Tony RoyFollow



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Excerpted from the longer Roy, Symbolic Logic, including chapter 1 and just the first parts of chapters 2 - 7.

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.


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

Answers to Selected Exercises


Publication Date



philosophy, logic, sentential logic


Logic and Foundations | Philosophy


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Sentential Logic