Peter Smith's Blog, page 68

An Invitation to Model Theory

[Updated] CUP have just emailed me information about this new book, coming out in March, An Invitation to Model Theory, by Jonathan Kirby.

The contents list and the description of the aim of the book look very promising: “[T]raditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics …”.

Daniel Nagase notes that there is currently a late draft linked at Kirby’s webpage. That link might not survive the actual publication of the book, so if you want to download to take a look at the book, hurry, hurry, while stocks last!

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IFL2: Table of Contents

I am posting here the detailed section-by-section Table of Contents of the first parts of IFL2.

Chapters 1 to 7 are introductory (informal notions of validity, proof, counterexample, etc.) Chapters 8 to 18 introduce the notion of formal PL languages, tautological entailment, the material conditional, etc. Chapters 19 to 22 introduce a natural deduction system for PL inferences. The detailed ToC gives a pretty good idea, I think, of what the chapters cover.

I won’t post all those chapters here in this blog (in part for copyright reasons, not wanting to upset CUP). I will however probably post the full ND chapters for comment when I’ve had another look at them. But drop me an email if you would be interesting in seeing all these chapters and perhaps commenting on (some of) them — under the usual rules, i.e. the chapters aren’t for further circulation. The book has already been much improved thanks to the kindness of strangers; but I’m sure there are more improvements to make!

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Seven books: Anton Chekhov

Once upon a very long time ago, there were — as well as the usual commercial cinemas — no less than three cinemas in Cambridge showing foreign and/or older films. There was the lovely small Arts Cinema in the middle of town; out along Mill Road there was the Kinema; and then there was the huge Rex Cinema in Magrath Avenue. The last two were very run down and had seen much better days. But they would, in term time in my student days, each show two programmes a week, each programme showing two films — often in mini-seasons, say of Garbo’s films, or Eisenstein’s films, or classic westerns, or the then-new French nouvelle vague. I and my friends saw a lot of films. And the seasons would repeat too for new generations of students. I must have seen Jules et Jim five or six  times if I saw it once.

One film I particularly fell in love with was that most perfect of literary adaptions, the 1960 Russian film of Chekhov’s “The Lady with the Little Dog”, Dama s sobachkoy. Seeing it again after all these years, it is still magically evocative, and so very true to Chekhov’s story as I soon discovered. For it was the film that introduced me to the writing, firstly in that old Penguin collection Lady with Lapdog and Other Stories. And I must have taken the now rather battered copy from the shelves most years since to re-read a story or two, though most often by far that title story again.

That book led to other collections of Chekhov stories, and eventually to the plays. One of the great theatre experiences of my life was seeing a touring production of Three Sisters in Aberystwyth when we were living there.  The staging and acting — I think originating from Theatr Clwyd — were brilliant. But what made the atmosphere in the theatre so intense was that so many of the audience there really did dream of going to Moscow, to Moscow. Or at least away from that remote part of Wales. There is a Chekhov story there …

 

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Seven books: Chekhov

Once upon a very long time ago, there were — as well as the usual commercial cinemas — no less than three cinemas in Cambridge showing foreign and/or older films. There was the lovely small Arts Cinema in the middle of town; out along Mill Road there was the Kinema; and then there was the huge Rex Cinema in Magrath Avenue. The last two were very run down and had seen much better days. But they would, in term time in my student days, each show two programmes a week, each programme showing two films — often in mini-seasons, say of Garbo’s films, or Eisenstein’s films, or classic westerns, or the then-new French nouvelle vague. I and my friends saw a lot of films. And the seasons would repeat too for new generations of students. I must have seen Jules et Jim five or six  times if I saw it once.

One film I particularly fell in love with was that most perfect of literary adaptions, the 1960 Russian film of Chekhov’s “The Lady with the Little Dog”, Dama s sobachkoy. Seeing it again after all these years, it is still magically evocative, and so very true to Chekhov’s story as I soon discovered. For it was the film that introduced me to the writing, firstly in that old Penguin collection Lady with Lapdog and Other Stories. And I must have taken the now rather battered copy from the shelves most years since to re-read a story or two, though most often by far that title story again.

That book led to other collections of Chekhov stories, and eventually to the plays. One of the great theatre experiences of my life was seeing a touring production of Three Sisters in Aberystwyth when we were living there.  The staging and acting — I think originating from Theatr Clwyd — were brilliant. But what made the atmosphere in the theatre so intense was that so many of the audience there really did dream of going to Moscow, to Moscow. Or at least away from that remote part of Wales. There is a Chekhov story there …

 

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IFL2: Propositional truth trees

[Reposted]

The first edition of An Introduction to Formal Logic did logic by trees. The main text of the second edition will do natural deduction, Fitch-style. But chapters on truth trees will still be available, as two online appendices. And these appendices will, indeed, together make a brisk stand-alone introduction to logic by trees for a reader who knows the basics about the languages of propositional and predicate logic.

Here, then, is the first appendix, on propositional truth trees (pp. 27). This is a slightly revised version from the one posted a few days ago. It is free to use and distribute. And the plan is for it to remain freely available, through the IFL2 page. Needless to say, all further comments/corrections gratefully received.

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Seven books: Georg Christoph Lichtenberg

It’s a thing on Twitter at the moment — people posting the covers of seven books that have meant something to them, without comment, and nominating others to join in and post their choices in turn. Actually, I’d prefer to see at least brief comments and explanations, for these can be half the interest and enjoyment; but it got me thinking about what books I’d choose (putting aside the likes of, say,  Anna Karenina and other books which have perhaps meant the most, but hardly need words of approbation from me!).

Here then is one I’d perhaps choose for my seven — appropriate at any rate to this day, for it happens to be the 220th anniversary of Lichtenberg’s death. I must have bought J. P. Stern’s Lichtenberg: A Doctrine of Scattered Occasions as a student — it was remaindered in Galloway and Porter of fond memory. I was told about the book, I think, by another student who had gone to talk to Stern about Wittgenstein. I’m not sure why I found Lichtenberg’s aphoristic take on the world, his disorderly mind, so appealing: a counter, perhaps, to my mathematician’s over-orderliness. And he can suggest so much in a striking hint  —  ‘He was astonished that cats have two holes cut in their fur at precisely the spot their eyes are’. Over the years, I have kept returning to his humane reflections, to his jottings on the complexity of our human world and of the natural world. I find something immensely likeable  about the man who reveals himself here.

There’s a much more recent and wider selection from his ‘Wastebooks’ to be found in  Georg Christoph Lichtenberg: Philosophical Writings (trans. Steven Tester, SUNY, 2012). But it is to Stern’s insightful book which I still return with pleasure.

(And talking of Twitter, Lichtenberg occasionally tweets @GeorgCL.)

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Seven books: Lichtenberg

It’s a thing on Twitter at the moment — people posting the covers of seven books that have meant something to them, without comment, and nominating others to join in and post their choices in turn. Actually, I’d prefer to see at least brief comments and explanations, for these can be half the interest and enjoyment; but it got me thinking about what books I’d choose (putting aside the likes of, say,  Anna Karenina and other books which have perhaps meant the most, but hardly need words of approbation from me!).

Here then is one I’d perhaps choose for my seven — appropriate at any rate to this day, for it happens to be the 220th anniversary of Lichtenberg’s death. I must have bought J. P. Stern’s Lichtenberg: A Doctrine of Scattered Occasions as a student — it was remaindered in Galloway and Porter of fond memory. I was told about the book, I think, by another student who had gone to talk to Stern about Wittgenstein. I’m not sure why I found Lichtenberg’s aphoristic take on the world, his disorderly mind, so appealing: a counter, perhaps, to my mathematician’s over-orderliness. And he can suggest so much in a striking hint  —  ‘He was astonished that cats have two holes cut in their fur at precisely the spot their eyes are’. Over the years, I have kept returning to his humane reflections, to his jottings on the complexity of our human world and of the natural world. I find something immensely likeable  about the man who reveals himself here.

There’s a much more recent and wider selection from his ‘Wastebooks’ to be found in  Georg Christoph Lichtenberg: Philosophical Writings (trans. Steven Tester, SUNY, 2012). But it is to Stern’s insightful book which I still return with pleasure.

(And talking of Twitter, Lichtenberg occasionally tweets @GeorgCL.)

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IFL2: Propositional truth trees

The first edition of An Introduction to Formal Logic did logic by trees. The main text of the second edition will do natural deduction, Fitch-style. But chapters on truth trees will still be available, as two online appendices. And these appendices will, indeed, together make a brisk stand-alone introduction to logic by trees for a reader who knows the basics about the languages of propositional and predicate logic.

Here, then, is the first appendix, on propositional truth trees (pp. 27). This is free to use and distribute. It should remain stably available, through the IFL2 page. Needless to say, all comments/corrections gratefully received.

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Conference on proof-theoretic semantics

There are so many really interesting-looking logic conferences these days. The Third Tübingen Conference on Proof-Theoretic Semantics, 27–30 March 2019 promises to be particularly good, and an earlier time-slice of me would have been very tempted to go. I do hope the organisers video the sessions, when speakers are happy about that, and put the the videos and/or the written papers online.

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IFL2: Two chapters on conditionals

How do you say enough about conditionals at an introductory level, to motivate the truth-functional material conditional to beginners? On the one hand, you want to avoid telling outright fibs or entirely glossing over problems. On the other hand, you don’t want to tangle with issues about conditionals to the point where the student reader  is left puzzled about why we are sticking with what has been made to seem such a dodgy rendition of the conditional. How to steer a helpful middle course?

Judging by the frequency of questions about the material conditional on math.stackexchange along the lines of “what is going on here!?”, this is a tricky issue for any entry-level lecture course or textbook. Here then is the latest version of my introductory efforsHere then is the latest version of my introductory effort for IFL2 (there’s another later chapter about rules of inference for the conditional in a Fitch-style ND system which reinforces the point made at the very end of these chapters).

Do point students to these chapters (if you think they might be helpful)! And/or send me comments (if you spot typos or can think of ways to improve them!).

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