Great Formal Machinery Works (eBook)

Theories of Deduction and Computation at the Origins of the Digital Age

Jan von Plato (Autor)

eBook Download: PDF

2017
400 Seiten
Princeton University Press (Verlag)
978-1-4008-8503-9 (ISBN)

Infos

Jan von Plato is professor of philosophy at the University of Helsinki. His books include Elements of Logical Reasoning and Structural Proof Theory.

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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 Schroder, 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 Godel 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.

Produkt-Details

• Erscheint lt. Verlag: 2.8.2017
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
• Themenwelt: Geisteswissenschaften ► Philosophie ► Logik
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Schlagworte: Accuracy and precision • Addition • Admissible Rule • algebraic equations • algebraic logic • algorithmic computability • angles • Arend Heyting • arithmetic • associative property • Assumptions • Axiom • axiomatic system • Axiom of reducibility • Axioms • basic notions • Begriffsschrift • Bertrand Russell • Big O notation • Bounded quantifier • Calculus • canonical form • Cauchy Sequence • classical arithmetic • Classical Logic • classical mathematics • commutative property • computable function • Computation • Conjunctive normal form • Connectives • consistency • Contemporary Logic • counterexample • David Hilbert • Decidability (logic) • Deduction • Deduction theorem • Deductive Reasoning • definable set • Dialectica interpretation • Digital Revolution • Direct proof • earth • Entscheidungsproblem • Equation • Ernst Schröder • Eugenio Beltrami • Existential instantiation • existential quantification • Finitary • finitary reasoning • Finitism • First-Order Logic • formal language • formal proof • Formal science • formal system • fundamental theorem • Gentzen • Gentzen's Consistency Proof • Geometry • George Boole • Gerard Gentzen • Gerhard Gentzen • Gödel • Göttingen • Gottlob Frege • Guiseppe Peano • Herbrand's theorem • Hermann Grassmann • heyting algebras • Higher-Order Logic • Hilbert • Hilbert's program • hypothetic reasoning • Incompleteness theorems • indirect proofs • inference • Information Age • intuistic arithmetic • Intuitionism • Intuitionistic Logic • Karl Menger • Kurt Gödel • Kurt Hensel • Lattice (order) • lattice theory • Leopold Kronecker • Logic • Logical conjunction • Logical connective • logical consequence • Logical disjunction • logical empiricism • logical reasoning • logical structure • logical truths • logicism • Material implication (rule of inference) • Mathematical Induction • Mathematical Logic • mathematical proofs • mathematical roots • Mathematics • Modal Logic • Moritz Schlick • Natural deduction • Natural number • Negation • non-Euclidan geometries • Notation • one-place predicates • parallel postulate • Paul Bernays • Peano • Peano axioms • Philosophy • Predicate logic • Predicate (mathematical logic) • Presburger arithmetic • prime factor • Prime number • Principia Mathematica • Programming language • Proof • Proof theory • Propositional Calculus • Provability Logic • pure thinking • quantificational inferences • Quantifier (linguistics) • Quantifier (logic) • real number • Recursive definition • Rudolf Carnap • Rule of inference • satisfiability • scientific notation • sequent • sequent calculus • Sheffer stroke • Special case • Summation • Tautology (logic) • Theorem • Theorems • theory • Thoralf Skolem • Transfinite induction • triangles • True arithmetic • Turing Machine • Universal instantiation • verificationism • Vienna Circle • Warren Goldfarb • Well-formed formula • Well-order • Wilhelm Ackermann • Zermelo–Fraenkel set theory
• ISBN-10: 1-4008-8503-5 / 1400885035
• ISBN-13: 978-1-4008-8503-9 / 9781400885039