Philosophy of Arithmetic

Psychological and Logical Investigations with Supplementary Texts from 1887–1901

Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 9401000603

Category: Mathematics

Page: 515

View: 4178

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.

The Philosophy of Arithmetic

Exhibiting a Progressive View of the Theory and Practice of Calculation, with an Enlarged Table of the Products of Numbers Under One Hundred

Author: Sir John Leslie

Publisher: N.A

ISBN: N.A

Category: Arithmetic

Page: 240

View: 4674


Arithmetic and Ontology

A Non-realist Philosophy of Arithmetic

Author: Philip Hugly,Charles Sayward

Publisher: Rodopi

ISBN: 9789042020474

Category: Mathematics

Page: 393

View: 9958

This volume documents a lively exchange between five philosophers of mathematics. It also introduces a new voice in one central debate in the philosophy of mathematics. Non-realism, i.e., the view supported by Hugly and Sayward in their monograph, is an original position distinct from the widely known realism and anti-realism. Non-realism is characterized by the rejection of a central assumption shared by many realists and anti-realists, i.e., the assumption that mathematical statements purport to refer to objects. The defense of their main argument for the thesis that arithmetic lacks ontology brings the authors to discuss also the controversial contrast between pure and empirical arithmetical discourse. Colin Cheyne, Sanford Shieh, and Jean Paul Van Bendegem, each coming from a different perspective, test the genuine originality of non-realism and raise objections to it. Novel interpretations of well-known arguments, e.g., the indispensability argument, and historical views, e.g. Frege, are interwoven with the development of the authors' account. The discussion of the often neglected views of Wittgenstein and Prior provide an interesting and much needed contribution to the current debate in the philosophy of mathematics.

The New Yearbook for Phenomenology and Phenomenological Philosophy

Author: Burt Hopkins,John Drummond

Publisher: Routledge

ISBN: 1317401247

Category: Philosophy

Page: 410

View: 2874

The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer.

Berkeley's Philosophy of Mathematics

Author: Douglas M. Jesseph

Publisher: University of Chicago Press

ISBN: 0226398951

Category: Philosophy

Page: 329

View: 2499

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a "science of abstractions." Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique treatments of geometry and arithmetic and his famous critique of the calculus in The Analyst. By putting Berkeley's mathematical writings in the perspective of his larger philosophical project and examining their impact on eighteenth-century British mathematics, Jesseph makes a major contribution to philosophy and to the history and philosophy of science.

Routledge Philosophy GuideBook to Frege on Sense and Reference

Author: Mark Textor

Publisher: Routledge

ISBN: 113693054X

Category: Philosophy

Page: 304

View: 6487

Gottlob Frege (1848-1925) is considered the father of modern logic and one of the founding figures of analytic philosophy. He was first and foremost a mathematician, but his major works also made important contributions to the philosophy of language. Frege’s writings are difficult and deal with technical, abstract concepts. The Routledge Philosophy Guidebook to Frege On Sense and Reference helps the student to get to grips with Frege’s thought, and introduces and assesses: the background of Frege’s philosophical work Frege’s main papers and arguments, focussing on his distinction between sense and reference the continuing importance of Frege’s work to philosophy of logic and language. Ideal for those coming to Frege for the first time, and containing fresh insights for anyone interested in his philosophy, this Guidebook is essential reading for all students of philosophy of language, philosophical logic and the history of analytic philosophy.

The Social Life of Numbers

A Quechua Ontology of Numbers and Philosophy of Arithmetic

Author: Gary Urton,Primitivo Nina Llanos

Publisher: University of Texas Press

ISBN: 0292786840

Category: Social Science

Page: 285

View: 336

Unraveling all the mysteries of the khipu—the knotted string device used by the Inka to record both statistical data and narrative accounts of myths, histories, and genealogies—will require an understanding of how number values and relations may have been used to encode information on social, familial, and political relationships and structures. This is the problem Gary Urton tackles in his pathfinding study of the origin, meaning, and significance of numbers and the philosophical principles underlying the practice of arithmetic among Quechua-speaking peoples of the Andes. Based on fieldwork in communities around Sucre, in south-central Bolivia, Urton argues that the origin and meaning of numbers were and are conceived of by Quechua-speaking peoples in ways similar to their ideas about, and formulations of, gender, age, and social relations. He also demonstrates that their practice of arithmetic is based on a well-articulated body of philosophical principles and values that reflects a continuous attempt to maintain balance, harmony, and equilibrium in the material, social, and moral spheres of community life.

Husserl-Arg Philosophers

Author: David A Bell

Publisher: Routledge

ISBN: 1136957847

Category: Philosophy

Page: 284

View: 5669

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

The Nature and Future of Philosophy

Author: Michael Dummett

Publisher: Columbia University Press

ISBN: 0231522185

Category: Philosophy

Page: 160

View: 2065

Philosophy is a discipline that makes no observations, conducts no experiments, and needs no input from experience. It is an armchair subject, requiring only thought. Yet that thought can advance knowledge in unexpected directions, not only through the discovery of new facts but also through the enhancement of what we already know. Philosophy can clarify our vision of the world and provide exciting ways to interpret it. Of course, philosophy's unified purpose hasn't kept the discipline from splintering into warring camps. Departments all over the world are divided among analytical and continental schools, Heidegger, Hegel, and other major thinkers, challenging the growth of the discipline and obscuring its relevance and intent. Having spent decades teaching in American, Asian, African, and European universities, Michael Dummett has felt firsthand the fractured state of contemporary practice and the urgent need for reconciliation. Setting forth a proposal for renewal and reengagement, Dummett begins with the nature of philosophical inquiry as it has developed for centuries, especially its exceptional openness and perspective-which has, ironically, led to our present crisis. He discusses philosophy in relation to science, religion, morality, language, and meaning and recommends avenues for healing around a renewed investigation of mind, language, and thought. Employing his trademark frankness and accessibility, Dummett asks philosophers to resolve theoretical difference and reclaim the vital work of their practice.

Logic and Philosophy of Mathematics in the Early Husserl

Author: Stefania Centrone

Publisher: Springer Science & Business Media

ISBN: 9048132479

Category: Philosophy

Page: 232

View: 6296

Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl’s early work as a more or less immature sketch of claims consolidated only in his later phenomenology, and unlike the majority of historians of logic she emphasizes the systematic strength and the originality of Husserl’s logico-mathematical work. The book attempts to reconstruct the discussion between Husserl and those philosophers and mathematicians who contributed to new developments in logic, such as Leibniz, Bolzano, the logical algebraists (especially Boole and Schröder), Frege, and Hilbert and his school. It presents both a comprehensive critical examination of some of the major works produced by Husserl and his antagonists in the last decade of the 19th century and a formal reconstruction of many texts from Husserl’s Nachlaß that have not yet been the object of systematical scrutiny. This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to analytical philosophers and phenomenologists with a background in standard logic.

Kant’s Philosophy of Mathematics

Modern Essays

Author: C.J. Posy

Publisher: Springer Science & Business Media

ISBN: 9401580464

Category: Philosophy

Page: 380

View: 2817

Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come.

Logical Investigations

Author: Edmund Husserl

Publisher: Routledge

ISBN: 1134548559

Category: Philosophy

Page: 432

View: 9810

Edmund Husserl is the founder of phenomenology and the Logical Investigations is his most famous work. It had a decisive impact on twentieth century philosophy and is one of few works to have influenced both continental and analytic philosophy. This is the first time both volumes have been available in paperback. They include a new introduction by Dermot Moran, placing the Investigations in historical context and bringing out their contemporary philosophical importance. These editions include a new preface by Sir Michael Dummett.