Cet article prend comme point de départ de sa réflexion les défis de l’éducation dans un « univers problématique », tel qu’il est analysé par Ricœur dans un entretien accordé à Anita Hocquard en 1985. Le caractère éminemment conflictuel de la tâche éducative nous amène à discuter les notions de traditionalité, de traditions et de tradition. Il s’agit, ainsi, de réfléchir autour de la lutte pour la reconnaissance, la légitimité et l’autorité des différentes traditions dans un contexte culturel où l’héritage (...) colonialiste s’est imposé comme le modèle qui délégitime les traditions plurielles qui coexistaient et rivalisaient avec cet héritage. Enfin, nous émettons l’hypothèse que la littérature représente une manière alternative de revitaliser ces héritages silencieux, sur la base d’une brève analyse du roman L’histoire de Poncia, de l’écrivaine brésilienne Conceição Evaristo. (shrink)

El objetivo de este artículo es hacer una reconstrucción racional del uso del examen de proporcionalidad en contextos de adjudicación judicial de derechos sociales constitucionales. Dicho trabajo de reconstrucción será desarrollado en dos pasos. En primer lugar, se tratará el interrogante referido a si el examen de proporcionalidad en su variante “por omisión” exhibe o no una estructura diferente con respecto a su, mucho más conocida e investigada, variante “por exceso”. En segundo lugar, se describirán las reglas y formas de (...) argumentación que están implícitas en el uso del examen de proporcionalidad por omisión y que componen a sus respectivos sub-exámenes de idoneidad, necesidad y proporcionalidad stricto sensu. Por último, se presentará un breve resumen a modo de conclusión. (shrink)

Drawing on Merleau-Ponty’s hypothesis about transcendental geology in the final phase of his work, this article examines the debate about the Anthropocene from the perspective of philosophy of history. Firstly, we follow the author through the preliminary materials for The Visible and The Invisible by situating transcendental geology within the book’s complex theoretical architecture, and by foregrounding the necessity of rethinking the notion of Earth through the reading that the French philosopher offers of Husserl’s phenomenology. We will thus focus on (...) the theme of the overturning of the Copernican doctrine in an ethico-practical perspective, showing that Merleau-Ponty’s ecology can be considered a philosophical ecology ante litteram. Finally, drawing on the hypothesis proposed by historians Bonneuil and Fressoz, the essay will attempt to highlight the relevance of Merleau-Ponty’s practical thought for the debate about the Anthropocene. (shrink)

Beginning with the relation between the question of Nature and the status of philosophy, this essay interprets the theme of the mirror through the chiasm between multiplicity and thought. This relation is not substantial dualism’s relation of the subject with the object, but rather, following the image used by Merleau-Ponty, it is like the relation between two mirrors facing each other, thus suggesting that the “subject” herself is a multiplicity. From thence, drawing inspiration from this quote in Eye and Mind, (...) “the Cartesian does not see himself in the mirror”, I formulate both the problem of the body and the question of intersubjectivity as a field of individuation for all possible forms of subjectivity. Following this theme, the essay retraces the use of the mirror in the Note on Machiavelli. Finally, given that the theme of subjectivity as a multiplicity is related to the theme of corporeality, the essay ends with an analysis of the idea of the body-mirror which, from an intersubjective point of view, becomes an expressive relation in which each body is mirror and expression of the whole universe, thus unlocking an existential monadology. (shrink)

La teoría del derecho de Robert Alexy. Análisis y crítica es un libro escrito por el profesor Jan-R. Sieckmann, de la Universidad Friedrich-Alexander de Erlangen-Nürnberg, y publicado en la prestigiosa serie de teoría jurídica y filosofía del derecho de la editorial Universidad Externado de Colombia. El libro sistematiza un conjunto de trabajos que tratan sobre la conocida teoría del derecho...

Este trabajo busca responder al siguiente interrogante: ¿es posible resolver confl ictos entre normas constitucionales que disponen derechos fundamentales sin necesidad de ponderar? Para ello expondremos la teoría que, para los casos de confl ictos constitucionales de derechos, propone reconstruir sistemas normativos. Esta teoría está representada en los trabajos de Moreso, Mendonca y Martínez Zorrilla y se presenta como una alternativa a la ponderación. Concluiremos que, si bien esta teoría puede resultar un buen complemento a la hora de formalizar las (...) decisiones judiciales sobre asuntos constitucionales, no puede reemplazar de plano a la ponderación, pues ésta siempre subyacería latente. Ello puede vislumbrarse con claridad en los casos donde derechos sociales fundamentales pretenden validez, en cuyo contexto la ponderación se presenta como algo conceptualmente necesario. (shrink)

The purpose of this article is to make a rational reconstruction of the use of the proportionality test in contexts of judicial adjudication of constitutional social rights. This reconstruction will be developed in two stages. Firstly, I will deal with the question of whether the proportionality test in its variation by omission (that is, in cases of positive rights) exhibits or not a different structure with respect to its (better known and developed) variation by excess (that is, in cases of (...) negative rights). Secondly, I will describe the rules and forms of argumentation implied in the use of the proportionality test by omission, which constitute its respective sub-tests of suitability, necessity and proportionality stricto sensu. Lastly, I will present a brief summary. (shrink)

Il saggio muove da una ricostruzione storico-concettuale dell’interpretazione merleau-pontyana del manoscritto di Husserl Rovesciamento della dottrina copernicana nell’interpretazione della corrente visione del mondo, con cui Merleau-Ponty è in dialogo sin dalla Fenomenologia della percezione, per ripercorrere gli sviluppi del tema della Terra nell’avanzare della riflessione merleau-pontyana sul corpo-proprio, sull’organismo vivente, sulla dimensione carnale dell’essere. La proposta di un ritorno alla Terra, intesa come Boden irriducibile dell’esperienza, trova infatti il suo risvolto ontologico nell’idea di Spielraum, che già Husserl definiva come “ambito (...) di possibilità”, e che in Merleau-Ponty assume il senso di un margine di gioco sempre aperto nella carne. Boden e Spielraum, non a caso tematizzati da Merleau-Ponty in due corsi paralleli tenuti al Collège de France nell’anno 1959-1960, permettono una rivalutazione del vivente secondo un modello che, contro il riduzionismo meccanicista, privilegi la spontaneità e la contingenza, e aprono allo sviluppo dell’ontologia porosa che il filosofo andrà proponendo negli ultimi anni. Ricostruendo la funzione della riflessione sulla corporeità e sul rapporto del vivente al mondo-ambiente in questa maturazione, si argomenterà che la critica che Merleau-Ponty muove al dualismo empirismo-idealismo trovi nell’idea di Terra un momento chiave, che contribuisce ad orientarla in direzione di una filosofia della carne. Questo passaggio riconfigura la Natura stessa, pensata non già come un originario, ma in quanto ambito di possibilità processuale e transindividuale, come quel quasi-oggetto, come lo definiva, ancora, Husserl, che presenta un’irriducibile resistenza ad un pensiero di sorvolo, proprio in quanto è condizione del pensiero stesso e ancoraggio della vita tutta.This essay begins with a historico-conceptual reconstruction of the Merleau-Pontian interpretation of Husserl’s manuscript, “Foundational Investigations of the Phenomenological Origin of the Spatiality of Nature,” with which Merleau-Ponty is in dialogue from Phenomenology of Perception onward, and revisits the development of the theme of the Earth in the progression of Merleau-Ponty’s reflection on le corps propre, the living organism, and the carnal dimension of being. The proposal for a return to the Earth, taken as irreducible Boden of experience, indeed finds its ontological reverse side in the idea of Spielraum, which Husserl already defined as a “milieu of possibilities,” and which in Merleau-Ponty takes on the sense of a margin of play always open in the flesh. Boden and Spielraum, two notions that Merleau-Ponty does not thematize by chance in the two parallel courses given at the Collège de France over the years 1959-1960, enable a reassessment of the living being according to a model that, against mechanistic reductionism, privileges spontaneity and contingency, and opens to the development of the porous ontology that the philosopher would propose in his final years. Reconstructing the function of reflection on corporeality, and on the relationship of the living being with its milieu in the process, it will be argued that the criticism directed by Merleau-Ponty against the dualism of empiricism-idealism finds in the idea of the Earth a key moment that contributes to orienting him in the direction of a philosophy of the flesh. This passage reconfigures Nature itself, no longer conceived of as an originating, but as a milieu of processual and transindividual possibilities, like that quasi-object, as Husserl again defined it, that presents an irreducible resistance against high-altitude thinking, precisely as the condition of thought itself and the anchorage of all life.Cet essai commence avec une reconstruction historico-conceptuelle de l’interprétation merleau-pontienne du manuscrit de Husserl, Renversement de la doctrine copernicienne, avec lequel Merleau-Ponty est en dialogue depuis la Phénoménologie de la perception, et revisite les développement du thème de la Terre dans la progression de la réflexion merleau-pontienne sur le corps propre, sur l’organisme vivant, sur la dimension charnelle de l’être. La proposition d’un retour à la Terre, prise comme Boden irréductible de l’expérience, trouve en effet son envers ontologique dans l’idée de Spielraum, que Husserl déjà définissait comme « milieu de possibilités » et qui chez Merleau-Ponty prend le sens d’une marge de jeu toujours ouverte dans la chair. Boden et Spielraum, deux notions que Merleau-Ponty ne thématise pas par hasard dans les deux cours parallèles donnés au Collège de France au cours de l’année 1959-1960, permettent une réévaluation du vivant selon un modèle qui, contre le réductionnisme mécaniste, privilégie la spontanéité et la contingence, et ouvrent au développement de l’ontologie poreuse que le philosophe allait proposer dans les dernières années. Reconstruisant la fonction de la réflexion sur la corporéité et sur le rapport du vivant avec son milieu dans ce processus, on argumentera que la critique dirigée par Merleau-Ponty contre le dualisme empirisme-idéalisme trouve dans l’idée de la Terre un moment clé qui contribue à l’orienter en direction d’une philosophie de la chair. Ce passage reconfigure la Nature elle-même, pensée non pas déjà comme un originaire, mais en tant que milieu de possibilités processuelles et transindividuelles, en tant que quasi-objet, comme le définissait, encore, Husserl qui offrait une résistance irréductible contre une pensée de survol, précisément en tant que condition de la pensée elle-même et ancrage de toute la vie. (shrink)

In the 1780s Kant’s critique of rational cosmology clearly identified the limits of theoretical cosmology in agreement with the doctrine of transcendental idealism of space and time. However, what seems to be less explored, and remains still a desideratum for the literature, is a thorough investigation of the implications of transcendental philosophy for Kant’s view of cosmology in the 1790s. This contribution fills this gap by investigating Kant’s view of teleology and measurement in the Critique of Judgment, exploring their implications (...) for Kant’s late view of cosmology. Considering the historical and scientific context in which Kant developed his reflections motivates my proposal to read Kant’s late view of the universe in terms of “functional cosmology.” -/- . (shrink)

Featuring original essays from leading scholars in philosophy and psychology, this volume investigates and rethinks the role of practical wisdom in light of the most recent developments in virtue theory and moral, social and developmental psychology. The concept of phronesis has long held a prominent place in the development of Aristotelian virtue ethics and moral education. However, the nature and development of phronesis is still in need of investigation, especially because of the new insights that in recent years have come (...) from both philosophy and science. The essays in this volume contribute to the debate about practical wisdom by elucidating its role in empirical psychology and advancing important new research questions. They address various topics related to practical wisdom and its development, including honesty, ecocentric phronesis, social cognitive theory, practical wisdom in limited-information contexts, Whole Trait Theory, skill models, the reciprocity of virtue, and challenges from situationism. Practical Wisdom will interest researchers and advanced students working in virtue ethics, moral psychology, and moral education. (shrink)

The activity of Wnt and Notch signalling is central to many cell fate decisions during development and to the maintenance and differentiation of stem cell populations in homeostasis. While classical views refer to these pathways as independent signal transduction devices that co‐operate in different systems, recent work has revealed intricate connections between their components. These observations suggest that rather than operating as two separate pathways, elements of Wnt and Notch signalling configure an integrated molecular device whose main function is to (...) regulate transitions between cell states in development and homeostasis. Here, we propose a general framework for the structure and function of the interactions between these signalling systems that is focused on the notion of ‘transition states’, i.e. intermediates that arise during cell fate decision processes. These intermediates act as checkpoints in cell fate decision processes and are characterised by the mixed molecular identities of the states involved in these processes.Editor's suggested further reading in BioEssays: Notch: Implications of endogenous inhibitors for therapy Abstract. (shrink)

Se presentan los resultados obtenidos en la tesis de maestría Sistema de talleres de trabajo educativo para la capacitación del profesor guía de Medicina en Nuevitas con el objetivo de demostrar el impacto a partir de su implementación en la brigada estudiantil. Se exponen las definiciones elaboradas y las contextualizaciones. Se concluye que el sistema contribuyó al adecuado desempeño del profesor guía y al desarrollo del modo de actuación de los estudiantes. La rapidez y la calidad que implicó en la (...) praxis educativa constituyó el resultado más importante en el contexto de la carrera de Medicina en la Filial. Results achieved through the master's thesis "Educational work workshops system for the Medicine degree guiding teacher training" in Nuevitas are presented, aimed at demonstrating its impact starting from its implementation on a class. Elaborate definitions and contexts are exposed. The conclusionreached through it was that the system contributed to the adequate guiding teacher's performance and to the development of students' behavior. The speed and quality it involved in educational praxis constituted the most important result in the context of the Medicine degree in La Filial town. (shrink)

A partir del enfoque desarrollador del proceso de enseñanza- aprendizaje y teniendo en cuenta las dificultades que se muestran con la literatura en la asignatura Historia de Cuba I para algunos contenidos, se presenta un sistema de medios con el objetivo de resolver estas dificultades. Se concluye que el sistema que se ofrece contribuye a la motivación del estudiante por el estudio de la asignatura; eleva la calidad de la clase; proporciona la asimilación y profundización del contenido, así como el (...) desarrollo de habilidades docentes, intelectuales y específicas; permite la participación activa y reflexiva de los estudiantes en la clase y facilita un mayor nivel de organización del contenido para la realización de las tareas docentes. Taking into consideration a developmental approach to the teaching-learning process and the instructional challenges linked to literature content of Cuban History I coursework, a system of teaching aids is presented. It is suggested that the proposed system enhances student motivation to study this subject, raises the quality of instructional lessons, favors the assimilation of the content, and improves the development of educational, intellectual and specific skills. It also allows for the active and reflexive participation of students in the lessons and facilitates a greater level of content organization for successful instruction. (shrink)

Se presenta un artículo con el objetivo de elaborar un sistema de talleres con la utilización de técnicas participativas para la autodirección estudiantil en la universidad médica, tema de gran relevancia en el desempeño del modelo del profesional. Este sistema contiene un conjunto de orientaciones teórico-metodológicas y herramientas de trabajo para ser implementadas por los estudiantes en la brigada, las cuales propician el fortalecimiento de su autodirección en analogía con el modelo del profesional. An article is presented with the objective (...) of elaborating a system of workshops with the use of collaborative techniques for the students’ self-direction in the medical university, issue of great relevance in the development of the future professional. This system contains a group of theoretical-methodological guidelines and working tools to be implemented by the students of the brigade, the ones that give the strength of its self-direction in analogy with the ideal professional. (shrink)

This paper has a twofold aim. On the one hand, we will discuss the much debated question of the source of normativity (which traditionally has nature and practical reason as the two main contenders to this role) and propose a new answer to it. Second, in answering this question, we will present a new account of practical wisdom, which conceives of the ethical virtues as ultimately unified in the chief virtue of phronesis, understood as ethical expertise. To do so, we (...) will first criticize the main current view of phronesis and its bearer (the phronimos), then offer another view of the nature of phronesis and of its relation to the other ethical virtues. Our proposal should not be intended as an interpretation of Aristotle’s own view; rather, it should be seen as a broadly Aristotelian theoretical proposal, which we believe can satisfyingly address most of the problems that afflict the more traditional accounts of practical wisdom. In section 2 of this paper, after criticizing first-nature naturalistic views of moral virtue, we take practical reason to be the cornerstone of second-nature naturalistic views; in section 3, we will outline criticisms to which, in our view, the traditional views of phronesis are ill-suited to respond, and, in section 4, we will outline our view of phronesis as ethical expertise – a view which in our view is immune to the above-mentioned criticisms – by spelling out the three main tenets of phronesis as ethical expertise: a conceptual thesis, an epistemic thesis, and the educational implications of the two. Finally, we will support our proposal with some empirical evidence taken from cognitive science. (shrink)

Practical wisdom eliminativism has recently been proposed in both philosophy and psychology, on the grounds of the alleged redundancy of practical wisdom (Miller 2021 ) and its purported developmental/psychological implausibility (Lapsley 2021 ). Here we respond to these challenges by drawing on an improved version of a view of practical wisdom, the “Aretai model”, that we have presented elsewhere (De Caro et al. 2021 ; Vaccarezza et al. 2023 ; De Caro et al. forthcoming ). According to this model, practical (...) wisdom is conceptualized: (i) as virtuousness _tout court_, i.e., as the _ratio essendi_ of the virtues, and (ii) as a form of ethical expertise. By appealing to the first thesis, we counter the charge of psychological implausibility, while we rely on the second thesis to address the accusation of redundancy. In conclusion we argue that the Aretai model implies a significant paradigm shift in virtue ethics. Practical wisdom emerges as both necessary and sufficient for virtuousness, thereby downsizing – without eliminating entirely – the role that individual virtues play in our ethical lives. (shrink)

Resumen La reseña, situada en la sección final de revistas especializadas, es un género textual típico del discurso científico, que ofrece información crítica acerca del contenido de una publicación reciente. El propósito del presente trabajo es enfocar el aspecto evaluativo del género reseña, ámbito propicio para la ocurrencia de diversas actividades de imagen de rol, de autocortesía, de cortesía y de descortesía. Este trabajo adopta el punto de vista discursivo-sociocultural para abordar los fenómenos de cortesía: Bravo y Kaul de Marlangeon. (...) Asimismo emplea la perspectiva de la teoría de la evaluación en el discurso, principalmente: Martin y Martin y White. El corpus ha sido extraído de reseñas de obras de autores hispanohablantes publicadas durante la última década en una selección de revistas internacionales de lingüística escritas en español: RILI, Signos, Discurso & Sociedad y Linred, donde se constata tanto el uso de los recursos evaluativos interconectados en el texto, como las diferentes actividades de imagen que desarrolla el reseñador. (shrink)

Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.

The recent discussions on the unity of virtue suffer from a lack of reference to the processes through which we interpret each other as moral agents. In the present paper it is argued that much light can be thrown on that crucial issue by appealing to a version of Donald Davidson’s Principle of Charity, which we call “Principle of Phronetic Charity”. The idea is that in order to treat somebody as a moral agent, one has first to attribute to them, (...) at least pro tempore, a significant degree of practical wisdom and, then, to assess and rationally adjust such attribution of competence via actual engagement with them – a process that may lead to different responses on the part of the interpreter. After expounding and defending the Principle of Phronetic Charity and the interpretive practices connected with it, we discuss the repercussions of our account on the issue of the epistemic access to virtue. We will show, in particular, that some important components of both disunitarianism and unitarianism have to be retained: in accordance with the former, we stress the role of concrete experience over pure speculation and, up to a point, the idea that virtues tend to form variegated ensembles; in accordance with the latter, we accept the claim that virtues are not attributed to moral agents in isolation. Ultimately, however, the account developed here rejects both the atomism of the disunitarian view and the holism of the “Unity of the Virtues”, since it is in fact a form of molecularism, according to which virtues come neither individually nor as a whole, but rather as clusters. (shrink)

According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then (...) propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices. (shrink)

Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, I (...) address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a (...) taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...) of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

This paper focuses on Kant's account of physical geography and his theory of the Earth. In spelling out the epistemological foundations of Kant's physical geography, the paper examines 1) their connection to the mode of holding-to-be-true, mathematical construction and empirical certainty and 2) their implications for Kant's view of cosmopolitan right. Moreover, by showing the role played by the mathematical model of the Earth for the foundations of Kant's Doctrine of Right, the exact relationship between the latter and physical geography (...) is highlighted. Finally, this paper shows how, in Kant's view, the progress of physical geography can be assured if and only if the free circulation of human beings is established and regulated by law. Therefore, examining the mutual relationship between the theory of Earth and the foundations of right opens new perspectives on the relationship between epistemology and practical philosophy within Kant's system. (shrink)

In this chapter, we will offer a sketch of the state of the art as concerns existing accounts of virtue acquisition in relation to automaticity. In particular, we will focus on the so-called “skill model,” which we aim to improve by questioning its rather common underlying dualistic picture of the mind. Then we will propose an account of skillful emotions by identifying the features that make them both automatic and embedded in an intelligent practice. Finally, we will show how this (...) view can help the skill model by offering a better description of emotion shaping in virtue acquisition. By doing so, we will contend that emotions contribute autonomously and actively to the skillfulness of the habits in which they are embedded. (shrink)

Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...) diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear. (shrink)

The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must (...) develop a specific form of enhanced manipulative imagination, in order to draw inferences from knot diagrams by performing epistemic actions. Moreover, it will be argued that knot diagrams not only can promote discovery, but also provide evidence. This case study is an experimentation ground to evaluate the role of space and action in making inferences by reasoning diagrammatically. (shrink)

Studying early modern medico-legal testimonies can enrich our understanding of witnessing, the focus of much research in the history of science. Expert testimonies were well established in the Roman Canon law, but the sphere of competence of expert witnesses—one of the grounds on which seventeenth-century physicians claimed social and intellectual authority—troubled contemporary jurists. By reconstructing these debates in Counter Reformation Rome, and by placing in them the testimonies given by Paolo Zacchia, one of the founding fathers of legal medicine, this (...) article discusses the epistemological and social issues surrounding the definition of expertise about the body in court. It shows how a high-ranking expert witness would define his competence versus the legal authority on the one hand, and versus lay and lower-status expert witnesses on the other. But it also explores the interactions between specific legal constraints, for example about eye witnessing, and the ways in which different kinds of witnesses would use the body as a source of evidence for testimony. While engaging with medico-legal issues including the ambiguous signs of childbirth and the visibility of pain, the article examines their meanings within Counter Reformation social controversies, including control over sexuality, imposition of discipline and the social status of physicians.Author Keywords: Legal medicine; Seventeenth-century Rome; Expert witnesses; Testimony; Body; Zacchia. (shrink)

In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal (...) notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron’s argument that idealizations do not help to carry the explanatory load at least for two reasons: mathematics is not independent of idealizations in modelling and idealizations help mathematics to carry the explanatory load of a model in different degrees. (shrink)

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability to (...) recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...) in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology. (shrink)

Investigar a los buenos profesores es complejo porque se corre el riesgo de generalizar trivializando sus características, por lo mismo, es fundamental no caer en la tentación de pensar que son ideales, puesto que son seres humanos que viven su existencia al igual que cada uno de nosotros, sólo que con compromiso y amor por lo que hacen. Gracias a las historias de vida pudimos entender el proceso de la profesionalización docente, develar sus principales complejidades y señalar tendencias válidas para (...) cualquier profesor que pueden ajustarse con flexibilidad a esos patrones. La construcción analítica nos aportó luces para entender y explicar qué es lo que hace a un profesor un Buen Profesor. Esto es, la valoración del sentido común, la improvisación, la conciencia del cambio, la reflexión y la acción pedagógica. Sus características pueden ser intencionalmente promovidas en las distintas etapas de formación profesional porque tienen la cualidad de generar entusiasmo, contagio con un compromiso pedagógico, social y político por el trabajo bien hecho. (shrink)

The distinction between propositional and doxastic justification is well-known among epistemologists. Propositional justification is often conceived as fundamental and characterized in an entirely apsychological way. In this chapter, I focus on beliefs based on deductive arguments. I argue that such an apsychological notion of propositional justification can hardly be reconciled with the idea that justification is a central component of knowledge. In order to propose an alternative notion, I start with the analysis of doxastic justification. I then offer a notion (...) of propositional justification, intersubjective propositional justification, that is neither entirely apsychological nor idiosyncratic. To do so, I argue that to be able to attribute propositional justification to a subject, we have to consider her social context as well as broad features of our human cognitive architecture. (shrink)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

a relação entre razão e natureza envolve um dos principais aspectos da crítica da teleologia de Kant. Visando destacar esta relação, investigarei o conceito de técnica da natureza, tal como introduzida na Crítica da faculdade de julgar. De acordo com Kant, a técnica da natureza permite as leis da razão a representarem o acordo dos princípios transcendentais da razão com a natureza. Deste modo, o conceito da técnica da natureza assume um papel prolífico ao expor, através de uma analogia com (...) as faculdades humanas, a atividade produtiva da natureza, como se sua atividade fosse orientada a fins.The relationship between reason and nature embodies one of the main aspects of Kant‟s critique of teleology. In order to highlight this relation, I shall investigate the concept of the technique of nature, as it has been introduced in Critique of the Power of Judgment. According to Kant, the technique of nature allows the laws of reason to represent the agreement of the transcendental principles of reason with nature. Thus, the concept of the technique of nature assumes a fruitful role by exposing, through an analogy with human faculties, the productive activity of nature, as if its activity were oriented towards ends. (shrink)

In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted in the (...) tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)