Tuesday, June 21, 2016

Brief reviews of logic textbooks

While I am still thinking about writing a book, I have to face the fact that I'm going to need a textbook at least for the introductory class in fall. I've collected all the books on my shelf that could vaguely be used as such, and am goin to briefly review tham all here, to try to determine which is the least bad.

Allen & Hand, Logic Primer:

  • Cons: No metatheory. Uses Lemmon-style natural deduction. No extra fluff/discussion: Would result in students complaining about having to take their own lecture notes.
  • Pros: Uses natural deduction. No extra fluff/discussion: Would require students to actually come to class and pay attention.

Button, Tim, forallx:

  • Cons: No metatheory.
  • Pros: Free. Motivates/defines subject matter. Accessible to philosophers. Uses Fitch-style natural deduction.

Carroll, Lewis, Symbolic Logic and Game of Logic:

  • Cons: Doesn't provide a good foundation to 21st C logic. Focuses on syllogisms and fallacies.
  • Pros: People like games. Designed with pedagogy in mind.

Clark, Gordon, Logic:

  • Cons: No predicate logic. No metatheory.
  • Pros: Defines and motivates logic. Covers informal reasoning, and the syllogism.

Copi, Irving M., Symbolic Logic:

  • Cons: Axiomatic rule of proofs (con), but with a large amount of rules of inference (pro).
  • Pros: Defines/motivates logic. Robust discussion of metatheory.

Copi, Irving M., Introduction to Logic:

  • Cons: Axiomatic rule of proofs (con), but with a large amount of rules of inference (pro). Discusses metatheory (pro) but only of propositional logic (con)
  • Pros: Defines/motivates logic. Discusses informal reasoning. Covers syllogisms and induction.

Ebbinhaus, Flum, Thomas, Mathematical Logic:

  • Cons: Terrifying to math phobes. Uses sequent calculus (but see pros).
  • Pros: Uses sequent calculus (but see cons). Explicit discussion of meta-theory.

Halmos, Paul, Algebraic Logic:

  • Cons: Would be terrifying for math phobes.
  • Pros:

Hilbert & Ackermann, Mathematical Logic:

  • Cons: Non-standard notation.
  • Pros: Extra cachet for using such a foundational historical source. Covers Aristotle!

Hodges, Wilfrid, Logic:

  • Cons: Has a strange definition of logic. Uses tableaux.
  • Pros: Has a lot of background/introductory/motivational material. Discusses metatheory.

Hurley, Patrick J., A Concise Introduction to Logic:

  • Cons: Similar style of proof system to Copi. No meta-theory.
  • Pros: Lots of informal reasoning/application to natural language. Discusses and motivates background notions and concepts. Covers syllogisms.

Lemmon, E.J., Beginning Logic:

  • Cons: Doesn't discuss term logic or informal logic. Doesn't use Fitch-style natural deduction.
  • Pros: Small/cheap. Discusses the scope/subject matter of logic. Discusses metatheory. Uses natural deduction.

Lewis and Langford, Symbolic Logic:

  • Cons: Starts off with algebra, which is both bad for the math phobes and doesn't explain why the study of logic is relevant to philosophy. Does not define the scope/subject matter of logic. Doesn't discuss history. Uses non-standard (from the point of view of the 2st C) notation. Has a complicated proof system. No informal logic. Metatheory (soundness/completeness) unclear.
  • Pros:

Lyndon, Roger C., Notes on Logic:/p>

  • Cons: Not discursive enough. Axiomatic proof theory.
  • Pros: Small.

Makinson, D.C., Topics in Modern Logic:

  • Cons: Axiomatic. Doesn't actually motivate/define logic.
  • Pros: Small, and presumably cheap. Some cool material on modified implication relations. Covers intuitionistic logic, and a bit of set theory.

Massey, Gerald J., Understanding Symbolic Logic:

  • Cons: Takes 125 pages to get to any sort of proof theory. Axiomatic proof theory.
  • Pros: Very detailed discussion of each of the connectives and all of the foundational material. Has a nice discussion of application to natural language. Explicit discussion of metatheory. Includes modal logic.

Mates, Benson, Stoic Logic:

  • Cons: I doubt I could get away with teaching only the Stoics!
  • Pros: Clearly grounded in philosophy. Small/cheap. Clear and straightforward discussion.

Mendelson, Elliott, Introduction to Mathematical Logic:

  • Cons: Would be terrifying for math phobes. Axiomatic proof theory.
  • Pros: Very detailed presentation of propositional and predicate logic. Explicit metatheoretical discussions. Tableaux are introduced AFTER the axiomatic system.

Quine, W.V.O., Methods of Logic:

  • Cons: I really don't like Quine.
  • Pros:

Smith, Peter, An Introduction to Formal Logic:

  • Cons: Uses tableaux.
  • Pros: Very discursive and accessible to philosophers. Goes slowly.

Smullyan, Raymond, First-Order Logic:

  • Cons: Starts off immediately with tableaux. Goes off too quickly: Hintikka's lemma is reached by p. 27!
  • Pros: Small/cheap.

Tomassi, Paul, Logic:

  • Cons: Uses tableaux.
  • Pros: Very discursive and accessible to philosophers. Motivates the scope and use of logic.

It looks like Button; Copi, Symbolic Logic; and Lemmon are the front-runners. Copi and Lemmon have the metatheory, but I'd have to introduce the alternative way of writing natural deductions. Button has my preferred method of natural deduction, but doesn't have any meta-theory.

I think it would be easier on the students for them to read their meta-theory in my draft book than it would be for me to translate Copi and Lemmon's proofs into another format. I think I will probably go with Button, heavily supplemented by my own notes.


  1. We would applaud you if you added metatheory to Button! (Yay open textbook license!)

    1. Other open and free textbooks: https://github.com/OpenLogicProject/OpenLogic/wiki/Other-Logic-Textbooks

    2. While I LOVE the idea of the licensing system Button uses and the ability to customize/add to it as one wills, I'm still undecided if that's the way I'd go -- I'm unsure, currently, how idiosyncratic I'd be, and hence whether what I'd have to say would be useful to/usable by others.

  2. Do you have thoughts on Gensler?

    1. Someone mentioned it on twitter; I've never come across it myself but will do so.

  3. Button has a metatheory book which builds upon forallx