{"id":328,"date":"2011-10-02T13:00:18","date_gmt":"2011-10-02T13:00:18","guid":{"rendered":"http:\/\/www.vince-inc.com\/vincent\/?p=328"},"modified":"2011-10-09T15:09:29","modified_gmt":"2011-10-09T15:09:29","slug":"proof-theory-history-and-philosophical-significance","status":"publish","type":"post","link":"https:\/\/www.vince-inc.com\/vincent\/?p=328","title":{"rendered":"Proof Theory: History and Philosophical Significance"},"content":{"rendered":"

Proof Theory<\/strong>
\n History and\u00a0Philosophical\u00a0Significance
\n<\/span><\/strong>Edited by
\nVincent F. Hendricks
\nStig Andur Pedersen
\nKlaus Frovin J\u00f8rgensen
\nSynthese<\/a>\u00a0Library Series, Kluwer Academic Publishers 2000<\/a><\/p>\n

 
\n
<\/p>\n

Abstract<\/a>\u00a0|\u00a0<\/span>Contributing\u00a0Authors<\/a>\u00a0|\u00a0Table\u00a0 of\u00a0Contents<\/a> | Cover<\/a>
\nReview – Bulletin of Symbolic Logic, volume 8, 2002<\/a> | Review – Annalen f\u00fcr Mathematique<\/a><\/span><\/p>\n

\n

 <\/p>\n

<\/a>ABSTRACT<\/strong><\/p>\n

This volume\u00a0in the Synthese Library Series is the result of\u00a0a conference held at the University of Roskilde, Denmark, October 31st – November 1st, 1997. The\u00a0aim was to provide a forum within which philosophers, mathematicians, logicians and historians of\u00a0mathematics could exchange ideas pertaining to the historical and philosophical\u00a0development of proof theory. Hence the conference was called Proof Theory: History and Philosophical\u00a0Significance. To quote from the conference abstract:<\/span><\/p>\n

Proof\u00a0theory was developed as part of Hilbert’s Program.\u00a0According to Hilbert’s Program one could provide mathematics with a firm and secure\u00a0foundation by formalizing all of mathematics and subsequently prove the consistency of\u00a0these formal systems by finitistic means.<\/span><\/p>\n

Hence\u00a0proof theory was developed as a formal tool through which\u00a0this goal should be fulfilled. It is well known that Hilbert’s Program in its original\u00a0form was unfeasible mainly due to G\u00f6del’s incompleteness theorems. Additionally it proved\u00a0impossible to formalize all of mathematics and impossible to even prove the consistency\u00a0of relatively simple formalized fragments of mathematics by finitistic\u00a0methods. In spite\u00a0of these problems, Gentzen showed that by extending Hilbert’s proof theory it would\u00a0be possible to prove the consistency of interesting formal systems, perhaps not by finitistic\u00a0methods but still by methods of minimal strength. This generalization of Hilbert’s original\u00a0program has fueled modern proof theory which is a rich part of mathematical logic with many\u00a0significant implications for the philosophy of mathematics.<\/span>
\n<\/span><\/p>\n

Although\u00a0a completely secure justification of mathematics is\u00a0impossible it is, however, possible to achieve many fundamental partial results concerning\u00a0relative consistency of theories, concerning the strength of axiomatic systems and finally concerning the\u00a0relationship between constructive, predicative and classical systems of\u00a0analysis.<\/span><\/p>\n

The\u00a0purpose of this meeting is to track the history of proof\u00a0theory and its role in the analysis of the philosophical foundations of mathematics from its first\u00a0primitive form in Hilbert’s original Program to its modern highly articulated form.\u00a0Accordingly, the\u00a0emphasis will be on historical and epistemological important episodes in the development of\u00a0proof theory, not on technical aspects. All lectures will be of such a nature that they can be\u00a0followed by mathematicians and philosophers without any professional training in proof theory butprovided with general knowledge of fundamental issues.<\/span><\/p>\n

<\/a>CONTRIBUTING AUTHORS<\/strong><\/p>\n

In order of\u00a0apperance:<\/span><\/p>\n

Solomon\u00a0Feferman<\/strong> is Professor of Mathematics and\u00a0Philosophy and Patrick Suppes Family Professor of Humanities and Sciences at Stanford\u00a0University. He is the author of In the Light of Logic and editor-in-chief of the Collected\u00a0Works of Kurt G\u00f6del. He is noted for his many contributions to logic and the foundations of\u00a0mathematics, in particular in the areas of proof theory and predicative systems of\u00a0mathematics.<\/span><\/span><\/p>\n

Leo\u00a0Corry<\/strong> teaches at the Cohn Institute for History\u00a0and Philosophy of Science, Tel Aviv University. His main research field is the history of mathematics in\u00a0the early 20th century.<\/span><\/span><\/p>\n

David\u00a0E. Rowe<\/strong> teaches history of mathematics and exact\u00a0sciences at Mainz University. His principal research interests center around mathematics in\u00a0Germany in the period from 1800 to 1945. Alongside foundations issues he has been studying\u00a0parallel developments in the foundations of physics connected with relativity\u00a0theory.\u00a0In connection with the latter, he has worked as a contributing editor for the Einstein\u00a0Editorial Project at Boston University since 1998.<\/span><\/span><\/p>\n

Wilfried\u00a0Sieg<\/strong> is Professor in the Department of\u00a0Philosophy at Carnegie Mellon University, Pittsburgh. He has been pursuing proof theoretic issues\u00a0ever since his graduate studies at Stanford University: consistency proofs for subsystems of\u00a0analysis, characterization of provably total functions for fragments of\u00a0arithmetic, and\u00a0automated search for natural deduction proofs in logic. The mathematical work has been\u00a0complemented by historical and philosophical analyses of the foundational work of\u00a0Hilbert and Bernays, but also of the emergemce of the concept of effective\u00a0calculability.<\/span><\/span><\/p>\n

Dirk\u00a0Van Dalen<\/strong> is Professor in the History of Logic\u00a0and Philosophy of Mathematics at Utrecht University. He is in charge of the Brouwer Project for\u00a0preparing and editing the unpublished manuscripts and correspondence of\u00a0Brouwer. He has\u00a0published the first volume of the Brouwer Biography.<\/span><\/span><\/p>\n

Moritz\u00a0Epple<\/strong> presently holds a Heisenberg fellowship in\u00a0the History of Mathematics. After graduating in physics and philosophy, he received a PhD in mathematical\u00a0physics from Tuebingen University. Since then, he has been teaching history of science and history\u00a0of mathematics at the universities of Mainz and Bonn.<\/span><\/span><\/p>\n

Erhard\u00a0Scholz<\/strong> is Professor of History of Mathematics at\u00a0the Department of Mathematics, University of Wuppertal. His main research interests include the\u00a0history of the 19th and 20th centuries. He contributes to the Hausdorff edition (Bonn).\u00a0Additional research interests concentrate on the historical interrelation between mathematics and\u00a0physics, centered around the work of Hermann Weyl.<\/span><\/span><\/p>\n

<\/a>TABLE OF CONTENT<\/strong><\/p>\n

\n

Preface<\/span><\/p>\n

Introduction: \u00a0Vincernt F. Hendricks, Stig Andur Pedersen and Klaus\u00a0Frovin J\u00f8rgensen<\/p>\n

Part I –\u00a0Review of Proof Theory<\/strong><\/p>\n

Chapter\u00a01.\u00a0<\/span>Solomon Feferman: Highlights in Proof\u00a0Theory<\/p>\n

 <\/p>\n

Part II –\u00a0The Background of Hilbert’s Proof Theory.<\/strong><\/p>\n

Chapter\u00a02.\u00a0<\/span>Leo Corry: The Empiricist Roots of\u00a0Hilbert’s Axiomatic Approach<\/p>\n

Chapter\u00a03.\u00a0<\/span>David Rowe: The Calm before the\u00a0Storm: Hilbert’s Early Views on Foundations<\/p>\n

Chapter\u00a04.\u00a0<\/span>Wilfried Sieg: Toward Finitist\u00a0Proof Theory<\/p>\n

Part III\u00a0– Brouwer and Weyl on Proof Theory and Philosophy of\u00a0Mathematics<\/strong><\/p>\n

Chapter\u00a05.\u00a0<\/span>Dirk Van Dalen: The Development\u00a0of Brouwer’s Intuitionism.<\/p>\n

Chapter\u00a06.\u00a0<\/span>Moritz Epple: Did Brouwer’sIntuitionistic Analysis Satisty its own\u00a0Epistemological\u00a0Standards?<\/p>\n

Chapter\u00a07.\u00a0<\/span>Solomon Feferman: The\u00a0Significance of Hermann Weyl’s Das Kontinuum.<\/p>\n

Chapter\u00a08.\u00a0<\/span>Erhard Scholz: Hermann Weyl on\u00a0the Concept of Continuum.<\/p>\n

Part IV –\u00a0Modern Views and Results from Proof Theory<\/strong><\/p>\n

Chapter\u00a09.\u00a0<\/span>Solomon Feferman: Relationships\u00a0between Constructive, Predicative and\u00a0Classical Systems of Analysis.<\/p>\n

Index<\/span><\/p>\n<\/blockquote>\n

<\/a>COVER<\/strong><\/p>\n

\"\"<\/span><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Proof Theory History and\u00a0Philosophical\u00a0Significance Edited by Vincent F. Hendricks Stig Andur Pedersen Klaus Frovin J\u00f8rgensen Synthese\u00a0Library Series, Kluwer Academic Publishers 2000   Abstract\u00a0|\u00a0Contributing\u00a0Authors\u00a0|\u00a0Table\u00a0 of\u00a0Contents | Cover Review – Bulletin of Symbolic Logic, volume 8, 2002 | Review – Annalen f\u00fcr Mathematique   ABSTRACT This volume\u00a0in the Synthese Library Series is the result of\u00a0a conference held […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_exactmetrics_skip_tracking":false,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"footnotes":""},"categories":[5,3],"tags":[],"class_list":["post-328","post","type-post","status-publish","format-standard","hentry","category-books","category-publications"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t