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The great formal machinery works [electronic resource] : theories of deduction and computation at the origins of the digital age

The great formal machinery works [electronic resource] : theories of deduction and computation at the origins of the digital age

Material type
E-Book(소장)
Personal Author
Von Plato, Jan.
Title Statement
The great formal machinery works [electronic resource] : theories of deduction and computation at the origins of the digital age / Jan von Plato.
Publication, Distribution, etc
Princeton, New Jersey ;   Woodstock, Oxfordshire :   Princeton University Press,   c2017.  
Physical Medium
1 online resource (xii, 378 p.) : ill.
ISBN
9781400885039 (electronic bk.) 1400885035 (electronic bk.) 9780691174174
요약
The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later.
General Note
Title from e-Book title page.  
Content Notes
An ancient tradition -- The emergence of foundational study -- The algebraic tradition of logic -- Frege's discovery of formal reasoning -- Russell : adding quantifiers to Peano's logic -- The point of constructivity -- The Göttingers -- Gödel's theorem : an end and a beginning -- The perfection of pure logic -- The problem of consistency.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Information technology --History. Computers --History.
Short cut
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245 1 4 ▼a The great formal machinery works ▼h [electronic resource] : ▼b theories of deduction and computation at the origins of the digital age / ▼c Jan von Plato.
260 ▼a Princeton, New Jersey ; ▼a Woodstock, Oxfordshire : ▼b Princeton University Press, ▼c c2017.
300 ▼a 1 online resource (xii, 378 p.) : ▼b ill.
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a An ancient tradition -- The emergence of foundational study -- The algebraic tradition of logic -- Frege's discovery of formal reasoning -- Russell : adding quantifiers to Peano's logic -- The point of constructivity -- The Göttingers -- Gödel's theorem : an end and a beginning -- The perfection of pure logic -- The problem of consistency.
520 ▼a The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Information technology ▼x History.
650 0 ▼a Computers ▼x History.
856 4 0 ▼3 EBSCOhost ▼u https://oca.korea.ac.kr/link.n2s?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1460141
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 004.09 Accession No. E14011890 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

Cover -- Title -- Copyright -- CONTENTS -- Preface -- Prologue: Logical Roots of the Digital Age -- 1. An Ancient Tradition -- 1.1. Reduction to the Evident -- 1.2. Aristotle’s Deductive Logic -- 1.3. Infinity and Incommensurability -- 1.4. Deductive and Marginal Notions of Truth -- 2. The Emergence of Foundational Study -- 2.1. In Search of the Roots of Formal Computation -- 2.2. Grassmann’s Formalization of Calculation -- 2.3. Peano: The Logic of Grassmann’s Formal Proofs -- 2.4. Axiomatic Geometry -- 2.5. Real Numbers -- 3. The Algebraic Tradition of Logic -- 3.1. Boole’s Logical Algebra -- 3.2. Schröder’s Algebraic Logic -- 3.3. Skolem’s Combinatorics of Deduction -- 4. Frege’s Discovery of Formal Reasoning -- 4.1. A Formula Language of Pure Thinking -- 4.2. Inference to Generality -- 4.3. Equality and Extensionality -- 4.4. Frege’s Successes and Failures -- 5. Russell: Adding Quantifiers to Peano’s Logic -- 5.1. Axiomatic Logic -- 5.2. The Rediscovery of Frege’s Generality -- 5.3. Russell’s Failures -- 6. The Point of Constructivity -- 6.1. Skolem’s Finitism -- 6.2. Stricter Than Skolem: Wittgenstein and His Students -- 6.3. The Point of Intuitionistic Geometry -- 6.4. Intuitionistic Logic in the 1920s -- 7. The Göttingers -- 7.1. Hilbert’s Program and Its Programmers -- 7.2. Logic in Göttingen -- 7.3. The Situation in Foundational Research around 1930 -- 8. Gödel’s Theorem: An End and a Beginning -- 8.1. How Gödel Found His Theorem -- 8.2. Consequences of Gödel’s Theorem -- 8.3. Two “Berliners” -- 9. The Perfection of Pure Logic -- 9.1. Natural Deduction -- 9.2. Sequent Calculus -- 9.3. Logical Calculi and Their Applications -- 10. The Problem of Consistency -- 10.1. What Does a Consistency Proof Prove? -- 10.2. Gentzen’s Original Proof of Consistency -- 10.3. Bar Induction: A Hidden Element in the Consistency Proof -- References -- Index -- .

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