A diplomacia das letras compreende a atividade literária de muitos homens de letras que estavam comprometidos nas questões públicas de seus estados, ou cuja carreira se dava em torno das cortes e centros de poder do Antigo Regime. Enquanto secretários, conselheiros, encarregados de negócios, próximos da política, eles tinham a possibilidade de observar as dinâmicas do poder e exprimir suas considerações sobre a história de seu tempo em sua produção literária (poemas, cartas, relatos de viagem, jornais etc.). Graças a estes (...) homens de letras, o conjunto dos valores da República das letras do século XVIII (a paz, a felicidade privada e pública, a tolerância etc.) entravam em cena na história política: sua luta por uma diplomacia disposta a abraçar os valores das Luzes mostra a importância da comunicação entre a cultura e a política, que é um dos mais fortes legados do século XVIII, e que deveria inspirar as relações internacionais ainda hoje. (shrink)

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception (...) of rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon –Enriques distinguishes between _ small-scale rigor _ and _ large-scale rigor _ and Severi between _ formal rigor _ and _ substantial rigor _. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we s... (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)

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)

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)

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)

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)

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)

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 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)

This paper intends to show how Schopenhauer‟s „eristic dialectics‟, defined by him as „the art of being right‟, arise from the combination of two lines of thought on dialectics: the Aristotelian tradition, in which dialects are understood as an argumentative discourse based on generally accepted notions; and the tradition set in motion by Kant, which understands dialectics as a logic of appearances or of illusion. The interpretation we favor, and which we intend to argue in this work, is the following: (...) while attempting to assimilate and to go beyond the teachings of both traditions, Schopenhauer sets forth the basic elements of a kind of communicative rationality in which the polemical functioning of language, understood as the effective instrument of a certain „will of power‟, becomes the sole factor which determines the consolidation of social beliefs and values. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2018 Heft: 220 Seiten: 173-198.

Going beyond Enlightenment critiques of ancien régime justice, historians are now exploring its distinctive procedures; courtrooms have become a fundamental site for recapturing early modern political and social dynamics. Historians of science and medicine can benefit too. Serving as expert witnesses was prominent among the activities of medical practitioners; and, especially in Continental Europe, natural and medical knowledge was routinely presented and contested in tribunals. This essay aims to promote further research on the resulting wealth of manuscript and printed sources (...) that give access to crucial social and epistemological issues. The voices of different actors, preserved in trial records, can extend our histories of the body. The relations among medical practitioners, and with the legal authorities, provide a hitherto neglected context within which to understand contemporary epistemological debates, from claims and challenges to expertise to the definition and production of evidence, including the status of signs, personal observation, and tests. (shrink)

Background Italy was the first European country to be involved with the COVID-19 pandemic. As a result, many healthcare professionals were deployed and suddenly faced end-of-life care management and its challenges. Aims To understand the experiences of palliative care professionals deployed in supporting emergency and critical care staff during the COVID-19 first and second pandemic waves. Research design A qualitative descriptive design was adopted, and in-depth interviews were used to investigate and analyse participants’ perceptions and points of view. Participants and (...) research context Twenty-four healthcare professionals (physicians, nurses, psychologists, physiotherapists, and spiritual support) from the most affected areas of Italy were recruited via the Italian society of palliative care and researchers’ network. Ethical considerations The University Institutional Board granted ethical approval. Participants gave written informed consent and agreed to be video-recorded. Findings The overarching theme highlighted participants’ experience supporting health professionals to negotiate ethical complexity in end-of-life care. Crucial topics that emerged within themes were: training emergency department professionals on ethical dimensions of palliative and end-of-life care, preserving dying patients’ dignity and developing ethical competence in managing end-of-life care. Conclusions Our study showed palliative care teams’ challenges in supporting health professionals’ ethical awareness in emergencies. However, while they highlighted their concerns in dealing with the emergency staff’s lack of ethical perspectives, they also reported the positive impact of an ethically-informed palliative care approach. Lastly, this study illuminates how palliative care professionals’ clinical and ethical competence might have assisted a cultural change in caring for dying patients during COVID-19 and future emergencies. (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)

Purpose: To explore the characteristics of the use of laughs and jokes during doctor-couple assisted reproductive technology visits.Methods: 75 videotaped doctor-couple ART visits were analyzed and transcribed in order to: quantify laugh and jokes, describing the contribution of doctors and couples and identifying the timing of appearance; explore the topic of laughs and jokes with qualitative thematic analysis.Results: On average, each visit contained 17.1 utterances of laughs and jokes. Patients contributed for 64.7% of utterances recorded. Doctor and women introduced the (...) majority of laughs and jokes. Visits with female physicians had significantly more laughs and jokes than visits with male doctors; no differences were found considering physicians’ age and years of experience, cause of infertility, and prognosis. Laughs and jokes were mainly recorded during history taking and information giving. Four core themes were identified, regarding the topic of laughs and jokes: health status, infertility treatment, organizational aspects, and doctor-patient interaction.Conclusion: Laughs and jokes are common in doctor-couple ART visits and are frequently used during the dialogue, covering a wide range of topics. Results seem to show that laughs and jokes are related to doctor’s personal characteristics, while are not associated with infertility aspects. Given the complexity of this communicative category, further studies are needed to explore the functions and the effects of laugh and jokes. (shrink)

SPECIAL SECTION: BUILDING UNIVERSES: THE PHILOSOPHICAL AND MATHEMATICAL UNDERPINNINGS OF COSMOLOGY (EIGHTEENTH–TWENTIETH CENTURIES) .

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)

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)

This contribution sheds light on the role of infinite idealization in structural analysis, by exploring how infinite elements and finite element methods are combined in civil engineering models. This combination, I claim, should be read in terms of a ‘complementarity function’ through which the representational ideal of completeness is reached in engineering model-building. Taking a cue from Weisberg’s definition of multiple-model idealization, I highlight how infinite idealizations are primarily meant to contribute to the prediction of structural behavior in Multiphysics approaches.

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)

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)

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)

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)

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)

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)

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)

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)

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of (...) rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon – Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely, objectivity as faithfulness to facts and objectivity as intersubjectivity. (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)