Peter Smith's Blog

Briefly, Thomas Forster tells me that he has acquired funding for two studentships in Wellington NZ (a delightful place!) for students who want to do a Ph.D. in set theory, in particular working with him on NF or perhaps some adjacent topic. He has an intriguing page of possible thesis topics here. Please spread the word if you have suitable students — and for more details, email Thomas.

The post Two Ph.D. studentships appeared first on Logic Matters.

An accessible, very readable, well-motivated, zestful book on ordinal analysis and proof theory would be a very good thing to have. Arai’s Ordinal Analysis with an Introduction to Proof Theory isn’t it. By a country mile. (I was asked for a verdict: so here it is.)

Let’s ignore the fact that there are far too many garbled non-sentences such as “We denote instead of when no confusion likely occurs” (p. 2). Let’s pretend the book has been translated into a closer approximation to English. It may for all I know be packed from end to end with technical truths. But that is little recommendation if it remains dreadfully hard-going, a very paradigm of how not to write an enjoyable and attractively helpful introduction to its topic. Who on earth is it intended for? If a reasonably logic-literate reader like myself finds it rebarbative, what hope a graduate student wanting to learn some proof theory?

Not that this sort of thing is so very exceptional: it is depressing how badly written many maths books are. But you can certainly cross this one off your Christmas list.

The post A very short, very blunt, book note appeared first on Logic Matters.

Most of the writing I have actually done this last week or so has been in tinkering with the category theory notes. For, sad to relate, I still find myself occasionally working through them. Until yesterday, however, it has just been a matter of making small changes for clarity and readability, and correcting a few trivial typos, with a view to making an updated version available later in the year.

But I have just been alerted to a non-trivial error in the current version (thanks to Edelcio Gonçalves de Souza of São Paulo). As it happens this is very timely, as the mistake occurs only a couple of chapters further on from where my re-readings had reached. So at least I am in the right frame of mind to be able readily to deal with it.

What’s the problem? Definition 95 says that in a category with a subobject classifier and an initial object 0, we can define a “falsehood” arrow as the characteristic arrow for . But that’s not good enough: if the characteristic arrow is to exist we need to be monic. So Definition 95 should add a suitable condition to ensure that that arrow is indeed monic, the natural candidate being that we are dealing with a cartesian closed category. In fact the following theorem is explicitly about such categories; and not too much damage is done because the later examples where arrows appear in Chapter 23 do also involve cartesian closed categories (though that isn’t spelt out properly).

But still some work needs to be done sorting things out more carefully. The material in Chapter 23 was originally much later in the book, in the context of talking about toposes, which are of course always cartesian closed. Evidently I forgot to explicitly pull forward all the needed assumptions when I moved the material to the current position. So many thanks to Edelcio for spotting this and for letting me know.

When we were in London a couple of weeks ago, we visited some of the Dutch rooms in the National Gallery — not least, to see once again their delightful, cheeringly humane, paintings by Pieter de Hooch, especially the The Courtyard of a House in Delft and A Woman and her Maid in a Courtyard. Which prompted me to get a second hand copy of one of the only books on the artist, Pieter de Hooch 1629–1684, an exhibition catalogue published almost thirty years (beautifully produced, as so often, by Yale UP). I have been enjoying this a great deal — the text is a bit stolid (the style of catalogue-writing has lightened with the years) but is very illuminating, and the full-page reproductions of the forty-one pictures by de Hooch in the original exhibition are just terrific. For calming relief after a bit of doom-scrolling, it’s hard to beat an art book like this.

There is a spectacular new CD from the Pavel Haas Quartet. Since their founder violist Pavel Nikl so sadly had to leave the PHQ because of family illness, three violists came and went in what must have been a distressingly unsettling way for the rest of the PHQ — so they drew breath and spent more than a year before settling on the young Slovak player Šimon Truszka as their new permanent member, with (it seems) huge success. I’ve now seen the quartet performing in its new line-up three times, and to my naive ears, Šimon Truszka is not only a wonderful player but a wonderful fit. And now comes the first CD with him as the violist, a recording of four of Martinů’s string quartets. Not the most immediately ingratiating music, but on repeated listening it becomes compelling. And the playing is surely at a stunning level. But don’t take my word for it – here’s a rave review from the Presto site. (Presto also have an interview with Veronika and Peter about Martinů — in which you learn they first met aged eleven, with Peter playing a piece by Martinů.)

I love the cover of the CD. It is difficult not to hear Veronika’s laughter a moment later.

And — an additional major treat! — here for the next month is a video of the PHQ playing at Wigmore Hall this week to great acclaim, starting with Martinů’s third quartet (followed by quartets by Korngold and Dvořák). Enjoy!

The post Footnotes to a fortnight: Category mistakes, Dutch courtyards, Martinů appeared first on Logic Matters.

Most of the writing I have actually done this last week or so has been in tinkering with the category theory notes. For, sad to relate, I still find myself occasionally working through them. Until yesterday, however, it has just been a matter of making small changes for clarity and readability, and correcting a few trivial typos, with a view to making an updated version available later in the year.

But I have just been alerted to a non-trivial error in the current version (thanks to Edelcio Gonçalves de Souza of São Paulo). As it happens this is very timely, as the mistake occurs only a couple of chapters further on from where my re-readings had reached. So at least I am in the right frame of mind to be able readily to deal with it.

What’s the problem? Definition 95 says that in a category with a subobject classifier and an initial object 0, we can define a “falsehood” arrow as the characteristic arrow for . But that’s not good enough: if the characteristic arrow is to exist we need to be monic. So Definition 95 should add a suitable condition to ensure that that arrow is indeed monic, the natural candidate being that we are dealing with a cartesian closed category. In fact the following theorem is explicitly about such categories; and not too much damage is done because the later examples where arrows appear in Chapter 23 do also involve cartesian closed categories (though that isn’t spelt out properly).

But still some work needs to be done sorting things out more carefully. The material in Chapter 23 was originally much later in the book, in the context of talking about toposes, which are of course always cartesian closed. Evidently I forgot to explicitly pull forward all the needed assumptions when I moved the material to the current position. So many thanks to Edelcio for spotting this and for letting me know.

When we were in London a couple of weeks ago, we visited some of the Dutch rooms in the National Gallery — not least, to see once again their delightful, cheeringly humane, paintings by Pieter de Hooch, especially the The Courtyard of a House in Delft and A Woman and her Maid in a Courtyard. Which prompted me to get a second hand copy of one of the only books on the artist, Pieter de Hooch 1629–1684, an exhibition catalogue published almost thirty years (beautifully produced, as so often, by Yale UP). I have been enjoying this a great deal — the text is a bit stolid (the style of catalogue-writing has lightened with the years) but is very illuminating, and the full-page reproductions of the forty-one pictures by de Hooch in the original exhibition are just terrific. For calming relief after a bit of doom-scrolling, it’s hard to beat an art book like this.

There is a spectacular new CD from the Pavel Haas Quartet. Since their founder violist Pavel Nikl so sadly had to leave the PHQ because of family illness, three violists came and went in what must have been a distressingly unsettling way for the rest of the PHQ — so they drew breath and spent more than a year before settling on the young Slovak player Šimon Truszka as their new permanent member, with (it seems) huge success. I’ve now seen the quartet performing in its new line-up three times, and to my naive ears, Šimon Truszka is not only a wonderful player but a wonderful fit. And now comes the first CD with him as the violist, a recording of four of Martinů’s string quartets. Not the most immediately ingratiating music, but on repeated listening it becomes compelling. And the playing is surely at a stunning level. But don’t take my word for it – here’s a rave review from the Presto site. (Presto also have an interview with Veronika and Peter about Martinů — in which you learn they first met aged eleven, with Peter playing a piece by Martinů.)

I love the cover of the CD. It is difficult not to hear Veronika’s laughter a moment later.

And — an additional major treat! — here for the next month is a video of the PHQ playing at Wigmore Hall this week to great acclaim, starting with Martinů’s third quartet (followed by quartets by Korngold and Dvořák). Enjoy!

The post Footnotes to a couple of weeks: Category mistakes, Dutch courtyards, Martinů appeared first on Logic Matters.

A great couple of days in London. The high point, a quite outstanding evening at Wigmore Hall — the wondrous Lea Desandre and Thomas Dunford (and the Jupiter ensemble) performing Dowland and Purcell.

Their new CD is terrific, and the live version of basically the same programme was even more so. One of the very best concerts we have been to in recent years, with Lea Desandre absolutely compelling. The barely controlled emotion as she sung Purcell’s “O let me weep, for ever weep” — interweaving with Louise Ayrton’s touchingly plangent baroque violin — made for an extraordinary experience. And as for Dido’s Lament …

Not that the concert was all sombre or doleful. For example, “O let me weep …” was followed immediately with sunlight in “Now the night is chased away.” Here’s a snatch from their rehearsal of that earlier in the day. And as you’ll see, while Jupiter are joined by four singers on the CD, in the concert — quite delightfully — the band themselves also provided, as it were, Lea’s occasional backing vocals. An evening to remember for a long time.

The post Songs of passion. appeared first on Logic Matters.

Not a logical week, but a great couple of days in London. The high point, a quite outstanding evening at Wigmore Hall — the wondrous Lea Desandre and Thomas Dunford (and the Jupiter ensemble) performing Dowland and Purcell.

Their new CD is terrific, and the live version of basically the same programme was even more so. One of the very best concerts we have been to in recent years, with Lea Desandre absolutely compelling. The barely controlled emotion as she sung Purcell’s “O let me weep, for ever weep” — interweaving with Louise Ayrton’s touchingly plangent baroque violin — made for an extraordinary experience. And as for Dido’s Lament …

Not that the concert was all sombre or doleful. For example, “O let me weep …” was followed immediately with sunlight in “Now the night is chased away.” Here’s a snatch from their rehearsal of that earlier in the day. And as you’ll see, while Jupiter are joined by four singers on the CD, in the concert — quite delightfully — the band themselves also provided, as it were, Lea’s occasional backing vocals. An evening to remember for a long time.

The post Footnote to the week: Songs of passion. appeared first on Logic Matters.

What have I been reading this week? I finished The Voyage Home, the most recent in Pat Barker’s wonderful series re-imaging episodes from the Trojan War. This time, it’s Agamemnon’s voyage home after the war, and his death at the hands of Clytemnestra and Aegisthus, which is re-told (mostly as seen through the eyes of a captive maid to Cassandra, the Trojan princess taken by Agamemnon as a trophy concubine). But you very probably know that, and won’t at all need me to tell you just how good Pat Barker’s trilogy is. So let me say something instead about a different book, which you might not know about.

I am a great admirer of A.E. Stallings poetry — the way her enticing surface formal play with rhyme and metre is married to depth and insight, the way she often gives new life to ancient voices (Persephone, Daphne, Penelope, …) yet her poems “come out of life’s dailiness”. Her This Afterlife: Selected Poems (2022) is full of subtle inventiveness, and — as a reviewer put it — she “demonstrates that in the right poet’s hands, the putative everydayness of the hic et nunc can be transformed into something every bit as rich and strange as even the most ancient myths.”  

But you probably know that too! However I only recently noted that Stallings’ had a new book out in April. Her Frieze Frame is on the rich and strange history of the Parthenon Marbles, and how “poets, painters, and their friends framed the debates around Elgin” and his acquisition (or should that be ‘looting’?) of the Marbles. I have just finished this too, and warmly recommend it.

The book began as a short lockdown essay, and has grown to become a quite fascinating scrapbook full of picaresque detail — ridiculous, infuriating, distressing, touching in turn. And as you’d expect, the writing can be wonderful. How about this, on the actress Melina Mercouri who became Greek Minster of Culture, and a passionate advocate for the return of the Marbles: “The Greeks loved her for this campaign and activism, quite apart from her acting; the Acropolis Metro Station is decorated with a famous photograph of her holding a summer bouquet, standing below the Parthenon on the Acropolis, so that she seems of a piece with one of the sturdy corner columns. In her fawn-colored trench coat, the same pale tawny color as the Pentelic marbles, with her weathered statuesque beauty, she could be a Caryatid on holiday, letting the wind run through her faded blonde hair and clutching the fresh flowers of the eternally recurring Greek spring.” Even if you know the basic story, this is just a terrific read.

I mused here a few weeks ago that it would be really good if there were a student-orientated(?) book which “played through some of the greatest hits from logic’s back catalogue” with zip and zest, engendering rather more excitement than e.g. the dutiful efforts in The History of Philosophical and Formal Logic (Bloomsbury 2017). Which got me wondering what an enticing chapter on Aristotle’s logic might look like. So the man himself has provided my other Greek reading this week. Along with a stash of hugely illuminating related articles, in particular by the estimable Jonathan Barnes.

Which has been pretty enjoyable — though it has certainly distracted me from what I was planning to be doing (getting back to updating the Study Guide) while also leaving me even more unsure how you’d do justice to Aristotle in a reasonably short piece.

It did strike me, though, that something that might be fun to do is to it take the often telegraphic lecture-notes that comprise the dozen pages of APr 1,2, 4–7 and — as it were — write out the lectures in a modern-reader-friendly way (or at least lectures as might have been given by a counterpart of Aristotle in some not too remote possible world). A devoted ancient philosophy student, with the translations and lengthy commentaries of Robin Smith and of Gisela Striker to hand (and ideally the original text too), can work things out. However that’s a big ask for someone whose first interest is in logic but who would be intrigued to get a real sense of how things started though without putting in too much time and energy.

A cheering small (very small) moment at the end of week. A mini Amazon review of the category theory book arrives online. “A superb introduction!” OK: I can raise a glass to that.

The post Greek readings appeared first on Logic Matters.

What have I been reading this week? I finished The Voyage Home, the most recent in Pat Barker’s wonderful series re-imaging episodes from the Trojan War. This time, it’s Agamemnon’s voyage home after the war, and his death at the hands of Clytemnestra and Aegisthus, which is re-told (mostly as seen through the eyes of a captive maid to Cassandra, the Trojan princess taken by Agamemnon as a trophy concubine). But you very probably know that, and won’t at all need me to tell you just how good Pat Barker’s trilogy is. So let me say something instead about a different book, which you might not know about.

I am a great admirer of A.E. Stallings poetry — the way her enticing surface formal play with rhyme and metre is married to depth and insight, the way she often gives new life to ancient voices (Persephone, Daphne, Penelope, …) yet her poems “come out of life’s dailiness”. Her This Afterlife: Selected Poems (2022) is full of subtle inventiveness, and — as a reviewer put it — she “demonstrates that in the right poet’s hands, the putative everydayness of the hic et nunc can be transformed into something every bit as rich and strange as even the most ancient myths.”  

But you probably know that too! However I only recently noted that Stallings’ had a new book out in April. Her Frieze Frame is on the rich and strange history of the Parthenon Marbles, and how “poets, painters, and their friends framed the debates around Elgin” and his acquisition (or should that be ‘looting’?) of the Marbles. I have just finished this too, and warmly recommend it.

The book began as a short lockdown essay, and has grown to become a quite fascinating scrapbook full of picaresque detail — ridiculous, infuriating, distressing, touching in turn. And as you’d expect, the writing can be wonderful. How about this, on the actress Melina Mercouri who became Greek Minster of Culture, and a passionate advocate for the return of the Marbles: “The Greeks loved her for this campaign and activism, quite apart from her acting; the Acropolis Metro Station is decorated with a famous photograph of her holding a summer bouquet, standing below the Parthenon on the Acropolis, so that she seems of a piece with one of the sturdy corner columns. In her fawn-colored trench coat, the same pale tawny color as the Pentelic marbles, with her weathered statuesque beauty, she could be a Caryatid on holiday, letting the wind run through her faded blonde hair and clutching the fresh flowers of the eternally recurring Greek spring.” Even if you know the basic story, this is just a terrific read.

I mused here a few weeks ago that it would be really good if there were a student-orientated(?) book which “played through some of the greatest hits from logic’s back catalogue” with zip and zest, engendering rather more excitement than e.g. the dutiful efforts in The History of Philosophical and Formal Logic (Bloomsbury 2017). Which got me wondering what an enticing chapter on Aristotle’s logic might look like. So the man himself has provided my other Greek reading this week. Along with a stash of hugely illuminating related articles, in particular by the estimable Jonathan Barnes.

Which has been pretty enjoyable — though it has certainly distracted me from what I was planning to be doing (getting back to updating the Study Guide) while also leaving me even more unsure how you’d do justice to Aristotle in a reasonably short piece.

It did strike me, though, that something that might be fun to do is to it take the often telegraphic lecture-notes that comprise the dozen pages of APr 1,2, 4–7 and — as it were — write out the lectures in a modern-reader-friendly way (or at least lectures as might have been given by a counterpart of Aristotle in some not too remote possible world). A devoted ancient philosophy student, with the translations and lengthy commentaries of Robin Smith and of Gisela Striker to hand (and ideally the original text too), can work things out. However that’s a big ask for someone whose first interest is in logic but who would be intrigued to get a real sense of how things started though without putting in too much time and energy.

A cheering small (very small) moment at the end of week. A mini Amazon review of the category theory book arrives online. “A superb introduction!” OK: I can raise a glass to that.

The post Footnotes to the week: Greek readings appeared first on Logic Matters.

Just before we went off to Zürich, we had our house painted outside (the doors, the windows, and so forth). It took fourteen days, not because we have a mansion but because a lot of preparatory work was needed, cutting out minor rot, repairing, filling, etc., and our decorator then did the most meticulous painting job. It looks terrific. But of course, the consequence is that lots of the inside paintwork now suddenly doesn’t seem quite so great. So I’ve been inspired to make a start on the long list of redecorating tasks that I’d been putting off.

Which is really quite enjoyable in its way, though horrendously time-consuming to do properly. And it requires concentration too. Whole mornings just disappear in a Zen-like state of careful brushwork. As a result, much less reading and writing of an even vaguely logical kind is getting done at the moment. Though I’m now a bit of an expert on Farrow & Ball’s thirty-seven whiter shades of pale …

One paper I did read this week with admiration is the logic-related piece among the ten papers selected for the latest volume of The Philosopher’s Annual. This is Nicholas DiBella’s “Cantor, Choice, and Paradox,” originally published in the Philosophical Review. Here’s the author’s abstract:

I propose a revision of Cantor’s account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor’s account if the Axiom of Choice is true, but its consequences differ from those of Cantor’s if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor’s account, blocks paradoxes—most notably, that a set can be partitioned into a set that is bigger than it—that can arise from Cantor’s account if the Axiom of Choice is false, illuminates the debate over whether the Axiom of Choice is true, is a mathematically fruitful alternative to Cantor’s account, and sheds philosophical light on one of the oldest unsolved problems in set theory.

That’s some conspectus! But the result is indeed impressive. Extremely lucidly written, engagingly novel, indeed suprisingly interesting and fruitful, but also judicious (not over-selling its claims). A model, I’d say, of how to write well at this level about logical matters.

Springer published last year — in the ongoing series ‘Outstanding Contributions to Logic’ — a volume of essays on Penelope Maddy’s work, edited by Sophia Arbeiter and Juliette Kennedy. I’ve been dipping in: but I have to report that I have been finding this mostly disappointing — which is no faulty of Maddy’s: she writes illuminating replies to (nearly all) the essays, which are probably the best thing about the book. But too many of the papers she is replying to strike me as, shall we say, unexciting. And not models of writing to be emulated.

I come to this volume with mixed views about Maddy’s work. For example, I was very engaged by her short book Defending the Axioms: On the Philosophical Foundations of Set Theory (2011); Luca Incurvati and I wrote an unpersuaded but not unfriendly review for Mind. On the other hand, I thought her later book The Logical Must: Wittgenstein on Logic (2014) quite misguided. Maddy says in her Introduction that her primary aim is “simply historical — to understand Wittgenstein better”. But a number of reviewers noted just how far Maddy seems to be from understanding the thrust of Wittgenstein’s thinking about logic (see, for example,  Martin Gustafsson’s review here).

Of course, it could be that the naturalistic view of logic Maddy adumbrates there is defensible even if she has gone badly wrong in thinking of it is as where Wiggenstein, properly understood, leads us. But I’m not persuaded. And I’m not helped to come to terms with her view by any of the papers contributed to this collection: the one that most engages with Maddy on Wittgenstein on logic is a 26 page ramble by Curtis Franks, “Wittgenstein’s Wayward Student: The Unauthorized Autobiography”. Not my cup of tea, to put it mildly.

No, the primary foci of the contributions (as you’d in fact expect) are firstly set theory (and in particular, ways of extending ZFC), and then Maddy’s contrasts between varieties of realisms and arealism about sets. Interesting/important topics, but I’ve decided against putting in the work to try to write up careful responses to the relevant pieces. Partly that’s because of the pressure of other things I want to be doing. And partly it’s because, when they get down to the nitty gritty, a number of the more technical contributions related to set theory are (to be honest) beyond my pay grade. For example, I’m not in a great position to engage usefully with e.g. John Steel writing on the generic multiverse (and he doesn’t make things easy for his reader — the paper he is replying to by Maddy and Toby Meadows is considerably more accessible and helpful).

The dust has yet to settle on recent debates about varieties of multiversism. For more debates, there are three “Conversations” involving set theorists reproduced at the end of the book. Then Maddy herself offers as the final essay in the collection an interesting new piece which aims to “isolate a surprising range of multiverse positions, revealing their sometimes-dubious metaphysical underpinnings and demonstrating that the distinction between multiversism and universism is often muddier than it might appear”. This is helpful.

One much older, less exotic, issue in the philosophy of set theory is how to construe talk of proper classes as contrasted with sets — which is arguably tied up with the question of how to regard logical classes (property-extensions) as contrasted with sets as explicated in the iterative conception. Maddy discussed the general problem long since in her 1983 JSL paper ‘Proper Classes’, where she reaches the interim conclusion that “In our search for a realistic theory of sets and classes, we [should] begin with two desiderata:
(1) classes should be real, well-defined entities;
(2) classes should be significantly different from sets.
The central problem is that it is hard to satisfy both of these.” She then proposed a theory to meet these desiderata, inspired by the structure of Kripke’s theory of truth.

Considerably later, Øystein Linnebo has a particularly insightful discussion in his ‘Pluralities and sets’ (J. Phil. 2010), again aiming for an account satisfying (1) and (2). So it intriguing to find him returning to the theme in the present collection in his contribution ‘Maddy on classes’. Here he argues that while Maddy’s original approach had promising features, her own development of the core idea was problematic. However, potential repairs run into more trouble, and Linnebo’s ultimate verdict is that “the picture that emerges is thus one of a failed research program”. But negative results are good to have! — and he concludes by suggesting another approach which (he argues) looks as if it should work better. I need to reflect some more: but this is a contribution worth reading and thinking about.

What about the discussions of Maddy on (anti)-realisms in this volume (see the review by Luca and myself for brief headlines about the issues)? I’ll mention the two best pieces. In rough terms, John Burgess complains (not entirely clearly) that Maddy strays too far in the direction of a nominalism and fictionalism about mathematics; going in the opposite direction Mary Leng (writing with her characteristic transparency) wants to push Maddy to take a step or two further towards her own brand of fictionalism. The replies perhaps help to better locate Maddy’s position — but puzzles remain.

Finally, although it is tedious to mention this, like others of the ‘Outstanding Contributions to Logic’ volumes, this one is oustandingly — not to say outlandishly, outrageously — expensive. Perhaps your university library has an e-copy available. Otherwise …

The post Footnotes to the week: Zen painting, the size of sets, Maddy appeared first on Logic Matters.

It is difficult to believe that Hugh Mellor died over five years ago: he was a very generous and loyal friend, and still much missed. And I have been thinking about him particularly this week, prompted by Tim Crane’s newly published biographical memoir for the British Academy. I think Tim does a really fine job, both on the man and his philosophy. Read his piece!

I am quite out of the loop now, on current discussions about causation, chance, time, dispositions, facts, and others of Hugh’s metaphysical preoccupations. My sense, though, is that his work is less read, less engaged with, than it surely deserves. For example, I see that the Stanford Encyclopaedia article on the metaphysics of causation in effect mentions him just once in passing. Why this lack of impact of Hugh’s major The Facts of Causation (1995) which says a lot on just this topic? Perhaps it is not irrelevant that that book is surprisingly hard going, as reviewers at the time noted. Oddly so, when his earlier books and indeed contemporaneous papers (and Hugh in conversation) were so lucid and accessible. The book’s arguments too could be unsatisfyingly brisk, as e.g. Dorothy Edgington found in her fine BJPS review article. But, echoing Tim, that doesn’t mean that there isn’t an original metaphysical story here about how causation, chance and the rest hang together, and one whose realist, anti-reductionist, themes have considerable attractions and deserve further exploration.

I’ve been rather distracted, then, from what I planned to be doing this week by dipping again into some of Hugh’s writing that you can find linked at hughmellor.com. And I was amused to come across this, in an interview published in Theoria in 2001. Noting that people postulate entities, such as properties, for various semantic purposes, Hugh continues:

It seems to me that before doing that, they should check what reasons there are for thinking there are such entities, as indeed they often do. That is why, for example, many logicians would prefer a logic or a semantics that did without sets, in which, to be honest, I doubt if anyone really believes. Talk about a set of things looks, to the outsider, like a way of using a singular term

Amusing, because the logic-related book I’ve been looking at this week is The Philosophy of Penelope Maddy, a substantial collection of papers published last year, mostly with replies by Maddy. The first group of six pieces is by a number of enthusiasts for sets, who most certainly believe in sets (Maddy herself countenances a more nuanced Arealism).

Now, it might be said that the sort of set that Hugh is sceptical about — e.g. a supposed set of heroes {Ramsey, Braithwaite, Reichenbach}, which arguably is really nothing over and above the men, plural — is not the kind of mathematical purely abstract object of the set-theorist’s dreams: so there is no lurking clash here. But the trouble is that set-theorists are wont to initially motivate their talk of sets with humdrum examples of sets of people, playing cards, and the like. And if such humdrum talk is indeed not really referring to special entities but is ripe for elimination in favour of frankly plural talk about people, cards and other whatnots, where exactly does that leave our supposed route into understanding what abstract set theory is about?

I’ll leave that question hanging as a tease! — but I want to return to say something more serious about the Maddy collection next week.

What have I been listening to? A year or two back, I really enjoyed a couple of earlier CDs of Scarlatti sonatas by the young Italian pianist Francesco Colli, so I was intrigued to see he has started releasing some Mozart discs, with the second out this month. But sadly, I think he tries more than a bit too hard to be inventive and imaginative. His approach works, perhaps, with the K331 Sonata where Colli manages in particular to make the hackneyed, oh-so-familiar, Alla Turca final movement sound fresh and full of wit. But he surely overdoes it with e.g. the delightful 12 Variations on ‘Ah, vous dirai-je maman’ (‘Twinkle, twinkle, little star’, to you). Elisabeth Brauß, for one, plays the piece with the gentler charm and affection it calls for, so listen to her instead.

The post Footnotes to the week: Mellor, Sets, Mozart appeared first on Logic Matters.