The Great Formal Machinery Works : : Theories of Deduction and Computation at the Origins of the Digital Age / / Jan von Plato.
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 computatio...
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von Plato, Jan, author. aut http://id.loc.gov/vocabulary/relators/aut The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / Jan von Plato. Princeton, NJ : Princeton University Press, [2017] ©2017 1 online resource (400 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Contents -- Preface -- Prologue -- 1. An Ancient Tradition -- 2. The Emergence of Foundational Study -- 3. The Algebraic Tradition of Logic -- 4. Frege's Discovery of Formal Reasoning -- 5. Russell: Adding Quantifiers to Peano's Logic -- 6. The Point of Constructivity -- 7. The Göttingers -- 8. Gödel's Theorem: An End and a Beginning -- 9. The Perfection of Pure Logic -- 10. The Problem of Consistency -- References -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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.Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Computer science Mathematics. Logic, Symbolic and mathematical History. Mathematics History. SCIENCE / History. bisacsh Arend Heyting. Begriffsschrift. Bertrand Russell. David Hilbert. Earth. Ernst Schröder. Eugenio Beltrami. Gentzen. George Boole. Gerard Gentzen. Gottlob Frege. Guiseppe Peano. Gödel. Göttingen. Hermann Grassmann. Heyting algebras. Hilbert. Karl Menger. Kurt Gödel. Kurt Hensel. Leopold Kronecker. Moritz Schlick. Paul Bernays. Peano. Principia Mathematica. Rudolf Carnap. Thoralf Skolem. Vienna Circle. algebraic equations. algebraic logic. algorithmic computability. angles. arithmetic. assumptions. axioms. basic notions. calculus. classical arithmetic. computation. connectives. contemporary logic. deduction. deductive reasoning. digital revolution. finitary reasoning. finitism. geometry. hypothetic reasoning. incompleteness theorems. indirect proofs. inference. information age. intuistic arithmetic. lattice theory. logic. logical empiricism. logical structure. logical truths. mathematical logic. mathematical proofs. mathematical roots. mathematics. negation. non-Euclidan geometries. notation. one-place predicates. parallel postulate. philosophy. programming language. proof. pure thinking. quantificational inferences. theorems. triangles. Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2017 9783110543322 print 9780691174174 https://doi.org/10.1515/9781400885039?locatt=mode:legacy https://www.degruyter.com/isbn/9781400885039 Cover https://www.degruyter.com/cover/covers/9781400885039.jpg |
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von Plato, Jan, von Plato, Jan, |
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von Plato, Jan, von Plato, Jan, The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / Frontmatter -- Contents -- Preface -- Prologue -- 1. An Ancient Tradition -- 2. The Emergence of Foundational Study -- 3. The Algebraic Tradition of Logic -- 4. Frege's Discovery of Formal Reasoning -- 5. Russell: Adding Quantifiers to Peano's Logic -- 6. The Point of Constructivity -- 7. The Göttingers -- 8. Gödel's Theorem: An End and a Beginning -- 9. The Perfection of Pure Logic -- 10. The Problem of Consistency -- References -- Index |
author_facet |
von Plato, Jan, von Plato, Jan, |
author_variant |
p j v pj pjv p j v pj pjv |
author_role |
VerfasserIn VerfasserIn |
author_sort |
von Plato, Jan, |
title |
The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / |
title_sub |
Theories of Deduction and Computation at the Origins of the Digital Age / |
title_full |
The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / Jan von Plato. |
title_fullStr |
The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / Jan von Plato. |
title_full_unstemmed |
The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / Jan von Plato. |
title_auth |
The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / |
title_alt |
Frontmatter -- Contents -- Preface -- Prologue -- 1. An Ancient Tradition -- 2. The Emergence of Foundational Study -- 3. The Algebraic Tradition of Logic -- 4. Frege's Discovery of Formal Reasoning -- 5. Russell: Adding Quantifiers to Peano's Logic -- 6. The Point of Constructivity -- 7. The Göttingers -- 8. Gödel's Theorem: An End and a Beginning -- 9. The Perfection of Pure Logic -- 10. The Problem of Consistency -- References -- Index |
title_new |
The Great Formal Machinery Works : |
title_sort |
the great formal machinery works : theories of deduction and computation at the origins of the digital age / |
publisher |
Princeton University Press, |
publishDate |
2017 |
physical |
1 online resource (400 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- Prologue -- 1. An Ancient Tradition -- 2. The Emergence of Foundational Study -- 3. The Algebraic Tradition of Logic -- 4. Frege's Discovery of Formal Reasoning -- 5. Russell: Adding Quantifiers to Peano's Logic -- 6. The Point of Constructivity -- 7. The Göttingers -- 8. Gödel's Theorem: An End and a Beginning -- 9. The Perfection of Pure Logic -- 10. The Problem of Consistency -- References -- Index |
isbn |
9781400885039 9783110543322 9780691174174 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA21 |
callnumber-sort |
QA 221 V6 42018 |
url |
https://doi.org/10.1515/9781400885039?locatt=mode:legacy https://www.degruyter.com/isbn/9781400885039 https://www.degruyter.com/cover/covers/9781400885039.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
510 - Mathematics |
dewey-full |
510.9 |
dewey-sort |
3510.9 |
dewey-raw |
510.9 |
dewey-search |
510.9 |
doi_str_mv |
10.1515/9781400885039?locatt=mode:legacy |
oclc_num |
984545641 |
work_keys_str_mv |
AT vonplatojan thegreatformalmachineryworkstheoriesofdeductionandcomputationattheoriginsofthedigitalage AT vonplatojan greatformalmachineryworkstheoriesofdeductionandcomputationattheoriginsofthedigitalage |
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ids_txt_mv |
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hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2017 |
is_hierarchy_title |
The Great Formal Machinery Works : Theories of Deduction and Computation at the Origins of the Digital Age / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2017 |
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