Philosophies of Arithmetic from Kant to Carnap
Author: Michael Potter
Publisher: Oxford University Press
ISBN: 019825041X
Category: Mathematics
Page: 305
View: 3847
How do we account for the truth of arithmetic? And if it does not depend for its truth on the way the world is, what constrains the world to conform to arithmetic? Reason's Nearest Kin is a critical examination of the astonishing progress made towards answering these questions from the late nineteenth to the mid-twentieth century. In the space of fifty years Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, and Carnap developed accounts of the content of arithmeticthat were brilliantly original both technically and philosophically. Michael Potter's innovative study presents them all as finding that content in various aspects of the complex linkage between experience, language, thought, and the world. Potter's reading places them all in Kant's shadow since it was hisattempt to ground arithmetic in the spatio-temporal structure of reality that they were reacting against; but it places us in Gödel's shadow since his incompleteness theorems supply us with a measure of the richness of the content they were trying to explain. This stimulating reassessment of some of the classic texts in the philosophy of mathematics reveals many unexpected connections and illuminating comparisons, and offers a wealth of ideas for future work in the subject.
The Routledge Companion to Twentieth Century Philosophy
Author: Dermot Moran
Publisher: Routledge
ISBN: 1134424035
Category: Philosophy
Page: 1040
View: 6906
Origins of Analytic Philosophy
Kant and Frege
Author: Delbert Reed
Publisher: A&C Black
ISBN: 1441123024
Category: Philosophy
Page: 224
View: 446
Author: Delbert Reed
Publisher: A&C Black
ISBN: 1441123024
Category: Philosophy
Page: 224
View: 446
Space, Number, and Geometry from Helmholtz to Cassirer
Author: Francesca Biagioli
Publisher: Springer
ISBN: 3319317792
Category: Philosophy
Page: 239
View: 4202
Set Theory and its Philosophy
A Critical Introduction
Author: Michael Potter
Publisher: Clarendon Press
ISBN: 0191556432
Category: Philosophy
Page: 360
View: 1616
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author: Michael Potter
Publisher: Clarendon Press
ISBN: 0191556432
Category: Philosophy
Page: 360
View: 1616
Ludwig Wittgenstein: Early Works: Oxford Bibliographies Online Research Guide
Author: Denis McManus
Publisher: Oxford University Press
ISBN: 0199810753
Category:
Page: 26
View: 3901
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: 9198
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.
Author: Gary Urton,Primitivo Nina Llanos
Publisher: University of Texas Press
ISBN: 0292786840
Category: Social Science
Page: 285
View: 9198
Kant-Studien
philosophische Zeitschrift
Author: N.A
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 4440
Author: N.A
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 4440
Philosophy of mathematics
an introduction
Author: David Bostock
Publisher: Blackwell Pub
ISBN: 9781405189910
Category: Mathematics
Page: 332
View: 1692
Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author’s personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals
Author: David Bostock
Publisher: Blackwell Pub
ISBN: 9781405189910
Category: Mathematics
Page: 332
View: 1692
Mathematical Reviews
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6472
The Concept 'Horse' Paradox and Wittgensteinian Conceptual Investigations
A Prolegomenon to Philosophical Investigations
Author: Dr Kelly Dean Jolley
Publisher: Ashgate Publishing, Ltd.
ISBN: 140948548X
Category: Philosophy
Page: 126
View: 5469
In The Foundations of Arithmetic, Gottlob Frege contended that the difference between concepts and objects was absolute. He meant that no object could be a concept and no concept an object. Benno Kerry disagreed; he contended that a concept could be an object, and that therefore the difference between concepts and objects was only relative. In this book, Jolley aims to understand the debate between Frege and Kerry. But Jolley's purpose is not so much to champion either side; rather, it is to utilize an understanding of the debate to shed light on the work of Ludwig Wittgenstein-and vice versa. Jolley not only sifts through the debate between Frege and Kerry, but also through subsequent versions of the debate in J. J. Valberg and Wilfred Sellars. Jolley's goal is to show that the central notion of Philosophical Investigations, that of a 'conceptual investigation', is a legacy of the Frege/Kerry debate and also a contribution to it. Jolley concludes that the difference between concepts and objects is as absolute in its way in Philosophical Investigations as it was in The Foundations of Arithmetic and that recognizing the absoluteness of the difference in Philosophical Investigations provides a beginning for a 'resolute' reading of Wittgenstein's book.
Author: Dr Kelly Dean Jolley
Publisher: Ashgate Publishing, Ltd.
ISBN: 140948548X
Category: Philosophy
Page: 126
View: 5469
Subject Guide to Books in Print
An Index to the Publishers' Trade List Annual
Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 2662
Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 2662
Wittgenstein's Notes on Logic
Author: Michael Potter
Publisher: Oxford University Press
ISBN: 0199215839
Category: Philosophy
Page: 310
View: 3416
Ramsey's Legacy
Author: Hallvard Lillehammer,D. H. Mellor
Publisher: Oxford University Press on Demand
ISBN: 0199279551
Category: Philosophy
Page: 182
View: 582
Anuario filosófico
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Philosophy
Page: N.A
View: 5383
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: 5327
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.
Author: Edmund Husserl
Publisher: Springer Science & Business Media
ISBN: 9401000603
Category: Mathematics
Page: 515
View: 5327
Origins of Objectivity
Author: Tyler Burge
Publisher: Oxford University Press
ISBN: 0199581401
Category: Philosophy
Page: 624
View: 7639
From Kant to Husserl
Author: Charles Parsons
Publisher: Harvard University Press
ISBN: 0674065425
Category: Philosophy
Page: 242
View: 9124
Organon F.
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Philosophy
Page: N.A
View: 7660
Con l'ali de l'intelletto
studi di filosofia e di storia della cultura
Author: Fabrizio Meroi
Publisher: Olschki
ISBN: 9788822254610
Category: Philosophy
Page: 405
View: 2450
Author: Fabrizio Meroi
Publisher: Olschki
ISBN: 9788822254610
Category: Philosophy
Page: 405
View: 2450