Proof Theory [electronic resource] : History and Philosophical Significance / edited by Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen.
Erişim Adresi
ISBN
9789401727969
Dil Kodu
İngilizce
Yer Numarası
DK/12993
Basım Bildirimi
1st ed. 2000.
Yayın Bilgisi
Dordrecht : Springer Netherlands : Imprint: Springer, 2000.
Fiziksel Niteleme
XII, 257 p. online resource.
Dizi
Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science, 2542-8292 ; 292
İçindekiler Notu
1. Review of Proof Theory -- Highlights in Proof Theory -- 2. The Background of Hilbert’s Proof Theory -- The Empiricist Roots of Hilbert’s Axiomatic Approach -- The Calm Before the Storm: Hilbert’s Early Views on Foundations -- Toward Finitist Proof Theory -- 3. Brouwer and Weyl on Proof Theory and Philosophy of Mathematics -- The Development of Brouwer’s Intuitionism -- Did Brouwer’s Intuitionistic Analysis Satisfy its own Epistemological Standards? -- The Significance of Weyl’s Das Kontinuum -- Herman Weyl on the Concept of Continuum -- 4. Modern Views and Results from Proof Theory -- Relationships between Constructive, Predicative and Classical Systems of Analysis.
Özet, vb.
hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.
Konu
Logic.
Mathematical logic.
Mathematics.
History.
Science __ Philosophy.
Logic.
Mathematical Logic and Foundations.
History of Mathematical Sciences.
Philosophy of Science.
Mathematical logic.
Mathematics.
History.
Science __ Philosophy.
Logic.
Mathematical Logic and Foundations.
History of Mathematical Sciences.
Philosophy of Science.
Kurum Adı
Eseri Alıntıla
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Dijital Kaynak
MARC Görünümü
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520 |ahiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.
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532 8 |aInaccessible, or known limited accessibility
532 8 |aNo reading system accessibility options actively disabled
532 8 |aPublisher contact for further accessibility information: accessibilitysupport@springernature.com
650 0|aLogic.
650 0|aMathematical logic.
650 0|aMathematics.
650 0|aHistory.
650 0|aScience|xPhilosophy.
650 14|aLogic.
650 24|aMathematical Logic and Foundations.
650 24|aHistory of Mathematical Sciences.
650 24|aPhilosophy of Science.
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700 1 |aPedersen, Stig Andur.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
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020 |a9789401727969|9978-94-017-2796-9
024 7 |a10.1007/978-94-017-2796-9|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/12993
245 10|aProof Theory|h[electronic resource] :|bHistory and Philosophical Significance /|cedited by Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen.
250 |a1st ed. 2000.
264 1|aDordrecht :|bSpringer Netherlands :|bImprint: Springer,|c2000.
300 |aXII, 257 p.|bonline resource.
336 |atext|btxt|2rdacontent
337 |acomputer|bc|2rdamedia
338 |aonline resource|bcr|2rdacarrier
347 |atext file|bPDF|2rda
490 1 |aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,|x2542-8292 ;|v292
505 0 |a1. Review of Proof Theory -- Highlights in Proof Theory -- 2. The Background of Hilbert’s Proof Theory -- The Empiricist Roots of Hilbert’s Axiomatic Approach -- The Calm Before the Storm: Hilbert’s Early Views on Foundations -- Toward Finitist Proof Theory -- 3. Brouwer and Weyl on Proof Theory and Philosophy of Mathematics -- The Development of Brouwer’s Intuitionism -- Did Brouwer’s Intuitionistic Analysis Satisfy its own Epistemological Standards? -- The Significance of Weyl’s Das Kontinuum -- Herman Weyl on the Concept of Continuum -- 4. Modern Views and Results from Proof Theory -- Relationships between Constructive, Predicative and Classical Systems of Analysis.
520 |ahiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.
532 8 |aAccessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format.
532 8 |aInaccessible, or known limited accessibility
532 8 |aNo reading system accessibility options actively disabled
532 8 |aPublisher contact for further accessibility information: accessibilitysupport@springernature.com
650 0|aLogic.
650 0|aMathematical logic.
650 0|aMathematics.
650 0|aHistory.
650 0|aScience|xPhilosophy.
650 14|aLogic.
650 24|aMathematical Logic and Foundations.
650 24|aHistory of Mathematical Sciences.
650 24|aPhilosophy of Science.
700 1 |aHendricks, Vincent F.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aPedersen, Stig Andur.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aJørgensen, Klaus Frovin.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
710 2 |aSpringerLink (Online service)
773 0 |tSpringer Nature eBook
776 08|iPrinted edition:|z9780792365440
776 08|iPrinted edition:|z9789048155538
776 08|iPrinted edition:|z9789401727976
830 0|aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,|x2542-8292 ;|v292
856 40|uhttps://doi.org/10.1007/978-94-017-2796-9
912 |aZDB-2-SHU
912 |aZDB-2-SXPR
912 |aZDB-2-BAE
950 |aHumanities, Social Sciences and Law (SpringerNature-11648)
950 |aPhilosophy and Religion (R0) (SpringerNature-43725)
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