Based on the Nietzschean conception of language as rhetoric, the aim is to show how the notion of constitutive artifice denies the naturalness of language and, at the same time, it is linked to the affirmation of an unconscious dimension operating in its functioning.

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)

Spatial and temporal scales are essential components of geological sciences; both are almost always imbricated in complex ways, challenging geoscientific knowledge among nonspecialists and students. The present paper focuses on the efforts made by the French naturalist Simon-Suzanne Nérée Boubée (1806–62) regarding popular education on geology. Though Boubée is poorly known nowadays, he experienced some prestige during his lifetime. He worked as an independent teacher, offering private as well as free public courses. Boubée, as a nineteenth-century science popularizer, repeatedly insisted (...) on his disposition for “spreading science for all.” He extensively published books and journals on geology, all aimed at popularizing geological scientific knowledge, considered to be of paramount relevance. This paper analyzes three visual examples extracted from his works: the Tableau Mnémonique des Terrains Primitifs, destiné au géologue voyageur, avec son explication (1831), the Tableau de l’État du Globe à ses différents âges (1832), and the Tableau figuratif de la structure minérale du globe, ou résumé synoptique du Cours de géognosie de M. N. Boubée (1839), supplemented with images from the travel guide Deux Promenades au Mont Doré (1834). Our goal is to understand Boubée’s efforts to synthesize information, scaling down geologic time and space into foldable materials that made geological knowledge cognitively and materially accessible to laypeople. (shrink)

Interessa ao educador científico contemporâneo compreender as relações entre ciência e religião, particularmente investigando como elas se dão entre seus estudantes e na realidade por eles vivenciada, posto que essa bagagem cultural está presente na sala de aula. Neste sentido, o presente trabalho objetiva identificar e analisar as principais características e tendências de investigações sobre as relações entre ensino de ciências e a religião, a fim de fornecer subsídios atualizados para quem o desejar ou necessitar. Para tanto, uma revisão de (...) referenciais teóricos sobre a relação ciência-religião é apresentada e, em sequência, reúnem-se e analisam-se produções científicas publicadas entre 2004 e 2020 com foco nas relações entre ensino de ciências e a religião. Entre os resultados observados destaca-se que as relações entre religião e ciência não são homogêneas dentro da escola (nem fora dela): diferentes estudantes, bem como diferentes professores, têm diferentes opiniões, atitudes, e visões de mundo sobre o tema. Além disso, os pesquisadores sugerem atuações pedagógicas frente às relações entre religião e ciência: os conhecimentos sobre a história da ciência bem como conhecimentos sobre a história das relações entre a ciência e a religião são relatados como ferramentas importantes e há unanimidade quanto à importância de combater a noção de conflito entre ciência e religião. (shrink)

Paying attention to the inner workings of mathematicians has led to a proliferation of new themes in the philosophy of mathematics. Several of these have to do with epistemology. Philosophers of mathematical practice, however, have not (yet) systematically engaged with general (analytic) epistemology. To be sure, there are some exceptions, but they are few and far between. In this chapter, I offer an explanation of why this might be the case and show how the situation could be remedied. I contend (...) that it is only by conceiving the knowing subject(s) as embodied, fallible, and embedded in a specific context (along the lines of what has been done within social and feminist epistemology) that we can pursue an epistemology of mathematics sensitive to actual mathematical practice. I further suggest that this reconception of the knowing subject(s) does not force us to abandon the traditional framework of epistemology in which knowledge requires justified true belief. It does, however, lead to a fallible conception of mathematical justification that, among other things, makes Gettier cases possible. This shows that topics considered to be far removed from the interests of philosophers of mathematical practice might reveal to be relevant to them. (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)

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)

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)

This paper argues that eighteenth-century Portuguese scientific policies promoted the inclusion of its main colony, Brazil, in the Enlightenment environment. This was accomplished by innovative initiatives, such as voyages to explore the colonial territory. Natural history activities, especially in mining, remained at the center of this political project and relied on co-opting groups of Portuguese in America. Based on the life of João da Silva Feijó, this article outlines the relevant connections between Feijó's scientific activities and the first Brazilian national (...) expedition in the 1850s, which led to discussion about developing the Brazilian nation. This analysis is aimed toward the growing consensus in historiography of the sciences that scientific activities practiced outside European centers gave rise to complex interactions involving the processes of mondialization of sciences and the construction of a local scientific context. (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)

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)

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)

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 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)

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)

Resumen El presente estudio, de carácter interpretativo-descriptivo, se ocupa de la relación existente entre el lenguaje verbal, la descortesía y las emociones en contextos de cultura hispanohablante. Se investiga dicha relación para algunos tipos de actos descorteses, correspondientes a tipos de una escala de intensificación de la fuerza de descortesía, Cortesía y conversación: de lo escrito a lo oral. Tercer Coloquio Internacional del Programa EDICE, Vol. 3. Valencia/estocolmo: Universidad de Valencia- Programa EDICE, Kaul de Marlangeon y Alba-Juez. 2012, A typology (...) of verbal impoliteness behaviour for the English and Spanish Cultures. Revista Española de Lingüística Aplicada 25, pp. 69–92), y la consiguiente construcción discursiva de las emociones presentes en ellos. A tal fin, se adopta el punto de vista sociocultural de la pragmática, necesario tanto para el análisis del discurso de cortesía como para el de las emociones intervinientes en los distintos tipos de actos de descortesía, éstos y aquéllas asociados a sus respectivos contextos socioculturales y situacionales. De igual forma, se acoge el punto de vista de la psicología social, especialmente aquél que pone el énfasis en la dependencia contextual de las emociones y las considera como una construcción social. El pertinente corpus de ejemplos ha sido recogido en diferentes contextos de cultura hispanohablante que validan una interpretación ingtercultural. Los resultados de la descripción émica muestran que en cada tipo de descortesía considerado concurren complejas experiencias emocionales, sobre todo negativas, activadoras de conductas agresivas y de su grado de intensidad o de intencionalidad. (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.

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)

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)

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)

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)

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

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.

The question of the dimensionality of space has informed the development of physics since the beginning of the twentieth century in the quest for a unified picture of quantum processes and gravitation. Scientists have worked within various approaches to explain why the universe appears to have a certain number of spatial dimensions. The question of why space has three dimensions has a genuinely philosophical nature that can be shaped as a problem of justifying a contingent necessity of the world. In (...) contrast to explanations of three-dimensionality based on anthropic arguments, we support the search for a theory that provides a justification for the dimensionality of space based on a combination of deductive and inductive reasoning applied to science. In doing so, we argue that Kant correctly approached the question in “Thoughts on the true estimation of living forces” by connecting space dimensionality and the inverse square law. In expounding the strategy of Kant’s argument, we describe the main features of a general Kantian explanation of the dimensionality of space and discuss them with respect to current accounts of explanation in the philosophy of science, such as inference to the best explanation and the deductive-nomological model. (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)

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 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)

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