In wonderland

A Cambridge story, from Arnie Koslow.

Back in the day, the Moral Sciences Club met in the rooms of Richard Braithwaite, then the Club’s chairman. A sofa at the front provided the regular seating for the nervous figure of Alfred Ewing at one end and the obscurely oracular John Wisdom at the other.

One meeting, the room is packed, and a latecomer hovers at the door, looking for somewhere to sit.

From the chair, Braithwaite booms “There is space on the sofa … between the March Hare and the Mad Hatter.”

A reading resolution kept!

For some while now, I’ve kept a list of the novels that I’ve being reading or re-reading  — my memory for this sort of thing being pretty bad. But the list used to grow depressingly slowly; so very many good (or better!) novels, with more coming out every month, and so little time, it seemed, to read them. This year, then, I made a New Year’s Resolution: really cut-back on non-work-related internet in the evenings. I’ve never been one for FaceBook, though Twitter can be addictive. But oh, how the hours can disappear on newspaper/magazine sites, other political sites (especially in these days of Brexit and Trump), arts/music sites, not to mention nerdy stuff …! So, as I say, I resolved to Cut Right Down.

And for once, this is a resolution that has been kept pretty well. In the last six months, I’ve now read as many novels as the whole of last year — and had much more enjoyable and relaxing evenings into the bargain. I can honestly recommend it hugely, both for pleasure and for eudaimonia.

There’s no real pattern or plan to my reading. I usually just take down from the shelves something old or new that appeals at the time — and the shelves are an pretty eclectic mix, given that Mrs Logic Matters and I both have a taste for browsing charity-shops for serendipitous finds. But I do nowadays make a happy rule of reading a Dickens every winter — so this year, I lapped up Dombey and Son (which I confess I hadn’t read before as an adult). And, since it is his bicentennial year, I thought I’d try to read or re-read a good amount of Turgenev, who I do find particularly appealing. More about him, perhaps, another time.

My big recent discovery has been the novels of Helen Dunmore. I was very taken with her late novel Exposure earlier in the year; here’s an insightful review by Kate Clanchy. And then a bit later I was in a charity shop — serendipity indeed! — as they were putting on the table a uniform set of completely-as-new recently reprinted paperback copies of her first ten novels which had been donated a few minutes before. So I snaffled the lot, and am now beginning to read her novels in chronological order. A poet as well as a novelist, Dunmore’s are beautifully written as well as wonderfully thoughtful books.

What else? Let me just mention three for reading on a summer’s night (or on the beach!) for sheer enjoyment. The latest Sarah Dunant, In the Name of the Family, takes up her fictional but historically rich version of the Borgias where Blood and Beauty leaves off. If you don’t know the earlier book, you really are missing a treat: if you do know it, you’ll have surely read the sequel already. Six months or so ago, Gail Honeyman’s Eleanor Oliphant is Completely Fine was top of the paperback bestseller lists. We’re usually a bit resistant to hype; but we started reading it in a bookshop on an enthusiastic recommendation — and were hooked. But the book I’ve enjoyed most of all in the last six months is one from 1979 which I’d never read before, Penelope Fitzgerald’s tragi-farce (her word) Offshore. Here’s a nice piece about it by Alan Hollinghurst. Sheer delight on many levels.

[Security, etc.]

[Just an update to say that I have now installed an SSL certificate so that this becomes a “secure” site served via https, which will stop some browsers telling you this isn’t a secure site. I’ve also moved domain registrar and done other stuff behind the scenes. Let me know if I have broken anything!]

It is not the case that p

You can of course very often express the negation of p  by saying ‘it’s not the case that p’.

But some logicians in intro texts incautiously claim more — saying something like “This is cumbersome, but it works in every case” (that’s a quote, but no names, no pack drill!).

However it surely overshoots to claim that prefixing  ‘it’s not the case that’ by itself produces the negation of what you start with in every case. Here are some examples:

  1. Jack loves Jill, or Jill is much mistaken about Jack’s feelings.
  2. It’s not the case that Jack loves Jill, or Jill is much mistaken about Jack’s feelings.

Aren’t both  true if Jill is sadly mistaken?

  1. Jack loves Jill and it’s not the case that Jill loves Jack.
  2. It’s not the case that Jack loves Jill and it’s not the case that Jill loves Jack.

Aren’t both false if Jill loves Jack?

  1. Jones, who is a Russian agent, loves caviar.
  2. It’s not the case that Jones, who is a Russian agent, loves caviar.

Aren’t neither true if Jones isn’t a Russian agent?

So what are your favourite counterexamples to the claim that ‘it’s not the case that p’ always expresses the negation of p?

Valuations again

[The original version of this post misread the quoted passage from Nick Smith’s book — see his comment! I’ve edited so that his comment still fits, but so that someone browsing through and not delving into comments doesn’t go away with the wrong impression!]

As a footnote to my last post, I want to consider a passage in Nick Smith’s Logic: The Laws of Truth.

Smith talks of giving a glossary for PL, a list like

A: Antelopes chew the cud,
F: Your best friend is my worst enemy,
N: Albany is capital of New York

(his examples). In such a case, he says (p. 33) that the sentence letter “represents” the proposition expressed using the sentence on the right, and we might wonder what “represents” means here. He also talks (p. 34) of a sentence letter “stand[ing] for” a proposition, and then (p.35) of a formula “express[ing]”  a proposition. I’d say that representing, standing for, and expressing are different — but let’s not nag about that. I think it is clear enough that Smith thinks of a glossary for some PL sentences as assigning them at least Fregean senses (i.e. truth-relevant meanings), so that they are meaningful and express propositions. Which is just fine by me, so long as we understand talk of propositions in a sufficiently neutral way.

Smith distinguishes between an argument’s being necessarily truth-preserving and its being necessarily truth-preserving in virtue of its form or structure. Some (e.g. me now in IFL2 though not in IFL1) would mark the difference as the difference between being valid and being logically valid. Smith, with about as much warrant from the tradition, reserves “valid” for  the second status. But we agree there’s a distinction to be made, and agree that what official stories about tautological validity, q-validity (as I’d call it), S5-validity and so give us are accounts of varieties of  necessary truth-preservation in virtue of form — special cases of logical validity for me, cases of validity for him. Which is again just fine by me.

But now consider this passage from p. 65:

An argument is invalid if there is a possible scenario in which the premises are true and the conclusion false. A truth table tells us whether there is such a possible scenario—but it also does more: if there is, it specifies the scenario for us (and if there is more than one, it specifies them all). For a given argument, we term a scenario in which the premises are true and the conclusion is false a counterexample to the argument. So a truth table does not merely tell us whether an argument is invalid: if it is invalid, we can furthermore read off a counterexample to the argument from the truth table.

Well, suppose we are working with the following glossary (nothing that Smith says, as far as I can see, bans this):

P: Kermit is emerald green
Q: Kermit is green

Or perhaps this glossary:

P: Jill has a twin
Q: Jill has a sibling

Or perhaps this glossary

P: Jill is much taller than Jack
Q: Jack is shorter than Jill.

Then in each case a truth-table tells us that the argument P, so Q is not necessarily-truth-preserving-in-virtue-of-PL-form (where PL form is the aspect of form, i.e. distribution of truth-functional connectives, that propositional logic latches onto). It doesn’t immediately follow from that that the argument is not necessarily-truth-preserving-in-virtue-of-form tout court, but let that pass. For the sake of argument, go with the verdict that the arguments in each case aren’t valid-in-Smith’s-sense. But of course, from the counterexample to tautological validity, meaning the valuation [P] = T, [Q] = F, we can’t in these cases read off a possible situation in which which the premiss is true and the conclusion false. In these cases, there simply is no such possible situation.

So has Smith has temporarily forgotten that, once we interpret PL atoms, this allows for relations of necessary connection of truth values that aren’t picked up by truth-tables? It turns out not so, contrary to my first impression — see his comment below. For when he talks about a counterexample as a “scenario” in which the premises are true and the conclusion is false, he is using “scenario”   in a special sense which is equivalent to (combinatorial) valuation and not — as the incautious reader whose eye skipped (me!) might assume — to mean, erm, scenario, i.e. situation in a possible world.

My original post then misrepresented my namesake: we agree that  combinatorially possible valuations as listed on lines of a truth-table may, given the interpretations of the atoms, not be valuations corresponding to possible scenarios in a natural sense, though they are ”scenarios” in his official (I’d say, misleadingly labelled!) sense. Good! Still, what I wanted to stress in my previous posting here is that the point we do agree on — however expressed — needs to be made loud and clear. Apologies to Nick for explicitly suggesting he’d fumbled the point as opposed, perhaps, to (like others I could mention!) not flagging it in the most perspicuous way.

Valuations, combinatorial vs ‘realizable’

This is request for references on an issue in very elementary logic!

To set the scene, suppose we take the atoms of a formal language for propositional logic to be interpreted. Yes, yes, I know that different authors take different official lines about how to treat their ‘P’s and ‘Q’s — hence the ‘suppose’! We are considering the approach where a formal language is indeed taken to be a language, with meaningful wffs, so inferences in the language really are genuine inferences, etc.

Perhaps then the glossary for a particular PL language reads

P: Water is H2O,
Q: Jill is married,
R: Jill is single.

So now consider, then, writing down a truth-table for a wff built from these atoms, as it might be ‘(P ∧ (QR))’. We of course standardly consider all combinatorially possible assignments of values to the three propositional atoms, giving us an eight-line table. But we might now remark that (according to most) there is no possible world at which ‘P’ is false. And (according to everyone, assuming it is the same Jill, etc. [oops, see comments!]) there is no possible world at which ‘Q’ and ‘R’ take the same value. Hence, of the combinatorially possible assignments of values to these three interpreted atoms, in fact only two (on the majority view) correspond to a possible world. In a word, in this case only two of the eight combinatorially possible valuations are “realizable” possible valuations — meaning realizable-at-some-possible-world.

Looking ahead, we define the tautological validity of an inference in an interpreted PL language in terms of truth-preservation on all combinatorially possible valuations of the relevant atoms. Whereas plain deductive validity is a matter of truth-preservation with respect to any possible world, which for PL wffs means truth-preservation on any valuation-realizable-at-some-possible-world. Which is why tautological validity implies validity for  inferences in a PL language, but not vice versa. (If, as some do, you prefer to build ‘in virtue of logical form’ into your official definition of validity, then replace talk of plain validity here with talk of necessary preservation of truth.)

OK, having set the scene, here’s the request. The point that combinatorially possible assignments of truth-value for an interpreted PL language may in some cases (depending on the intepretations of the atoms) not correspond to possible worlds, is an entirely elementary one. But which elementary texts (or sets of detailed online notes) make the point particularly clearly? At some point a couple of months ago, I did read a text — online I think — which handled this particularly clearly, and used a better word than “realizable” (heavens, what was it??).  But like an idiot I didn’t take notes at the time. So any suggestions/pointers?

(Full disclosure: This is one of the many issues that I want to handle better in IFL2 than in IFL1, and so I’d really like to check my draft treatment against versions elsewhere — and also like to see how others who are clear in the propositional case handle the analogous distinction when it comes to predicate logic.)

The Epistemic Lightness of Truth

Using my hefty discount at the CUP shop, I bought a copy of The Epistemic Lightness of Truth: Deflationism and its Logic by Cezary Cieśliński when it came out at the very end of last year. I mentioned it briefly here, saying that first impressions were very good. I then read some more;  but, life being as it is, I got distracted, and I never returned to say more about what struck me as an excellent book — a must-read if you are tempted by/interested in a broadly deflationist approach to truth.

In fact, I’ve not been keeping up quite closely enough with the literature here to give a fully informed judgement of Cieśliński’s achievement without more homework than I have had time for. However, Leon Horsten is in as good a position as anyone to assess the state of play. And he has now written an extensive and detailed review for Notre Dame Philosophical Reviews. His summary judgement? “I cannot praise this book too highly. I predict that it will constitute indispensable reading for any researcher in the field (professional or postgraduate) for years to come.” So read the very helpful review. Order the book for your library. And let’s hope that CUP issue a more modestly priced paperback sooner rather than later.

At Kettle’s Yard

Edge III, 2012, Antony Gormley

To cheer up after a depressing work day yesterday — one of those days you lose faith in the book you are writing — a cheering outing to the newly opened exhibition at Kettle’s Yard, with five works by Antony Gormley, an exhibition which makes wonderful use of the spaces in the new galleries there. Very striking and thought provoking.

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.

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