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)

Recordando a Bachelard a medio siglo de su muerte (2011) -- Filosofia de la relatividad (2011) -- La proliferación de los conceptos de especie en la biología evolucionista (2010).

Volume 19, Issue 9, September 2019, Page 37-39.

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)

A critical survey of the main philosophical theories about events and event talk, organized in three main sections: (i) Events and Other Categories (Events vs. Objects; Events vs. Facts; Events vs. Properties; Events vs. Times); (ii) Types of Events (Activities, Accomplishments, Achievements, and States; Static and Dynamic Events; Actions and Bodily Movements; Mental and Physical Events; Negative Events); (iii) Existence, Identity, and Indeterminacy.

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)

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)

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)

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.

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 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)

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 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)

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)

Roberto Esposito is one of the most prolific and important exponents of contemporary Italian political theory.

This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as (...) a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics. (shrink)

1 The epistemology of Otto Hölder This special issue is devoted to the philosophical ideas developed by Otto Hölder (1859-1937), a mathematician who made important contributions to analytic functions and group theory. Hölder’s substantial work on the foundations of mathematics and the general philosophical conception outlined in this work are, however, still largely unknown. Up to the present, philosophical interest in Hölder’s work has been limited to his axiomatic formulation of a theory of..

Peano’s axioms for arithmetic, published in 1889, are ubiquitously cited in writings on modern axiomatics, and his Formulario is often quoted as the precursor of Russell’s Principia Mathematica. Yet, a comprehensive historical and philosophical evaluation of the contributions of the Peano School to mathematics, logic, and the foundation of mathematics remains to be made. In line with increased interest in the philosophy of mathematics for the investigation of mathematical practices, this them...

Peano’s axioms for arithmetic, published in 1889, are ubiquitously cited in writings on modern axiomatics, and his Formulario is often quoted as the precursor of Russell’s Principia Mathematica. Yet, a comprehensive historical and philosophical evaluation of the contributions of the Peano School to mathematics, logic, and the foundation of mathematics remains to be made. In line with increased interest in the philosophy of mathematics for the investigation of mathematical practices, this them...

Two views of Plato’s politics in the Republic predominate in the literature. Political organicism is the view that the polis is an organism and implies that individual happiness is defined by an individual’s contribution to the polis’s good. Individualism is the view that the polis is reducible to individuals, which implies that the polis’s good is nothing but individual happiness aggregated. This article develops a middle-of-the-road view called weak organicism, which qualifies Plato’s organicism and includes a Platonic account of the (...) mereological relations of the polis. These relations imply that individuals as such are not structurally dependent on the whole polis, thereby making conceptual space for Plato’s expressly stated thesis that the polis’s good is over and above individual happiness without necessarily implying that individual happiness is reducible to the polis’s good, which the literature generally supposes to be a corollary of political organicism. (shrink)

This book provides a collection of chapters on the development of scientific philosophy and symbolic logic in the early twentieth century. 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 scholarship contained provides a rich historical and philosophical understanding of these groups and research areas. Specifically, the contributions focus on a detailed investigation of the relation between structuralism and modern mathematics. In addition, this book provides a closer understanding of the relation between symbolic logic and previous traditions such as syllogistics. This volume also informs the reader on the relation between logic, the history and didactics in the Peano School. This edition appeals to students and researchers working in the history of philosophy and of logic, philosophy of science, as well as to researchers on the Vienna Circle and the Peano School. (shrink)

Oxford: Oxford University Press 2011, x + 245 pp. £44.00 (hardcover). ISBN 978-0-19-960620-7.

In this article Roberto Balzani, the mayor of Forlì, remembers Roberto Ruffilli, 25 years after his murder. The remembrance reconstructs the steps of his academic career and of his political commitment. Ruffilli graduated at the Catholic University of Milan; his researches in contemporary history placed him in an original position if compared with the Italian studies of the time. The constant attention towards the history of administration and the transformations of the state is the basis on which Ruffilli (...) built his proposals concerning the reform of the insitutional and political system. Balzani concludes the article by affirming that the problems of today aren't any different, that is why Ruffilli's proposals still demonstrate their modernity. (shrink)

According to a leading view, emotions such as admiration, contempt, pride, and shame are important vehicles of agential development. Through admiration and contempt, we establish models and countermodels against which to shape our character; through pride and shame, we get a sense of how we measure up to them. Critics of this view object that these emotions always deliver uncompromising evaluations: admiration casts people in a completely positive light, while contempt casts aspersion on them. Therefore, insofar as they lack the (...) capacity for nuance, these emotions are systematically unfitting and misleading. This paper discusses this objection as originally formulated by John Doris as well as Macalester Bell’s response. Drawing from research on emotional intentionality, it will be argued that Doris’ and Bell’s accounts are respectively misguided criticisms and inadequate defences of these emotions. Their mistake lies in an invalid transition from the claim that these emotions are intentionally directed towards persons to the claim that they deliver global evaluations of those towards whom they are directed. By rejecting this inference, it will be shown that these emotions can deliver nuanced and fitting evaluations in a way Doris’ objection overlooks and Bell’s response precludes us from articulating. (shrink)

This book by Roberto Esposito - a leading Italian political philosopher - is a highly original exploration of the relationship between human bodies and societies. The original function of law, even before it was codified, was to preserve peaceful cohabitation between people who were exposed to the risk of destructive conflict. Just as the human body's immune system protects the organism from deadly incursions by viruses and other threats, law also ensures the survival of the community in a life-threatening (...) situation. It protects and prolongs life. But the function of law as a form of immunization points to a more disturbing consideration. Like the individual body, the collective body can be immunized from the perceived danger only by allowing a little of what threatens it to enter its protective boundaries. This means that in order to escape the clutches of death, life is forced to incorporate within itself the lethal principle. Starting from this reflection on the nature of immunization, Esposito offers a wide-ranging analysis of contemporary biopolitics. Never more than at present has the demand for immunization come to characterize all aspects of our existence. The more we feel at risk of being infiltrated and infected by foreign elements, the more the life of the individual and society closes off within its protective boundaries, forcing us to choose between a self-destructive outcome and a more radical alternative based on a new conception of community. (shrink)

Neste artigo, temos como objetivo perscrutar o funcionamento da verbo-visualidade de uma perspectiva dialógica do discurso, utilizando, como material de análise, uma videomontagem humorística acerca do ator político Dilma Rousseff, durante a campanha presidencial brasileira do ano de 2010. Primeiramente, procuramos refletir acerca de alguns pressupostos teórico-metodológicos de Bakhtin e de Brait, qual seja, o de verbo-visualidade, alicerçado na concepção bakhtiniana de linguagem. Em um segundo momento, detivemo-nos na análise do texto objeto do artigo, que se pautou na seguinte indagação: (...) como contribuem e funcionam os elementos verbais e visuais para produção e direcionamento de sentidos na videomontagem? Nossa hipótese é a de que os discursos carregados pela montagem criam uma trilha ideológica de sentido que leva os interlocutores a interpretar a então candidata como uma pessoa sem discurso, manipulável. Diante do exposto, tentaremos demonstrar a hipótese que sustentamos. (shrink)

This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent calculi (...) for S*fde, dS*fde, crossS*fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar, Hallden, Deutsch and Daniels, we provide a general recipe to define containment logics, we explore the single-premise/single-conclusion fragment of S*fde, dS*fde, crossS*fdeand the connections between crossS*fde and the logic Eq of equality by Epstein. Also, we present S*fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley, and we briefly examine three further systems that are closely related to our main logics. Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues. (shrink)

As the worlds of economics, politics, culture, and communications face a growing wave of globalization that will likely continue, ethical challenges for journalists have also gone global. I propose a clear division between ethics codes for media owners, the public, and professional journalists and present a set of considerations and specific rules applicable only to the last group. In this article I advocate a universal code of journalistic ethics but point out problems and warn against dangers that have made the (...) application of such codes difficult in the past. A universal code should consider the voluntary nature of such an endeavor, the cultural and economic differences in various journalistic traditions, and the problem of producing solutions acceptable to all involved. (shrink)

Comparative study of the knowledge of IVF in medical students of universities with different ethical and humanistic valuesEstudo comparativo do conhecimento das técnicas de reprodução assistida em estudantes de Medicina de universidades com diferentes ideários éticos e humanísticosIn vitro fertilization continues to be presented as a relatively simple solution to produce a pregnancy without exposing the medical and ethical problems that this represents. This project consisted of conducting a survey to medical students from three medical schools in Mexico City with (...) different ethical and humanistic ideas with the aim of evaluating knowledge about IVF techniques and their ethical implications. The survey was applied to 404 medical students. Students in schools with personalistic ethics had a greater recognition of the bioethical principles involved in the use of these techniques. Knowledge of the technique and ethical issues involved in assisted reproduction could improve the sensitivity of medical students to ethical dilemmas that arise in their professional practice.Para citar este artículo / To reference this article / Para citar este artigoCantú-Quintanilla G, Vidal-Sentíes C, Marcó-Bach FJ, Camargo-Prieto F, Aguiñaga-Chiñas N, Contreras-Estrada D. Estudio comparativo del conocimiento de las técnicas de reproducción asistida en estudiantes de medicina de universidades con diferentes idearios éticos y humanísticos. Pers Bioet. 2020;24:166-176. DOI: https://doi.org/10.5294/pebi.2020.24.2.4Recibido: 04/09/2019Aceptado: 05/08/2020Publicado: 27/11/2020. (shrink)

L’article a pour but d’analyser la conception de la géométrie et de la mesure présentée dans Intuition et Raisonnement [Hölder 1900], « Les axiomes de la grandeur et la théorie de la mensuration » [Hölder 1901] et La Méthode mathématique [Hölder 1924]. L’article examine les relations entre a) la démarcation introduite par Hölder entre géométrie et arithmétique à partir de la notion de ‘concept donné’, b) sa position philosophique par rapport à l’apriorisme kantien et à l’empirisme et c) le choix (...) du postulat de la continuité de Dedekind parmi les axiomes de la théorie des grandeurs. L’article montre que les choix faits au niveau axiomatique sont reliés au cadre épistémologique et que l’originalité de Hölder consiste surtout dans son analyse au cas par cas des procédures déductives en mathématiques.The aim of the paper is to analyze Hölder’s understanding of geometry and measurement presented in Intuition and Reasoning [Hölder 1900], “The Axioms of Quantity and the Theory of Measurement” [Hölder 1901], and The Mathematical Method [Hölder 1924]. The paper explores the relations between a) Hölder’s demarcation of geometry from arithmetic based on the notion of given concepts, b) his philosophical stance towards Kantian apriorism and empiricism, and c) the choice of Dedekind’s continuity in the axiomatic formulation of the theory of magnitudes. The paper shows that the choices made at the axiomatic level reflect Hölder’s epistemological framework, and individuates the originality of his approach in the case by case analysis of deductive procedures. (shrink)

L’article a pour but d’analyser la conception de la géométrie et de la mesure présentée dans Intuition et Raisonnement [Hölder 1900], « Les axiomes de la grandeur et la théorie de la mensuration » [Hölder 1901] et La Méthode mathématique [Hölder 1924]. L’article examine les relations entre a) la démarcation introduite par Hölder entre géométrie et arithmétique à partir de la notion de ‘concept donné’, b) sa position philosophique par rapport à l’apriorisme kantien et à l’empirisme et c) le choix (...) du postulat de la continuité de Dedekind parmi les axiomes de la théorie des grandeurs. L’article montre que les choix faits au niveau axiomatique sont reliés au cadre épistémologique et que l’originalité de Hölder consiste surtout dans son analyse au cas par cas des procédures déductives en mathématiques. (shrink)