Paolo Mancosu's Books

The Philosophy of Mathematical Practice

By: Paolo Mancosu

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The Philosophy of Mathematical Practice

By: Paolo Mancosu

There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

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460

Publisher

Oxford University Press on Demand

Published Date

ISBN 10

0199296456

ISBN 13

9780199296453

The Adventure of Reason

Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

By: Paolo Mancosu

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The Adventure of Reason

Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

By: Paolo Mancosu

Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

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Page Count

631

Publisher

OUP Oxford

Published Date

ISBN 10

0191021997

ISBN 13

9780191021992

Abstraction and Infinity

By: Paolo Mancosu

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Abstraction and Infinity

By: Paolo Mancosu

Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism.

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240

Publisher

Oxford University Press

Published Date

ISBN 10

0191063800

ISBN 13

9780191063800

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

By: Paolo Mancosu

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Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

By: Paolo Mancosu

Includes bibliographical references and index.

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286

Publisher

Oxford University Press, USA

Published Date

ISBN 10

0195084632

ISBN 13

9780195084634

Zhivago's Secret Journey

From Typescript to Book

By: Paolo Mancosu

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Zhivago's Secret Journey

From Typescript to Book

By: Paolo Mancosu

Paolo Mancosu continues an investigation he began in his 2013 book Inside the Zhivago Storm, which the New York Book Review of Books described as "a tour de force of literary detection worthy of a scholarly Sherlock Holmes". In this book Mancosu extends his detective work by reconstructing the network of contacts that helped Pasternak smuggle the typescripts of Doctor Zhivago outside the Soviet Union and following the vicissitudes of the typescripts when they arrived in the West. Mancosu draws on a wealth of firsthand sources to piece together the long-standing mysteries surrounding the many different typescripts that played a role in the publication of Doctor Zhivago, thereby solving the problem of which typescript served as the basis of the first Russian edition: a pirate publication covertly orchestrated by the Central Intelligence Agency (CIA). He also offers a new perspective, aided by the recently declassified CIA documents, by narrowing the focus as to who might have passed the typescript to the CIA. In the process, Mancosu reveals details of events that were treated as top secret by all those involved, vividly recounting the history of the publication of Pasternak's epic work with all its human and political ramifications.

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Page Count

283

Publisher

Hoover Press

Published Date

ISBN 10

081791966X

ISBN 13

9780817919665

An Introduction to Proof Theory

Normalization, Cut-Elimination, and Consistency Proofs

By: Paolo Mancosu,Sergio Galvan,Richard Zach

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An Introduction to Proof Theory

Normalization, Cut-Elimination, and Consistency Proofs

By: Paolo Mancosu,Sergio Galvan,Richard Zach

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

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336

Publisher

Oxford University Press

Published Date

ISBN 10

0192649299

ISBN 13

9780192649294

Abstraction and Infinity

By: Paolo Mancosu

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Abstraction and Infinity

By: Paolo Mancosu

Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems.

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231

Publisher

Oxford University Press

Published Date

ISBN 10

0198746822

ISBN 13

9780198746829

From Brouwer to Hilbert

The Debate on the Foundations of Mathematics in the 1920s

By: Paolo Mancosu

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From Brouwer to Hilbert

The Debate on the Foundations of Mathematics in the 1920s

By: Paolo Mancosu

Most contemporary work in the foundations of mathematics takes its start from the groundbreaking contributions of, among others, Hilbert, Brouwer, Bernays, and Weyl. This book offers an introduction to the debate on the foundations of mathematics during the 1920s and presents the English reader with a selection of twenty five articles central to the debate which have not been previously translated. It is an ideal text for undergraduate and graduate courses in the philosophy of mathematics.

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337

Publisher

Oxford University Press on Demand

Published Date

ISBN 10

0195096320

ISBN 13

9780195096323

Analytic Philosophy and the Later Wittgensteinian Tradition

By: Paolo Tripodi

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Analytic Philosophy and the Later Wittgensteinian Tradition

By: Paolo Tripodi

This book aims to explain the decline of the later Wittgensteinian tradition in analytic philosophy during the second half of the twentieth century. Throughout the 1950s, Oxford was the center of analytic philosophy and Wittgenstein – the later Wittgenstein – the most influential contemporary thinker within that philosophical tradition. Wittgenstein's methods and ideas were widely accepted, with everything seeming to point to the Wittgensteinian paradigm having a similar impact on the philosophical scenes of all English speaking countries. However, this was not to be the case. By the 1980s, albeit still important, Wittgenstein was considered as a somewhat marginal thinker. What occurred within the history of analytic philosophy to produce such a decline? This book expertly traces the early reception of Wittgenstein in the United States, the shift in the humanities to a tradition rooted in the natural sciences, and the economic crisis of the mid-1970s, to reveal the factors that contributed to the eventual hostility towards the later Wittgensteinian tradition.

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Page Count

276

Publisher

Springer Nature

Published Date

ISBN 10

1137499907

ISBN 13

9781137499905

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

By: Paolo Mancosu

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Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

By: Paolo Mancosu

1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.

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290

Publisher

Oxford University Press, USA

Published Date

ISBN 10

0195132440

ISBN 13

9780195132441

Moscow Has Ears Everywhere

New Investigations on Pasternak and Ivinskaya

By: Paolo Mancosu

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Moscow Has Ears Everywhere

New Investigations on Pasternak and Ivinskaya

By: Paolo Mancosu

The conflict between Soviet Communists and Boris Pasternak over the publication of Doctor Zhivago did not end when he won the Nobel Prize, or even when the author died. Paolo Mancosu tells how Pasternak's expulsion from the Soviet Writers' Union left him in financial difficulty. After Pasternak's death, Olga Ivinskaya, his companion, literary assistant, and the inspiration for Zhivago's Lara, also received some of the Zhivago royalties. After the KGB intercepted Pasternak's will on her behalf, the Soviets arrested and sentenced her to eight years of labor camp. The ensuing international outrage inspired a secret campaign in the West to win her freedom. Mancosu's new book provides extraordinary detail on these events, in a thrilling account that involves KGB interceptions, fabricated documents, smugglers, and much more. Included are letters of Pasternak and Ivinskaya from the Hoover Institution Library and Archives.

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424

Publisher

Hoover Press

Published Date

ISBN 10

0817922466

ISBN 13

9780817922467

Syllogistic Logic and Mathematical Proof

By: Paolo Mancosu,Massimo Mugnai

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Syllogistic Logic and Mathematical Proof

By: Paolo Mancosu,Massimo Mugnai

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.

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Page Count

238

Publisher

Oxford University Press

Published Date

ISBN 10

0198876947

ISBN 13

9780198876946

An Introduction to Proof Theory

Normalization, Cut-Elimination, and Consistency Proofs

By: Paolo Mancosu,Sergio Galvan,Richard Zach

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An Introduction to Proof Theory

Normalization, Cut-Elimination, and Consistency Proofs

By: Paolo Mancosu,Sergio Galvan,Richard Zach

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431

Publisher

Oxford University Press

Published Date

ISBN 10

0192895931

ISBN 13

9780192895936

Inside the Zhivago Storm

The Editorial Adventures of Pasternak’s Masterpiece. Anno Quarantasettesimo

By: Paolo Mancosu

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Inside the Zhivago Storm

The Editorial Adventures of Pasternak’s Masterpiece. Anno Quarantasettesimo

By: Paolo Mancosu

In Inside the Zhivago Storm. The Editorial Adventures of Pasternak’s Masterpiece, Paolo Mancosu, Professor of Philosophy at the University of California at Berkeley, provides a riveting account of the story of the first publication of Doctor Zhivago and of the subsequent Russian editions in the West. Exploiting with scholarly and philological rigor the untapped resources of the Feltrinelli archives in Milan as well as several other private and public archives in Europe, Russia, and the USA, Mancosu reconstructs the relationship between Pasternak and Feltrinelli, the story of the Italian publication, and the pressure exercised on Feltrinelli by the Soviets and the Italian Communist Party to stop publication of the novel in Italy and in other countries.

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Page Count

890

Publisher

Feltrinelli Editore

Published Date

ISBN 10

885881441X

ISBN 13

9788858814413

Book's by Paolo Mancosu

The Philosophy of Mathematical Practice

The Philosophy of Mathematical Practice

The Adventure of Reason

The Adventure of Reason

Abstraction and Infinity

Abstraction and Infinity

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Zhivago's Secret Journey

Zhivago's Secret Journey

An Introduction to Proof Theory

An Introduction to Proof Theory

Abstraction and Infinity

Abstraction and Infinity

From Brouwer to Hilbert

From Brouwer to Hilbert

Analytic Philosophy and the Later Wittgensteinian Tradition

Analytic Philosophy and the Later Wittgensteinian Tradition

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Moscow Has Ears Everywhere

Moscow Has Ears Everywhere

Syllogistic Logic and Mathematical Proof

Syllogistic Logic and Mathematical Proof

An Introduction to Proof Theory

An Introduction to Proof Theory

Inside the Zhivago Storm

Inside the Zhivago Storm

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