Epistemology versus Ontology [electronic resource] : Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf / edited by P. Dybjer, Sten Lindström, Erik Palmgren, B.G. Sundholm.
Erişim Adresi
ISBN
9789400744356
Dil Kodu
İngilizce
Yer Numarası
DK/8353
Basım Bildirimi
1st ed. 2012.
Yayın Bilgisi
Dordrecht : Springer Netherlands : Imprint: Springer, 2012.
Fiziksel Niteleme
XXVIII, 388 p. online resource.
Dizi
Logic, Epistemology, and the Unity of Science, 2214-9783 ; 27
İçindekiler Notu
Introduction.-On the Philosophical Work of Per Martin-Löf: Göran Sundholm -- Notes on the contributors -- Part 1. Philosophy of Logic and Mathematics -- Chapter 1. Kant and Real Numbers: Mark van Atten -- Chapter 2. Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing: Juliet Floyd -- Chapter 3. Truth and Proof in Intuitionism: Dag Prawitz -- Chapter 4. Real and Ideal in Constructive Mathematics: Giovanni Sambin -- Chapter 5. In the Shadow of Incompleteness: Hilbert and Gentzen: Wilfried Sieg -- Chapter 6. Evolution and Logic: Jan Smith -- Chapter 7. The “Middle Wittgenstein” and Modern Mathematics: Sören Stenlund -- Chapter 8. Primitive Recursive Arithmetic and Its Role in the Foundations of Arithmetic: historical and Philosophical Reflections: William Tait -- Part 2. Foundations -- Chapter 9. Type Theory and Homotopy: Steve Awodey -- Chapter 10. A Computational Interpretation of Forcing in Type Theory: Thierry Coquand; Guilhem Jaber -- Chapter 11. Program Testing and the Meaning Explanations of Intuitionistic Type Theory: Peter Dybjer -- Chapter 12. Normativity in Logic: Jean-Yves Girard -- Chapter 13. Constructivist versus Structuralist Foundations: Erik Palmgren -- Chapter 14. Machine Translation and Type Theory: Aarne Ranta -- Chapter 15. Constructive Zermelo-Fraenkel Set Theory, Powerset, and the Calculus of Constructions: Michael Rathjen -- Chapter 16. Coalgebras as Types determined by their Elimination Rules: Anton Setzer -- Chapter 17. Second Order Logic, Set Theory and Foundations of Mathematics: Jouko Väänänen.
Özet, vb.
This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
Konu
Logic.
Mathematical logic.
Knowledge, Theory of.
Ontology.
Mathematics.
History.
Logic.
Mathematical Logic and Foundations.
Epistemology.
Ontology.
History of Mathematical Sciences.
Mathematical logic.
Knowledge, Theory of.
Ontology.
Mathematics.
History.
Logic.
Mathematical Logic and Foundations.
Epistemology.
Ontology.
History of Mathematical Sciences.
Diğer Yazarlar
Kurum Adı
Eseri Alıntıla
Referansları kullanmadan önce gözden geçirmeniz ve varsa gerekli düzeltmeleri yapmanız önerilir.
Dijital Kaynak
MARC Görünümü
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245 10|aEpistemology versus Ontology|h[electronic resource] :|bEssays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf /|cedited by P. Dybjer, Sten Lindström, Erik Palmgren, B.G. Sundholm.
250 |a1st ed. 2012.
264 1|aDordrecht :|bSpringer Netherlands :|bImprint: Springer,|c2012.
300 |aXXVIII, 388 p.|bonline resource.
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490 1 |aLogic, Epistemology, and the Unity of Science,|x2214-9783 ;|v27
505 0 |aIntroduction.-On the Philosophical Work of Per Martin-Löf: Göran Sundholm -- Notes on the contributors -- Part 1. Philosophy of Logic and Mathematics -- Chapter 1. Kant and Real Numbers: Mark van Atten -- Chapter 2. Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing: Juliet Floyd -- Chapter 3. Truth and Proof in Intuitionism: Dag Prawitz -- Chapter 4. Real and Ideal in Constructive Mathematics: Giovanni Sambin -- Chapter 5. In the Shadow of Incompleteness: Hilbert and Gentzen: Wilfried Sieg -- Chapter 6. Evolution and Logic: Jan Smith -- Chapter 7. The “Middle Wittgenstein” and Modern Mathematics: Sören Stenlund -- Chapter 8. Primitive Recursive Arithmetic and Its Role in the Foundations of Arithmetic: historical and Philosophical Reflections: William Tait -- Part 2. Foundations -- Chapter 9. Type Theory and Homotopy: Steve Awodey -- Chapter 10. A Computational Interpretation of Forcing in Type Theory: Thierry Coquand; Guilhem Jaber -- Chapter 11. Program Testing and the Meaning Explanations of Intuitionistic Type Theory: Peter Dybjer -- Chapter 12. Normativity in Logic: Jean-Yves Girard -- Chapter 13. Constructivist versus Structuralist Foundations: Erik Palmgren -- Chapter 14. Machine Translation and Type Theory: Aarne Ranta -- Chapter 15. Constructive Zermelo-Fraenkel Set Theory, Powerset, and the Calculus of Constructions: Michael Rathjen -- Chapter 16. Coalgebras as Types determined by their Elimination Rules: Anton Setzer -- Chapter 17. Second Order Logic, Set Theory and Foundations of Mathematics: Jouko Väänänen.
520 |aThis book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
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650 0|aMathematical logic.
650 0|aKnowledge, Theory of.
650 0|aOntology.
650 0|aMathematics.
650 0|aHistory.
650 14|aLogic.
650 24|aMathematical Logic and Foundations.
650 24|aEpistemology.
650 24|aOntology.
650 24|aHistory of Mathematical Sciences.
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001 807060
003 TR_AnAIT
005 20260127003346
007 cr nn 008mamaa
008 120710s2012 ne | s |||| 0|eng d
020 |a9789400744356|9978-94-007-4435-6
024 7 |a10.1007/978-94-007-4435-6|2doi
041 |aeng
049 |aTürk Tarih Kurumu Kütüphanesi
050 4|aBC1-199
072 7|aHPL|2bicssc
072 7|aPHI011000|2bisacsh
072 7|aQDTL|2thema
082 04|a160|223
090 |aDK/8353
245 10|aEpistemology versus Ontology|h[electronic resource] :|bEssays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf /|cedited by P. Dybjer, Sten Lindström, Erik Palmgren, B.G. Sundholm.
250 |a1st ed. 2012.
264 1|aDordrecht :|bSpringer Netherlands :|bImprint: Springer,|c2012.
300 |aXXVIII, 388 p.|bonline resource.
336 |atext|btxt|2rdacontent
337 |acomputer|bc|2rdamedia
338 |aonline resource|bcr|2rdacarrier
347 |atext file|bPDF|2rda
490 1 |aLogic, Epistemology, and the Unity of Science,|x2214-9783 ;|v27
505 0 |aIntroduction.-On the Philosophical Work of Per Martin-Löf: Göran Sundholm -- Notes on the contributors -- Part 1. Philosophy of Logic and Mathematics -- Chapter 1. Kant and Real Numbers: Mark van Atten -- Chapter 2. Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing: Juliet Floyd -- Chapter 3. Truth and Proof in Intuitionism: Dag Prawitz -- Chapter 4. Real and Ideal in Constructive Mathematics: Giovanni Sambin -- Chapter 5. In the Shadow of Incompleteness: Hilbert and Gentzen: Wilfried Sieg -- Chapter 6. Evolution and Logic: Jan Smith -- Chapter 7. The “Middle Wittgenstein” and Modern Mathematics: Sören Stenlund -- Chapter 8. Primitive Recursive Arithmetic and Its Role in the Foundations of Arithmetic: historical and Philosophical Reflections: William Tait -- Part 2. Foundations -- Chapter 9. Type Theory and Homotopy: Steve Awodey -- Chapter 10. A Computational Interpretation of Forcing in Type Theory: Thierry Coquand; Guilhem Jaber -- Chapter 11. Program Testing and the Meaning Explanations of Intuitionistic Type Theory: Peter Dybjer -- Chapter 12. Normativity in Logic: Jean-Yves Girard -- Chapter 13. Constructivist versus Structuralist Foundations: Erik Palmgren -- Chapter 14. Machine Translation and Type Theory: Aarne Ranta -- Chapter 15. Constructive Zermelo-Fraenkel Set Theory, Powerset, and the Calculus of Constructions: Michael Rathjen -- Chapter 16. Coalgebras as Types determined by their Elimination Rules: Anton Setzer -- Chapter 17. Second Order Logic, Set Theory and Foundations of Mathematics: Jouko Väänänen.
520 |aThis book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
650 0|aLogic.
650 0|aMathematical logic.
650 0|aKnowledge, Theory of.
650 0|aOntology.
650 0|aMathematics.
650 0|aHistory.
650 14|aLogic.
650 24|aMathematical Logic and Foundations.
650 24|aEpistemology.
650 24|aOntology.
650 24|aHistory of Mathematical Sciences.
700 1 |aDybjer, P.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aLindström, Sten.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aPalmgren, Erik.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aSundholm, B.G.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
710 2 |aSpringerLink (Online service)
773 0 |tSpringer Nature eBook
776 08|iPrinted edition:|z9789400744349
776 08|iPrinted edition:|z9789400744363
776 08|iPrinted edition:|z9789401782388
830 0|aLogic, Epistemology, and the Unity of Science,|x2214-9783 ;|v27
856 40|uhttps://doi.org/10.1007/978-94-007-4435-6
912 |aZDB-2-SHU
912 |aZDB-2-SXPR
950 |aHumanities, Social Sciences and Law (SpringerNature-11648)
950 |aPhilosophy and Religion (R0) (SpringerNature-43725)
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