Study Guide

Beginning Mathematical Logic again

I have uploaded a slightly revised version of Part I of the Study Guide, with just a few changes to the arm-waving chat and a couple of additions to the recommendations in the Computation/Arithmetic/Gödel’s Theorem chapter. You can download it here.

I’m working away at Part II, mostly enjoying the (re)reading around. An earlier time-slice of myself might have persisted in reading the less fun books out of a misplaced sense of duty. Now I tend to think that if someone really can’t be bothered to write with transparent clarity and make some honest attempt to take their reader along with them by e.g. providing enough signposts along the way, then maybe I can’t be too bothered about struggling with their ill-written texts. So I move on much more quickly to find something more logically entertaining.

Beginning Mathematical Logic: A Study Guide

I’ve renamed the old Teach Yourself Logic study guide; it is now more aptly called Beginning Mathematical Logic: A Study Guide. And there is now a new version of Part I of the Guide (all 95 pages of it) which you can download from here. It’s taken some time to settle on a style for the expanded Guide (though in the end I have not worried too much about keeping the level of the “overviews” of various topics consistent in level), and also it’s a judgement call where to place e.g. a quick introduction to second-order logic.

If you read the PDF from within a browser (as opposed to downloading it and using a PDF reader) it seems best to use Firefox on a Mac. Because then, if you go back after clicking a link, you are returned to your place in the Guide: Safari returns you unhelpfully to the beginning of the Guide.

All comments/corrections gratefully received as always — but perhaps better to use email until I can sort out the comment handling on the blog. The comments will arrive in my admin dashboard but won’t be visible.

Back to the Study Guide

These have been depressing times, despite good vaccine news, no? Grey winter days do not lift the lockdown spirits. So an unproductive period for me. I don’t think I’m alone in this either.

Regrouping, I realize I’ve been trying to juggle too many balls at the same time recently. So — with apologies to Catarina Dutilh Novaes — I’m going to hang fire on blogging chapter-by-chapter about her interesting The Dialogical Roots of Induction (this is such a wide-ranging book, and it would take me too much time to do the homework to do it detailed justice). I might put together some brisker comments later. I’m also going to back off from the idea of doing some podcasts. I need to focus, and since both are downloaded a lot, I’m going to concentrate over the next few months on completing (i) the new version study guide and (ii) the notes on category theory. Which probably won’t make for many interesting blog posts here!

OK; so I have now uploaded the latest version of the partial Logic: A Study Guide, with a new twelve page chapter on elementary set theory. There is an overview of the topics, and I’ve slightly revised my preference-ordering of recommended texts. It’s been fun (and embarrassingly instructive) to revisit some of those basic set theory book; so I hope that some students will find the results useful!

Logic: A Study Guide now “launched”

I’ve now retired the mid 2020 version of the TYL guide, and marked the new year by officially launching a replacement, retitled as Logic: A Study Guide. (Although the Guide’s title has changed, its webpage address stays the same, so as not to break external links.)

The Guide now takes the form of two PDFs. The first contains the rewritten Chapters 1 to 7. That’s three preliminary chapters about the aims and structure of the Guide, and then four chapters on very-elementary (“naive”) set theory, FOL, elementary model theory, and arithmetic/Gödel’s theorems. These have already been posted here, and many thanks for the most useful comments so far.

The second PDF contains Chapters 8 onwards, renumbered but otherwise unrevised from the last version of TYL. As the weeks and months go by, the first PDF should grow as more newly revised chapters are added, and the second PDF will correspondingly shrink. Or at least, that’s the plan!

Logic: A Study Guide — Naive set theory

I’ve decided to divide the coverage of set theory in the Guide into three different chapters. There will now be two chapters in Part I. A short initial chapter on naive set theory, meaning the bits and pieces of notation, concepts and constructions that are often taken for granted in even very elementary logic books. Mathematicians shouldn’t need the chapter, but it could well be useful for philosophers without much mathematical background. This chapter therefore now comes before the chapters on FOL, model theory, and arithmetic. Then, after those chapters, there will be the main chapter on elementary set theory (a first real encounter at the level of e.g. Enderton’s book or a little more). A later chapter on hard-core set theory (large cardinals, forcing, and the like) belongs in Part III.

So I’ve now inserted the draft chapter on naive set theory (and made a few changes too to other chapters, responding to a few comments and suggestions). Here then is the current version of Part I of Logic: A Study Guide, still lacking its main chapter on set theory, which I hope will follow fairly shortly.

Logic: A Study Guide — Computability, arithmetic, Gödel

I mentioned a couple of days ago that, in the last four months, the newly available PDFs of my Intro to Formal Logic and Intro to Gödel’s Theorems have both been downloaded over 3.5K times (and that’s ignoring an initial flurry of downloads of the Gödel book by people who clicked on a probably misleading link posted elsewhere). In the same period — without any advertising at all — the Teach Yourself Logic Study Guide has been downloaded 7.5K times. I mention this to explain again why I feel I ought to give the TYL project some love and spend some quality time updating the Guide: if it is being downloaded that much, with a big surge at the beginning of semesters, it must be being recommended as useful. So I guess I really ought to make sure it is as useful as it can be, and indeed make sure it reflects what I now think about which texts to recommend.  The last full version was a pretty rough-and-ready layered accumulation of bits and pieces of various vintages: it is well past time for an end-to-end rewrite. But heavens, it’s necessarily a slow job, as I revisit texts old and new!

Anyway … here now is the latest version of the new-style Guide up to the rewritten Chapter 6. This reworked chapter covers three inter-connected topics: (a) the elementary informal theory of arithmetic computability, (b) an introduction to formal theories of arithmetic and how they represent computable functions, which leads up to (c) Gödel’s epoch-making incompleteness theorems

My reading recommendations for this chapter haven’t changed a lot. But a feature of the revised Guide is that (after the preliminary chapters), each chapter has a section (or two) giving an extended overview of its theme, from five to ten pages long. These overviews are supposed to be elementary indicators of some of the topics covered by the recommended reading.  They can certainly be skipped (that’s clearly signalled): the overviews are included just for those who might find this kind of preliminary  orientation helpful. It is difficult to know just how to pitch them, and I will no doubt later revisit the set of overviews to make them more uniform in style and level (so comments appreciated!).

I realize now that the Teach Yourself Logic Study Guide has been so-called for over eight years. Maybe I shouldn’t change the “brand” name after all ….

Logic: A Study Guide — Basic Model Theory

I’m continuing work on the update for Teach Yourself Logic: A Study Guide. So there are now five chapters in the new Logic: A Study Guide.

There are three preliminary chapters, giving an introduction for philosophers, an introduction for mathematicians, and a guide-to-the-Guide. Then there is a long chapter on FOL. I’ve previously posted versions of these.

The fifth chapter is on entry-level model theory. There’s an overview introducing a few elementary results, intended to give a flavour of the enterprise. There follows the usual sort of reading guide.

Here then is the Guide including this new  chapter. Need I add? — all comments very gratefully received.

In particular I’m sure I can do better at the end of the displayed box on p. 34. I say earlier in the chapter that — although the focus is of course on standard first-order model theory — it is worth at this stage knowing just a bit about second-order logic/theories (so you get e.g. a glimmer of why first-order arithmetic isn’t categorical which a second-order arithmetic can be). But what short and accessible reading on second-order logic would you recommend at this stage? Later in the Guide we’ll be taking a serious look at the topic: but what brisk (perhaps arm-waving but still helpful) intro could be offered at this point?

Logic: A Study Guide

The Teach Yourself Logic study guide has, as I said a couple of posts ago, grown over the years in a really rather haphazard and disorganized way. Looking at it again, more carefully,  the guide really need to be rewriten from the ground up. And, to add to the guide’s usefulness, it would be very good to begin each chapter/major section with a short essay (up to half a dozen pages, say) giving some orientation, briefly surveying the relevant area of logic.

So all that is what I plan to do. And it should be fun to put it together. However, it will be really quite time-consuming, writing the essays and revisiting the large literature to re-assess my various current recommendations. So I intend to work on TYL’s planned descendant — Logic: A Study Guide — in intermittent stages over the coming months, posting the new chapters for comments as I go along.

I’ve made a start. And now will be a very good time to make suggestions for improvement for the early chapters on the more elementary material (i.e. the core math logic topics covered in what are now Chapters 4 and 5). TYL is downloaded a great deal: so tell me what what you think!  — all comments and advice will, as always, be very gratefully received.

Update to the TYL Guide

I have uploaded a half-year “maintenance upgrade” to the Teach Yourself Logic Guide. There are just a few additional entries, a few changes in existing entries, minor re-writing here and there, and then some re-arrangement of material to make it easier for the two different readerships — philosophers and mathematicians — to navigate the beginning of the Guide.

I really must give this project some more love and attention over the coming months (it’s been rather neglected as I have been concentrating on IFL2). In the first half of this year the Guide was downloaded over 15K times from this site, and looked at another 5K times on my academia page (I do still find those stats rather startling). So obviously — patchy and half-baked though it is in many places — there remains some real need for such a Guide. So I guess I should do my best to make it as good as I can. And it is fun enough to work on when in the right frame of mind.

Any suggestions for improvement are of course always welcome!  I surely must have missed some recent texts which might be worth looking at. Though I do suspect that the culture of “research assessments” over recent years — where writing such books (as opposed to papers read by eleven people) can count for so very little — puts many people off devoting their energies to writing introductory or mid-level texts.

Tim Button’s Set Theory: A Open Introduction

Tim Button wrote up his Cambridge lecture notes for a course on set theory for philosophers, previously taught by Michael Potter and then Luca Incurvati, as Open Set Theory which he then contributed to the Open Logic Project, and the resulting Set Theory: An Open Introduction can now be downloaded from this page on the Project’s site. The result, as you would expect from this author, is very good. It makes an excellent, and free, alternative to e.g. Enderton’s famous introductory book. It is particularly clear in marking off the initial informal (naive) development of the theory of sets, cardinals, ordinals etc. from the ensuing elaboration of an official iterative conception of the hierarchy and the formal development of an axiomatization of ZFC. It is perhaps just occasionally uneven in level; but when I do a half-yearly update of the Teach Yourself Logic Study Guide in a few weeks time, this will get promoted to a top recommendation.

I’ll be checking out again more of Open Logic’s offerings, for this project seems to have developed very well. In particular, I’ll also be recommending Richard Zach’s Incompleteness and Computability, which you can download here. More in TYL 2020.5. 

Scroll to Top