We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)
The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve cannot be (...) so treated and involve additional tools–leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat’s manuscript but it is Breger who tampers with Fermat’s procedure by moving all terms to the left-hand side so as to accord better with Breger’s own interpretation emphasizing the double root idea. We provide modern proxies for Fermat’s procedures in terms of relations of infinite proximity as well as the standard part function. (shrink)
Classically, an osculating circle at a point of a planar curve is introduced technically, often with formula giving its radius and the coordinates of its center. In this note, we propose a new and intuitive definition of this concept: among all the circles which have, on the considered point, the same tangent as the studied curve and thus seem equal to the curve through a microscope, the osculating circle is this that seems equal to the curve through a microscope within (...) microscope. (shrink)
We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to \ that has a point of continuity when restricted to any non-empty compact subset, then f is of Baire class 1. We use this property of the restrictions to compact sets to give a generalisation of Baire’s grand theorem for functions of any Baire class.
Responding to questions put to him at a Roundtable held at Villanova University in 1994, Jacques Derrida leads the reader through an illuminating discussion of the central themes of deconstruction. Speaking in English and extemporaneously, Derrida takes up with unusual clarity and great eloquence such topics as the task of philosophy, the Greeks, justice, responsibility, the gift, the community, the distinction between the messianic and the concrete messianisms, and his interpretation of James Joyce. Derrida convincingly refutes the charges of (...) relativism and nihilism that are often leveled at deconstruction by its critics and sets forth the profoundly affirmative and ethico-political thrust of his work. The "Roundtable" is marked by the unusual clarity of Derrida's presentation and by the deep respect for the great works of the philosophical and literary tradition with which he characterizes his philosophical work. The Roundtable is annotated by John D. Caputo, the David R. Cook Professor of Philosophy at Villanova University, who has supplied cross references to Derrida's writings where the reader may find further discussion on these topics. Professor Caputo has also supplied a commentary which elaborates the principal issues raised in the Roundtable. In all, this volume represents one of the most lucid, compact and reliable introductions to Derrida and deconstruction available in any language. An ideal volume for students approaching Derrida for the first time, Deconstruction in a Nutshell will prove instructive and illuminating as well for those already familiar with Derrida's work. (shrink)
Far more telling than mere biography, this collection of the extant letters exchanged between philosopher Jacques Maritain and social activist Saul Alinsky reveals a deep and intimate friendship, however unexpected and unlikely. Indeed, to all who knew or knew of them the dignified, prominent philosopher and the earthy, truculent genius of social reform seemed antithetical to one another in almost every way. The Maritain-Alinsky correspondence began in 1945, shortly after they met, and continued until Alinsky's death in 1972. The (...) tone and content of the letters vary widely, ranging from expressions of mutual admiration and friendship, to details of the triumphs and tragedies of their personal lives, to anguished considerations of death and immortality. In their letters Maritain and Alinsky offer each other personal expressions of strong mutual support - as well as judicious warnings and slightly apprehensive distancing - for the different works each had undertaken at various times in his respective careers. They also discuss the Catholic church, taking ironic jibes at clerical pomposity and exchanging praise of the socially aware. Though it is difficult to tell whether either man had a significant influence on the thought and work of the other, their correspondence attests that the philosopher and the provocateur, so different in personality, educational backgrounds, demeanor, and intellectual affinities, enjoyed a surprisingly intimate and extraordinary friendship. With context and interpretation of the letters provided by the editor, this intriguing collection of lively, moving letters not only reveals the depths of a most improbable friendship, it also goes far in exposing the humanity behind the personas. (shrink)
The following interview took place between Jacques Bouveresse and Hilary Putnam on May 11, 2001 in Paris at the Collège de France. Sandra Laugier was present, preserved the transcription, and proposed that we publish the text here. It was translated into English by Marie Kerguelen Feldblyum LeBlevennec and lightly edited by Jacques Bouveresse, Juliet Floyd, and Sandra Laugier. Themes covered in the interview include the question of Wittgenstein’s importance in contemporary philosophy, Putnam’s development with respect to realism, especially (...) in philosophy of mathematics, and the differences and motivations for realism in mathematics, physics, and ethics. The editors thank Marie Kerguelen Feldblyum LeBlevennec for her translation, and Jacques Bouveresse, Mario De Caro, and Sandra Laugier for permission to publish this transcription. (shrink)
Responding to questions put to him at a Roundtable held at Villanova University in 1994, Jacques Derrida leads the reader through an illuminating discussion of the central themes of deconstruction. Speaking in English and extemporaneously, Derrida takes up with unusual clarity and great eloquence such topics as the task of philosophy, the Greeks, justice, responsibility, the gift, the community, the distinction between the messianic and the concrete messianisms, and his interpretation of James Joyce. Derrida convincingly refutes the charges of (...) relativism and nihilism that are often leveled at deconstruction by its critics and sets forth the profoundly affirmative and ethico-political thrust of his work. The “Roundtable” is marked by the unusual clarity of Derrida’s presentation and by the deep respect for the great works of the philosophical and literary tradition with which he characterizes his philosophical work. The Roundtable is annotated by John D. Caputo, the David R. Cook Professor of Philosophy at Villanova University, who has supplied cross references to Derrida’s writings where the reader may find further discussion on these topics. Professor Caputo has also supplied a commentary which elaborates the principal issues raised in the Roundtable. In all, this volume represents one of the most lucid, compact and reliable introductions to Derrida and deconstruction available in any language. An ideal volume for students approaching Derrida for the first time, Deconstruction in a Nutshell will prove instructive and illuminating as well for those already familiar with Derrida’s work. (shrink)
Jacques Derrida: Law as Absolute Hospitalityãeepresents a comprehensive account and understanding of Derridaâe(tm)s approach to law and justice. Through a detailed reading of Derridaâe(tm)s texts, Jacques de Ville contends that it is only by way of Derrida's deconstruction of the metaphysics of presence, and specifically in relation to the texts of Husserl, Levinas, Freud and Heidegger - that the reasoning behind his elusive works on law and justice can be grasped. Through detailed readings of texts such as To (...) speculate âe" on Freud, Adieu, Declarations of Independence, Before the Law, Cogito and the history of madness, Given Time, Force of Law and Specters of Marx, De Ville contends that there is a continuity in Derridaâe(tm)s thinking, and rejects the idea of an âe~ethical turnâe(tm). Derrida is shown to be neither a postmodernist nor a political liberal, but a radical revolutionary. De Ville also controversially contends that justice in Derridaâe(tm)s thinking must be radically distinguished from Levinasâe(tm)s reflections on âe~the otherâe(tm). It is the notion of absolute hospitality - which Derrida derives from Levinas, but radically transforms - that provides the basis of this argument. Justice must on De Villeâe(tm)s reading be understood in terms of a demand of absolute hospitality which is imposed on both the individual and the collective subject. A much needed account of Derrida's influential approach to law,ãeeJacques Derrida: Law as Absolute Hospitalityãeewill be an invaluable resource for those with an interest in legal theory, and for those with an interest in the ethics and politics of deconstruction. (shrink)
Chora L Works documents the unprecedented collaboration, initiated in 1985, between philosopher Jacques Derrida and architect Peter Eisenman on a project for the Parc de la Villette in Paris. Woven into the volume are discussion transcripts, candid correspondence, and essays, as well as sketches, presentation drawings, and models. Derrida and Eisenman's design process was guided by Plato's chora text from the Timeaus; their unique reciprocal relationship was an interchange - and transformation - of voices.
In  we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of  allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions).
When I first contacted Jacques Rancière in March 2017, nearly three-and-a-half years before the completion of this interview, a few basic questions were growing heavy. Questions limited to current political climates, trending philosophical systems, specific literary works, designated historical shifts, or particular Rancièrean terms would be reluctantly put aside in pursuit of certain elemental distinctions that might better inform the rest. The original proposal was to work around such slippery paradoxes as resistance, and to readdress tangible material like the (...) letter, but the overall idea, communicated from the start, was to produce a sort of reintroduction to Rancière's thought, for myself and an intended... (shrink)
In this 2004 interview — translated into English and published in its entirety for the first time — Jacques Derrida reflects upon his practices of writing and teaching, about the community of his readers, and explores questions related to corporeity and textuality, sexual difference, desire, politics, Marxism, violence, truth, interpretation, and translation. In the course of the interview, Derrida discusses the work of Martin Heidegger, Hans-Georg Gadamer, Maurice Blanchot, Hélène Cixous, Jean Genet, Paul Celan, and many others.
Prodigiously influential, Jacques Derrida gave rise to a comprehensive rethinking of the basic concepts and categories of Western philosophy in the latter part of the twentieth century, with writings central to our understanding of language, meaning, identity, ethics and values. In 1993, a conference was organized around the question, 'Whither Marxism?’, and Derrida was invited to open the proceedings. His plenary address, 'Specters of Marx', delivered in two parts, forms the basis of this book. Hotly debated when it was (...) first published, a rapidly changing world and world politics have scarcely dented the relevance of this book. (shrink)
One of Jacques Derrida’s richest and most provocative works, Life Death challenges and deconstructs one of the most deeply rooted dichotomies of Western thought: life and death. Here Derrida rethinks the traditional philosophical understanding of the relationship between life and death, undertaking multidisciplinary analyses of a range of topics, including philosophy, linguistics, and the life sciences. In seeking to understand the relationship between life and death, he engages in close readings of Freudian psychoanalysis, the philosophy of Nietzsche and Heidegger, (...) French geneticist François Jacob, and epistemologist Georges Canguilhem. Derrida gave his “Life Death” seminar over fourteen sessions between 1975 and 1976 at the École normale supérieure in Paris as part of the preparation for students studying for the agrégation, a notoriously competitive qualifying exam. The theme for the exam that year was “Life and Death,” but Derrida made a critical modification to the title by dropping the coordinating conjunction. The resulting title of Life Death poses a philosophical question about the close relationship between life and death. Derrida argues that death must be considered neither as the opposite of life nor as the truth or fulfillment of it, but rather as that which both limits life and makes it possible. Through these captivating sessions, Derrida thus not only questions traditional understandings of the relationship between life and death, but also ultimately develops a new way of thinking about what he calls “life death.”. (shrink)
Frederick Watkins’ 1953 edition of Rousseau’s _Political Writings_ has long been noted for being fully accurate while representing much of Rousseau’s eloquence and elegance. It contains what is widely regarded as the finest English translation of _The Social Contract_, Rousseau’s greatest political treatise. In addition, this edition offers the best available translation of the late and important _Government of Poland_ and the only published English translation of the fragment _Constitutional Project for Corsica_, which, says Watkins, provides the clearest possible demonstration (...) of the practical implications of Rousseau’s political thought. (shrink)
One of the most influential and controversial thinkers of the twentieth-century, Jacques Derrida’s ideas on deconstruction have had a lasting impact on philosophy, literature and cultural studies. Jacques Derrida: Basic Writings is the first anthology to present his most important philosophical writings and is an indispensable resource for all students and readers of his work. Barry Stocker’s clear and helpful introductions set each reading in context, making the volume an ideal companion for those coming to Derrida’s writings for (...) the first time. The selections themselves range from his most infamous works including Speech and Phenomena and Writing and Difference to lesser known discussion on aesthetics, ethics and politics. (shrink)
We discuss in the paper the following problem: Given a function in a given Baire class, into "how many" (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union.