IFL

IFL2 update … and online lectures?

IFL2 should be published this month. You can admire the cover and “look inside” at an excerpt here, courtesy of CUP  (though the first chapter is not particularly representative). There’s more info at the book’s homepage here. I’m gradually populating the page of worked answers to the end-of-chapter exercises. And hey ho, there’s already a corrections page of typos …

I’ve been turning over in my mind the idea of putting online some series of 30 minute lectures associated with the book. At the moment I’m rather minded to provide these as “voice-over-slide-show” videos, probably with some very short talking-head interludes (so the lectures aren’t just coming from a disembodied oracle!). Since you can grow proofs in real time in a video in a way in which you can’t in a printed book, a supplementary series of videos on propositional natural deduction might indeed be quite helpful to students: so that’s where I’d start.

However, delving online for guidance about how best to do this, I’m getting lost! There is a lot of “how to/how not to” advice out there, and it is difficult to know where to start. So if anyone has any recommendations for guidance for similar projects which they have found useful, do please let me know here! [I’d be creating the videos on a Mac, using Beamer for the slides.]

Covered in blue …


So here’s the cover for IFL2 (click for a larger version).  The painting, my choice, is Kandinsky’s Blue Painting (Blaues Bild) from January 1924. It has been slightly cropped by CUP’s designers but I do think it still makes for a good-looking cover. I’m really very pleased with the result.

I’m working away putting answers to end-of-chapter exercises online (currently I’m having fun with quantifier natural deduction).  This is actually rather a good task to have on the go right now. It is distracting enough to keep my mind off other things during a long afternoon stuck at home; but it hardly demands prolonged concentration trying to get my head round Difficult Stuff.  I’m making some very slight improvements to the exercises as I go along which can be incorporated into the final final book version when CUP call for it in a week or two. And so  on we go.

I’d like, though, to get back to thinking about category theory. Here’s one question: category theorists, or some influential ones among them at any rate, seemingly work with a non-standard conception of sets: but what is it, exactly (when you try to cash out the ‘bag of dots’ metaphor that gets trotted out)? As a warm up exercise (although I don’t think he tackles this question) I’m going to be sitting down to read carefully Luca Incurvati’s recent Conceptions of Set and the Foundations of Mathematics. If your library subscribes to the Cambridge Core system, you should be able to get it online. I’ll start posting about this book, chapter by chapter, in the next few days.

 

More natural deduction exercises

We are keeping our social distance, ducking out of meetings, avoiding cafés, having at least some food supplies delivered rather than going to the shops, and so on — all in all, erring on the side of caution, given age considerations. Keep calm and carry on. What else can you do?

So I’ve had a  bit more time than expected to plough on with getting answers to IFL2 exercises online (discovering along the way that one of the exercises asked students to prove a falsehood — I live and learn: fortunately I can still change the final final PDF for the book).

By my lights, the key thing for philosophy students is to understand the principles behind a natural deduction system (and ideally, to get some sense of what are the deep ideas, and what are matters of presentational choice). Doing a few exercises no doubt helps understanding. Getting expert at proof-discovery goes beyond what is really necessary. Still, I can’t resist: I have now provided very extensive worked answers — over forty pages — with a lot of hints and tips for proof discovery. You will find the exercises and answers here. I hope they will be of some interest even to those not using IFL2 (e.g. users of forall x).

Exercises for QL natural deduction next … is there no end to the fun?

Some IFL2 exercises

Thirty-seven of the forty-two chapters of IFL2 have sets of exercises at the end. So that’s many merry hours to be spent, putting answers to all the exercises online. What joy. And yes, this is pretty time-consuming, to say the least.

But, when taken just a chapter or two at a time, writing up the answers without worrying too much about typographical niceties is quite diverting. And unlike the business of writing the book itself, it is not at all stress-inducing — after all, any slip-ups or silly mistakes or other infelicities can be instantly corrected when noticed, rather than being preserved for ever in embarrassing print.

Here then is the slowly growing page with links to (1) some of the sets of exercises, and then to (2) corresponding sets of answers. Since the exercises are available independently of the book,  many of these sets with their answers could eventually be useful to students even if they are not actually using IFL2.

The most recent additions are two sets of questions covering propositional natural deduction proofs for negation and conjunction,  and then for disjunction too, with extensive answer sets  — talking through strategies for finding the solutions rather in the manner of an examples class. Next up, examples for proofs using the conditional, and more. Watch this space.

Better late than never …

So here we are: four hundred and twenty pages of logical goodness, written with insight, clarity, zest, and wit, making it an unmissable read for students new and old.

Well, that’s the theory ….

Kind friends and relations have said it is mostly not bad, give or take. On a good day, I can almost agree.

So, after a ridiculously protracted re-writing, I really will have to let this second edition of my Intro to Formal Logic go into the world this week and then take its chances. There’s a couple of (small) remaining tasks and then off to CUP with it!

I won’t tell you how many things that I ought to have realized decades ago when I started teaching this stuff that I’ve learnt (at last) in putting this edition together. That would be just too embarrassing. But better late than never …

Natural deduction for quantifier logic

It’s very late in the day, as I hope to get IFL2 finally off to the Press within the next fortnight or so. But since the natural deduction chapters are new to the second edition it is understandable (I hope!) that I am still worrying away at them, tinkering here and there. Here then is the latest version of the three main chapters on QL proofs. Any last minute corrections and/or helpful comments (other than, perhaps, “use a different proof system”) will still be most welcome …

There is no real novelty here except perhaps by mistake: though one feature of the handling of QL proofs is the sharp distinction made between dummy names (parameters) and fixed-interpretation proper names, as I think this makes for conceptual clarity.

Some context for these chapters: As background, the reader will already be familiar with a Fitch-style system for propositional logic (pretty similar to The Logic Book‘s system, but with an absurdity constant and EFQ). The reader will also have done a lot of prior work on the language of QL, at least in an initial way,  hopefully coming to these chapters with a decent understanding of the quantifier/variable notation, and a lot of practice at translations. They won’t, however have met yet the identity predicate, and QL= proofs will come later.

Empty domains, again

Here’s a rewritten four-page chapter from IFL2 on empty domains. Difficult to know how to handle this topic. Many intro texts just skate over the issue. An earlier draft perhaps said a bit too much a bit too confusingly. Hope this strikes a better balance. Last-minute comments always welcome!

(By the way, “sets*” with a star is my usage in the book for when I really mean sets as objects in their own right — the ones that play a starring role in full-blown set* theory — as opposed to when I’m occasionally using lightweight talk of virtual classes which can be translated away.)

Back to categories

IFL2 is off to the proof-reader. So, for some weeks, time to think of other things.

A while back, I constructed a webpage linking to online materials on category theory at an introductory/middling  level, including lecture notes, (legally available!) books, and videos of lectures, more than 50 items altogether. Here it is!

I initially wrote this really for my own use, to keep track of things I found. But the page has got over 25K visits in the last year, so obviously some others are finding it useful too.

This page of links hasn’t had much attention in recent months while IFL2 was occupying my mind. However, I’ve just now updated it, removed a couple of dead links and corrected some others. Please do let me know of appropriate recent materials I should be adding to the list — and do spread the word to students who might find it useful.

Logic exercises: a first batch

I have put online a first batch of the end-of-chapter exercises for IFL2. There are PDFs of each set of exercises in stand-alone form, and then PDFs of worked answers (in some cases with an amount of discussion).

These should be of some use to beginning students, whether or not they are following a version of IFL. The exercises relate to the opening seven chapters, introducing notions like validity, soundness, proof, form, proposition, etc. in very informal ways.

Sound the trumpet!

A full PDF of IFL2 is off to CUP! Again. And not for the last time, because there’s the whole process of sending it out a proof-reader still to be gone through. But it’s a major step on the road. The book is at last in a stable state, and it is — let’s hope — very minor tinkering from here on in.

Heavens, this all seems to have been a great deal of work. Remind me again why I agreed to do a second edition?

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