Authors

Tony RoyFollow

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Description


From the preface: There is, I think, a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. While courses in mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first course may also leave these untreated, and fail explicitly to lay down the definitions upon which the second course is based. The aim of this text is to integrate material from these courses and, in particular, to make serious mathematical logic accessible to students I teach. The first parts introduce classical symbolic logic as appropriate for beginning students; the last parts build to Gödel’s adequacy and incompleteness results. A distinctive feature of the last section is a complete development of Gödel’s second incompleteness theorem.

Contents

Front Matter

I The Elements: Four Notions of Validity

1 Logical Validity and Soundness

2 Formal Languages

3 Axiomatic Deduction

4 Semantics

5 Translation

6 Natural Deduction

II Transition: Reasoning About Logic

7 Direct Semantic Reasoning

8 Mathematical Induction

III Classical Metalogic: Soundness and Adequacy

9 Preliminary Results

10 Main Results

11 More Main Results

IV Logic and Arithmetic: Incompleteness and Computability

12 Recursive Functions and Q

13 Gödel’s Theorems

14 Logic and Computability

Concluding Remarks

Answers to Selected Exercises

Bibliography

Publication Date

7-30-2016

Keywords

philosophy, logic, Godel's theorems

Disciplines

Logic and Foundations | Philosophy

Comments

This text may be found in additional formats at

http://rocket.csusb.edu/~troy/int-ml.html

Symbolic Logic

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