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)

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 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)

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)

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)

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)

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)

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)

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 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)

Computational tools might tempt us to renounce complete cer- tainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correct- ness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be (...) too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding. (shrink)

According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof. I challenge this view while accepting that mathematical justification requires arguments that are put forward as proofs. I argue that certain fallacious putative proofs considered by the relevant subjects to be correct can confer mathematical justification. But mathematical justification doesn’t come for cheap: not just any argument will do. I suggest that to successfully transmit justification an argument (...) must satisfy specific standards, some of which are social. I contrast my view with Huemer’s inferential conservatism, which makes mathematical justification too easy to get. Although in this article I focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs. (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)

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)

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)

John P. Burgess is the John N. Woodhull Professor of Philosophy at Princeton University. He obtained his Ph.D. from the Logic and Methodology program at the University of California at Berkeley under the supervision of Jack H. Silver with a thesis on descriptive set theory. He is a very distinguished and influential philosopher of mathematics. He has written several books: A Subject with No Object (with G. Rosen, Oxford University Press, 1997), Computability and Logic (with G. Boolos and R. Jeffrey, (...) 5th ed., Cambridge University Press, 2007), Fixing Frege (Princeton University Press, 2005), Mathematics, Models, and Modality (Cambridge University Press, 2007), Philosophical Logic (Princeton University Press, 2009), Truth (with A. G. Burgess, Princeton University Press, 2011), Saul Kripke: Puzzles & Mysteries (Polity Press, 2012), Rigor & Structure (Oxford University Press, 2015), and Set Theory (Cambridge Elements, Forthcoming). In this interview, Professor Burgess talks about how his interests in mathematics and philosophy developed and relate to each other. He then answers questions about specific themes of his philosophical work, with a focus on issues pertaining to philosophy of mathematics. (shrink)

Giacomo Leopardi, a major Italian poet of the nineteenth century, was also an expert in evil to whom Schopenhauer referred as a “spiritual brother.” Leopardi wrote: “Everything is evil. That is to say, everything that is, is evil; that each thing exists is an evil; each thing exists only for an evil end; existence is an evil.” These and other thoughts are collected in the Zibaldone, a massive collage of heterogeneous writings published posthumously. Leopardi’s pessimism assumes a polished form in (...) his literary writings, such as Dialogue between Nature and an Islander (1824)—an invective against nature and the suffering of creatures within it. In his last lyric, Broom, or the flower of the desert (1836), Leopardi points to the redeeming power of poetry and to human solidarity as placing at least temporary limits on the scope of evil. (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.

ABSTRACT Francis Bacon and René Descartes have traditionally been presented as leaders of opposed philosophical currents. However, more and more studies show important continuities between their philosophies. This article explores one of them: their perspectives on medicine. The dominion over nature and the instinct for self-preservation are the central elements of the theoretical framework within which they inserted their assessments of medicine. Medicine is valued as the most outstanding discipline for its benefits for the care of the human being. Departing (...) from this start-point, one finds further coincidences about the status, practice, and reform of medicine. (shrink)

Este capítulo se propone explorar cómo el replanteo de las causas finales en la ciencia natural suscitado por la Revolución Científica impactó en el desarrollo del materialismo y el ateísmo del Siglo de las luces. Con el surgimiento de la ciencia moderna en Europa, en el siglo XVII ocurrieron cambios sustantivos en la concepción de la causalidad. Ciertos estudios pioneros sobre el tema, sostenían que la nueva ciencia anulaba las causas finales y establecía que todos los fenómenos naturales debían explicarse (...) en términos de materia y movimiento (Burtt, 1952:98‒99; Schmitt, 1983:5). Más tarde, otros especialistas —con argumentos más sólidos y pruebas más convincentes— mostraron que la causalidad final no fue anulada por completo; siguió presente en muchos autores, aunque ya no como parte indispensable de la explicación científica, sino como un componente ontológico de la naturaleza (Osler, 1996 y 2001). Ahora bien, ¿qué sucedió con las causas finales en el siglo XVIII europeo, época de profundas turbulencias políticas y controversias filosóficas, en la cual el materialismo, el ateísmo y el deísmo fueron ganando terreno? Para hacer un recorte dentro de la vasta variedad de posiciones existentes en este escenario, comenzaremos por repasar la posición sobre las causas finales de Francis Bacon (1561‒1626), quien fue una figura muy influyente en la Ilustración. 2 Luego, analizaremos la recepción de esa posición por parte de algunos autores británicos (D. Stewart, S. Parker) y franceses en el siglo XVIII (D'Alembert, Naigeon, Diderot, Cabanis). (shrink)

¿Qué entendemos hoy por canon en el ámbito de la filosofía? El sentido más habitual de esta palabra remite a una lista o catálogo de autores y de textos que se consideran fundamentales con respecto a un determinado recorte de la filosofía y a veces a la filosofía en su totalidad. Este sentido de canon, por extensión, suele tener una connotación de norma, precepto o regla, en la medida en que la lista de obras o autores es juzgada como necesaria (...) para alcanzar un conocimiento o dominio de la filosofía. Está ligado con la formación de los filósofos en el marco de una institución de enseñanza. El propósito de este trabajo es deconstruir este sentido de canon, considerando sus elementos como piezas de un modelo que puede armarse, desarmarse y rearmarse. Antes de esta deconstrucción, será necesario hablar del lugar donde se construye y delinear cuáles son sus rasgos definitorios, incluyendo sus modos de construcción y reproducción. A ello estará dedicada la primera sección de este texto. Las tres secciones que siguen se concentrarán en cada de las piezas básicas que constituyen los cánones filosóficos: los autores, las obras y los temas. (shrink)

The article critically develops Nietzsche's presence in Heidegger's second great work, Contributions to Philosophy. Heidegger considers Nietzsche the last metaphysicist. However, being Western Metaphysics' zenith is the greatest thing that can be said of a thinker, since being the one who brings to completion a school of thought makes one, at the same time, the precursor of the ‘other’ begining and thus his concept of God's dead, nihilism and truth really can open the door to a kind of post-metaphysical thought, (...) as Heidegger would say, the thought of the history od being. Therefore, between Nietzsche's "God is dead" and Heidegger's "last God" there exists continuity and parallelism that needs future development. (shrink)

This chapter will explore the reception of Condillac in Argentina from the nineteenth century to the early twentieth century, focusing on two cases. First, the reception by nineteenth-century professors of idéologie (Juan Crisóstomo Lafinur, Juan Manuel Fernández de Agüero, Luis José de la Peña, and Diego Alcorta) that was mediated by the interpretations of Antoine Destutt de Tracy, Pierre Jean Cabanis, and Pierre Laromiguière. Second, the reception in the early twentieth century by José Ingenieros, whose narrative was conditioned by his (...) own political and philosophical agenda. In each case, we can identify different receptions that must be interpreted not only in light of the philosophical concerns of the authors who made them but also in light of the wider cultural and political context in which they emerged. In the first half of the nineteenth century, Condillac was received as a philosopher who integrated the new philosophical canon that would replace the Scholastic canon that had been imposed by the colonial regime. In the early twentieth century, Ingenieros inserted Condillac into a narrative that, starting with Bacon and Locke, culminated in positivism, a current that, in his view, offered the best framework to make Argentina shine in the concert of civilized nations. (shrink)

In the last few decades, the historiographical categories rationalism and empiricism have been criticized for their limitations to explain the complex positions and the links held by the philosophers tradiotnally attached to them. This narrative was firstly conceived by Kantian German historians and began to become standard at the turn of the twentieh century. Nonetheless, nineteenth-century French historiography developed other narratives by which early modern philosophers were classified according to alternative criteria. In the first edition of Histoire comparée des systémes (...) de philosophie (1804), Joseph-Marie Degérando distinguishes three first-order early modern schools founded by Bacon, Descartes and Leibniz, respectively. Degérando introduces the empiricism and rationalism distinction as one among others, and not as the fundamental one. In addition, he separates empiricism from experimental philosophy. The last one, along with speculative philosophy, is said to conciliate senses and reason. As a result, this account offers philosophical groupings different from those constructed by the standard narrative. Furthermore, it draws on labels and classification criteria which were part of the early modern philosophical discourse. (shrink)

La concepción según la cual la naturaleza es un todo ordenado donde prevalece la regularidad en las propiedades y procesos que caracterizan a las distintas especies recorre el pensamiento occidental desde la filosofía antigua griega hasta nuestros días. Diferentes teorías científicas sobre innumerables aspectos y objetos de la naturaleza elaboradas a lo largo de los siglos, e incluso teorías contrapuestas entre sí, asumieron el orden y la regularidad del mundo como un supuesto innombrado, como un a priori histórico sobre el (...) cual se sustentaron. Existen varias vías posibles de examinar históricamente la construcción y la evolución de una concepción tan vasta y duradera. La que aquí propongo consiste en estudiar la concepción del orden a partir de analizar la excepción y la anomalía que lo alteran o subvierten. En este caso me dedicaré a estudiar las perspectivas aristotélicas, tardo-escolásticas y baconianas sobre los monstruos, también conocidos como “fenómenos preternaturales”. (shrink)

L'esistenza del commento di Alessandro di Afrodisia al De generatione aristotelico, perduto nella versione greca e nella traduzione araba, è attestata da numerose fonti arabe, tra le quali Averroè, nel suo commento alla stessa opera. L'A. rintraccia la presenza, la tipologia e la distribuzione delle citazioni tratte dal commento di Alessandro nel Kitab al-Tasrif, un'opera del corpus alchemico attribuita a Gabir ibn Hayyan. Secondo l'A., la sezione interessata dalle citazioni assembla tre diversi tipi di testi: 1) lemmi del De generatione (...) in traduzione araba; 2) frammenti lacunosi della traduzione araba del commento di Alessandro; 3) interventi di collegamento. Una più ampia discussione si trova in un saggio visibile sulla pagina "publicationslist" dell'autore: "Alessandro di Afrodisia sulle 'contrarietà tangibili' (De gen. et corr. II.2): fonti greche e arabe a confronto" in: Aristotele e Alessandro di Afrodisia nella tradizione araba, a c. di C. D'Ancona e G. Serra, “Il Poligrafo”, Padova 2002, pp. 151-189. Notasi che il testo ricostruito di Alessandro in GC 2.2-5 è stato pubblicato da E. Gannagé nella serie ACA, che però non menziona il contributo di SF, dalla cui iniziativa, dalle cui analisi e dalla cui ricostruzione integrale, svolta sul manoscritto arabo Paris. 5099, la ricerca prese l'avvio. (shrink)

The historiographical narrative describing early modern European philosophy as the confrontation between rationalism and empiricism and its overcoming through the Kantian synthesis had a huge spread in Argentina. This article investigates the genesis of this traditional account in the universities of Córdoba, Buenos Aires and La Plata between 1780 and 1920. It offers an introduction concerning the formation of this narrative in Europe and a survey of the teaching of early modern philosophy in Argentina during that period. It concludes that, (...) although some of its components are found during the nineteenth century, it was only in the second decade of the twentieth century that the traditional narrative was formulated in its entirety, in parallel with the introduction of Kantianism in Argentine. However, the construction of this narrative is not merely explained by this fact but also by the weight that the history of philosophy gained in the syllabus as part of the demands involved in the shaping of the academic philosophical field. Finally, this paper suggests ways to reconfigure and renew the canon. (shrink)

This paper will address the nineteenth-century reception of Bacon as an exponent of materialism in Joseph de Maistre and Karl Marx. I will argue that Bacon’s philosophy is “quasi-materialist.” The materialist components of his philosophy were noticed by de Maistre and Marx, who, in addition, pointed out a Baconian materialist heritage. Their construction of Bacon’s figure as the leader of a materialist lineage ascribed to his philosophy a revolutionary import that was contrary to Bacon’s actual leanings. This contrast shows how (...) different the contexts were within which materialism was conceived and valued across the centuries, and how far philosophical and scientific discourses may be transformed by their receptions, to the point that in many cases they could hardly be embraced by the authors of these discourses. (shrink)

Hace un tiempo G. Rees señaló la importancia del razonamiento cuantitativo en el programa de la renovación del saber propuesto por F. Bacon, renovando la imagen tradicional de su método. Con la intención de proseguir el replanteo iniciado por Rees de los conceptos centrales del método baconiano, me propongo reexaminar el significado de la experimentación y de los instrumentos científicos, lo cual implica al mismo tiempo considerar la relación entre razón y sentidos. Para ello, examinaré el significado de los sentidos (...) como fuentes del conocimiento, la función de la experimentación y de los instrumentos para superar las limitaciones de los sentidos, la inserción de datos cuantitativos en el marco experimental, el concepto de sutilidad de la naturaleza y el sentido metodológico de la anatomía baconiana. Como conclusión señalo que en el método baconiano los sentidos están subordinados a la razón, ya que tanto los experimentos como los instrumentos científicos están sujetos a la autoridad de la razón para alcanzar la verdad y evitar sus errores. (shrink)

La idea de que la tarea de la ciencia consiste en dar cuenta de las leyes de la naturaleza comenzó a establecerse durante el siglo XVII mientras se estaba delineando la nueva imagen de la ciencia y de la naturaleza. Si bien distintos estudios historiográficos coinciden en situar el origen del concepto moderno de ley de la naturaleza en este siglo, sus interpretaciones son divergentes en varios sentidos. En este trabajo, me dedicaré en primer lugar a repasar brevemente y analizar (...) en forma crítica los resultados de estos estudios historiográficos, agrupándolos en cuatro grandes líneas de lectura. En segundo lugar y a modo de conclusión a partir de lo arrojado por esos estudios, enumeraré los factores fundamentales que considero ineludibles para realizar un abordaje historiográfico satisfactorio y completo de este problema. (shrink)

One of the main philosophical works by Alexander of Aphrodisias, De principiis, is lost in its original Greek text, but it is preserved in three extant Medieval Semitic versions, one in Syriac and two in Arabic, which were written in the Near East between 500 and 950 AD. These versions are not totally identical and, as we have shown in 2012, they are in a rather complex textual relationship. As we will show in this article, a tentative reconstruction of the (...) lost text should be based upon an attentive and point‑to‑point comparative analysis of some aspect of all three versions. We have tentatively called the abore way “critical translation”. (shrink)

Os escritos de Francis Bacon dedicados à filosofia abundam em imagens, metáforas, comparações e alegorias destinadas a ilustrar e apresentar com eloquência suas ideias. Solidamente formado na cultura humanista de seu tempo, Bacon adotou com destreza os recursos da retórica e nutriu-se de um amplo espectro da literatura clássica greco-latina, assim como também dos escritos bíblicos. Em especial, a mitologia clássica (a que dedicou seu De sapientia veterum (1609) - Da sabedoria dos antigos) foi um de seus recursos predilteos na (...) hora de valer-se de alegorias para tornar acessível a um público amplo e não especializado os conteúdos mais inovadores, profundos e abstrusos de sua filosofia.1 Tudo isso converte algumas de suas obras em excelentes peças da literatura filosófica, nas quais Bacon põe em prática sua grande plasticidade como escritor, que, delicadamente e sem tropeços, transporta seus leitores da beleza da poesia e fantasia para os conceitos mais abstratos, sempre em busca de representar suas ideias filosóficas e de transformar a realidade por meio delas. Neste texto, apresentarei brevemente algumas das imagens pelas quais ele quis retratar aspectos fundamentais do seu projeto de restauração do saber. (shrink)

La concepción cusana de la possibilitas / materia (posibilidad / materia) está directamente ligada con la doctrina de los modos de ser (modi essendi) sobre los que el Cusano se explaya, con diversos grados de profundidad, en varias de sus obras, entre las que se cuenta De docta ignorantia (1440), De conjecturis (1440), De Mente (1450), De venatione sapientiae (1462) y De ludo globi (1463). A lo largo de esas obras Nicolás de Cusa aborda dos aspectos centrales de la posibilidad (...) / materia, estrechamente relacionados entre sí: el aspecto ontológico y el aspecto gnoseológico. En la primera sección de este artículo expondremos la caracterización ontológica de la posibilidad / materia en el marco de los distintos modos de ser. En la segunda sección nos dedicaremos a desarrollar las perspectivas de Cusa acerca del conocimiento del modo de ser de la posibilidad o materia . (shrink)

En estas páginas se publican mis respuestas a una encuesta incluida en el libro Galfione, María Carla y Moine, Facundo José, eds., La inquietud por la filosofía. Ensayos sobre canon, historia y crítica, Córdoba, Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades, 2023, pp. 178-182. Las preguntas de la encuesta son las siguientes: 1. ¿Cree que tiene sentido hacer hoy historia de la filosofía, como objeto de investigación y/o enseñanza? ¿Por qué y cómo?; 2. ¿Pueden ayudar las reflexiones de (...) Foucault para esa historia, como "caja de Herramientas"? ¿Por qué? ¿Cómo?; 3. ¿Qué hacer con el canon filosófico? ¿Hay que conservarlo, transmitirlo, inculcarlo?; 4. ¿Cómo entiende la crítica en tanto actividad reflexiva que atraviesa el discurso filosófico? ¿Encuentra alguna potencialidad o productividad en pensar la crítica de cara al canon filosófico?; 5. ¿Cree conveniente, a la hora de pensar el pasado y el presente del saber filosófico, inscribirlo en un presente, en determinadas instituciones, en un marco que lo excede histórica y discursivamente? ¿Qué entiende que resulta del saber filosóficoposicionado en esos marcos?; 6. ¿Cuál cree que es el grado de persistencia del pasado o del canon al pensar la filosofía en su exigente vínculo con el presente? O, de otro modo, ¿tiene la historia de la filosofía y su práctica algún lugar en la constitución del presente? (shrink)

The first part of this paper will provide a reconstruction of Francis Bacon’s interpretation of Academic scepticism, Pyrrhonism, and Dogmatism, and its sources throughout his large corpus. It shall also analyze Bacon’s approach against the background of his intellectual milieu, looking particularly at Renaissance readings of scepticism as developed by Guillaume Salluste du Bartas, Pierre de la Primaudaye, Fulke Greville, and John Davies. It shall show that although Bacon made more references to Academic than to Pyrrhonian Scepticism, like most of (...) his contemporaries, he often misrepresented and mixed the doctrinal components of both currents. The second part of the paper shall offer a complete chronological survey of Bacon’s assessment of scepticism throughout his writings. Following the lead of previous studies by other scholars, I shall support the view that, while he approved of the state of doubt and the suspension of judgment as a provisional necessary stage in the pursuit of knowledge, he rejected the notion of acatalepsia. To this received reading, I shall add the suggestion that Bacon’s criticism of acatalepsia ultimately depends on his view of the historical conditions that surround human nature. I deal with this last point in the third part of the paper, where I shall argue that Bacon’s evaluation of scepticism relied on his adoption of a Protestant and Augustinian view of human nature that informed his overall interpretation of the history of humanity and nature, including the sceptical schools. (shrink)

L’identité et la datation de Nicolas le Péripatéticien, l’auteur d’un sommaire de la philosophie d’Aristote, ont fait l’objet d’un article récent de Silvia Fazzo paru dans la Revue des Études Grecques. Contre la datation courante, fondée sur l’identification de Nicolas à l’historien de grand renom Nicolas Damascène , Fazzo a montré que Nicolas avait probablement vécu au cours de la période couvrant les IIIe au Ve siècles ap. J.-C., et plus problablement à l’époque de l’empereur Julien l’Apostat . Cette (...) hypothèse trouve un appui dans un nouveau fragment en traduction hébraïque découvert par Mauro Zonta, dans lequel Nicolas cherche à expliquer la Trinité de Dieu au moyen de la doctrine aristotélicienne des causes: Dieu est un, en tant que sa substance est une, mais Dieu est également trois, puisqu’il est à la fois causes motrice, formelle et finale du monde. Dans la mesure, évidemment réduite, où un fragment si court est susceptible de datation, l’époque de Julien paraît la plus probable. (shrink)

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, vindicating why (...) it is not vulnerable to diachronic Dutch Book arguments. Moreover, the diachronic Dutch Books against the ‘halfer’ solutions fail to undermine the standard arguments for Conditionalization. The main upshot that emerges from my discussion is that the disagreement between different solutions does not challenge the applicability of Bayesian reasoning to centered settings, nor the commitment to Conditionalization, but is instead an instance of the familiar problem of choosing the priors. (shrink)

Este libro, por un lado, propone nuevas perspectivas y materiales de estudio sobre algunos de los temas, autores y textos clásicos de la filosofía moderna; por otro lado, invita a descubrir rarezas, temas, autores y textos poco conocidos o ignorados, que lleven a renovar el canon de la filosofía moderna. Realiza una revisión crítica de las categorías empirismo y del racionalismo modernos y dedica artículos a una serie de filósofas modernas con el fin de renovar el canon filosófico moderno.

This article discusses Margaret Cavendish's position on reality and fiction in dreams and her role within the moderate skepticism of her philosophy. While Cavendish argues that there is no distinction between dream-like and waking depictions, she does not consider the difference between fact and fiction to be sharp or relevant. We will argue that, although Cavendish promotes a philosophical discourse that articulates reason –that seeks to know reality— and fancy —which constructs fictions—, considers that only "elevated" poetic fantasies are competent (...) for the construction of this discourse. (shrink)

Es muy habitual que se presenten los grandes lineamientos de la filosofía moderna en el marco del paradigma epistemológico y apelando a la distinción de dos corrientes filosóficas fundamentales, el empirismo y el racionalismo. Se trata de categorías analíticas construidas para interpretar y caracterizar retrospectivamente a ciertos filósofos de la modernidad. Pero no fueron términos ni conceptos utilizados por los actores mismos6. John Locke, George Berkeley y David Hume no se llamaban a sí mismos empiristas, ni René Descartes, Baruch Spinoza (...) y Gottfried W. Leibniz se autodenominaban racionalistas. En este capítulo, profundizaremos algunos puntos esbozados en el capítulo anterior. En primer lugar, expondremos las definiciones que han recibido el empirismo y el racionalismo dentro del paradigma epistemológico, que si bien ha sido criticado y redefinido en las últimas décadas, sigue siendo sostenido en la actualidad. En esa misma sección, analizaremos en qué medida las figuras del canon moderno establecido por el paradigma sostienen o no las tesis racionalistas y empiristas que les atribuyen esas definiciones tradicionales. Finalmente, resumiremos algunas críticas que ha recibido la narrativa tradicional y presentaremos una propuesta de resignificación de ambas categorías que nos parece más atinada. (shrink)

Lo personal es político. Revisito la potente frase de Carol Hanish (1970) que sigue resonando en las luchas y discursos feministas desde que se hiciera pública a comienzos de 1970. Me permito reversionarla, con gran libertad, para marcar el pulso de este texto y contar, a partir de mi relación con la filosofía, cómo lo personal pasó a ser político en el interés por conocer las filósofas modernas e interpelar y rearmar el canon filosófico. Con ello, los y las invito (...) a reflexionar sobre la perspectiva de género en la historiografía filosófica, las formas de construcción del canon y sus repercusiones en la enseñanza de la filosofía. (shrink)

Drawing an analogy between modal structuralism about mathematics and theism, I o er a structuralist account that implicitly de nes theism in terms of three basic relations: logical and metaphysical priority, and epis- temic superiority. On this view, statements like `God is omniscient' have a hypothetical and a categorical component. The hypothetical component provides a translation pattern according to which statements in theistic language are converted into statements of second-order modal logic. The categorical component asserts the logical possibility of the (...) theism struc- ture on the basis of uncontroversial facts about the physical world. This structuralist reading of theism preserves objective truth-values for theistic statements while remaining neutral on the question of ontology. Thus, it o ers a way of understanding theism to which a naturalist cannot object, and it accommodates the fact that religious belief, for many theists, is an essentially relational matter. (shrink)

This paper will analyze three historical cases (Francis Bacon, Galileo Galilei and Margaret Cavendish) that exemplify the complexity of the interaction between science and religion in the Scientific Revolution and confirm the interpretation of J. H. Brooke, according to which, in this historical context –rather than a separation- a differentiation took hold between them. We will hold that although these authors agreed in proposing the separation of science and religion as an ideal, each in their own way made an articulation (...) between the two that in the long run prevented a complete separation. This articulation was due to both epistemic and extra-epistemic reasons and manifests a tension that was characteristic of the Scientific Revolution. (shrink)

Las narraciones que presentan la filosofía moderna como un periodo particular de la historia de la filosofía, al igual que las narraciones sobre otros periodos de la historia de la filosofía, son deudoras tanto de determinadas concepciones de la filosofía como de ciertas concepciones de su historia y de la historia. La mirada hacia el pasado filosófico se sitúa en un presente que, implícitamente o no, delimita el campo de lo que es considerado como filosofía y de lo propiamente filosófico, (...) delimitación que implica una selección de las manifestaciones que caracterizan la filosofía, como, por ejemplo, sus autores, sus problemas, sus escenarios y sus formas discursivas. Dicho de otra manera, al narrar una historia de la filosofía se determinan de alguna manera quiénes son filósofes, qué temas son filosóficos, dónde se hace filosofía y cómo se escribe filosofía, entre otras cosas. A su vez, la narración histórica de las expresiones de ese pasado asume ciertas posiciones acerca de la historicidad de lo filosófico, de sus relaciones con los diferentes ámbitos de su emergencia, de sus métodos de investigación y de las modalidades discursivas deseables para esta narración. (shrink)