Le fragment 129 d'Empédocle fait état du savoir prodigieux et du pouvoir des prapides d'un Super-Sage du passé en qui les sources citatrices et les interprètes modernes reconnaissent trop facilement Pythagore de Samos. Le but de la présente étude est de reprendre à nouveaux frais l'examen de ces six vers afin d'ouvrir le débat autour de la sagesse et des pouvoirs attribués à la figure anonyme du Super-Sage. Interprétant « Empédocle à partir d'Empédocle », mais aussi à l'aide des références (...) culturelles majeures de son temps, on essaie d'examiner quel type de sagesse était attribué à cette figure par le poète philosophe, de quelles conditions, physiologiques ou autres, relève l'acquisition de cette dernière et en quoi consiste son caractère exceptionnel. Empedocle's fragment 129 praises the exceptional knowledge and the power of the prapides of a Super-Sage of the past. In this sage both ancient testimonies and modern interpreters all too easily recognize Pythagoras of Samos. The aim of the present paper is to re-examine these six verses in order to open up the discussion on the wisdom and powers attributed to this unnamed figure. Interpreting « Empedocles by Empedocles », and also taking into account the major cultural references of his time, we try to define what kind of wisdom was attributed to this distinguished sage, under which conditions, physiological or otherwise, he was able to acquire it, and what constitutes the exceptional character of his knowledge. (shrink)

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical (...) realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philosophy, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy". Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly ("trust only the methods of science" for example), so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second (...) Philosopher". mhis Second Philosopher begins from perceptual common sense experimentation, theory formation and testing, working all the while to asses, correct and improve her methods as she goes. Second Philosophy is then the result of the Second Philosopher's investigations. Maddy delineates the Second Philosopher's approach by tracing her reactions to various familiar skeptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing her methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. She then undertakes to practice Second Philosophy in her reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized. (shrink)

Ce livre, issu du programme « Présocratiques Grecs/Présocratiques Latins » financé par l’Agence Nationale de la Recherche (ANR) et dirigé par André Laks et Carlos Lévy, est le fruit d’une tentative fort intéressante de mettre l’accent sur la question de la spécificité de la transmission et de l’utilisation latine des présocratiques. Car sans nul doute, dans le domaine des études présocratiques, les témoignages issus de la tradition latine ne se trouvent pas au même niveau que ceux provenant d...

Les études recueillies dans cet ouvrage collectif sont issues, dans leur grande majorité, de communications et de débats dans le cadre du séminaire du « Centre Léon Robin de Recherches sur la Pensée Antique » (UMR 8061, Université de Paris IV-Sorbonne, CNRS et ENS), consacré, pendant les années 2005-2007, à la Physique et la Métaphysique chez Aristote. Les contributions, rédigées ou traduites en français, sont soigneusement struc­turées et caractérisées par une argumentation claire et approf...

Penelope Deutscher reconsiders the role of procreation in Foucault's thought, especially its proximity to risk, mortality, and death. Foucault's Futures brings together his work on sexuality and biopolitics to provide new insights into the conflicted political status of reproductive conduct and what it means for feminism and critical theory.

We adopt and extend the concept of ‘noncooperative space’ to analyze how (aspirant) black women intellectual activists attempt to sustain their efforts within settings that publicly endorse racial equality, while, in practice, the contexts remain deeply racist. Noncooperative spaces reflect institutional, organizational, and social environments portrayed by powerful white agents as conducive to anti-racism work and promoting racial equality but, indeed, constrain individuals who challenge racism. Our work, which is grounded in intersectionality, draws on an autoethnographic account of racially motivated (...) domestic violence suffered by our lead author. Our analysis suggests that (aspirant) black women intellectual activists must develop courage to sustain their ‘voice’ within noncooperative spaces. However, the three interlinked dimensions of noncooperative spaces—namely, deceiving design, hegemonic actors’ indifference to racism, and (some assimilated gatekeepers’) false equivalence—may gradually erode a black female scholar’s courage. This forces her ‘voice’ to vanish temporarily, or even permanently. Courage is thus fragile and depletable. Yet, courage can be regenerated, resulting in regaining voice. Consequently, we propose courageous collective action by white allies and black and brown individuals who voluntarily and officially cooperate within and across various spaces to achieve racial equality. (shrink)

Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.

Traditional accounts of the feminist history of philosophy have viewed reason as associated with masculinity and subsequent debates have been framed by this assumption. Yet recent debates in deconstruction have shown that gender has never been a stable matter. In the history of philosophy 'female' and 'woman' are full of ambiguity. What does deconstruction have to offer feminist criticism of the history of philosophy? _Yielding Gender_ explores this question by examining three crucial areas; the issue of gender as 'troubled'; deconstruction; (...) and feminist criticism of the history of philosophy. The first part of the book discusses the work of Judith Butler, Jacques Derrida, and contemporary French feminist philosophy including key figures such as Luce Irigiray. Particular attention is given to the possibilities offered by deconstruction for understanding the history of philosophy. The second part considers and then challenges feminist interpretations of some key figures in the history of philosophy. Penelope Deutscher sketches how Rousseau, St. Augustine and Simone de Beauvoir have described gender and argues that their readings of gender are in fact empowered by gender's own contradiction and instability rather than limited by it. (shrink)

A novel treatment of an issue central to much current work in metaphysics: the distinction between the essential and accidental properties of individuals. Mackie challenges widely held views, and arrives at what she calls "minimalist essentialism," an unorthodox theory according to which ordinary individuals have relatively few interesting essential properties. Mackie's clear and accessible discussions of issues surrounding necessity and essentialism mean that the book will appeal as much to graduate students as it will to seasoned metaphysicians.

The human microbiome has become one of the dominant biomedical frameworks of the contemporary moment that may be understood to be post-Pasteurian. The recognitions the human microbiome opens up for thinking about the biological self and the individual have ontological and epistemological ramifications for considering what and who the human being is. As this article illustrates, the microbiopolitics of the human microbiome challenges the immunitarian Pasteurian model in which the organismic self shores itself up and defends itself against a microbial (...) non-self or other. Instead, this theory presents the human organism as comprised of multiple ecosystems and as a multitude, suggesting that the thanatopolitical attempts to wipe out microbial others (evident in the overuse and misuse of antibiotics, for example) are giving way to an affirmative microbiopolitics grounded in generative multispecies relationality. This article sets out to make the case for this affirmative microbiopolitics. (shrink)

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of (...) the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments. (shrink)

The effort to fit simple logical truths–like `if it's either red or green and it's not red, then it must be green'–into Kant's account of knowledge turns up a position more subtle and intriguing than might be expected at first glance.

This ambitious book explores the relationship between time and history and shows how an appreciation of long-term time helps to make sense of the past. The book is devoted to a wide-ranging analysis of the way different societies have conceived and interpreted time, and it develops a theory of the threefold roles of continuity, gradual change, and revolution which together form a "braided" history. Linking the interpretative chapters are intriguing brief expositions on time travel, time cycles, time lines, and time (...) pieces, showing the different ways in which human history has been located in time. In its global approach the book is part of the new shift toward “big history,” in which traditional period divisions are challenged in favor of looking at the entire past of the world from start to end. The approach is thematic. The result is a view of world history in which outcomes are shown to be explicable, once they happen, but not necessarily predictable before they do. This book will inform the work of historians of all periods and at all levels, and contributes to the current reconsideration of traditional period divisions (such as Modernity and Postmodernity), which the author finds outmoded. (shrink)

The Logical Must is an examination of Wittgenstein's philosophy of logic, early and late, from an austere naturalistic perspective called "Second Philosophy.".

The work of Robert Hooke on acoustics and music theory is a larger subject than might seem the case from studies of his career so far available. First, there are his experiments for the Royal Society which can be defined as purely acoustical, which anticipate later experiments performed by men such as J. Sauveur and E. Chladni. Second, there are passages in many of his writings which by extensive use of musical analogy attempt to account for all physical phenomena of (...) the universe, which operates on the principles of ‘harmony’ and ‘dissonance’. It is in this context that the hitherto unpublished manuscript presented at the end of this paper should be considered. This essay, which combines both the older tradition of the ‘praise of music’ and the newer consideration of the physical nature of musical sound, illustrates a particular aspect of Hooke's thought which exercised a profound influence on all his studies. (shrink)

Pursues the theoretical level of the two‐tiered epistemology of set theoretic realism, the level at which more abstract axioms can be justified by their consequences at more intuitive levels. I outline the pre‐axiomatic development of set theory out of Cantor's researches, describe how axiomatization arose in the course of Zermelo's efforts to prove Cantor's Well‐ordering Theorem, and review the controversy over the Axiom of Choice. Cantor's Continuum Hypothesis and various questions of descriptive set theory were eventually shown to be independent (...) of the standard axioms, and new axiom candidates—Gödel's Axiom of Constructibility, on the one hand, determinacy and large cardinal axioms, on the other—offer dramatically different solutions. This situation presents a new epistemic challenge to the set theoretic realist: on what grounds can we adjudicate between new axiom candidates? (shrink)

Outlines a physicalistic version of set theoretic realism, and compares and contrasts it with Field's nominalism, with structuralism, and with modalism. I conclude that, despite metaphysical differences, versions of all these views share the new challenge raised in Ch. 4: how are new axiom candidates to be rationally evaluated?

Begins with a review of Benacerraf's metaphysical challenge to mathematical realism based on sets: how, for example, can number theory be the study of particular sets when other sets with the same structural relations would seem to do just as well? The set theoretic realist gives the straightforward response that numbers are not particular sets, but properties of sets. I close with a digression on the prospects for ‘Frege numbers’—i.e. numbers construed as proper classes.

Begins with a presentation and elaboration of Benacerraf's epistemic challenge to realism: how can we gain knowledge of an acausal world of non‐spatio‐temporal abstracts? I then outline a theory of perception based in part on neurological theories of Hebb and developmental evidence from Piaget, and I argue in these terms that we can, in fact, perceive sets of medium‐sized physical objects. This account of perception is elaborated into an account of physical and mathematical intuition, faculties that produce various rudimentary beliefs (...) that underlie the simplest physical and set theoretic assumptions. I conclude by comparing and contrasting this epistemology with some controversial passages from Gödel's writings. (shrink)

The early sections describe the pre‐theoretic realism of the mathematician, survey the basic forms of realism in philosophy, and attempt to disentangle the issues of realism from debates over the nature of truth. The final section begins by laying out traditional Platonism, intuitionism, and formalism. Quine's famous critique of Carnap's conventionalism then leads to Quine's realism, and Putnam's developments thereof, while a different sort of mathematical realism is found in Gödel's writings. Set theoretic realism emerges as an effort to build (...) on the strengths of Quine's and Gödel's realisms, while avoiding their weaknesses and filling in their lacunae. (shrink)

This second edition encourages the integration of technology into a pedagogically sound learning sequence for primary mathematics.

Professor Deutscher studies Beauvoir's philosophy on "otherness" not just through her famous views on gender (in her celebrated 1949 work The...

A plea for natural philosophy --On the question of realism --Hume and Reid --Moore's hands --Wittgenstein on hinges --A note on truth and reference --The philosophy of logic --A Second Philosophy of logic --Psychology and the a priori sciences --Do numbers exist? --Enhanced if-thenism.

Sexual difference as a basis of equality : an introduction to Irigarayan politics -- Irigaray on language : from the speech of dementia to the problem of sexual indifference -- Rethinking the politics of recognition : the declaration of Irigarayan sexuate rights -- Irigarayan performativity : is this a question of can saying it make it so? -- Sexuate genre : ethics and politics for improper selves -- Anticipating sexual difference : mediation, love, and divinity -- Interrogating an unasked question (...) : is there sexual difference? -- The impossible friend : traversing the heterosocial, the homosocial, and the successes of failure -- Sexed discourse and the language of the philosophers : to be two -- Effacement redoubled? : between the Orient and the Occident. (shrink)

Carpendale & Lewis (C&L) view enculturation as the internalization of cultural concepts given in social interactions. They claim that enculturation implies relativism and fails to take into account both the constructive activity of the child and the gradual nature of development. Their view is contrasted with the notion of the child as both enculturated and enculturing throughout the course of development.

Ludwig Wittgenstein gave priority to aesthetics over other disciplines due to its invaluable capacities for revealing certain aspects of the nature of human understanding and for guiding our actions toward an ethical life. Although Wittgenstein did not focus on these issues in a systematic way, these worries were present in his philosophy during his lifetime. That is why I use a very wide range of his writings, from the Tractatus to letters and diaries. Aesthetic inquiries can throw light upon the (...) existence of an intransitive understanding–that is, a kind of knowledge that cannot be expressed by language shared by all competent users of a language. I also discuss Wittgenstein’s conception of ethics in order to explain the close relationship that he proposed between ethics and aesthetics. I hope this will clarify why he believed there was so much to learn from paintings, films, music, poems, or novels. I compare works of art and religious belief and how the former can help us to guide our lives as the latter does. I do this while extending the scope and claiming the importance of aesthetic education, given that it can help us to deal with our nature and with our history. (shrink)

It’s often said that set theory provides a foundation for classical mathematics because every classical mathematical object can be modeled as a set and every classical mathematical theorem can be proved from the axioms of set theory. This is obviously a remarkable mathematical fact, but it isn’t obvious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring (...) to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational. (shrink)

The work of the distinguished philosopher Sarah Kofman has, since her tragic death in 1994, become a focus for many scholars interested in contemporary French philosophy. The first critical collection on her thought to appear in English, Enigmas evaluates Kofman's most important contributions to philosophy, psychoanalytic theory, feminism, and literary theory. These insightful essays range from analyses of Kofman's first book, L'Enfance de l'art, to her last, L'Imposture de la beauté. This unique volume represents the major themes in Kofman's scholarship: (...) literature and aesthetics; philosophy and metaphor; women, feminism, and psychoanalysis; and Jews and German nationalism. Selected essays explore and diagnose Kofman's personal struggles as they are reflected in her writing. (shrink)