HOME > 상세정보

상세정보

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

자료유형
E-Book(소장)
개인저자
Von Plato, Jan.
서명 / 저자사항
The great formal machinery works [electronic resource] : theories of deduction and computation at the origins of the digital age / Jan von Plato.
발행사항
Princeton, New Jersey ;   Woodstock, Oxfordshire :   Princeton University Press,   c2017.  
형태사항
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.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Information technology --History. Computers --History.
바로가기
EBSCOhost   URL
000 00000cam u2200205 a 4500
001 000045981725
005 20190425164142
006 m d
007 cr
008 190424s2017 njua ob 001 0 eng d
010 ▼a 2017938675
020 ▼a 9781400885039 (electronic bk.)
020 ▼a 1400885035 (electronic bk.)
020 ▼a 9780691174174
035 ▼a 1460141 ▼b (N$T)
035 ▼a (OCoLC)992119144 ▼z (OCoLC)984545641
037 ▼a 22573/ctt1vwjsfh ▼b JSTOR
040 ▼a N$T ▼b eng ▼e rda ▼e pn ▼c N$T ▼d IDEBK ▼d N$T ▼d YDX ▼d EBLCP ▼d OCLCF ▼d CNCGM ▼d OCLCQ ▼d JSTOR ▼d UWW ▼d DEGRU ▼d UAB ▼d MCW ▼d CEF ▼d OH1 ▼d 211009
050 0 0 ▼a T58.5
082 0 4 ▼a 004.09 ▼2 23
084 ▼a 004.09 ▼2 DDCK
090 ▼a 004.09
100 1 ▼a Von Plato, Jan.
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)

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/e-Book 컬렉션/ 청구기호 CR 004.09 등록번호 E14011890 도서상태 대출불가(열람가능) 반납예정일 예약 서비스 M

컨텐츠정보

목차

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 -- .

관련분야 신착자료