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.
Psychological and Logical Investigations with Supplementary Texts from 1887–1901
Author: Edmund Husserl
Publisher: Springer Science & Business Media
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
(considered as a Branch of Mathematical Science) and the Elements of Algebra
Author: John Walker
Containing Also a History of Arithmetic
Author: Edward Brooks
Author: William Russell (writing master.)
Author: William RUSSELL (Writing Master and Accountant.)
With Numerous Problems, Curious and Useful, Solved by Various Modes ...
Author: Uriah Parke
Author: John WALKER (Fellow of Trinity College, Dublin.)
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.
A Non-realist Philosophy of Arithmetic
Author: Philip Hugly,Charles Sayward
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.
Author: Burt Hopkins,John Drummond
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.
Author: Douglas M. Jesseph
Publisher: University of Chicago Press
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.
A Quechua Ontology of Numbers and Philosophy of Arithmetic
Author: Gary Urton,Primitivo Nina Llanos
Publisher: University of Texas Press
Category: Social Science
Edmund Husserl and the Quest for a Rigorous Science of Philosophy
Author: Marvin Farber
Publisher: SUNY Press
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.
Author: Michael Dummett
Publisher: Columbia University Press
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.
Author: Stefania Centrone
Publisher: Springer Science & Business Media
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.
Author: C.J. Posy
Publisher: Springer Science & Business Media