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. These volumes are available in hardcopy. In addition, both the text and answers to selected exercises are available as PDF downloads.
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.
- Symbolic Logic, Volume 1
- Symbolic Logic, Volume 2
These are hardcopy (paperback) volumes available from Amazon Direct Printing. I do recommend working from the hardcopy: For a text that you do not merely read but rather work through, it makes a difference to see more than a “screen’s worth” at a time, mark on pages, and such—and the price is right: the hardcopy is available at the zero-royalty, lowest-allowable rate (around $14.00/volume).
- Symbolic Logic, Full Text
- Symbolic Logic, Answers to Selected Exercises
These are freely available PDF files. Note that the full text is continuously paginated (with unified index and bibliography) so that page numbers do not match directly with printed versions. The answer file appends answers to the full text; however, the answer page size is larger than that of the main text—where this can cause unexpected behavior in viewers; thus the answer file is best mainly for viewing answers; appending answers does, however, have the advantage that links between text and answers are live.
Other useful files:
- 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
- For instructors: Complete Answers to Exercises / request password
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.