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2010, ISBN: 9048151058

[EAN: 9789048151059], Neubuch, [SC: 0.0], [PU: Springer Netherlands], ARITHMETIC; ALGORITHMS; CONSTRUCTIVISM; LOGIC; PROGRAMMINGLANGUAGE; SEQUENTCALCULUS; SETTHEORY, Druck auf Anfrage Neu… Meer...

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Truth, Proof and Infinity - pocketboek

2010, ISBN: 9789048151059

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[ED: Softcover], [PU: Springer / Springer Netherlands], Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, b… Meer...

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Truth, Proof and Infinity / A Theory of Constructive Reasoning / P. Fletcher / Taschenbuch / Synthese Library / Paperback / X / Englisch / 2010 / Springer Netherland / EAN 9789048151059 - Fletcher, P.
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Truth, Proof and Infinity / A Theory of Constructive Reasoning / P. Fletcher / Taschenbuch / Synthese Library / Paperback / X / Englisch / 2010 / Springer Netherland / EAN 9789048151059 - pocketboek

2010

ISBN: 9789048151059

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[ED: Taschenbuch], [PU: Springer Netherland], Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in term… Meer...

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Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it… Meer...

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P. Fletcher:
Truth, Proof and Infinity - pocketboek

2010, ISBN: 9048151058

[EAN: 9789048151059], Neubuch, [PU: Springer Netherlands], ARITHMETIC ALGORITHMS CONSTRUCTIVISM LOGIC PROGRAMMINGLANGUAGE SEQUENTCALCULUS SETTHEORY PHILOSOPHIE ALLGEMEINES LEXIKA PROGRAMM… Meer...

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Truth, Proof and Infinity: A Theory of Constructive Reasoning P. Fletcher Author

Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Löf have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.

Gedetalleerde informatie over het boek. - Truth, Proof and Infinity: A Theory of Constructive Reasoning P. Fletcher Author


EAN (ISBN-13): 9789048151059
ISBN (ISBN-10): 9048151058
Gebonden uitgave
pocket book
Verschijningsjaar: 2010
Uitgever: Springer Netherlands Core >1 >T
480 Bladzijden
Gewicht: 0,719 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2011-01-15T22:33:59+01:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2024-03-20T13:17:12+01:00 (Amsterdam)
ISBN/EAN: 9789048151059

ISBN - alternatieve schrijfwijzen:
90-481-5105-8, 978-90-481-5105-9
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: fletcher, goodman martin
Titel van het boek: three infinity, proof theory, truth, 276


Gegevens van de uitgever

Auteur: P. Fletcher
Titel: Synthese Library; Truth, Proof and Infinity - A Theory of Constructive Reasoning
Uitgeverij: Springer; Springer Netherland
470 Bladzijden
Verschijningsjaar: 2010-12-07
Dordrecht; NL
Gedrukt / Gemaakt in
Gewicht: 0,735 kg
Taal: Engels
192,59 € (DE)
197,99 € (AT)
212,50 CHF (CH)
POD
X, 470 p.

BC; Logic; Hardcover, Softcover / Philosophie/Allgemeines, Lexika; Philosophie: Logik; Verstehen; Arithmetic; algorithms; constructivism; logic; programming language; proof; sequent calculus; set theory; Mathematical Logic and Foundations; Theory of Computation; Philosophy of Science; Logic; Mathematical Logic and Foundations; Theory of Computation; Philosophy of Science; Mathematik: Logik; Mathematische Grundlagen; Theoretische Informatik; Wissenschaftsphilosophie und -theorie; BB

1. Introduction and Statement of the Problem.- 2. What’s Wrong with Set Theory?.- 3. What’s Wrong with Infinite Quantifiers?.- 4. Abstraction and Idealisation.- 5. What are Constructions?.- 6. Truth and Proof of Logical Formulae.- 7. The Need for a Theory of Constructions.- 8. Theories of Constructions.- 9. Hilbert’s Formalism.- 10. Open-endedness.- 11. Analysis.- 12. Introduction to Part II.- 13. Design of the Term Language.- 14. The Term Language.- 15. From the Term Language to the Expanded Term Language.- 16. The Expanded Term Language.- 17. The Protological Sequent Calculus.- 18. Commentary on the Protological Axioms and Rules.- 19. From Protologic to Expanded Protologic.- 20. Expanded Protologic.- 21. From Expanded Protologic to the Coding of Trees.- 22. The Coding of Trees.- 23. The Expanded Term Language as a Functional Programming Language.- 24. Introduction to Part III.- 25. From the Coding of Trees to Logic.- 26. Logic.- 27. From Logic to the Calculus of Proof Functions.- 28. Calculus of Proof Functions.- 29. From Calculus of Proof Functions to the Logic of Partial Terms.- 30. Logic of Partial Terms.- 31. From Logic of Partial Terms to Heyting Arithmetic.- 32. Heyting Arithmetic.- 33. From Heyting Arithmetic to Peano Arithmetic.- 34. Peano Arithmetic.- 35. Conclusions on Arithmetic.- 36. Introduction to Part IV.- 37. From Expanded Protologic to the Second-Order Coding of Trees.- 38. The Second-Order Coding of Trees.- 39. From the Second-Order Coding of Trees to Second-Order Logic.- 40. Second-Order Logic.- 41. From Second-Order Logic to Second-Order Calculus of Proof Functions.- 42. Second-Order Calculus of Proof Functions.- 43. From Second-Order Calculus of Proof Functions to Second-Order Logic of Partial Terms.- 44. Second-Order Logic of Partial Terms.- 45. From Second-Order Logic of Partial Terms to Second-Order Heyting Arithmetic.- 46. Second-Order Heyting Arithmetic.- 47. From Second-Order Heyting Arithmetic to Second-Order Peano Arithmetic.- 48. Second-Order Peano Arithmetic.- 49. Conclusions on Analysis.- References.- Index of symbols.- Index of axioms, theorems and rules of inference.- Index of names.- Index of topics.

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