Proof Theory: History and Philosophical Significance: 292 (Synthese Library) - Hardcover

 
9780792365440: Proof Theory: History and Philosophical Significance: 292 (Synthese Library)
Hardcover
ISBN 10: 0792365445 ISBN 13: 9780792365440
Verlag: Springer, 2000

Inhaltsangabe

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.

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Reseña del editor

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.

Reseña del editor

The conference on Proof Theory: History and Philosophical Significance held in 1997 at the University of Roskilde, Denmark, tracked the history of proof theory and its role in the analysis of the philosophical foundations of mathematics since Hilbert's original program to its modern, highly articulated form. This volume is a collection of papers presented at the conference. It can be read with profit and pleasure by philosophers, mathematicians, computer scientists and scholars with no professional training in proof theory, provided they have a general knowledge of foundational issues.

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Verlag
Springer
Erscheinungsdatum
2000
Sprache
Englisch
ISBN 10 
0792365445
ISBN 13 
9780792365440
Einband
Tapa dura
Anzahl der Seiten
276
Herausgeber
Hendricks Vincent F., Pedersen Stig Andur, Jørgensen Klaus Frovin
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
CMN Printpool Inh. Mathis Neumann
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