Logic: A Study Guide — First Order Logic

Updated with corrected link!

I have started working occasionally on an update for Teach Yourself Logic: A Study Guide. It now has a slightly different format — and a marginally snappier title, Logic:  A Study Guide.

After three preliminary chapters — an “Introduction for Philosophers”, a shorter “Introduction for Mathematicians”, and a chapter on “Using this Guide” — the first substantial chapter of the new Guide gives, as you would expect, basic reading recommendations on first order logic. Here then is a draft of those preliminary chapters together with the new Chapter 4. (The earlier chapters will only be of any interest to those not familiar with the general intention of the Guide: everyone else can start reading at p. 12.)

All comments and suggestions very gratefully received, as always.


“Ok, it looks prettier, but the principal recommendations haven’t changed!” I’m afraid not. I have been doing a lot of enjoyable and indeed instructive re-reading over the last couple of weeks, but I do seem to have ended up not changing my verdicts about very much. Fancy that!

“So after all that effort, it’s a bit like Ford Prefect updating his entry for the Earth in the Hitchhiker’s Guide to the Galaxy from ‘Harmless’ to ‘Mostly harmless’?” Harsh but embarrassingly close to the truth …

… Still, there are enough minor changes, perhaps, to make it all worth while!

5 thoughts on “Logic: A Study Guide — First Order Logic”

  1. I’m not sure whether these comments are more relevant to your study guide or to your Introduction to Formal Logic.

    I find it useful in an introductory text to say something near the start about terminology. Every discipline has its own technical terms. Often these are common English words that are put to a precise and particular use that may differ from their familiar meaning. When we learn physics we have to learn to use the words ‘force’, ‘power’, ‘momentum’, ‘energy’, etc., in a precise fashion. The same is true in logic. Words such as ‘argument’, ‘valid’, ‘entailment’, ‘interpretation’, ‘model’, ‘theory’, ‘satisfaction’, are among the terms used in logic that differ from their ordinary meanings. In particular, ‘valid’ is one that nearly all newcomers to logic have difficulty with. People are accustomed to using it as an evaluative term meaning that an argument is good or persuasive, and it takes considerable practice to get used to using it to describe an argument in which if the premises are true the conclusion follows necessarily. My experience is that this needs to be emphasised.

    It may be helpful to say something about the history of logic. Logic was originally concerned with what distinguishes a good argument from a bad argument. It was concerned with grounds, reasons and justifications. Over the last 120 years or so logic has evolved into a more purely formal discipline and much of what used to be considered logic is now part of epistemology. This distinction is something that causes confusion among students. They may have trouble accepting, for example, that an argument is not invalid because it has irrelevant premises, or premises that don’t provide a reason to accept the conclusion. Or that an argument with inconsistent premises is always valid. Or that any circular argument is valid.

    I’d also like to say that I’m pleased that you mention non-classical logics. Introductions to logic are invariably introductions to classical logic, but they usually fail to say so. This sometimes leaves students with the impression that classical logic is the only logic. There are good reasons why classical logic is the most important and the most commonly used logic and should be the first one a student learns, but it doesn’t hurt to point out from the start that it is one of many.

    1. In particular, ‘valid’ is one that nearly all newcomers to logic have difficulty with. People are accustomed to using it as an evaluative term meaning that an argument is good or persuasive, and it takes considerable practice to get used to using it to describe an argument in which if the premises are true the conclusion follows necessarily

      There seems to be a common use of ‘valid’ that’s even further from its use in logic. People will say, for example, that all opinions are valid, and they don’t mean they’re all persuasive. (I’ve found it difficult to work out quit what they do mean.)

    2. On terminology, etc.: I agree. That’s why I spend quite a bit of time — some would say too much time! — at the beginning of IFL explaining some basic logical terminology (and stressing how the logician’s usage of e.g. “valid” differs from everyday).

      On history of logic: I meant to include carry over from TYL a short section pointing to a few pieces on the history of FOL. Now done. Thanks for the prompt!

      On non-classical logics: yes, always covered in TYL and will be in the revised Guide.

  2. I have gotten some valuable use out of your guide. Thank you. I would like to mention, though, that while it’s perfectly reasonable to say that you are not interested in covering elementary logic in your guide if you don’t want to, and despite sort of seeming to want to distance yourself from the condescending phrase “baby logic,” you use it at least five times in the book, which seems to me to me a little unnecessarily unfriendly.

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