This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a worskhop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical (...) conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio Leòn-Sànchez and Ana Leòn-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro. (shrink)

Este artículo explora el concepto de trauma colectivo y su aplicación en el contexto histórico y social de las sociedades latinoamericanas. La transferencia del término «trauma colectivo» desde el campo del conocimiento psicológico a la esfera social e histórica plantea preguntas sobre su legitimidad y marco conceptual. El estudio examina la fidelidad de esta transferencia conceptual y su relación con la comprensión psicoanalítica temprana de los fenómenos traumáticos. El contexto cultural europeo de finales del siglo xix y principios del (...) siglo xx proporcionó la base para teorizar las consecuencias de experiencias intensas y violentas, lo que resultó en el concepto de «neurosis traumática», influenciado significativamente por el trabajo de Freud. El artículo discute la apropiación de herramientas psicoanalíticas en la crítica histórica y cultural para comprender eventos que desafían marcos tradicionales y la inteligibilidad social, como el Holocausto. La noción del trauma como una fuerza enigmática y recurrente en la experiencia histórica se explora a través del enfoque de los estudios del trauma. El artículo pone de relieve a destacados y destacadas académicas en este campo y su uso de conceptos psicoanalíticos, demostrando la preservación y aplicación significativa de estas nociones en la comprensión de fenómenos históricos y colectivos. Al acortar la brecha entre las experiencias psicológicas individuales y los traumas colectivos, los estudios del trauma ofrecen un enfoque único para interpretar y representar eventos que resisten las narrativas históricas tradicionales. (shrink)

The objective of this work was to construct and validate an instrument for assessing resilience to suicide attempts in a Spanish clinical population that has made a previous attempt, and to verify its efficacy for predicting future suicide reattempts at 6 months. For the construction of a Scale of Resilience to Suicide Attempts the theoretical-rational strategy was used. The constructed SRSA-18 consisted of 18 items and 3 subdimensions, had high internal consistency and a high positive correlation with the Suicide Resilience (...) Inventory-25, SRI-25, and to a lesser extent with general resilience scales such as the Connor-Davidson Resilience Scale, CD-RISC and the Resilience Scale of 14 items, RS-14. Additionally, a specific SRSA-18 score predicted future suicide reattempts 6 months after the first attempt. This new scale assesses in a brief and rapid way, through protective factors rather than risk factors, the level of resilience to the suicide attempt in specific clinical subpopulations in hospital emergency services, being able to prevent suicide reattempts with higher lethality. (shrink)

La crisis sanitaria mundial ha propiciado un fecundo debate iusfilosófico en lo referente a la protección de los derechos humanos. El nuevo escenario exige respuestas nuevas por parte de la filosofía del derecho. En este trabajo se somete a crítica la teoría del garantismo constitucional de Luigi Ferrajoli, cuestionándose su idoneidad como marco de referencia para afrontar los mencionados desafíos. La crítica se centra en la concepción ferrajoliana de la democracia y en su proyección cosmopolita. Se argumentará que la (...) extensión del constitucionalismo más allá del Estado debe realizarse a partir de un cosmopolitismo gradual y realista. (shrink)

El objetivo de este trabajo es analizar la percepción que tienen los estudiantes en su primer año universitario sobre la enseñanza de competencias de pensamiento histórico en Bachillerato. El estudio se basa en los recuerdos de los estudiantes en relación con las competencias de pensamiento histórico trabajadas en el instituto en las clases de las asignaturas de Historia. Los objetivos específicos son dos. Primero, conocer con qué frecuencia recuerdan que se enseñaban competencias de pensamiento histórico en las clases de Historia. (...) Segundo, saber su opinión sobre la relevancia de estas competencias para la enseñanza de la historia. La metodología empleada es cuantitativa basada en el análisis de medidas de tendencia central, a partir de los datos extraídos de un cuestionario semiestructurado denominado CUPECH. La muestra no probabilística está formada por 264 estudiantes de primer curso de las universidades de Murcia, León, Granada y Valencia. Para los estudiantes, la competencia de identificación de causas y consecuencias fue la que más trabajaron en las clases de Historia y la que valoran como más relevante para la enseñanza de esta disciplina. Por el contrario, la dimensión ética o el análisis y contraste de fuentes fueron las menos trabajadas. Por tanto, se concluye que es necesario reforzar el trabajo de competencias históricas en la etapa educativa de Bachillerato para mejorar el pensamiento histórico del alumnado. (shrink)

O presente artigo trata da influência exercida pela filosofia kantiana na actualidade a partir da chamada crise da Modernidade ilustrada. Os autores começam por analisar o posicionamento original kantiano, incidindo especialmente na sua concepção do criticismo e do transcendentalismo. Esta análise é feita a partir da perspectiva da aberta pela Kritik der Urteilskraft enquanto marco do sistema da razão, capaz de incorporar a finitude da mesma. Seguidamente são analisadas a recepção e a transformação do pensamento kantiano a partir de (...) duas correntes filosóficas actuais: o Racionalismo Crítico de Karl Popper e Hans Albert, e a Pragmática Transcendental da linguagem de KarlOtto Apel. Em ambos os casos se compara o seu modo próprio de incorporar as noções de crítica e transcendentalidade com a concepção original de Kant. (shrink)

De un tiempo a esta parte, siguen surgiendo una gran cantidad de estudios científicos de notoria calidad dedicados a la recuperación y el análisis de la vida y obra de un buen número de mujeres que destacaron en los campos de la ciencia o el arte. Así, por distintos motivos, parecían haber sido olvidadas o relegadas a un segundo plano, una omisión que, tristemente, se ha perpetuado con el paso de los años...

La ciudadanía y lo político. Ciudadanía y crisis de la democracia liberal en un mundo en transformación es un texto provocador, que desafía directamente a las esferas de poder económico, político y social en el marco de la corrupción. Deja al descubierto las entrañas cancerígenas de una política enferma de poder, donde priman los intereses particulares o políticos sobre los intereses del pueblo. El libro es una lanza que atraviesa las profundidades que erosionan nuestra sociedad, realizando así un análisis (...) riguroso desde distintas aristas, que tienen un elemento común: la corrupción política. A lo largo de las páginas se ofrece un enorme panorama sobre el papel de la ciudadanía dentro de la sociedad, que reclama a gritos una revolución desalienante frente a la cleptoestructura. Es así como, el papel de la ciudadanía es el centro de la reflexión analítica que nos presenta Joan Lara Amat y León. (shrink)

A la luz de algunas críticas recientes, en el marco de este texto se busca impulsar un debate que tiene lugar en dos frentes: por una parte, la lógica del origen de la lógica y, por otra parte, la relación entre psicoanálisis y marxismo. Para ello se recuperan algunos textos publicados por Alain Badiou hacia finales de la década de 1960, en los que polemiza con Jacques-Alain Miller alrededor de los concepto de "sutura" y "sujeto" (Zizek), para situar tanto (...) las diversas posiciones como las coherentes reconsideraciones a lo largo de su trayectoria intelectual. En efecto, desde "El concepto de modelo" hasta su más reciente trilogía (Teoría del sujeto, El ser y el acontecimiento y Lógica de los Mundos), se propone una perspectiva que lejos de establecer jerarquías y subordinaciones busca promover conexiones a partir de las especificidades y las diferencias a través de esa vía particular que es la filosofía. De este modo resulta posible apreciar que, pese a su crítica respecto de la primacía de la lógica del significante, los conceptos propuestos por Jacques Lacan funcionaron como una notoria fuente de inspiración para Badiou, especialmente en relación con el sujeto del inconsciente. (shrink)

Este trabajo comienza ofreciendo, a modo de «status quaestionis», una panorámica de la atención que se ha prestado a la obra ensayística de Sánchez Ferlosio, desde las lecturas propuestas en los años noventa del siglo pasado por autores del círculo de nuestro autor hasta los estudios y artículos aparecidos tras su muerte, en 2019. A continuación, se presentan algunas aportaciones relevantes de Ferlosio al pensamiento contemporáneo. Concretamente, se analiza el «aprecio por lo perecedero» como uno de estas aportaciones y, además, (...) se explica cómo este aprecio surge en el marco de una «actitud reflexiva ante el lenguaje». Por último, se procede a un balance crítico de las posiciones de Sánchez Ferlosio con respecto a los asuntos mencionados. (shrink)

Greek ancient and early modern geometry necessarily uses diagrams. Among other things, these enter geometrical analysis. The paper distinguishes two sorts of geometrical analysis and shows that in one of them, dubbed “intra-confgurational” analysis, some diagrams necessarily enter as outcomes of a purely material gesture, namely not as result of a codifed constructive procedure, but as result of a free-hand drawing.

Bajo el título "La época de lo social y otros escritos sobre Política y Seguridad Social", se recogen en este volumen doce importantes ensayos de Antonio Perpiñá, publicados entre los años 1946 y 1980, todos ellos a propósito del devenir histórico de la política social y la formación de las instituciones de derecho público que fueron asumiendo en el pasado siglo la doble función de previsión y protección social, desde el Instituto Nacional de Previsión (INP) de 1908 al desarrollo (...) del sistema estatal de la Seguridad Social tras la Ley de Bases de 1963. Precede a estos artículos un extenso estudio preliminar dedicado a la presentación biográfico-intelectual del autor y su papel en el proceso de institucionalización académica en España tanto de la Sociología como disciplina específica, como de la teoría de la Política y de la Seguridad Social, temas todos ellos a los que el autor madrileño dedicó numerosos e importantes estudios, muy celebrados además en su momento. Con esta edición se superan treinta años de olvido de quien cumplió un papel sin duda importante en el desarrollo de la sociología hecha en España durante el siglo XX, primer catedrático de Sociología General del Instituto Social León XIII (UPSA), por cuyas aulas pasaron buena parte de los máximos exponentes de la sociología científica de aquellos años y posteriores: Salustiano del Campo, José Castillo, J. Díez Nicolás, A. Ortí Benlloch, Jesús Mª Vázquez, F. Sánchez López, Carmelo Lisón, M. Martín Serrano, J. Jiménez Blanco, J. M. López Cepero, M. Lizcano, Carlos Ollero, J. J. Toharia, etc. Cierra el libro un elenco bibliográfico exhaustivo con el conjunto de su obra, también elaborado por el editor. Recopilación antológica de ensayos sobre teoría de la Política Social y de la Seguridad Social del iuspublicista y sociólogo español Antonio Perpiñá Rodríguez (1910-1984). Edición, Estudio Preliminar, Bibliografía y notas: Juan C. Valderrama. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Formal Technique and Epithalamial Setting in the Song of the Parcae (Catullus 64.305–22, 328–36, 372–80)Marcos Ruiz SánchezThe present study aims to analyze the technique of verbal reminiscences and the structure of the frame of the song of the Parcae, one of the most important sections in poem 64 and the most controversial in meaning, together with the implications these verbal echoes have for the meaning of the text.Catullus’ poem (...) 64 was undoubtedly conceived by the author himself as his masterpiece and it appears as such in the very centre of the collection. We know from poem 95 that Cinna, Catullus’ poet friend and companion on his journey to the East, took nine years to write a similar poem, the epyllion entitled Zmyrna. Cinna’s work was famous for its obscurity, but also poem 35 mentions the time spent by another poet from Catullus’ circle of friends in writing a poem on the Magna Mater. Both references reveal the meticulousness (the labor limae) with which the neoteric poets composed their most important works.This explains the reason for the compositional virtuosity that can frequently be discovered in poem 64. An example of this is the repeated use of verbal reminiscences throughout the poem. 1 For the author this procedure serves various purposes: to provide a frame for the descriptive sections or direct speech; to link the different events by underlining the causal relations between them; to confer a symbolic nature on the text, and so forth. Before we turn to the introduction of the Parcae and their song, which is the main focus of this paper, it will be useful to illustrate Catullus’ technique of simultaneous ring composition and forward [End Page 75] cross-reference through verbal echoes from verses 112–15. This one case and its allusive network may serve as an example, among many, of this compositional virtuosity of Catullus. When he describes the hero Theseus emerging from the labyrinth after slaying the Minotaur, he does so in the following terms:inde pedem sospes multa cum laude reflexit errabunda regens tenui vestigia filo, ne labyrintheis e flexibus egredientem tecti frustraretur inobservabilis error.(64.112–15)These verses are an echo, after the elaborated Homeric simile used by the author to refer to the death of the monster, of those in which Catullus previously described the fears of Ariadne enamoured by Theseus’ fortune:cum saevum cupiens contra contendere monstrum aut mortem appeteret Theseus aut praemia laudis! non ingrata tamen frustra munuscula divis promittens tacito succepit vota labello.2 (64.101–4)In both cases the narration centres on the favours granted Theseus by Ariadne: in the first with the supplications she directs to the gods; in the second with the gift of the ball of thread which enables the hero to escape from the labyrinth.It is not difficult to discover a closer relation between the two passages. In the first, Theseus wishes to fight the monster: cum saevum cupiens contra contendere monstrum /... Theseus. The expectation thus raised with regard to possible narratives is answered in verse 110, which evokes the previous verse: sic domito saevum postravit corpore Theseus.The hero wishes for death or glory: 3 aut mortem appeteret Theseus [End Page 76] aut praemia laudis This verse is taken up later in the following passage: inde pedem sospes multa cum laude reflexit (64.112). If Theseus wished for death or the reward of glory, Ariadne’s help enabled him to avoid one and achieve the other. The reappearance of the term frustra (102) in the verb frustraretur (115) stresses the heroine’s intervention. 4In verses 112–15 we find, moreover, the stylistic recourse of etymologically related words that had been used by the poet in the previous simile (indomitus turbo, 107; exturbata, 108; domito, 110). Reflexit (112) and errabunda vestigia (113) are echoed again in labyrintheis flexibus (114) and inobservabilis error (115), such that the verses are ordered as follows: A (112), B (113), A′ (114), B′ (115).The repetitions stress the difficulty in returning and the importance of Ariadne’s help. Theseus’ life depends on the tenuous thread that governs his steps. Reflexit and flexibus emphasize the tortuousness... (shrink)

Faith-based organizations are a key player in major sectors of activity for maintaining the welfare state, including health, education, and social services. This paper uses a multivariate regression model in an attempt to identify the factors that affect the relationship between work engagement and flourishing. The paper also discusses the empirical research gap that has been identified in the literature about the moderated effect of human values on this relationship. This study is based on a sample of 142 nuns of (...) a congregation belonging to a religious organization with an international scope and a Catholic inspiration. The case of religious women who have chosen to live a life consistent with the charism of the congregation constitutes a paradigmatic and unique environment to investigate the potential alignment of personal values with professional activity. Two important conclusions are derived from this work. First, the more engaged nuns are in their work (social action to serve the poorest and most disadvantaged people), the more they flourish in their working environment and in their personal lives. Second, certain personal values reinforce the relationship between the professional role (work engagement) and the personal role (flourishing). (shrink)

AI research is being challenged with ensuring that autonomous agents learn to behave ethically, namely in alignment with moral values. Here, we propose a novel way of tackling the value alignment problem as a two-step process. The first step consists on formalising moral values and value aligned behaviour based on philosophical foundations. Our formalisation is compatible with the framework of (Multi-Objective) Reinforcement Learning, to ease the handling of an agent’s individual and ethical objectives. The second step consists in designing an (...) environment wherein an agent learns to behave ethically while pursuing its individual objective. We leverage on our theoretical results to introduce an algorithm that automates our two-step approach. In the cases where value-aligned behaviour is possible, our algorithm produces a learning environment for the agent wherein it will learn a value-aligned behaviour. (shrink)

COVID-19 confinement has supposed a challenge to the whole wide world, especially in athletes that have frustrated their expectations about training programs and competitions. Specifically, competition cyclists during confinement had lot of difficulties to train due to the need to train outside their homes. However, the increase of online training sessions, or virtual training tools could help to overcome training difficulties due to confinement although there are not studies that analyse the effects of using these types of tools in cyclists. (...) This study aims to test how the use of online training tools in competition cyclists during confinement is related to training frequency and duration, and emotions. 329 cyclists filled an online questionnaire about feelings during confinement and the use of online training tools, before and during confinement. Results showed that the use of online training tools was associated with higher frequency and duration of trainings. Moreover, those who used these tools felt more positively about their future and preparation to compete, feeling more energy than those who did not used online tools. In addition, cyclists that started using these online tools (including virtual roller training) during confinement increased the frequency of training. In conclusion the use of online training tools for cycling could be appropriate to maintain training levels and energy and positive feelings about their future. (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams (...) are supposed to have an appropriate relation with these objects. I take this relation to be a quite peculiar sort of representation. Its peculiarity depends on the two following claims that I shall argue for: ( i ) The identity conditions of EPG objects are provided by the identity conditions of the diagrams that represent them; ( ii ) EPG objects inherit some properties and relations from these diagrams. (shrink)

The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...) can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and genuine IA, and argue that no genuine sound IA is available or easily forthcoming. We then submit that this holds also in the particularly relevant case in which indispensability is conceived as explanatory indispensability. (shrink)

Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it (...) applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of different instances of$AC$and$FC$(§3). We turn to the possible interpretations of$FC$(§4), and advance a Semantic$FC$(§4.1), arguing that while it suits Frege’s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (§4.1.2), for reasons only partly similar to those offered by Crispin Wright (§4.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege’s conception of real numbers and magnitudes (§4.2). We argue that an Architectonic version of$FC$is indeed faithful to Frege’s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$to Frege and appreciating the role of the Architectonic$FC$can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (§5). (shrink)

Apresentação do Dossiê "Contribuições formativas da Filosofia".

Breathing fresh air into the philosophy of mathematics Content Type Journal Article DOI 10.1007/s11016-010-9470-8 Authors Marco Panza, IHPST, 13, rue du Four, 75006 Paris, France Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest (...) to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning the definition of natural and real numbers. (shrink)

The paper argues that Frege’s primary foundational purpose concerning arithmetic was neither that of making natural numbers logical objects, nor that of making arithmetic a part of logic, but rather that of assigning to it an appropriate place in the architectonics of mathematics and knowledge, by immersing it in a theory of numbers of concepts and making truths about natural numbers, and/or knowledge of them transparent to reason without the medium of senses and intuition.

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

The aim I am pursuing here is to describe some general aspects of mathematical proofs. In my view, a mathematical proof is a warrant to assert a non-tautological statement which claims that certain objects (possibly a certain object) enjoy a certain property. Because it is proved, such a statement is a mathematical theorem. In my view, in order to understand the nature of a mathematical proof it is necessary to understand the nature of mathematical objects. If we understand them as (...) external entities whose 'existence' is independent of us and if we think that their enjoying certain properties is a fact, then we should argue that a theorem is a statement that claims that this fact occurs. If we also maintain that a mathematical proof is internal to a mathematical theory, then it becomes very difficult indeed to explain how a proof can be a warrant for such a statement. This is the essential content of a dilemma set forth by P. Benacerraf (cf. Benacerraf 1973). Such a dilemma, however, is dissolved if we understand mathematical objects as internal constructions of mathematical theories and think that they enjoy certain properties just because a mathematical theorem claims that they enjoy them. (shrink)

The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called “Plato’s problem,” in line with the program of a philosophy of mathematical practice. It then provides a sketch of a platonist solution, following the same perspective. This solution disregards as nonsensical the question of the existence of abstract, and specifically mathematical, objects, by rather focusing on the modalities of our access to them: objects (in general, both concrete and abstract) are regarded (...) as individual contents that we have (or can have) a de re epistemic access to. The question of the existence of mathematical objects is then replaced by that of the modalities of our de re epistemic access to individual mathematical contents. (shrink)

The philosophy of mathematical practice is not only a research topic, but overall a disciplinary field that is extending its importance and attracting the interest of an increasing number of scholars from different communities. The book edited by Paolo Mancosu provides a comprehensive and vivid account of the philosophy of mathematical practice, by showing it at work on different and multifarious topics, and by suggesting a substantial agenda for its development. This is also a momentous programme for the philosophy of (...) mathematics as a whole, aiming at "bringing some fresh air" into it. Furthermore, Mancosu's book gives voice to a community of scholars working in this area that does not only include the authors of the essays contained in it, but also a large group of scholars sharing their approach and often collaborating with them. (shrink)

This longitudinal study explored patterns of basic psychological needs and self-determined motivation, as well as its association with the teaching style and the physical activity enjoyment in a group of students. The sample consisted of 200 secondary education students (105 girls and 95 boys) aged 11 to 13 years (M= 12.65,SD= 0.79) at the start of the study. Students were assessed twice in a 22 month-period. Descriptive analyses were conducted between major variables at both time points, and to explore the (...) number and nature of clusters, we relied on latent profile analysis. The statistical analyses showed three different patterns: downward, stable and upward, with different outcomes and determinants. The downward pattern was associated with more negative enjoyment and a controlling style, while the upward pattern with more positive enjoyment and autonomy support. This study, which was based on a person-centered approach, provided a bigger picture of the interplay between autonomy, competence, relatedness, self-determined motivation, autonomy/control support, and physical activity enjoyment. (shrink)

In this paper we would like to attempt to shed some light on the way in which diagrams enter into the practice of ancient Greek geometrical analysis. To this end, we will first distinguish two main forms of this practice, i.e., trans-configurational and intra-configurational. We will then argue that, while in the former diagrams enter in the proof essentially in the same way they enter in canonical synthetic demonstrations, in the latter, they take part in the analytic argument in a (...) specific way, which has no correlation in other aspects of classical geometry. In intra-configurational analysis, diagrams represent in fact the result of a purely material gesture, which is not codified by any construction canon, but permitted only by the practice of the method of analysis and synthesis. (shrink)

Editorial NoteThe following Discussion Note is an edited transcription of the discussion on G. Aldo Antonelli’s paper “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals”, held among participants at the IHPST-UC Davis Workshop Ontological Commitment in Mathematics which took place, in memoriam of Aldo Antonelli, at IHPST in Paris on December, 14–15, 2015. The note’s and volume’s editors would like to thank all participants in the discussion for their contributions, and Alberto Naibo, Michael Wright and the personnel (...) at IHPST for their technical support. (shrink)

François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète’s major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète’s ‘new algebra’ relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of (...) analysis based on the use of formal methods. However, Viète’s algebraic analysis is not an analysis in the same sense as his cryptanalysis is. In Aristotelian terms, the first is a form of 'analysis,' while the second is a form of 'diaresis.' While the first is a top-down argument from the point of view of the human subject, since it is an argument going from what is not actual to what is actual for such a subject, the second one is a bottom-up argument from this same point of view, since it starts from what is first for us and proceed towards what is first by nature.Keywords: Analysis; Cryptanalysis; Algebra; Aristotle; Viète. (shrink)

The book contains eight papers previously published in English—three of which also appeared in Mancosu's papers collection —and now translated into French (two of them are co-authored with J....