Peter Smith's Blog, page 74

As when the dove



To distract you from Trump, Brexit, and other woes, the wonderful Lucy Crowe sings “As when the dove” from Handel’s Acis and Galatea. The whole new recording from the Early Opera Company under Christian Curnyn on Chandos is terrific.

The post As when the dove appeared first on Logic Matters.

Thin Objects

Øystein Linnebo’s book Thin Objects: An Abstractionist Account is out from OUP. If you’ve been following his contributions to debates on neo-Fregean philosophy of mathematics and related issues over some fifteen years, you won’t be surprised by the general line; but you will be pleased to have the strands of thought brought together in a shortish and (at least relative to the topic) accessible book. If you are new to Linnebo’s brand of neo-neo-neo-Fregeanism, this is your chance to catch up!

I confess that, having read Frege at an impressionable age, I still rather want something broadly Fregean to be right. I want there to be mathematical objects OK, but for them to be “thin”, to use Linnebo’s word — which he cashes out (perhaps not entirely happily, I’d say) as “not making a substantial demand on the world”. Linnebo gets his thin objects, Frege-style — his Platonism on the cheap — by conjuring the objects into being by abstraction principles. But unlike Frege and the Hale/Wright neo-Fregeans, Linnebo insists that the defensible and harmless principles need to be predicative. And it is well known that predicative abstraction principles by themselves are too weak to be useful for the foundations of much mathematics. Linnebo’s distinctive response is to allow indefinite iteration of abstraction principles (what he calls “dynamic” abstraction). But allowing completed infinite iterations would seem to entangle us in some pretty robust commitments again; so Linnebo wants to regiment his ideas about dynamic abstraction by going modal.

Does this work? Is getting thinness at the cost of going modal a good trade? I’ll let you know (given world enough and time).

The post Thin Objects appeared first on Logic Matters.

IFL2 Chapters 18 to 20: Propositional truth trees

Back then to the excitements of the second edition of An Introduction to Formal Logic. I have been revising the revisions of the chapters on propositional trees. I’ve streamlined the presentation, and some material is relegated to an online Appendix (yet to come). So there are now three short chapters, just 26 pages plus 3 pages of Exercises (also yet to come), as opposed to four chapters and 39 pages in the first edition. I do hope the result is still a very clear introduction to the truth-tree method.

All comments and/or corrections (either here or to the email address in the watermarked header) are as always most welcome.

[Added: I should say that tree-rules for biconditionals and examples with biconditionals are a topic for the planned end-of-chapter Exercises.]

The post IFL2 Chapters 18 to 20: Propositional truth trees appeared first on Logic Matters.

Postcard from Cornwall

Another year, another (logic-free!) fortnight in St Mawes, in Cornwall. It is good to go at this time, as it is mostly still very quiet and the walking is at its best. The weather, though, can often be very changeable. But this time, we were particularly lucky, and there were a lot of very good days; and for once we got to see, for example, the charming Elizabethan house and garden at Trerice in the sun. Sheer delight.

I mostly tried to avoid the news for the two weeks. It is no surprise to now find that Brexit still continues to be a train-wreck. (Cornwall, away from the tourist trade, is one of the poorest areas of Europe; it will lose a great deal of EU support funding. You can put it down to the fundamental mendaciousness of the referendum campaign that there was a local majority for leaving …)

You can easily drive from Cambridge to Cornwall in a day, but it is much more enjoyable to break the journey. This year, in one direction, we stopped over at edge of Gloucester, wanting to see the cathedral which we had never visited. It is quite wonderful. But oh, the surrounding city centre seems so shabby and run-down (to the point that we felt quite uncomfortable about venturing back to eat in the city in the evening). It is indeed depressing how many of the old county towns of England have become hollowed-out, undignified, wrecks.

The post Postcard from Cornwall appeared first on Logic Matters.

The Pavel Haas, remixed

Photo: Marco Borggreve

Sadly we can’t get to the Wigmore Hall concert tonight to hear the Pavel Haas for the first time in their (wonderfully promising) new line up.

It must have been a great blow to them when their founder violist Pavel Nikl had to leave the Quartet in 2016 because of family illness. His replacement Radim Sedmidubský is a fine player, but somehow (to me at any rate) he never felt an entirely comfortable fit for the quartet; and, for whatever reason, he left at the end of 2017. The Pavel Haas played a few concerts with Pavel Nikl again, but he hasn’t been able to rejoin them. And so they teamed up with the young composer/conductor/violist Jiří Kabát, and played a few concerts earlier in year, and he has now officially joined the Quartet.

Every sign is that this promises to be a happy match with another very serious and gifted musician who can play with the intense commitment of the other three. Though that’s too solemn a way to put it —  a Facebook post from the Quartet after their first official outing together showed beaming smiles all round with the simple comment “Feeling wonderful”. Very much hope to catch them in London in September …

The post The Pavel Haas, remixed appeared first on Logic Matters.

IFL2 Chapter 23: Translations

Here’s another draft chapter from the planned second edition of IFL. This one discusses some general issues about translating to and from the formal language(s) of quantificational logic, and also gives lots of worked examples. Purists might, I suppose, be upset by the reliance on Loglish as half-way house to aid understanding and translation; but by my lights this would be being too pernickety by half! Comments on the last section in particular would be welcome.

The post IFL2 Chapter 23: Translations appeared first on Logic Matters.

Cranks

Once upon a time, a certain mathematics professor, one William Dilworth, joined the ranks of those purporting to rebut Cantor’s diagonal argument and aiming to show that that set theory (as we know and love it) is founded on mistake — indeed “Logicians’ axiomatic set theory is meaningless in mathematics.  They have been working in wrong mathematics and exerting their efforts in vain over the past sixty years.” Underwood Dudley gave Dilworth a mention in his entertaining squib Mathematical Cranks. Dilworth sued for defamation. [HT to a FOM posting …]

The case was dismissed, then went to appeal. The dismissal was upheld on appeal in a decision written by Richard Posner. From the decision:

A crank is a person inexplicably obsessed by an obviously unsound idea—a person with a bee in his bonnet. To call a person a crank is to say that because of some quirk of temperament he is wasting his time pursuing a line of thought that is plainly without merit or promise … To call a person a crank is basically just a colorful and insulting way of expressing disagreement with his master idea, and it therefore belongs to the language of controversy rather than to the language of defamation.

That seems to me an excellent characterisation of a crank! But it does prompt the thought that, by that token, an awful lot of philosophers are either cranks or expend a great deal of ink on cranks …

Or am I just getting cranky in my old age?

The post Cranks appeared first on Logic Matters.

IFL2 Chapters 21, 22: QL languages

Here is the second instalment of some draft chapters planned for the second edition of my Introduction to Formal Logic. This time, there are two short chapters — still only eighteen pages. I introduce here the syntax and interpretational semantics of QL languages.

As far as syntax goes, my preference is for distinguishing parameters/dummy names from free variables (and banning wffs with dangling free variables, and wffs with repeated or  vacuous quantiers). And as far as semantics goes, at this stage we are just learning to translate in and out of formal languages, using Loglish as a half-way house. Hopefully there is nothing that should jar too much for expert readers, even when they might prefer to do things another way.

As always, comments most welcome (even if just ‘that was OK, so keep going!’). So here are Chapters 21 and 22, to follow on from Chapter 20 in the previous blog post.

The post IFL2 Chapters 21, 22: QL languages appeared first on Logic Matters.

IFL2 Chapter 20: Quantifiers

Over the next few weeks, I plan to post here draft versions of some individual chapters  from the slowly evolving second edition of my Introduction to Formal Logic. I’m at the stage where feedback would be most welcome!

Seeking reactions to a four hundred page book would be a really big ask, so I’m not going to do that. But I do hope that a few friendly readers might be tempted at least to look intermittently at some relatively short chapters!

All comments, then,  most gratefully received, whether you are a student or a teacher — I’d especially like to know about places where I am less than ideally clear. And if you have some snappier examples or explanatory turns of phrase for me to steal, that would be great! Though, however wise and well-intentioned, I guess it is a bit late in the day for reactions along the lines of  ‘you really should be writing a quite different book’! You can either comment here or by email (address on the draft chapters).

OK: please do remember IFL is intended as a genuinely introductory book (it is based on my pre-retirement first year lecture course). This first instalment is the chapter motivating the quantifier/variable notation and the design of formal languages for quantificational logic.

The post IFL2 Chapter 20: Quantifiers appeared first on Logic Matters.

Five books — Philosophical Logic, from the back catalogue

As noted in a recent post, I’ve  recently been reading an old discussion by Geach of ‘any’ vs ‘every’. I’d largely forgotten what his view was — I hadn’t revisited my dusty copy of the relevant book for decades. But that got me thinking: what five books on philosophical logic from back in the day (say, the quarter century or so on from 1950), books that are little read these days, are well worth revisiting, and still could be/should be recommended to budding philosophers to round out their education?

Here are five suggestions. No doubt I’ve forgotten about some that are equally worthwhile. Given more time (and fewer things I ought to be doing instead), I might have been inspired to write longer, separate, blog posts on each of these books. But I’ll have to be content with a brief paragraph on each. So taking them in order of publication, let’s begin with …

Peter Geach, Reference and Generality (Cornell U.P., originally 1962: third edition 1980). Cheerfully abuses some ideas to be found in various medieval logicians and in early Russell, in order to bring out the wisdom to be found in Frege. Tendentious, and you’ll want to read Gareth Evans on pronouns as a counterbalance, but this is full of good things, and written with great verve and clarity.

Next, Arthur Prior, The Objects of Thought  (OUP, 1971). This is Prior’s unfinished, and somewhat uneven book, edited from his drafts after his death by Geach and Kenny. If you don’t know it, the book is divided into two parts. The first concentrates on the logical properties of propositions, their relation to facts and sentences (Prior an early enthusiast for Ramsey). The second part is on  intentionality and discusses the relationship between different theories of naming and different accounts of belief. Of course these have been the topics of intense investigation in the near half-century since Prior was writing — but he is still definitely worth reading.

The next might seem to be an odd suggestion for an under-read book from those days. Doesn’t every well-brought up budding philosopher read their Quine? Well, not so much these days, or that’s the impression I get. And if they do read him, they probably miss what seems to me one of his most engaging books — W.V.O Quine, The Roots of Reference (Open Court, 1973). Even if you dispute the details the way Quine handles it, his project of considering a sequence of more and more sophisticated linguistic practices and asking at what level we need to discern reference to objects still seems to me exactly what we need. Quine’s wonderful style is, as always, a bonus.

For a very different book, written at the end of the  heyday of one kind of ‘linguistic philosophy’, we have Alan White,  Modal Thinking (Blackwell, 1975). As White says in the preface “Much attention has recently been given to formal modal logic and to various of its problems, but little to the actual nature of those concepts of our everyday thinking for which the formal logic was ostensibly designed”. Which is still pretty much as true now as it was then. He has chapters on ‘possibility’, ‘can’, ‘may’, ‘probability’, ‘certainty’, ‘necessity’, ‘must’, ‘obliged’,  ‘ought’, ‘the nature of modality’. White’s linguistic claims are not always compelling, but there is a lot of philosophically important concept-mapping and distinction-drawing. Again, an easy read. (If you like Ian Hacking’s wonderful paper ‘All kinds of possibility’, then you’ll get a lot out of Whit’s book too – and if you don’t know Hacking’s paper, it really is a must-read!)

Finally — and not just as an act of Cambridge piety — let me mention a book which is probably gathering as much dust in your library as the other four combined: Casimir Lewy, Meaning and Modality (Cambridge, 1976). Although the last published, this is by far the most old-school of the books, based on lectures that Lewy had famously been giving in Cambridge for some twenty years. And it an austere book. For example, he expends a lot on ink on the relationship  between the claims ‘vixen’ means ‘female fox’, ‘vixen’ means female fox, and the concept of being a vixen is identical with the concept of being a female fox. Lewy mostly leaves it to reader to draw the moral from his discussion for more substantive claims of philosophical analysis. But still, it seems to me that the philosophical distinctions he draws out from his apparently thin examples remain  important ones — and ones you still frequently find people getting confused about (‘confused’, in a strong Polish accent, being a favourite word of Lewy’s). The final chapters on entailment — and Lewy’s forgotten paradoxes of entailment — are still very much worth reading too.

So there are my five recommendations — any other suggestions of overlooked books on philosophical logic from that era that we should blow the dust off?

The post Five books — Philosophical Logic, from the back catalogue appeared first on Logic Matters.