Search Results - "Plato, Jan"

Logic as Calculus and Logic as Language: Too Suggestive to be Truthful? by von Plato, Jan

“…The paper focuses on the inferential role of quantifiers in Frege, Peano and Russell. Two aspects of the early years of mathematical logic are discussed: the…”
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Gödel’s Reading of Peano’s Arithmetices Principia by von Plato, Jan

“…In preparation for his article on Russell’s mathematical logic (1944), Gödel read carefully Peano’s Arithmetices Principia. His six pages of summary in the…”
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GENERALITY AND EXISTENCE: QUANTIFICATIONAL LOGIC IN HISTORICAL PERSPECTIVE by VON PLATO, JAN

“…Frege explained the notion of generality by stating that each its instance is a fact, and added only later the crucial observation that a generality can be…”
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KURT GÖDEL'S FIRST STEPS IN LOGIC: FORMAL PROOFS IN ARITHMETIC AND SET THEORY THROUGH A SYSTEM OF NATURAL DEDUCTION by VON PLATO, JAN

“…What seem to be Kurt Gödel's first notes on logic, an exercise notebook of 84 pages, contains formal proofs in higher-order arithmetic and set theory. The…”
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Gentzen's Proof of Normalization for Natural Deduction by von Plato, Jan

“…Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen (Investigations into logical reasoning) that he was…”
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From mathematical axioms to mathematical rules of proof: recent developments in proof analysis by Negri, Sara, von Plato, Jan

“…A short text in the hand of David Hilbert, discovered in Göttingen a century after it was written, shows that Hilbert had considered adding a 24th problem to…”
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Von Neumann Explains His Game Theory to Gödel, September 1940 by von Plato, Jan

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From mathematical axioms to mathematical rules of proof: recent developments in proof analysis by Negri, Sara, von Plato, Jan

“…A short text in the hand of David Hilbert, discovered in Göttingen a century after it was written, shows that Hilbert had considered adding a 24th problem to…”
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Cut Elimination in the Presence of Axioms by Negri, Sara, von Plato, Jan

“…A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a…”
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Proof-theoretical analysis of order relations by Negri, Sara, Plato, Jan von, Coquand, Thierry

“…A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to…”
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Martin Davis on Computability, Computational Logic, and Mathematical Foundations by E. Omodeo and A. Policriti (eds.): SWITZERLAND: SPRINGER, OUTSTANDING CONTRIBUTIONS TO LOGIC, 10, 2016, 464 PP., US $ 129.00, ISBN-13: 978-3-319-41841-4 by von Plato, Jan

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90 years of Gödel’s incompleteness theorems: Logic and computation by Baaz, Matthias, Ertel, Marcel, Kahle, Reinhard, Piecha, Thomas, von Plato, Jan

“…Abstract This volume is one of two special issues collecting articles by invited speakers of the conference ‘Celebrating 90 Years of Gödel’s Incompleteness…”
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Gentzen's Proof Systems: Byproducts in a Work of Genius by von Plato, Jan

“…Gentzen's systems of natural deduction and sequent calculus were byproducts in his program of proving the consistency of arithmetic and analysis. It is…”
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From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction by Von Plato, Jan

“…The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first…”
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From Axiomatic Logic to Natural Deduction by von Plato, Jan

“…Recently discovered documents have shown how Gentzen had arrived at the final form of natural deduction, namely by trying out a great number of alternative…”
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Gödel, Gentzen, Goodstein: The Magic Sound of a G-String by von Plato, Jan

“…There can be beauty and depth and surprise in a mathematical result. At some rare occasions there is more: a touch of magic. Reuben Louis Goodstein (1912-1985)…”
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David Hilbert’s lectures on the foundations of arithmetic and logic 1917–1933. Edited by William Ewald and Wilfried Sieg. Springer, Berlin, Heidelberg and New York, 2013, xxv + 1062 pp by von Plato, Jan

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Gödel’s Reading of Peano’s Arithmetices Principia by von Plato, Jan

“…RésuméPour préparer son article sur la logique mathématique de Russell (1944), Gödel a lu attentivement les Arithmetices Principia de Peano. Les six pages…”
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Logic as Calculus and Logic as Language: Too Suggestive to be Truthful? by von Plato, Jan

“…RésuméLe présent article porte sur le rôle inférentiel des quantificateurs chez Frege, Peano et Russell. Nous abordons ici deux aspects qui caractérisent la…”
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Rereading Gentzen by Von Plato, Jan

“…Issue Title: History of Logic…”
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