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Bringing together the histories of mathematics, computer science, and linguistic thought, 'Language and the Rise of the Algorithm' reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians well before the computer age - how do you draw the line between computational rules and the complexities of making systems comprehensible to people? By attending to this question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day.

Semantics. --- intellectual history, history of mathematics, algorithms, Gottfried Wilhelm Leibniz, Nicolas de Condorcet, George Boole, programming languages, machine learning. --- Semiotics --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Mathematical linguistics --- Algorithms --- Formal languages --- Mathematical notation --- Language and languages --- Computer programming --- History. --- Philosophy.

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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 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.

Information technology --- Computers --- History. --- 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.