Philosophy Of Logic And Mathematics

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Philosophical and Mathematical Logic

Author : Harrie de Swart
Publisher : Springer
ISBN 13 : 3030032558
Total Pages : 539 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Philosophical and Mathematical Logic by : Harrie de Swart

Download or read book Philosophical and Mathematical Logic written by Harrie de Swart and published by Springer. This book was released on 2018-11-28 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo

Philosophy of Logic and Mathematics

Author : Gabriele M. Mras
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110657880
Total Pages : 559 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Philosophy of Logic and Mathematics by : Gabriele M. Mras

Download or read book Philosophy of Logic and Mathematics written by Gabriele M. Mras and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-18 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.

Three Views of Logic

Author : Donald W. Loveland
Publisher : Princeton University Press
ISBN 13 : 140084875X
Total Pages : 344 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Three Views of Logic by : Donald W. Loveland

Download or read book Three Views of Logic written by Donald W. Loveland and published by Princeton University Press. This book was released on 2014-01-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

Philosophy of Logic

Author :
Publisher : Elsevier
ISBN 13 : 9780080466637
Total Pages : 1218 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Philosophy of Logic by :

Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter

LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science

Author : Andrea Iacona
Publisher : Springer Nature
ISBN 13 : 3030648117
Total Pages : 228 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science by : Andrea Iacona

Download or read book LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science written by Andrea Iacona and published by Springer Nature. This book was released on 2021-05-10 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a logic manual which includes an elementary course and an advanced course. It covers more than most introductory logic textbooks, while maintaining a comfortable pace that students can follow. The technical exposition is clear, precise and follows a paced increase in complexity, allowing the reader to get comfortable with previous definitions and procedures before facing more difficult material. The book also presents an interesting overall balance between formal and philosophical discussion, making it suitable for both philosophy and more formal/science oriented students. This textbook is of great use to undergraduate philosophy students, graduate philosophy students, logic teachers, undergraduates and graduates in mathematics, computer science or related fields in which logic is required.

Early Writings in the Philosophy of Logic and Mathematics

Author : Edmund Husserl
Publisher : Springer
ISBN 13 : 0792322622
Total Pages : 505 pages
Book Rating : 4.7/5 (923 download)

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Book Synopsis Early Writings in the Philosophy of Logic and Mathematics by : Edmund Husserl

Download or read book Early Writings in the Philosophy of Logic and Mathematics written by Edmund Husserl and published by Springer. This book was released on 1993-12-31 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary intent of this volume is to give the English reader access to all the philosophical texts published by Husserl between the appearance of his first book, Philosophie der Arithmetik, and that of his second book, Logische Untersuchungen- roughly, from 1890 through 1901. Along with these texts we have included a number of unpublished manuscripts from the same period and dealing with the same or closely related topics. A few of the texts here translated (the review of Pahigyi, the five "report" articles of 1903-1904, the "notes" in Lalande's Vocabulaire, and the brief discussion. article on Marty of 1910) obviously fall outside this time period, so far as their publication dates are concerned; but in content they seem clearly confined to it. The final piece translated, a set of personal notes that date from 1906 through 1908, provides insight into how Husserl experienced his early labors and their results, and into how he saw their relation to work before him: a phenomenological critique of reason in all of its forms. Thus the texts here translated - which obviously are to be read in conjunction with his first two books - cover the progression of Husserl's Problematik from the relatively narrow one of clarifying the epistemic structure of general arithmetic, to the all-encompassing one of establishing in principle, through phenomenological research, the line between legitimate and illegitimate claims to know or to be rational, regardless of the domain concerned.

Phenomenology, Logic, and the Philosophy of Mathematics

Author : Richard L. Tieszen
Publisher : Cambridge University Press
ISBN 13 : 0521837820
Total Pages : 369 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Phenomenology, Logic, and the Philosophy of Mathematics by : Richard L. Tieszen

Download or read book Phenomenology, Logic, and the Philosophy of Mathematics written by Richard L. Tieszen and published by Cambridge University Press. This book was released on 2005-06-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.

Mathematics, Logic, and their Philosophies

Author : Mojtaba Mojtahedi
Publisher : Springer Nature
ISBN 13 : 3030536548
Total Pages : 493 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Mathematics, Logic, and their Philosophies by : Mojtaba Mojtahedi

Download or read book Mathematics, Logic, and their Philosophies written by Mojtaba Mojtahedi and published by Springer Nature. This book was released on 2021-02-09 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

Language, Logic, and Mathematics in Schopenhauer

Author : Jens Lemanski
Publisher : Springer Nature
ISBN 13 : 3030330907
Total Pages : 318 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Language, Logic, and Mathematics in Schopenhauer by : Jens Lemanski

Download or read book Language, Logic, and Mathematics in Schopenhauer written by Jens Lemanski and published by Springer Nature. This book was released on 2020-06-08 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

The Philosophy of Mathematical Practice

Author : Paolo Mancosu
Publisher : OUP Oxford
ISBN 13 : 0191559091
Total Pages : 460 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Philosophy of Mathematical Practice by : Paolo Mancosu

Download or read book The Philosophy of Mathematical Practice written by Paolo Mancosu and published by OUP Oxford. This book was released on 2008-06-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

Lectures on the Philosophy of Mathematics

Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Philosophy of Logic (Routledge Revivals)

Author : Hilary Putnam
Publisher : Routledge
ISBN 13 : 1317832574
Total Pages : 76 pages
Book Rating : 4.3/5 (178 download)

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Book Synopsis Philosophy of Logic (Routledge Revivals) by : Hilary Putnam

Download or read book Philosophy of Logic (Routledge Revivals) written by Hilary Putnam and published by Routledge. This book was released on 2014-04-04 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

Philosophy of Mathematics

Author : Paul Benacerraf
Publisher : Cambridge University Press
ISBN 13 : 1107268133
Total Pages : pages
Book Rating : 4.1/5 (72 download)

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Book Synopsis Philosophy of Mathematics by : Paul Benacerraf

Download or read book Philosophy of Mathematics written by Paul Benacerraf and published by Cambridge University Press. This book was released on 1984-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

Introduction to Mathematical Philosophy

Author : Bertrand Russell
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introduction to Mathematical Philosophy by : Bertrand Russell

Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Logic for Philosophy

Author : Theodore Sider
Publisher : Oxford University Press
ISBN 13 : 0192658816
Total Pages : 305 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Logic for Philosophy by : Theodore Sider

Download or read book Logic for Philosophy written by Theodore Sider and published by Oxford University Press. This book was released on 2010-01-07 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

The Oxford Handbook of Philosophy of Mathematics and Logic

Author : Stewart Shapiro
Publisher : Oxford University Press
ISBN 13 : 0190287535
Total Pages : 856 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis The Oxford Handbook of Philosophy of Mathematics and Logic by : Stewart Shapiro

Download or read book The Oxford Handbook of Philosophy of Mathematics and Logic written by Stewart Shapiro and published by Oxford University Press. This book was released on 2005-02-10 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

A Profile of Mathematical Logic

Author : Howard DeLong
Publisher : Courier Corporation
ISBN 13 : 0486139158
Total Pages : 322 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis A Profile of Mathematical Logic by : Howard DeLong

Download or read book A Profile of Mathematical Logic written by Howard DeLong and published by Courier Corporation. This book was released on 2012-09-26 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.