Textbook for symbolic logic, beginning at a level appropriate for beginning students, and continuing through Gödel’s completeness and incompleteness theorems. The text naturally divides into two volumes, the first for reasoning in logic, and the second for reasoning about it. Available on this page are the different sections of the text (formatted for either single- or double-sided printing), and answers to selected exercises (formatted on large pages, and best viewed on a larger monitor). Consistent with the license, I am happy for anyone to use this material. And I appreciate comments—which you may make via the Textbook Blog!
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 completeness and ıncompleteness results. A distinctive feature of the last section is a complete development of Gödel’s second ıncompleteness theorem. Complete preface/contents to the textbook.
Textbook files (ver 10.28 — November 27, 2022):
Sentential Logic, first parts of chapters 1–7: SntL_single-sided and SntL_double-sided
Symbolic Logic: Volume I, all of chapters 1–8: SLVI_single-sided and SLVI_double-sided
Symbolic Logic: Volume II, all of chapters 9–14: SLVII_single-sided and SLVII_double-sided
Symbolic Logic, complete text: SL_single-sided and SL_double-sided
Symbolic Logic: Answers to Selected Exercises (there is also a Complete Answers to Exercises for instructors / request password)
Some other useful files:
- Symbolic Logic: most recent version (November 27, 2022)
- A course of study for Symbolic Logic: assignment schedule
- Ruby recursive program files: running Ruby / recursive1.rb
- Turing machine files: running the simulator / state.rb / turing_machine.rb / suc.rb / blank.rb
- If you are interested in \LaTeX: getting started with LaTeX / derivations in LaTeX / test.tex / preamble.tex
Symbolic Logic: An Accessible Introduction to Serious Mathematical Logic by Tony Roy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Note that this license is compatible with the production of classroom readers and such.