So August was the first full month for Logic Matters with its snappy new web host, and with its sparse new look. Everything seems to have settled down to be working pretty satisfactorily (though some further minor tinkering remains to be done when I am in the mood). The stats are pretty much in line with the previous averages — just under 40K unique visitors in the first month. Or so they say. I’m never sure quite what to read into such absolute numbers.

Relative numbers are more reliable, no doubt. And one consistency is that — month by month — the Study Guide gets downloaded more than the Three Big Red Logic Books combined. So really that settles what I need to do next. Namely, eschew all kinds of logical distractions and concentrate on actually finishing rewriting the damned thing: no more procrastination. So that’s my plan for the next ten weeks. I have a time-table. And, if things don’t go too far adrift, I hope to start posting excerpts from the new version here by the end of the month. Who knows? — I might even get a few useful comments/suggestions from new contributors …

Rowsety MoidI’m wondering if it makes sense to comment on the existing rewrite of chapters 1-9, and whether they’re going to be rewritten too.

Peter SmithI’m working through those chapters right now, re-organising some material as I go. Now is probably a good time for any rather general comments that could still affect my thinking about the overall shape of the Guide. (The current plan is to drop a separate Part III, and just have a few suggestions for more advanced readings added to the relevant earlier chapters. This is partly to keep the length under better control and partly because Part III isn’t really so needed — once people are launched on a sensible reading course, and have made their way into a topic, they should be able to find their own way to any advanced literature that might interest them. So I’m focussing more — as the new title has it — on

BeginningMathematical Logic.)Rowsety MoidI’ve started reading chapters 1-9. Some comments:

The titleI liked the old title and the way it put teaching yourself front and centre. Still, TYL wasn’t completely without problems as a title, because there’s a series of ‘Teach Yourself’ books that aren’t reading guides, and that could affect what people expect. (The logic book in that series seems to be

Logic: A Complete Introduction: Teach Yourself.)One thing I like about the new title is that it makes it clear the guide is about mathematical logic, which should avoid having people come in expecting readings on Aristotelian syllogisms, informal fallacies, or (who knows?) whatever Hegel thought ‘logic’ meant. (Strictly speaking, it doesn’t stick to mathematical logic, though, since it includes ‘other logics’: relevant, free, plural.)

The target readershipIt eventually becomes clear enough. However, different things are said at different points: philosophers and mathematicians (p v), “beginning graduate students in philosophy” (p 3), “philosophy students” (also p 3), “mathematics students” (p 7). Some sections — such as ‘How to prove it’ and ‘briefer introduction for mathematicians’ — seem aimed at undergraduates; and p 12 says Parts I and II are ‘at an advanced undergraduate / beginning graduate student level’ (which seems about right).

That isn’t a major problem, but it looks like some tightening-up is possible, and I expect many prospective readers will want to answer quite quickly ‘is this for me?’

It is assumed that you will by default be using library copies of books (p vi)Is that still the right assumption to make?

Part IIII quite like the separate Part III. And, while it’s probably true that people who are ready to read advanced literature

canfind their own way, they might still find it interesting and helpful to read what someone who knows a lot about logic and has evaluated many books has to say about some of the advanced books available. Even people who aren’t yet ready to take on advanced books can find it interesting.Also, the three-part guide has been a success. Do you have any information on what people especially like about it, or about what sorts of people download it and why? I wouldn’t want the guide to change in a way that inadvertently made it less appealing.

OTOH, it makes sense to focus on parts I and II, and to control the length (especially with the new overview sections adding to it). So I’m not

opposedto dropping Part III, and it could be restored if that later seems right.Chapter 3: The Guide, and how to use itI think it takes an awfully long time (especially considering two whole chapters have already gone by) to get to what I think is one of the most useful sections in the entire guide, ‘3.6 Strategies for self-teaching from logic books’. And though the journey to 3.6 might be shortened by the absence of Part III, there still ought to be something about where the ‘vertical’ division between what’s covered and what’s more advanced lies.

I don’t have a specific suggestion here, but if you can see a good way to make the ‘strategies’ section easier to get to, or easier to spot, it could be worth doing it.

Overview sections — mission creep?I think they’re a good idea, and there’s helpful information in them; they do represent a fairly fundamental change in the purpose of the guide, though, taking it away from being a guide to other readings and towards being an introduction in itself.

There’s a danger of going too far in that direction. The FOL overview is 9 pages long and gets quite detailed and formula-dense towards its end. Also, while tree systems work very well for some people, the don’t for everyone. (I end up wondering how they’d be used for a much larger proof than appears in typical examples.) The overview doesn’t show a Fitch-style proof or (fortunately, imo) sequents, and if it shouldn’t go into all that (I think it shouldn’t), should it go into so much detail about the proof styles it does show? Is it important for the reader to be told all that before they even open a logic book (if we suppose they’re going to read what the guide says about the books first)?

Also, from a mathematical logic POV, does it make sense to go very far into the details of formal proof systems? In my experience, anyway, a proof system is introduced primarily so that we can reason about it (and prove certain important theorem such as completeness), not so it would actually be used. I took every mathematical logic course available when I was a student (several were), but the only course where the students did formal proofs was an intro logic course in the Philosophy department.

Chapter 4: A little informal set theoryI like most of this.

It’s good that it discusses different used of ‘naive’. (I’m inclined to give the Halmos book much of the blame for the confusion around ‘axiomatic’ and ‘naive’ and for the still present tendency to talk about presentations of set theory as ‘naive’ or not, in a way that doesn’t happen for any other part of mathematics. I think Stillwell’s

Naive Lie theoryis the only place I’ve ever seen it elsewhere.)I think section 4.3, ‘Virtual classes, real sets’, makes too much of this issue, gives it too much prominence, and (for a discussion of this length, in one of the most introductory parts of the guide) brings it in too soon. I think that, at a minimum, the section should be cut back to little more than its first paragraph, the Quine quote and the ‘virtual classes’ terminology, the Kunen paragraph (and its quote), and something like the final paragraph.

I also think that defining ‘set’ (section 4.1) in a way that says it “exists over and above its members” puts too much emphasis on the set’s existence. I prefer what Button says on his p 14, “a set is a collection of objects, considered as a single object”; or what Enderton says on his p 1, “a set is a collection of things (called its members or elements), the collection being regarded as a single object.”

I don’t think there is a widespread confusion about sets in which people think that the set, as an object in its own right, is playing a significant role every time sets are used, so that it had better be explained that it doesn’t, at length, and very soon after sets are first introduced.

A more general point is that, when someone who knows a lot about a subject is presenting introductory material, it can often happen — I’ve certainly done it — that they’re aware of an issue (or that some people think there’s an issue), and so they raise it themself in a way that unnecessarily complicates the subject (at that stage) or gives students the impression that something is more questionable than it actually is.

Peter SmithMany thanks for these characteristically helpful comments!

TitleI have wavered to and fro about changing the title, but plumped in the end for the revised one because, as you say, it “makes it clear the guide is about mathematical logic”.

What counts as “mathematical logic” is moot. One might think mathematical treatments of aspects of mathematical reasoning

oughtto count; but as you point out, not all traditionally do. But anyway, the new Guide version has a bit less about “other logics”; and I’ll double check that this straying outside the traditional core topics is properly flagged up as such!Target readershipThat’s very useful. I agree that some tidying is definitely called for; and I think I’ve done better in the new version.

Library copies?Yes, the new Preface comes a lot nearer to frankly acknowledging straight out that students will be using something like libgen or Z-library!

Part IIIThe material won’t all disappear. The plan is that, e.g., a snappier version of the suggestions for advanced reading on model theory will now appear as the final section of the model theory chapter. I think that should work at least as well, and probably better.

How to use the GuideHaving a Preface and TWO Introductions was overkill. So things in the version currently online do take too long to get going! I’ve speeded that up. But there’s a separate point: might what is now §3.6 be better placed at/near the beginning of that chapter? I’ll think about this, but at first sight, a good suggestion!

Mission creepYes! The overviews in the current online version were going too far beyond a “checklist” and I’ve been somewhat cutting them back — and in particular I have radically reducing the section in the FOL chapter on proof-styles. So it is good to get this feedback, encouraging me in the right direction.

Finally, set theoryThis is very useful. I’ll think some more about these points. Again, many thanks!