Modern Logic — A Survey

1. Front Matter

   Pages i-viii

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. The General Sense and Character of Modern Logic

      • J. M. Bochenski

      Pages 3-14

   3. The Growth of Logic Out of the Foundational Research in Mathematics

      • Stanislaw J. Surma

      Pages 15-33

3. Pure Logic

   1. Front Matter

      Pages 35-35

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   2. Proof Theory

      • Kurt Schütte

      Pages 37-43

   3. Model Theory

      • Angus Macintyre

      Pages 45-65

   4. Constructivist Approaches to Logic

      • G. Kreisel

      Pages 67-91

   5. Infinitary Logics

      • Jon Barwise

      Pages 93-112

   6. Many-Valued Logics

      • A. Rose

      Pages 113-129

   7. Modal and Relevance Logics: 1977

      • Nuel D. Belnap Jr.

      Pages 131-151

4. The Interplay Between Logic and Mathematics

   1. Front Matter

      Pages 153-153

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   2. Logic and the Foundations of Mathematics

      • E. Casari

      Pages 155-166

   3. Logic and Set Theory

      • Gaisi Takeuti

      Pages 167-171

   4. Recursion Theory

      • Hans Hermes

      Pages 173-195

   5. The Interplay Between Logic and Mathematics: Intuitionism

      • A. S. Troelstra

      Pages 197-221

   6. Logic and Probability

      • Jens Erik Fenstad

      Pages 223-233

   7. Logic and Category Theory

      • Gonzalo E. Reyes

      Pages 235-252

5. The Relevance of Logic to other Scientific Disciplines

   1. Front Matter

      Pages 253-253

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   2. Logic and the Methodology of Empirical Sciences

      • Evandro Agazzi

      Pages 255-282

Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recom­ prehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be con­ sidered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a diSCipline, is that one has succeeded in isolating the 'scientific core' of it, by restricting the somehow vague and redundant generality of its original 'philosophical' configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By follOwing this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition.

• deontic logic
• foundation
• growth
• history
• history of literature
• linguistics
• logic
• model
• optics
• predicate logic
• quantum mechanics
• rhetoric
• science
• subject
• tradition

• Dept. of Philosophy, University of Genoa, Italy

  Evandro Agazzi

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