• Mathematics

Reason's Nearest Kin

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.

    • Philosophy

The Routledge Companion to Twentieth Century Philosophy


Author: Dermot Moran
Publisher: Routledge
ISBN: 1134424035
Category: Philosophy
Page: 1040
View: 6906
The twentieth century was one of the most significant and exciting periods ever witnessed in philosophy, characterized by intellectual change and development on a massive scale. The Routledge Companion to Twentieth Century Philosophy is an outstanding authoritative survey and assessment of the century as a whole. Featuring twenty-two chapters written by leading international scholars, this collection is divided into five clear parts and presents a comprehensive picture of the period for the first time: major themes and movements logic, language, knowledge and metaphysics philosophy of mind, psychology and science phenomenology, hermeneutics, existentialism, and critical theory politics, ethics, aesthetics. Featuring annotated further reading and a comprehensive glossary, The Routledge Companion to Twentieth Century Philosophy is indispensable for anyone interested in philosophy over the last one hundred years, suitable for both expert and novice alike.

    • Philosophy

Origins of Analytic Philosophy

Kant and Frege
Author: Delbert Reed
Publisher: A&C Black
ISBN: 1441123024
Category: Philosophy
Page: 224
View: 446

    • Philosophy

Space, Number, and Geometry from Helmholtz to Cassirer


Author: Francesca Biagioli
Publisher: Springer
ISBN: 3319317792
Category: Philosophy
Page: 239
View: 4202
This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

    • Philosophy

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.

Ludwig Wittgenstein: Early Works: Oxford Bibliographies Online Research Guide


Author: Denis McManus
Publisher: Oxford University Press
ISBN: 0199810753
Category:
Page: 26
View: 3901
This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.

    • Social Science

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.

Kant-Studien

philosophische Zeitschrift
Author: N.A
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 4440

    • Mathematics

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

    • Mathematics

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6472

    • Philosophy

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.

    • American literature

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

    • Philosophy

Wittgenstein's Notes on Logic


Author: Michael Potter
Publisher: Oxford University Press
ISBN: 0199215839
Category: Philosophy
Page: 310
View: 3416
This is the first book-length study of Wittgenstein's first philosophical work, The Notes on Logic . Since Wittgenstein is one of the most important figures in the history of philosophy, and one of the few who attracts the interest of non-philosophers, the book is likely to be of unusually wide interest. Using a challenging blend of biography and philosophy, it draws new conclusions about the nature of the Notes , about the genesis of theTractatus (which draws on material from them), and about Wittgenstein's highly individualistic working methods.

    • Philosophy

Ramsey's Legacy


Author: Hallvard Lillehammer,D. H. Mellor
Publisher: Oxford University Press on Demand
ISBN: 0199279551
Category: Philosophy
Page: 182
View: 582
The Cambridge philosopher Frank Ramsey (1903-1930) died tragically young, but had already established himself as one of the most brilliant minds of the twentieth century. Besides groundbreaking work in philosophy, particularly in logic, language, and metaphysics, he created modern decision theory and made substantial contributions to mathematics and economics. In these original essays, written to commemorate the centenary of Ramsey's birth, a distinguished international team ofcontributors offer fresh perspectives on his work and show how relevant it is to present-day concerns.Each of the ten essays addresses fundamental and contentious issues, including success semantics, propositions, infinity, conditionals, conceptual analysis, decision theory, and intergenerational justice. They also shed light on the intellectual context in which Ramsey developed his thought, including his relationship with such leading thinkers as John Maynard Keynes, Bertrand Russell, and Ludwig Wittgenstein. The volume will be indispensable reading for anyone interested in the recent historyof philosophy and economics, as well as for practitioners and students of logic, metaphysics, philosophy of mathematics, philosophy of science, philosophy of mind, decision theory, and welfare economics.

    • Philosophy

Anuario filosófico


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Philosophy
Page: N.A
View: 5383

    • Mathematics

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.

    • Philosophy

Origins of Objectivity


Author: Tyler Burge
Publisher: Oxford University Press
ISBN: 0199581401
Category: Philosophy
Page: 624
View: 7639
Tyler Burge's study investigates the most primitive ways in which individuals represent the physical world. By reflecting on the science of perception and related psychological and biological sciences, Burge outlines the constitutive conditions for perceiving the physical world, thus locating the origins of representational mind.

    • Philosophy

From Kant to Husserl


Author: Charles Parsons
Publisher: Harvard University Press
ISBN: 0674065425
Category: Philosophy
Page: 242
View: 9124
Main description: In From Kant to Husserl, Charles Parsons examines a wide range of historical opinion on philosophical questions, from mathematics to phenomenology. Amplifying his early ideas on Kant's philosophy of arithmetic, Parsons uses Kant's lectures on metaphysics to explore how his arithmetical concepts relate to the categories. He then turns to early reactions by two immediate successors of Kant, Johann Schultz and Bernard Bolzano, to shed light on disputed questions regarding interpretation of Kant's philosophy of mathematics. Interested, as well, in what Kant meant by 0pure natural science,0 Parsons considers the relationship between the first Critique and the Metaphysical Foundations of Natural Science. His commentary on Kant's Transcendental Aesthetic departs from mathematics to engage the vexed question of what it tells about the meaning of Kant's transcendental idealism.Proceeding on to phenomenology, Parsons examines Frege's evolving idea of extensions, his attitude toward set theory, and his correspondence, particularly exchanges with Russell and Husserl. An essay on Brentano brings out, in the case of judgment, an alternative to the now standard Fregean view of negation, and, on truth, alternatives to the traditional correspondence view that are still discussed today. Ending with the question of why Husserl did not take the 0linguistic turn,0 a final essay included here marks the only article-length discussion of Husserl Parsons has ever written, despite a long-standing engagement with this philosopher.

    • Philosophy

Organon F.


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Philosophy
Page: N.A
View: 7660

    • Philosophy

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