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Language, Truth and Logic in Mathematics : Jaakko Hintikka Selected Papers - Jaakko Hintikka

Language, Truth and Logic in Mathematics

Jaakko Hintikka Selected Papers

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Published: 31st December 1997
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One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.

Origin of the Essays
Introduction
What Is Elementary Logic? Independence-Friendly Logic as the True Core Area of Logicp. 1
A Revolution in Logic?p. 27
A Revolution in the Foundations of Mathematics?p. 45
Is There Completeness in Mathematics after Godel?p. 62
Hilbert Vindicated?p. 84
Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematicsp. 106
Standard vs. Nonstandard Logic: Higher-Order, Modal, and First-Order Logicsp. 130
The Skeleton in Frege's Cupboard: The Standard versus Nonstandard Distinctionp. 144
An Alternative Concept of Computabilityp. 174
What is the Logic of Parallel Processing?p. 189
Model Minimization - An Alternative to Circumscriptionp. 212
New Foundations for Mathematical Theoriesp. 225
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792347668
ISBN-10: 0792347668
Series: Jaakko Hintikka Selected Papers
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 250
Published: 31st December 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 2.54
Weight (kg): 0.54