Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing through Godel's completeness and incompleteness theorems. The text naturally divides into two volumes, the first for reasoning in logic, the second for reasoning about it.
The first volume includes parts I and II of the text. Part I introduces the complete classical predicate calculus with equality, including both axiomatic and natural derivation systems. Part II transitions to methods for reasoning about logic, including direct reasoning from definitions and mathematical induction.
The second volume includes parts III and IV of the text. Part III develops basic results in classical metalogic, including the soundness and completeness of the predicate calculus. Part IV moves to Gödel’s incompleteness theorems: the first that, under certain constraints, no theory is sufficient to prove one of P or not-P for every sentence P of its language; the second that none is sufficient to prove its own consistency.
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 Completeness
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
philosophy, logic, Godel's theorems
Logic and Foundations | Philosophy
Roy, Tony, "Symbolic Logic" (2023). Books. 1.