Gunky Pluralities

Philosophers have been squeezed out of most traditional areas of physics by fancy scientists with their “experiments” and their “research budgets”, but one thing they’ve managed to cling on to is mereology. We’ve even reclassified it as metaphysics so the physicists won’t accidentally stumble across it when looking for a book on something more important. Mereology is the theory of parts and wholes. Mereologists try to answer questions like these:

• Is there a great big object which all the other objects are parts of?
• When x is a proper part of y, is there always another object z which is the rest of y?
• Does anything even have proper parts? (A proper part of x is a part of x that isn’t x itself.)
• Could there be two different objects made out of the same parts at the same time?
• Could there be something all of whose parts had multiple parts?

The last question is about gunk. I wrote here once before about gunk, when describing an argument by David Hume against the possibility of gunk. You have to be a little bit careful when defining gunk, because what seem like equivalent definitions might not be equivalent if you accept some other exotic principles about parthood, or at least reject some mundane ones. One fairly careful definition of gunk would be “something all of whose parts have proper parts”, but that doesn’t really get at what we had in mind if we allow that things can be proper parts of each other.

Now, parts and wholes aren’t the only game in town when it comes to gathering objects together. Somebody once told me that Bolzano identified like fifteen different ways of gathering objects together. Maybe it wasn’t fifteen, but I’m pretty sure it was a lot. Although perhaps this person was pulling my leg.

Anyway, one alternative to making a whole out of some objects is to make a plurality out of them. A broom is an object made of a brush and a handle. A brush and a handle are a plurality whose members are a brush and a handle. (Sets are different again; two things form a set, but they are a plurality.) Now, you might think that there’s no distinction here: a broom just is a brush and a handle. If that’s what you think then I’m actually on your side, but most people who work on this stuff don’t think that’s right. (One person who works on this stuff and thinks it is right is Meg Wallace, of whose work on both this and other things I am a fan.) The mainstream view is that a broom can’t be a brush and a handle, because (apart from anything else) a broom is one thing and a brush and a handle are two things. Anyway, let’s make the distinction.

It turns out that a lot of the candidate principles governing wholes and their parts are analogous to candidate principles governing pluralities and their subpluralities. Let’s say that Tom and Harry are among Tom, Dick and Harry. Let’s also say that Tom is among Tom, Dick and Harry, and that Tom, Dick and Harry are among Tom, Dick and Harry, but not properly among them. And let's allow that "some things, the xs, are F" can be true even if only one thing is F, so some things are (each!) Buzz Aldrin. Now we have a language in which to ask similar questions about pluralities and subpluralities to the ones we asked about parts and wholes.

• Are there some things, the xs, such that whenever there are some things they’re among the xs?
• When the xs are properly among the ys, are there always some things, the zs, that are the rest of the ys?
• Are any things properly among any other things?
• Could there be some things, the xs and the ys, such that any things among the xs were also among the ys and vice versa, but the xs weren’t the ys?
• Could there be some things, the xs, such that whenever some things the ys were among the xs there were some things, the zs, properly among the ys?

Call some xs that fit the definition in the last question a gunky plurality. Could you have gunky pluralities? Are they ridiculous? I asked Twitter if they were ridiculous, and the eight respondents were evenly split on the matter.

Am I an experimental philosopher yet?

I was a little bit surprised. I think gunky pluralities are coherent, but in the past I’ve never detected much enthusiasm for them. While a Twitter poll with eight respondents doesn’t give much of an indication of the frequency of a position among any population apart from the people who responded to it, I was quite surprised to see that four people, not including me, saw the tweet who don’t think gunky pluralities are ridiculous. Maybe they didn’t understand the question. I did phrase it in terms of membership instead of in terms of amongness, but if anything I’d expect that to make the position seem more ridiculous, not less.

Now, I’m invested in gunky pluralities being coherent because I think composition’s identity and amongness is parthood, and so if gunky pluralities are incoherent then gunk is incoherent, and nobody wants to be committed to that. (Someone with a fancy research budget might come along and make a fool of you.) But even if you don’t think composition’s identity, and I suppose even if you don’t think merelogical gunk is possible, you can still make sense of the question about gunky pluralities. Are they ridiculous or aren’t they?

I think that Hume and Leibniz probably took the view that they were ridiculous. Hume may well have been thinking only about mereological gunk, and I’m pretty sure Leibniz was, but it would have been kind of weird to endorse their arguments for the mereological case and not the analogous arguments for the pluralities case. It’s possible of course that they didn’t really see a distinction, Bolzano not having arrived on the scene until the following century. Hume credited his argument to a Monsieur Malezieu, who I guess is probably this guy, although his English Wikipedia article could use some work and his French one doesn't mention Hume. Here are some quotes for you:

It is evident, that existence in itself belongs only to unity, and is never applicable to number, but on account of the unites, of which the number is composed. Twenty men may be said to exist; but it is only because one, two, three, four, &c. are existent, and if you deny the existence of the latter, that of the former falls of course. It is therefore utterly absurd to suppose any number to exist, and yet deny the existence of unites; [...]

But the unity, which can exist alone, and whose existence is necessary to that of all number, is of another kind, and must be perfectly indivisible, and incapable of being resolved into any lesser unity. (Hume, Treatise on Human Nature, 1.2.2)

And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things. (Leibniz, Monadology, translated by Robert Latta, proposition 2)

It’s also true that our language gets a bit strained when we try to talk in a way that never presupposes that the thing we’re referring to is just one thing. You’ll have noticed that when I was trying to do it earlier. On the other hand, there doesn’t seem to be any reason you can’t construct a logic that can accommodate gunky pluralities. You might struggle to get a model theory in terms of sets that didn’t make a certain kind of person a bit grumpy, but this kind of person is already grumpy about variable-domain model theory for modal logic, so you’ll be in good company. (It may be that their grumpiness is warranted, but my impression is that even if the objection in the case of modal logic succeeds, the analogous objection would be question-begging in the case of gunky pluralities. But I’m pretty open to being wrong about that.) One possibility is that the idea of gunky pluralities is one of those things that’s ridiculous without being incoherent. I don’t really get what the problem is supposed to be, though. If you think they’re ridiculous, and it seems at least four of you do, let me know why in the comments!

Cocksure certainties

I was reading an opinion piece in the Observer by Nick Cohen yesterday, and I came across this paragraph:

As the opposition collapsed last week, Paul Mason insisted that Labour must be transformed from a party that seeks to govern into a “social movement”. Mason, along with Michael Gove, Boris Johnson and Milne, is part of a group of journalists who have poisoned public life by taking braggart swagger and cocksure certainties of newspaper punditry into politics. But in this instance, he was authentically reflecting “the people” or, rather, that tiny section of “the people” who pay £3 and click on a link to show they agree with him.

My first thought was that it was strange for a political newspaper pundit to talk about political newspaper punditry in such uncharitable terms. It might be fair enough for a reality TV star to criticize Donald Trump for poisoning public life by taking the cartoonish offensiveness and fakery of reality TV into politics, but this seems different. Political newspaper punditry seems too similar to public life for braggart swagger and cocksure certainties to be OK in one but not in the other. Perhaps you’ll disagree with me about that. But there’s something else I wanted to pick up on in the paragraph. It’s the cocksure certainty expressed with such braggart swagger in the last sentence. I think it might not be quite accurate.

Here are the results of the leadership election Jeremy Corbyn won last year:

You’ll notice that Corbyn did much better than any of the other candidates among members, and among registered supporters, and among affiliated supporters. From what Cohen said, you’d think that Corbyn won the election because of the votes of the people who had paid £3 to be able to vote in the leadership election. Those people are the “registered supporters” column. But if Corbyn is winning in all the columns, then what Cohen said is quite misleading. Unless I’ve misread something.

I don’t know if he really thinks Corbyn won the election on the back of the £3 voters. It seems a weird thing for him to be wrong about. But since people are discussing Corbyn’s leadership a lot at the moment, it’s worth getting this right. When Corbyn was elected, the big split wasn’t between the party and the clicktivists. It was between the party membership, the clicktivists and the members of affiliated organizations on the one hand, and the Labour MPs on the other. Maybe the split is in a different place now, but that’s where it was last year.

Now, I understand that Nick Cohen thinks that the platform that most Labour MPs want the Labour party to present is closer to the views of the electorate as a whole than Corbyn's platform is. That's a genuine concern. But it's very different from the idea that Labour's leadership is out of touch because the election was hijacked by a group of fairweather enthusiasts with £3 to spare. If Labour is out of touch with the people, then it's out of touch at every level but the MPs. (The MPs may of course be out of touch as well. We don't really know a great deal about the people's view on Angela Eagle, Owen Smith, or whoever the Parliamentary Labour Party wants to replace Corbyn with.)

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I did try asking him on Twitter whether he thinks that Corbyn only won because of the £3 voters, but he didn’t reply. That’s completely understandable: he’s famous and I’m sure people tweet at him all the time. Here’s the tweet:

How to link to things on Twitter

Twitter is fun. One of the fun things you can do on it is link to things you think people will like. Another is you can retweet things other people have tweeted. And nowadays when you retweet something you can add a little comment of your own. Without a comment it comes up on people’s feeds like this:

And with a comment, your followers see something like this:

Now, you may have noticed that what Janine and Carl have done is to combine the two fun things about Twitter that I mentioned earlier: they have retweeted things with links in them. But while Janine’s followers can click on the link to open it, Carl’s followers can’t. At least, not if they’re using Twitter on any of the devices I’ve ever used. You can’t click on a link in a quoted tweet! What you have to do, as far as I can tell, is click on the quoted tweet to open it up, either in a new tab or by leaving the main twitter feed page, and then click on the link. This involves a lot more clicking and mouse-moving, and if Richard Thaler and co have taught us anything it’s that making people do things like open new tabs will make them less likely to open a link. You want people to open the link, don’t you? Well, maybe sometimes you don’t. You might be quoting the tweet for some other reason. But if you do want people to open your link, you should repeat it in your comment, like this:

Got that? See the difference? When you quote a tweet with a link in it, repeat the link in your comment. Unless you don’t want people to click on the link. And it’s not just Carl I’m talking to; he was just the first example in my Twitter feed. I hardly ever see anyone else doing it right. Do it right! You’ll save your followers time, and the things you’re trying to make viral will be more likely to go viral.