What do you think of Enderton’s Mathematical Introduction to Logic?

Now I’m back from my Bahamian break, I’m intermittently doing some reading, preparing for another version of the Teach Yourself Logic Guide to be put online at the end of the month. I’ve just been taking another look at Enderton’s much used, and often recommended, A Mathematical Introduction to Logic (to which I perhaps gave rather short shrift before). It strikes me as a good book, meeting it again after a long gap, now in the guise of its second edition. But it also strikes me as tougher going than it purports to be. So my summary verdict, from the draft page-and-a-bit that I’ll be adding to the appendix on the Big Books on Mathematical Logic, is that Enderton’s Chs 1 and 2 would make good supplementary reading if you’ve already read a more user-friendly text on first-order meta-theory, and that his even-more-action-packed Ch.3 would make good consolidatory reading if you’ve already read something more introductory on incompleteness (like IGT, for example!).

But what do/did you think of Enderton’s text as a teacher/student? I’d be interested to hear as it is still recommended so often.

[Added: Well, in the end, I didn’t really wait for answers before posting the new version of TYL which has a long entry on the book. But I’d still be interested to know how my comments play.]

4 thoughts on “What do you think of Enderton’s Mathematical Introduction to Logic?”

1. When I learned mathematical logic as an undergraduate years ago, I had the 1st edition of Enderton as the text in one course and Mendelson in another. (I’m no longer sure how I ended up taking two such courses, but I think the one that used Enderton was more advanced.) On the whole, I preferred Enderton, although that edition of Mendelson was the one that had the interesting sketch of a proof of the consistency of arithmetic. Enderton’s book was ‘nicer’ somehow and made the subject more interesting. We (students) thought the course and book difficult, though in a good way, and we kept our interest in logic. (Most of us went on to take the graduate model theory intro which used Chang and Keisler or Bell and Slomson as the text, depending on the year.)

I think you’re probably right that Enderton is better as supplementary or consolidatory reading than as a first intro; but I think it presents the subject from an interesting perspective and is still worth reading.

I’m a bit surprised to hear of Enderton in philosophy courses. My experience was that the philosophy and maths departments weren’t interested in enough of the same things where logic was concerned, and Enderton’s book deservedly had “Mathematical” in its title. (At the time one of my logic courses started, the guy teaching it and the one who was teaching a logic course in the philosophy department that term sat in on each other’s classes; but within a few weeks, they decided their interests were too different and stopped.) (On the other hand, you’re a philosopher who’s interested in mathematical logic, so there must be considerable overlap after all.)

Anyway, while looking around on the web, I noticed Enderton has written a brief Author’s Commentary on the book. It might be useful, if you haven’t already read it.

Amazon has been listing a 3rd edition of Enderton for ages now, but I’ve seen no sign of it appearing, and Amazon US currently has its publication date as February 29, 2020 (!). Amazon UK claims 29 Mar 2013.

1. Interesting! I agree that Enderton is ‘nicer’ than Mendelson and more exciting in some ways: indeed still worth reading. Thanks a lot for the link to Enderton’s Commentary (which I didn’t know): I’ll take a look.

As for philosophers using the book, I meant in mathematical logic courses in grad school in the past (I don’t know how those are now doing in the USA nowadays … they aren’t in robust health here).

2. I first learned serious logic from Enderton, which Pen Maddy used for her year-long logic sequence at Notre Dame. (To my great good fortune, she came to Notre Dame fresh out of grad school for several years before heading west.) I found the book quite challenging but learned a huge amount from it; it is still a “go to” reference work for me. One very big improvement in the 2nd edition I hadn’t noticed: The 1st edition opened with a “Chapter 0” on induction and recursion, which flummoxed me utterly as a first-year grad student. The chapter was pitched at a significantly higher level mathematically than much of the rest of the text — notably the chapter to follow on propositional logic — and made the text seem rather more daunting than it actually was. But, wisely, that chapter has been replaced by a much friendlier and more useful overview of basic set theory in the 2nd edition.

3. Enderton passed away three years ago. I’m afraid the 3rd edition of his book will not be published.

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