Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing through Godel's completeness and incompleteness theorems.
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.
I The Elements: Four Notions of Validity
1 Logical Validity and Soundness
2 Formal Languages
3 Axiomatic Deduction
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
Answers to Selected Exercises
philosophy, logic, Godel's theorems
Logic and Foundations | Philosophy
Roy, Tony, "Symbolic Logic" (2016). . 1.