los otros grupos simplemente las sigan como si tuvieran un deber de hacerlo. Para ello, servirá como referencia el análisis del caso de las disimiles normas migratorias entre California y Texas dentro de Estados Unidos. (shrink)

The sociological work of Elias is studied, together with his characteristic outcast position, typical of judaism at the end of the century. From such judaic root stems the metapolitical approach observed in the process of civilization from the platform of a Human Genre already assume as formed and defined by the civilized conscience. The idea of a metapolitical (extraterritorial) platform is determined, and its possible historical and political efficiency. Finally, the work focuses on the limits of the civilization process, contrasting (...) N. Elias and G. Bueno conceptions on the issue. Hence a third alternative which observs such limit of history and its superation in the “antropological field” – through the a structural, technoscientific and objective development of society – springs as a source from where the “ultramoderne spirit” described at the end of the issue finds its origins. (shrink)

The philosophy of mathematical practice sometimes investigates the social constitution of mathematics but does not always make explicit the philosophical-normative framework that guides the discussion. This chapter investigates some recent proposals in the philosophy of mathematical practice that compare social facts and mathematical objects, discussing similarities and differences. An attempt will be made to identify, through a comparison with three different perspectives in social ontology, the kind of objectivity attributed to mathematical knowledge, the type of representational or non-representational semantics adopted, (...) and the justificatory or coordinative role entrusted to axiomatics. After a brief introduction to key issues in social ontology, Sect. 3 of the chapter offers a survey of contributions by Feferman, Ferreirós, and Cole, highlighting a difference between approaches based on rules, practices, and intentional states, respectively. Section 4.1 also discusses results by Carter, Collin, Giardino, and Pantsar, focusing on differences between the objectivity of knowledge and objectivity of objects and showing that many authors combine a realist, structuralist, and pragmatist perspective, as well as the idea that objectivity comes in degrees. Section 4.2 focuses on the kind of semantics that is adopted in socially oriented approaches. A representational semantics is preferred by authors grounding their views on mental states, whereas a non-representational semantics best fits with views based on practices. Section 5 considers how axiomatics can be understood in a social perspective. Axiomatics generally plays a justificatory role also in theories that aim to explain the social constitution of mathematical knowledge. Yet, if one shifts from approaches based on mental states to approaches anchored on rules or habits, axiomatics can be viewed as an institution based on obligations, functions, coordination problems, and agent’s actions and roles, thus playing an organizational and coordination role. (shrink)

The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior (...) analytics is used to distinguish between conceptions that share the same name but are substantively different: for example the search for a broader genus including all mathematical objects; the search for a common character of different species of mathematical objects; and the effort to treat magnitudes as numbers. (shrink)

Involutive Stone algebras were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of truth values, and (...) hence not only preserving the value $1$. Among other things, we prove that Six is a many-valued logic that can be determined by a finite number of matrices. Besides, we show that Six is a paraconsistent logic. Moreover, we prove that it is a genuine Logic of Formal Inconsistency with a consistency operator that can be defined in terms of the original set of connectives. Finally, we study the proof theory of Six providing a Gentzen calculus for it, which is sound and complete with respect to the logic. (shrink)

Confidentiality is a central bioethical principle governing the provider–patient relationship. Dating back to Hippocrates, new laws have interpreted it for the age of precision medicine and electronic medical records. This is where the discussion of privacy and technology often ends in the scientific health literature when Internet-related technologies have made privacy a much more complex challenge with broad psychological and clinical implications. Beyond the recognised moral duty to protect patients’ health information, clinicians should now advocate a basic right to privacy (...) as a means to safeguard psychological health. The article reviews empirical research into the functions of privacy, the implications for psychological development and the resigned sentiment taking hold regarding the ability to control personal data. The article concludes with a call for legislative, educational and research steps to readjust the equilibrium between the individual and ‘Big Data’. (shrink)

This paper tackles the question of whether the order of concepts was still a relevant aspect of scientific rigour in the 19th and 20th centuries, especially in the case of authors who were deeply influenced by the Leibnizian project of a universal characteristic. Three case studies will be taken into account: Hermann Graßmann, Giuseppe Peano and Kurt Gödel. The main claim will be that the choice of primitive concepts was not only a question of convenience in modern hypothetico-deductive investigations, but (...) sometimes also the result of philosophical investigations onto the foundation of scienti­fic disciplines. The question of the "right" order of concepts is an ideal to be followed rather than a task that can be fulfilled, but remains nonetheless an essential part of the axiomatic enterprise. This paper aims to question whether there is in fact such a stark contrast, as there is often claimed to be in the literature, between the debates relating to the right order of concepts and the foundational questions concerning modern axiomatics. The scientific rupture determined by the appearance of hypothetico-deductive systems in mathema­tics and logic should thus not be dissociated from some relevant continuities concerning the ideal of knowledge as the search for a general theory of concepts deriving from some fundamental elements. (shrink)

This paper tackles the question of whether the order of concepts was still a relevant aspect of scientific rigour in the 19th and 20th centuries, especially in the case of authors who were deeply influenced by the Leibnizian project of a universal characteristic. Three case studies will be taken into account: Hermann Graßmann, Giuseppe Peano and Kurt Gödel. The main claim will be that the choice of primitive concepts was not only a question of convenience in modern hypothetico-deductive investigations, but (...) sometimes also the result of philosophical investigations onto the foundation of scienti­fic disciplines. The question of the "right" order of concepts is an ideal to be followed rather than a task that can be fulfilled, but remains nonetheless an essential part of the axiomatic enterprise. This paper aims to question whether there is in fact such a stark contrast, as there is often claimed to be in the literature, between the debates relating to the right order of concepts and the foundational questions concerning modern axiomatics. The scientific rupture determined by the appearance of hypothetico-deductive systems in mathema­tics and logic should thus not be dissociated from some relevant continuities concerning the ideal of knowledge as the search for a general theory of concepts deriving from some fundamental elements. (shrink)

This article contributes to the literature on national varieties of socially responsible investment (SRI) by demonstrating how Scandinavian SRI developed from the 60s and onwards. Combining findings on Scandinavian SRI with insights from previous research and institutional theory, the article accounts for the role of changes in societal values and norms, the mechanisms by which SRI practices spread, and how investors adopt and transform practices to suit their surrounding institutional contexts. Especially, the article draws attention to how different categories of (...) investors act as institutional entrepreneurs during specific historical periods, and how these roles come to shift as institutional rule systems of varying societal levels change. Thus, the insights gained are useful in the future research agenda concerned with advancing knowledge on idiosyncrasies and commonalities of national SRI manifestations, and to understand the reasons underlying such characteristics. (shrink)

The question of the applicability of mathematics is an epistemological issue that was explicitly raised by Kant, and which has played different roles in the works of neo-Kantian philosophers, before becoming an essential issue in early analytic philosophy. This paper will first distinguish three main issues that are related to the application of mathematics: indispensability arguments that are aimed at justifying mathematics itself; philosophical justifications of the successful application of mathematics to scientific theories; and discussions on the application of real (...) numbers to the measurement of physical magnitudes. A refinement of this tripartition is suggested and supported by a historical investigation of the differences between Kant’s position on the problem, several neo-Kantian perspectives, early analytic philosophy, and late 19th century mathematicians. Finally, the debate on the cogency of an application constraint in the definition of real numbers is discussed in relation to a contemporary debate in neo-logicism, in order to suggest a comparison not only with Frege’s original positions, but also with the ideas of several neo-Kantian scholars, including Hölder, Cassirer, and Helmholtz. (shrink)

I argue that curiosity about the world deserves attention as a moral virtue, even apart from the role it may play in (the more generally praised) love of wisdom. First, close relationships and caring are reasonably considered part of a well-lived life, and curiosity is important for caring both about people and about things in the world. Second, curiosity helps us to define an appropriate way for persons to be affected by certain situations. Perhaps most important, curiosity can help one (...) to live well because it addresses the most fundamental existential task humans face, the need to see their lives as meaningful. I argue that curiosity is a distinctive virtue but suggest that related virtues (e.g., receptivity, reverence) may contribute to different kinds of worthy engagement with the world. (shrink)

The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) and prove for it (...) results which correspond to many major classical model theories, taken from Shoenfield [5]. In particular we prove counterparts of the theorems of o-Tarski and Chang-o-Suszko, Craig-Robinson and the Beth definability theorem. (shrink)

Background The COVID-19 pandemic has influenced the approach to the health-disease system, raising the question about the principles of bioethics present in physician–patient relations. The principles while widely accepted may not be sufficient for a comprehensive ethical analysis. Therefore, the aim of this study was to explore the perception of these principles and the physician–patient relationship during a hospital stay through a qualitative approach. Method Sixteen semi-structured interviews took place to know the patients’ perception during their 2020 hospitalization for COVID-19. (...) The data was analyzed through the constant comparison method, creating categories and comparing them. In the end, seven categories were established and were grouped in three: bioethical principles (dignity, charity, vulnerability, autonomy), doctor-patient relationship (participant commitment, informed consent, health staff-patient relationship) and the experience of the disease (illness, the role of the family). Results The research found that most patients described a positive experience, with the feeling of having been well cared for with no sense of discrimination or injustice done. The majority also reported that their autonomy was respected in the treatment decisions. The evaluation of these attitudes is an area of opportunity, especially when the patients' vulnerability is at risk. Conclusions The ethics of virtue offers a better reflection of how human beings manifest themselves by emphasizing the development of virtuous character and behaviors that allow them to realize their values in life. Authorized by the Research Ethics Committee with registration: DI/18/105-B/3/308. (shrink)

Desde la tradición de los estudios de gubernamentalidad y sus resonancias en las sociologías políticas y de la educación, en este artículo se recuperan los debates vigentes en torno a las nociones de gubernamentalidad, gobierno y biopolítica desarrolladas en la vasta obra de Michel Foucault y sus continuadoras/es para enlazarlas con las discusiones sobre el objeto de estudio y el campo teórico de la política educativa, enfatizando el potencial analítico que ofrece su grilla de inteligibilidad para los fenómenos educativos propios (...) de las sociedades posdisciplinares. En esa dirección, este trabajo esboza una serie de propuestas epistemológicas, teóricas y metodológicas producidas a partir de una investigación empírica recientemente finalizada (Aguirre, 2022), de corte descriptivo y de carácter cualitativo. En vistas a estos propósitos, se producen diálogos interdisciplinares a la vez que se tensionan y discuten algunos supuestos clásicos y tradicionales de la política educativa, para incitar una renovación analítica que posibilite el estudio de las relaciones sociales de autogobierno y gobierno de las/os otras/os en tanto articulaciones históricas entre el saber, el poder y la subjetividad. Finalmente, se exponen algunos indicios y propuestas para el abordaje sociológico de los fenómenos educativos contemporáneos, que convocan y promueven la necesidad de producir ciertos desplazamientos epistemológicos en el campo teórico de la política educativa, así como invitan a la reconfiguración de sus objetos de estudio en el marco de la adscripción a un enfoque posestructuralista. (shrink)

This article examines humanist works written in the immediate aftermath of Stefano Porcari's failed conspiracy against Pope Nicholas V. While they were designed to flatter the pope and support papal claims to temporal power, these works use images and adopt rhetorical startegies that are republican and not, as one would expect, imperial in origin. The humanists were so devoted not only to classical form, but also to Roman republican ideals that they sometimes present Porcari positively, have heroes of the Roman (...) republic comment on the modern papacy, and construct a strained theory of papal liberty. (shrink)

T echnocrati c fundamentalis m (neocons ) an d theocrati c fundamentalis m (teocons) ar e t w o manifestation s o f politica l though t v e r y restrict i v e o f democra c y . Th e f irst on e ha s a highe r incidenc e i n th e f iel d o f econo m y an d th e secon d on e i n tha t o f the (...) religion , bu t bot h imp l y a stron g challeng e fo r th e democrati c State . Thi s a r ticl e deals wit h th e mor e o r les s fo r ma l conjunctio n bet w ee n bot h kind s o f fundamentalism , that appear s an d acts , e v e n a t a globa l l e v el , a s a v e r y conse r v at i v e reactio n agains t the mai n demand s o f c i vi c laicis m an d o f pr o g ress i v e policies . Th e autho r maintain s that th e an s w e r t o thes e n e w fundamentalisms , li k e t o th e ol d d o gmatisms , i s no t a t all th e relat i vism , bu t th e critica l an d aut o critica l thought . Th e poin t i s t o ad v ance , with thi s critica l attitude , i n th e const r uctio n o f n e w democrati c fo r mulations , pr o vided wit h a mor e stron g fundamen t i n te r m s o f ethica l l e gitima c y an d socia l l e gitimation. (shrink)

In 1 Corinthians 15:35–58, Paul combats disagreement in the Corinthian church over the nature of the resurrection. Paul’s argument for the physicality of the resurrection, and his location of the individual’s resurrection within a larger transformation and restoration of all creation, changes how the contemporary church understands and teaches Christian hope, sanctification, and mission.

Supervenience is one of the 'hot discoveries' of analytic philosophy, and this collection of essays on the topic represents an examination of it and its application to major areas of philosophy. The interest in supervenience has much to do with the flexibility of the concept. To say that x supervenes on y indicates a degree of dependence without committing one to the view that x can be reduced to y. Thus supervenience is a relationship that has the potential of replacing (...) the traditional notion of dependence, while performing at least part of the function reductive relationships were supposed to fulfil. Moreover, since it is a topic-neutral concept, supervenience has a wide range of applicability. (shrink)

Cause and effect relationships play a central role in how we perceive and make sense of the world around us, how we act upon it, and ultimately, how we understand ourselves. Almost two decades ago, computer scientist Judea Pearl made a breakthrough in understanding causality by discovering and systematically studying the “Ladder of Causation” [Pearl and Mackenzie 2018], a framework that highlights the distinct roles of seeing, doing, and imagining. In honor of this landmark discovery, we name this the Pearl (...) Causal Hierarchy (PCH). In this chapter, we develop a novel and comprehensive treatment of the PCH through two complementary lenses, one logical-probabilistic and another inferential-graphical. Following Pearl’s own presentation of the hierarchy, we begin by showing how the PCH organically emerges from a well-specified collection of causal mechanisms (a structural causal model, or SCM). We then turn to the logical lens. Our first result, the Causal Hierarchy Theorem (CHT), demonstrates that the three layers of the hierarchy almost always separate in a measure theoretic sense. Roughly speaking, the CHT says that data at one layer virtually always underdetermines information at higher layers. Since in most practical settings the scientist does not have access to the precise form of the underlying causal mechanisms – only to data generated by them with respect to some of PCH’s layers – this motivates us to study inferences within the PCH through the graphical lens. Specifically, we explore a set of methods known as causal inference that enable inferences bridging PCH’s layers given a partial specification of the SCM. For instance, one may want to infer what would happen had an intervention been performed in the environment (second-layer statement) when only passive observations (first-layer data) are available. We introduce a family of graphical models that allows the scientist to represent such a partial specification of the SCM in a cognitively meaningful and parsimonious way. Finally, we investigate an inferential system known as docalculus, showing how it can be sufficient, and in many cases necessary, to allow inferences across PCH’s layers. We believe that connecting with the essential dimensions of human experience as delineated by the PCH is a critical step towards creating the next generation of AI systems that will be safe, robust, human-compatible, and aligned with the social good. (shrink)

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between P and , is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of (...) contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively . I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between P and (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory. (shrink)

We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. 18 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when (...) [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text]. (shrink)

The turn of the last century was a key transitional period for the development of symbolic logic and scientific philosophy. The Peano school, the editorial board of the Revue de Métaphysique et de Morale, and the members of the Vienna Circle are generally mentioned as champions of this transformation of the role of logic in mathematics and in the sciences. The articles contained in this volume aim to contribute to a richer historical and philosophical understanding of these groups and research (...) areas in Italy, France and Austria. Specifically, the contributions focus on the following topics: a detailed investigation of the relation between structuralism and modern mathematics; different notions of definition and interpretation at the turn of last century; a closer understanding of the relation between the Vienna Circle, the Peano School and French philosophy in the first half of the twentieth century. (shrink)

Recent years have featured the existence of a variety of structuralisms, with an important partition between methodological versus philosophical structuralism. Inside philosophical structuralism, many trends can be identified, corresponding to various ontological stances. We argue here that another main partition has contributed to organize structuralism in the twentieth century, rooted in different technical and theoretical interests. This partition is largely transversal to the ones classically identified. Concretely, the paper will focus on possible differences between an arithmetical and logical notion of (...) structure that can be traced back to the writings of Bertrand Russell and Rudolf Carnap, and a mathematical notion of structure, exemplified in the works by Bourbaki. This coexistence gives rise to a fundamental ambiguity that affects contemporary structuralism. Philosophically, in one case the attention is rather centered on a foundational and reductionist perspective, as featured by the Whitehead-Russell Principia and the Carnapian project of the Aufbau: the scientific construction of the world around the idea of structure. In the other, the focus is on epistemological and dynamical issues, as exemplified by two key issues in Bourbaki’s treatise: understanding the architecture of mathematics, offering a tool-kit to mathematicians. These two distinct meanings still coexist inside contemporary scientific practices and lead to different theoretical interests, as we will show thanks to various recent examples. (shrink)

Giuseppe Veronese (1854-1917) est connu pour ses études sur les espaces à plusieurs dimensions ; moins connus sont les écrits « philosophiques », qui concernent les fondements de la géométrie et des mathématiques et qui expliquent les raisons pour la construction d’une géométrie non-archimédienne (une dizaine d’années avant David Hilbert) et la formulation d’un concept de continu, qui contient des éléments infinis et infiniment petits. L’article esquissera quelques traits saillants de son épistémologie et analysera le rapport entre géométrie et intuition (...) spatiale, en comparant les conceptions de l’espace géométrique dans les œuvres de Veronese, Helmholtz et Poincaré. Selon Veronese l’espace intuitif, de même que l’espace géométrique, n’est pas euclidien et il n’a pas un nombre déterminé de dimensions : on peut donc avoir l’intuition aussi bien d’un espace à quatre dimensions que d’un continu non-archimédien. (shrink)

"The Third Edition of Philosophical Foundations of Adult Education presents seven theoretical approaches to adult education: liberal, progressive, behaviorist, humanist, radical/critical, analytic, and postmodem. The book gives the historical grounding as well as the basic principles for each approach. In this edition each chapter has been revised and brought up to date. The chapter on radical adult education incorporates recent developments in radical education, phenomenology, feminist educational theory, and critical social theory. The book contains an entirely new chapter on postmodem (...) adult education.". (shrink)

The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity conditions required (...) by the modern version of the theory of proportions. Secondly, Grassmann’s conception of mathematical knowledge will be investigated. Parting from the traditional definition of mathematics as a science of magnitudes, Grassmann considered mathematical forms as particulars rather than universals: the classification of the branches of mathematics was thus based on different operational rules, rather than on empirical criteria of abstraction or on the distinction of different species belonging to a common genus. It will be argued that a different notion of generalization is thus involved, and that the knowledge of mathematical forms relies on the understanding of the rules of generation of the forms themselves. Finally, the paper will analyse if Grassmann’s approach in the first edition of the Ausdehnungslehre should be explained in terms of the notion of purity of method, and if it clashes with Grassmann’s later conventionalism. Although in the second edition the features of the operations are chosen by convention, as it is the case for the anti-commutative property of the multiplication, the choice is oriented by our understanding of the resulting forms: a simplification in the algebraic calculus need not correspond to a simplification in the ‘dimensional’ interpretation of the result of the multiplicative operation. (shrink)

Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct, off a small definable subset, that is, a definable set internal to (...) the predicate. For certain dense pairs of geometric topological fields without the independence property, whenever the underlying set of a definable group is contained in the dense-codense predicate, the group law is locally definable in the reduct as a geometric topological field. If the reduct has elimination of imaginaries, we extend this result, up to interdefinability, to all groups internal to the predicate. (shrink)

Originally published in 1985, this is a short meditation by a great old man on people relating to other people who are dying, and the need for all of us to open ...

Giuseppe Veronese (1854-1917) est connu pour ses études sur les espaces à plusieurs dimensions ; moins connus sont les écrits « philosophiques », qui concernent les fondements de la géométrie et des mathématiques et qui expliquent les raisons pour la construction d’une géométrie non-archimédienne (une dizaine d’années avant David Hilbert) et la formulation d’un concept de continu, qui contient des éléments infinis et infiniment petits. L’article esquissera quelques traits saillants de son épistémologie et analysera le rapport entre géométrie et intuition (...) spatiale, en comparant les conceptions de l’espace géométrique dans les œuvres de Veronese, Helmholtz et Poincaré. Selon Veronese l’espace intuitif, de même que l’espace géométrique, n’est pas euclidien et il n’a pas un nombre déterminé de dimensions : on peut donc avoir l’intuition aussi bien d’un espace à quatre dimensions que d’un continu non-archimédien. (shrink)

In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in -definable groups — which are examples of locally definable spaces. We show that the various concepts of connectedness associated (...) to these groups, which have appeared in the literature, are non-equivalent. (shrink)

The paper advocates an epistemological interpretation of the Peano School axiomatics. The construction of axiom systems is presented as a cognitive enterprise unveiling the internal dynamics, evolution, and architecture of axiomatic systems as well as connections to applications. This approach reveals that the study of the relation between axioms and theorems not only serves to reduce a theory to a minimum number of principles and increase the certainty or justification of the latter, but also to study alternative settings of a (...) given mathematical theory. The paper explains why the Peanian conception of axiomatics differs from axiomatic deductivism, if-thenism and scientific deductivism, and analyzes Peano’s conception of rigor. The paper also postulates that Peano had a set-theoretic but also an algorithmic conception of function, and prioritized functions over relations. Two seemingly contradictory aspects of Peano’s axiomatics, global and local reasoning, are illustrated through the examples of rigor and simplicity. Finally, the paper claims that Peano’s axiomatics was a dynamic mathematical enterprise rather than an a priori axiomatization grounded on logical principles, which explains the difference with respect to Frege’s project. (shrink)

On March 8, 1987, the Sandinista Liberation Front published its statement on the relation of women's struggles to the Nicaraguan revolution. The author argues that this official statement is consistent with the views of modern feminists on some key points relating to the need to eliminate women's double day, promote women's self-organization, and wage an ideological struggle against sexism if women's subordination is to be eliminated. The author believes that the Sandinista Front's emphasis on ideological struggle and political organization represents (...) an important break with more economistic, orthodox Marxist approaches to analyzing the condition of women and has important implications for Marxist feminism. (shrink)

Deux courants de pensée jouent un rôle important dans la philosophie des mathématiques contemporaine. Le structuralisme, s’il n’est pas une idée nouvelle, continue de se déployer en des directions multiples – de la pratique mathématique jusqu’à ses dimensions ontologiques –, et de faire l’objet d’études, par exemple en direction des modalités de sa genèse. L’épistémologie historique, dont la conception classique a été largement enrichie récemment, est également au cœur de débats qui renouvellent la philosophie des sciences bien au-delà de ses (...) problématiques classiques. Son usage en mathématiques requiert toutefois des analyses spécifiques du fait de leurs idiosyncrasies, des notions comme celle de rigueur, d’expérience ou d’ontologie y ayant un sens et une charge historique différentes de celles qu’elles ont dans les sciences de la nature. Le propos de cet article sera de mettre en situation certains de ces débats en se concentrant sur un des phénomènes les plus significatifs du xxe siècle mathématique: le structuralisme de Bourbaki. Il s’intéressera en particulier aux potentialités de l’épistémologie historique, en cherchant à montrer que ses outils permettent de mieux comprendre certains enjeux du structuralisme. L’accent sera mis en particulier sur deux notions clés dans les travaux de Rheinberger, Daston et Hacking, celles d’objets et de concepts épistémiques. (shrink)

In Crull it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky, is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in (...) quantum mechanics, such as the measurement problem or the emergence of classicality. (shrink)

The Consistent Histories (CH) formalism aims at a quantum mechanical framework which could be applied even to the universe as a whole. CH stresses the importance of histories for quantum mechanics, as opposed to measurements, and maintains that a satisfactory formulation of quantum mechanics allows one to assign probabilities to alternative histories of a quantum system. It further proposes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account, but that (...) different realms can be mutually incompatible. Finally, some of its proponents offer an “evolutionary” explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work questions the validity of claims offered by CH proponents asserting that it solves many interpretational problems in quantum mechanics. In particular, we point out that the interpretation of the framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. Our claim is that by doing so, CH overlooks the main interpretational problems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality. (shrink)