The Very Short Teach Yourself Logic Guide

The full TYL Study Guide is a 96 page PDF. That’s full of good things, including detailed descriptions of lots of books, including alternative suggestions to the top recommendations. But some readers may just want the unvarnished headline news. So here, excerpted from the current version of the full Guide, is a one-webpage mini-guide to some particularly good entry-level reading on the standard core mathematical logic curriculum (a step up from baby logic). NB:

This is a short Guide to getting started on teaching yourself mathematical logic (a serious and time-consuming business) not a short introduction to mathematical logic!

It’s assumed you have access to a university library (so cost/availability in print is not a factor in the choosing what to recommend).

There’s nothing here about extensions of classical logic like modal logic or variants like relevance logic. They are treated in the full Guide. The only extras that get mentioned are second order and intuitionistic logic.

These are, to repeat, entry-level readings. Advice on more advanced topics and more sophisticated texts is also in the full Guide.

You can tackle Sections 2, 3, 4 in any order.

1. Basic first-order logic

Read Ian Chiswell and Wilfrid Hodges, Mathematical Logic (OUP 2007) for a natural deduction approach, followed by

Christopher Leary and Lars Kristiansen, A Friendly Introduction to Mathematical Logic (Milne Library, 2015 – first edn. by Leary alone, Prentice Hall 2000) up to §3.2, or Herbert Enderton, A Mathematical Introduction to Logic (Academic Press 1972, 2002) up to §2.5, for an axiomatic approach.

If you struggle slightly, or just want a comfortingly manageable additional text: Derek Goldrei’s Propositional and Predicate Calculus: A Model of Argument (Springer, 2005) is explicitly designed for self-study. Read Chs. 1 to 5 (except for §§4.4, 4.5).

Then for overview/revision/sideways looks at other ways of doing things: Wilfrid Hodges, ‘Elementary Predicate Logic’, in the Handbook of Philosophical Logic, Vol. 1, ed. by D. Gabbay and F. Guenthner, (Kluwer 2nd edition 2001, but little changed from 1st edition). Read first twenty short sections.

2. Beginning model theory

Derek Goldrei, Propositional and Predicate Calculus: A Model of Argument (Springer, 2005) §§4.4, 4.5 and then Ch. 6 on ‘Some uses of compactness’ — gives a very clear introduction to some model theoretic ideas. That should smooth the path to reading the main text:

Maria Manzano, Model Theory, Oxford Logic Guides 37 (OUP, 1999).

3. Beginning computability theory/Gödel’s theorems

Peter Smith, An Introduction to Gödel’s Theorems (CUP 2007, 2nd edition 2013), highlights incompleteness but has something on the general theory of computability.

The particularly clear Richard Epstein and Walter Carnielli, Computability: Computable Functions, Logic, and the Foundations of Mathematics (Wadsworth 2nd edn. 2000) tackles computability first.

Tougher but classic: George Boolos, John Burgess, Richard Jeffrey, Computability and Logic (CUP 5th edn. 2007)

4. Beginning set theory

Start with Herbert B. Enderton, The Elements of Set Theory (Academic Press, 1977): or alternatively with

Derek Goldrei, Classic Set Theory (Chapman & Hall/CRC 1996) (subtitle ‘For guided independent study’).

Additional introductory reading:

Karel Hrbacek and Thomas Jech, Introduction to Set Theory (Marcel Dekker, 3rd edition 1999).

Yiannis Moschovakis, Notes on Set Theory (Springer, 2nd edition 2006).

Michael Potter, Set Theory and Its Philosophy (OUP, 2004).

5. Extras

On second-order logic:

Herbert Enderton, A Mathematical Introduction to Logic (Academic Press 1972, 2002), Ch. 4. And/or Dirk van Dalen, Logic and Structure, Ch. 4.

For a fuller story: Stewart Shapiro, Foundations without Foundationalism: A Case for Second-Order Logic, Oxford Logic Guides 17 (Clarendon Press, 1991), Chs. 3–5.

On intuitionistic logic: