Sunday, May 21, 2017

Bad Deal Or No Deal

Consider these two statements:
  • Eating no bread is better than eating any mouldy bread.
  • Any bread at least as good to eat as no bread is not mouldy.

To avoid ambiguity, let’s put them into Mickey Mouse first order logic:
  • (x)[[Mouldy(x) & Bread(x)] → Better(eatingNoBread,eating(x))]
  • (x)[[Bread(x) & ¬Better(eatingNoBread,eating(x))] → ¬Mouldy(x)]

The two formulations are equivalent: they are both false iff there is some mouldy bread the eating of which is no worse than eating nothing. But there’s a difference of emphasis. The first formulation is something you might say if you were taking an uncompromising line on bread: if mouldy bead is all there is, you’d rather have nothing. The second formulation is something you might say if you were taking a compromising line on mouldiness: it can’t be mouldy or you wouldn’t recommend eating it at all. But a difference in emphasis is not a difference in commitment. Asserting either commits you to the same things.

Now, the government’s line on the Brexit negotiations is apparently that no deal is better than a bad deal. People take this as meaning that they’re taking an uncompromising line on deals, and they take it to embody an attitude of cavalier intransigence. But consider these two statements:
  • Reaching no deal is better than reaching any bad deal.
  • Any deal at least as good as no deal is not bad.

And in MMFOL:
  • (x)[[Bad(x) & Deal(x)] → Better(reachingNoDeal,reaching(x))]
  • (x)[[Deal(x) & ¬Better(reachingNoDeal,reaching(x))] → ¬Bad(x)]

The second formulation seems to embody an attitude of roundheaded compromise. Don’t criticize this underwhelming deal, they say, because it’s better than nothing. But the two formulations are formulations of the same commitment. In the mouldy bread case the speaker enjoys a certain amount of latitude because of whatever vagueness and subjectivity there is in the word “mouldy”. In the Brexit case the speaker enjoys latitude because of whatever vagueness and subjectivity there is in the word “bad”.

Now with the mouldy bread case, the speaker is at least committing themselves to something. That’s because some bread is determinately mouldy. Suppose the only food available is determinately mouldy bread, and you say that eating no bread is better than eating any mouldy bread. Half the party eats the bread, against your advice, and half the party goes hungry. One half has a better time and you are open to praise or criticism as a result.

Now consider the Brexit case. While we don’t have a whole party to divide up into people taking your advice and people not taking it, we can still compare the actual world with our dimly assigned probability distributions over the space of counterfactual situations. But the government can always evade criticism, whatever consensus history arrives at on the relative merits of no deal and the available deals. Obviously the government are also the people taking the decision, unless they lose the election, and so they could be open to criticism for taking one option if history judges that other available options would have turned out better. There’s no escapting that. But the particular claim that no deal is worse than a bad deal is entirely hedged.

Take any deal you like. If we decide that it’s worse than no deal, the government says it’s bad and takes the credit for being right. If we decide that it’s better than no deal, the government can just say that it wasn’t a bad deal. Similarly, nobody needs to praise the government however things turn out either. If history judges that the available deal was worse than no deal, the opponent can say that of course there are some deals worse than no deal, but there are plenty of bad deals better than no deal too, and if we’d been able to get one of those then the government would have turned it down and been wrong to do so. The word ‘bad’ and the associated concept are flexible enough that nobody ever needs to admit they were wrong about whether no deal is worse than a bad deal. The government shouldn’t be criticized for taking a bad line; they should be criticized for empty, commitment-free rhetoric.

Monday, May 1, 2017

The After Dinner Circuit

It was recently reported that Barack Obama is getting paid $400,000 to give a speech to a Wall Street bank. Obama’s a great speaker, but a lot of people seem to think nobody’s $400,000 great, and so the transaction smacks of corruption. The thinking is that the bank must be getting more than just a speech for their money.


Now, I don’t know if it’s true that the speech alone isn’t worth that much to the bank. There’s a lot of money flying around in banking, and the stakes are high. Maybe if people come to your dinner rather than your competitor’s dinner, you might get a big deal that makes the money back. Or maybe hosting dinners with Obama attracts employees that could otherwise only be attracted with those enormous banker’s bonuses that we love reading about.


But let’s suppose that the speech isn’t worth that much to the bank, and they’re getting something else. Or maybe it is worth it to them but they're still getting something else, because that's how the after dinner speech market works. One possibility is that Obama made a shady deal where he did the bank some kind of regulatory favour while he was in office, on the understanding that they would pay him $400,000, which they are now laundering as a speaking fee. I think that's unlikely, but it’s beyond the scope of this blogpost to persuade you to agree with me that it's unlikely.


What I think is much more likely is that there’s a general understanding that Wall Street banks, and other big businesses, are willing to pay massive speaking fees to politicians after they leave office, and that they offer the gigs to politicians who are friendly to Wall Street and so on while they’re in office, and that on some level this influences the way politicians govern. This kind of thing is insidious and I can see it affecting basically everyone to some extent, without anyone doing anything they could be prosecuted for. That’s not ideal.


What can we do about this? One thing we could do is demand that politicians declare future conflicts of interest. If you’re taking a gig in the medium-to-near future that would constitute a conflict of interest if you had it now, then you need to declare it as if you had it now. I don’t see that it makes sense to have laws or strong norms about present conflicts of interest while relying on the honour system for future conflicts of interest. But let’s assume that’s not going to happen. What can individuals do?


Some people think Obama shouldn’t take this kind of gig. He should set an example, he needs to go high where other people go low, and so on. Even if his governing wasn’t influenced by the prospect of lucrative speaking gigs, he needs to extinguish any suspicion that it was.


Some other people think Obama should take the money. Everyone takes the money, and it’s unfair to demand he make all the sacrifices, especially when the new president brazenly doesn’t care about all his own conflicts of interest and spends government money at his own businesses all the time.


Here’s what I think. It’s too late for Obama. Whatever influence the speaking fees had on his presidency, they’ve had it already. We know he wasn’t planning to eschew the speaking fees, and changing his mind now won’t change whatever decisions he took during his presidency. If he was running for future office, things would be different. But he probably isn’t, and so it’s too late. Obama showed a lot of things were possible, but he can’t show that saving politics from the after dinner circuit is possible. And if he had been planning to do this, regulating Wall Street on the merits and to hell with the speaking fees, then he should have said something about it sooner. Like, when he was in office, or even before that.


It’s not too late for everyone. If you’re in office now, or you’re running for office in the future, and you don’t want politicians to be influenced by the prospect of future speaking fees, pledge not to take them. Or if you aren’t willing to go that far, then at least pledge not to take the really big fees. It’s simple, it’s easy for people to understand, and it doesn’t rely on backwards causation.


Saturday, April 15, 2017

Meet Me Halfway

A logician goes to an island of knights and knaves. Knights always tell the truth; knaves always lie. One of the locals says “either I’m a knave or there’s gold on this island”. Is there gold on the island?

This kind of puzzle is a staple of the puzzle books of Raymond Smullyan, and Forever Undecided: A Puzzle Guide To Gödel is no exception. This isn’t just a compendium of brainteasers intended solely for entertainment though; Smullyan has a serious purpose. He’s explaining some of the main results in provability logic by recasting them in terms of the beliefs of logicians with various characteristics when faced with this sort of knight/knave puzzle. It’s a clever idea, and very much the kind of clever idea you would expect Raymond Smullyan to have.

It’s helpful to cast results like Gödel’s incompleteness theorems and Löb’s theorem in different terms, and especially in fairly concrete terms about things people say or the output of a computer program. It helps to explain the content of the results, and helps readers understand their significance. One thing Smullyan is pretty keen to get across is that the impossibility of a system of arithmetic proving its own consistency doesn’t give any reason for thinking such systems aren’t consistent. This makes sense, since we already knew that an inconsistent system could prove its own consistency - inconsistent systems prove everything - so if a system says it’s consistent that’s no reason to think it is. If you ask a resident of the knight-knave island if they’re a knight, knights and knaves will both say they are. Similarly, if you want to know if a system’s consistent, you shouldn’t ask the system itself, and the fact people didn’t properly figure this out until Gödel discovered that consistent systems wouldn’t answer the question doesn’t change that.

As well as discussing the results, the book also contains lots of exercises, with reasonably generous solutions. These are analogous to the kind of exercises you might get in a textbook on provability logic, except they’re expressed in different terms. Now, you might think that doing it in terms of knights and knaves and so on would make the whole thing so much fun that the hard work of getting your head round this material wouldn’t feel like hard work, and before you knew it you’d have all the proofs of the main results in provability logic at your fingertips. This was not my experience. The material is just as hard, and now you have to learn a bunch of new terminology. It isn’t Smullyan’s fault that this stuff is hard, but there are things I think he could have done to make it a bit easier.

First, the book doesn’t have an index, and the chapter headings are often whimsical (“It ain’t necessarily so!”), vague (“More Consistency Predicaments”), or related to the island-hopping framing device (“In Search of Oona”). This makes it difficult to go back and remind yourself of material when it comes up again. This is bad enough when reading a novel, but in a textbook it’s not really excusable. Smullyan hasn’t set out to write a textbook, but he wanted the material to be comprehensible to someone who (unlike me) was approaching it for the first time, and an index and analytic table of contents would have helped with that a lot.

Second, the book introduces a lot of new terminology: reasoners of type 1, 2, 3, 4, 1*, G, G* and Q; normal, regular, peculiar, modest, conceited, reflexive and stable reasoners; Gödelian systems, Löbian systems, and so on. Being a doofus, I wasn’t able to keep all the definitions in my head. Since there was no convenient way of looking them up, a lot of the time I couldn’t understand the exercises until I looked at the solutions to see what followed from a reasoner being regular or stable or of type 3 or whatever. This isn’t really satisfactory, so I skipped a lot of the exercises and solutions, and when I didn’t skip the exercises I often didn’t really know what I was being asked. An appendix in the back saying what all these definitions mean would have been a great help. The last chapter gives a summary of the main results, but that’s not the same thing and doesn’t make the exercises more comprehensible. I’m considering writing an appendix myself and sticking it in the back in case I or anyone else reads my copy of the book again. It’d take some work though, as the definitions are scattered throughout the book and there’s no index.

So, who’s the book for? I think you’d really enjoy the book if you liked whimsical logic puzzles and were already very familiar with the technical material. (I like whimsical logic puzzles but was only reasonably familiar with the technical material.) You’d also probably get some scholarly benefit from reading the book if your understanding of the proofs of the results was better than your understanding of what the results amount to. I’m the opposite, and I expect that’s normal for people who encounter it through studying philosophy. I guess if you encountered it through studying maths then things might be the right way round for you. Who else would like the book? Well, someone who liked puzzles and would be interested in provability logic but hadn’t seen any of the results before would probably like the book at first but find it became a bit of a slog about 100 pages in. If they’re the sort of person who can read a maths textbook without looking at the index, the contents page or a list of definitions used in the book, then they’d probably be fine. Here’s what Smullyan says about the target audience in the preface:

I have lectured a good deal on all this material to such diverse groups as bright high school students and Ph.D.’s in mathematics, philosophy, and computer science. The responses of both groups were equally gratifying - they were intrigued. Indeed, any neophyte who is good at math or science can thoroughly master this entire book (though some application will be needed), yet many an expert will find here a wealth of completely new and fresh material.

I think that’s a bit optimistic, and if he wanted neophytes to apply themselves and master the entire book then he should have met them halfway with an index, and appendix and a better contents page. But I’ve no doubt people enjoyed the lectures.

Wednesday, April 12, 2017

Lost Voices Of History

Bertrand Russell was a great philosopher, and he also had a great voice. Since he was a celebrity who died in 1970, he was on TV a lot and you can have a listen to his voice on Youtube. If you hear a voice in your head when you read, as I do but as not everyone does, then I recommend reading Russell in Russell’s voice. It’s fun! With a lot of great philosophers, of course, we don’t have this luxury. There aren’t any recordings of their voices and nobody knows what they sounded like. This seems to me an avoidable shame.

People will presumably continue to do Michael Caine impressions for at least a while after Michael Caine dies, and my understanding is that most people’s Michael Caine impression owes at least as much to copying other people’s impressions as to copying Caine himself. That’s why they all sound the same but they don’t sound like Michael Caine. The Michael Caine impression voice is easy to do, and Michael Caine’s voice is hard to do, and here we are.

It seems to me that the Michael Caine impression voice could be preserved indefinitely, even if all the recordings of his voice and the impression voice were destroyed and no more were ever produced. People would copy each other, and hundreds of years into the future people would still be doing impressions of Michael Caine. And that would be a fine thing.

At least as fine a thing would be if this had actually happened with historical public figures: people had done impressions of them for the amusement of people familiar with the original, the way the impression sounded had become common knowledge, the ability to do the impression had become part of every self-respecting person’s conversational repertoire, and then 470 years on we were all still doing impressions of Henry VIII.

I can’t think of anyone this has happened with in the Anglosphere. All the impressions we do nowadays are of people we have recordings of. Perhaps there are or have been communities who did preserve their ancestors’ voices over the centuries in this way; if you know of any then tell us about it in the comments. It would seem strange to me if that hadn’t happened, but English speakers seem not to have preserved any, so maybe that’s how things are.

Wednesday, March 22, 2017

A Love Poem About Donkeys

March 4 was National Grammar Day in America, and someone I follow on Twitter was running a competition for grammar-themed haikus. I wrote one. It didn’t win. You can see the winners here. But in case you missed it, here is mine.

Donkeys donkeys love
Love donkeys donkeys donkeys
Donkeys love love love.

Sunday, March 12, 2017

Stop Reporting Surveys Wrong

There’s a common mistake in the way findings of surveys are reported. It annoys me every time I see it, and when I saw it again yesterday it annoyed me enough to write on my blog about it. Here’s a screenshot of a tweet promoting the article. Can you spot the mistake?


Vox white evangelicals muslims more discrimination.png


Pretty awful, right?


So, the survey asked people which groups they thought faced a lot of discrimination in the United States today. 44% of white evangelicals said Muslims did, and 57% of white evangelicals said Christians did. So more white evangelicals think Christians face a lot of discrimination than think Muslims do. But that’s not what the headline says.


The headline says that white evangelicals think Christians face more discrimination than Muslims. And it follows from the survey’s findings that at least 13% of them do think this, since at least 13% think Christians face a lot and don’t think Muslims do. But it’s still open that 87% think that Muslims face more discrimination. I guess it probably isn't as high 87%, but we just don't know what the figure is. If a survey just finds that at least 13% of people in a group think something, it’s misleading to report the survey as finding that the group as a whole thinks that thing. And if that thing is both false and a dangerous and foolish thing to think, as in this case, it’s especially important not to misleadingly report the group as thinking it.


Now, you might say that from the results of the survey it’s more or less certain that most white evangelicals think Christians face more discrimination than Muslims. I don’t think it is. But even if it is, the reader can be the judge of that. Report what the survey says, and let the reader draw their own conclusions. Or argue for a conclusion. But don’t just misreport the findings of the survey.

Sunday, February 26, 2017

The Bleak Future Of Boycotts

You’ve probably been there yourself. I know I have. A news story comes out about a company doing some nefarious thing and you decide to express your dissatisfaction by boycotting them. When I was a kid there was something about Nestlé and baby milk, and I suddenly found out just how many things are made by Nestlé. Every so often there’s one about McDonald’s, and more recently there have been boycott-inducing stories about Uber and Byron Burgers. I don’t know whether it achieves what it’s supposed to achieve. I joined in with the Byron Burgers thing, and I didn’t have to decide about the Uber one because I don’t have a smartphone.

It seems like a good idea in principle. A company does something you disapprove of, and you try to stop them doing it by withholding your custom. Or maybe you’re not trying to change their behaviour but you just don’t want to give these ne’erdowells the benefit of your custom, even if it means forgoing their products and services. Cutting off one’s nose to spite someone else’s face makes a certain amount of sense.

Lately I’ve noticed some boycotts being encouraged to protest more mainstream associations like Donald Trump and the Daily Mail. The idea is that if you don’t like Trump then you boycott companies run by people that do, and if you don’t like the Daily Mail then you boycott companies that advertise in the Mail.

In principle this doesn’t make any less sense than using boycotts to protest less controversially awful things. If you think advertising in the Daily Mail is as bad as whatever Nestlé and Byron Burgers did, then it doesn’t really matter that lots of people think the Daily Mail is great. But I worry about where it leads.

It seems to be the received wisdom that politics, at least in America, is becoming more polarized and tribal. If members of one tribe boycott a lot of the companies belonging to the other, the way they already kind of do with media outlets, then you’ll end up with two parallel economies. That’s bad for competition, presumably, but it also might lead to governments from one tribe punishing companies from the other. That sounds bad. I hope it doesn’t happen.