Round squares

Most people think that roundness and squareness are incompatible. Circles have curved sides and no corners, while squares have straight sides and four corners. Meinong is sometimes interpreted as having thought there was a round square, but he thought it was a non-existent object, and may even have thought that its having incompatible properties explained its non-existence. But I’ve recently started wondering whether round squares could have existed after all.

If I understood rightly, I was told on Friday that if space was curved in an odd enough way then things in it could be round and square. It sounds like the sort of thing that might be true. That’s not what I’ve been wondering about though; I’m suspecting that round squares might even fit into both Euclidean space and ordinary space.

The problem comes from multiple location. If things can be wholly in two places at once, then I don’t see how round squares could be impossible. The simplest way multiple location could allow round squares is if absolutely anything could be absolutely anywhere and in any number of places. Then an object could be in a round region and a square region, thereby being a round square, since things are the same shapes as their locations.

Prima facie, one can plausibly deny that the possibilities for multiple location are this permissive. However, if multiple location is possible at all I’d have definitely thought that a point-sized object could be at two points at once. (Maybe there really is only one of each kind of point particle and each is in a lot of places. Feynman talked about something like this in his Nobel lecture.) Now take continuum-many point-sized objects, and let them each have two locations. The first locations could be arranged into a square and the second locations could be arranged into a circle. The square region and circular region wouldn’t even have to be the same size, although they could be. The object made out of these point particles would thereby have a circular location and a square location, so it would be a round square.

If this argument works, I suppose it could be used to argue that shape wasn’t an intrinsic property of objects, but rather a property they had in virtue of where they were. That’s weird of course, but multiple location is weird. I’m actually quite attracted to the view that how things are and where they are have a fairly loose relationship, but now I’m starting to worry that if it’s true then analogous arguments to the one about shape will show that almost no properties of located things are intrinsic, and that way lies madness. Or supersubstantivalism.

Computers are amazing

Not philosophy this time I'm afraid. Many people are surprised that computers aren't more reliable. Well I'm surprised they aren't less reliable. Much less.

Say what you like about computers, but they're complicated. Babbage's difference engine certainly looks complicated, Turing machines don't look complicated but they usually are, and now that modern computers are connected by the internet what we're really dealing with is a massive uber-computer of biological complexity. (I think Pascal's proto-calculator was pretty simple, but I'd have been surprised if that wasn't reliable.)

Complicated things break. Murphy's law always struck me as a bit silly, but I'd have thought we could safely say that if enough things can go wrong, something will. Well, with computers there are so many things going on that it amazes me that something doesn't always go wrong. But it doesn't! Usually when you type in a web address you get to the site you want, when you save a file it's still there a year later, emails get through and so on.

Of course the reason people get so annoyed with computers is that they rely on them too much. People don't save their work often enough, they put themselves in situations where they'll miss a deadline if the printer's playing up and they put too much trust in the sanitary status of files from dubious sources. I'm as bad as the next person in this regard, but I don't get annoyed with the computer when something goes wrong. I get annoyed with myself, because it's my fault. Same with train delays, but that's another post.

Thinking about my appendix

Fairly famously, Russell thought that you could only have singular thoughts about things you were directly acquainted with. For Russell this meant you could only have singular thoughts about your present experiences and maybe yourself. Nobody thinks that anymore, but we do mostly agree that Russell was on to something. If there’s a guy in Wisconsin called Hank that I’ve never met, I can’t think about him because I don’t know about him. I can wonder generally about whether there’s a guy called Hank and he’s happy, but I can’t wonder whether Hank himself is happy. I can’t think about people I don’t know about (in the relevant sense of ‘know about’).

Now, I’ve never seen my appendix, and hopefully I never will. I don’t even really know where it is. I can’t feel it, and I’m not aware of it doing anything. But I’m pretty sure I can think about my appendix. I can wonder where it is, what it looks like, and whether it’s one day going to kill me.

One explanation for my ability to think about my appendix is that I know I’ve got one, and only one. If I’m acquainted with something, and I know it’s got one and only one of something, then I can think about the second thing via the first. I know about Russell and I know he had exactly one mother, so I can think about Russell’s mother via Russell. That doesn’t sound too crazy a result.

It does come out awfully permissive, though. Presumably my red blood cells are all slightly different sizes, so I’ve got exactly one largest red blood cell, so I can think about that. In the same way I can think about the oldest man in Hawaii, the first child born in the 22nd century (who Kaplan called ‘Newman I’), the centre of gravity of the Pacific Ocean and other such tenuous acquaintances. In fact I can think about the satisfier of any definite description I know to be satisfied, through my acquaintance with the world. I can think about the shortest spy, even if the shortest spy is an alien on another planet.

Now you can say that in these cases only the thing I’m acquainted with directly sits in the content of the thought, so when I’m thinking about the shortest spy I’m really just thinking about the universe or spies in general, and when I’m thinking about Clinton’s mother I’m really just thinking about Clinton and mothers in general. Perhaps that’s right. But then I never really think about my appendix either. What I’d like to do is find a principled way of drawing the line somewhere between my appendix and the shortest spy, and I don’t know how to do that.

Selfishness and squeamishness

Since I studied Mill as a first year undergraduate I’ve never seen the alleged counterintuitive results of impartial consequentialism (IC) as a cost to the theory. I’m not saying there aren’t good objections to IC, but the counterintuitive results always seemed quite a positive thing. It’s possible that justice or significant relationships demand that we let the world be a little worse than we have to, or maybe a lot worse. But isn’t that a shame? To my mind it’s simply perverse to look at the world IC asks us to live in and turn it down, actively seeking loopholes in the theory which allow us to live in a worse one. Of course it’s disingenuous to cast the point in precisely these terms: the counterintuitive results aren’t just about the world IC asks us to inhabit, but also about what it asks us to do. But it’s partly about the world it asks us to inhabit. I think all these complaints generally fall into one of two categories: selfish objections and squeamish objections.

I guess it’s pretty obvious where I’m going with this, so I’ll try to keep it short. An example of a selfish objection is that IC demands the rich give away most of their money, because rehydrating a faraway diarrhoea sufferer has better consequences than buying a pint. There’s the objection that giving away your money would just buy Mugabe a new solid gold bathtub, but IC only demands we give away our money if it would really help. Supposing it would help, I don’t see what the problem is supposed to be. We can spend the money improving the world or spend it on ourselves. Whose side would we expect morality to be on?

An example of a squeamish objection is the one that says IC sometimes demands framing an innocent man to stop a bloody riot, pushing a fat guy in front of a runaway train to stop it killing five workmen down the line, or voting tactically to keep the crazies out. It’s understandable that people don’t want to do these things, and sometimes in the long run it can help if people follow some rules, but IC factors in the long run and still sometimes asks us to get our hands dirty. I’m not sure which side you’re meant to be on when you watch Sartre’s Les Mains Sales, but I know which side I was on. Sometimes the only thing necessary for evil to triumph is for good people to act as if everyone was good.

I think that objections to IC stemming from significant personal relationships are a bit of column one and a bit of column two. Suppose I have to choose between saving my cat or two strangers’ cats from a burning building. (If the owner-cat relationship isn’t significant enough, change the example to friends, wives, mothers, children, whatever.) I’d rather save mine, but that’s selfish. It’d be unpleasant to let my cat burn, but that’s squeamish. You get the point.

There’s the demandingness objection to consider, but I don’t see that it’s properly separate. There are conflicts between following IC and indulging our selfishness and squeamishness. Maybe morality doesn’t always demand that we follow IC, but if we’re asking morality what the best thing to do is, I don’t know why we’d expect it to indulge us. If we’re looking for objections to IC I think we should look elsewhere than at our selfish and squeamish intuitions.

Counterpart theory

The other day I was trying to explain to another philosopher what counterpart theory was in terms which didn’t make me sound like a maniac for sympathising with it, and it wasn’t that easy.

I said that according to a counterpart theorist, she could have been a chef because the world could have contained somebody who was very like her, except she was a chef. (I glossed over technicalities about multiple counterparts and multiple good candidates.) This contrasts with a transworld identity theorist, who says that she could have been a chef because the world could have had her in it being a chef. Similarity is vague and context dependent and identity isn’t, so counterpart theory makes de re modal predication vague and context dependent, and transworld identity theory doesn’t.

I think this is more or less right, but there’s a problem with it. In my explanation of counterpart theory I talked about how the world could have been, and taken at face value that’s a de re modal predication of the world. Now, some people don’t think the world exists, like compositional nihilists, and for them I suppose there’s a difference between a de dicto modal statement and a de re modal predication of the world. Either way you’re having to talk about ways things could have been. If we give a counterpart-theoretic gloss of how I could have been, why don’t we give the same sort of gloss of the way things in general could have been? And if we take ways the things in general could have been as primitive, why not do the same with ways I could have been?

Well, if you’re a modal reductionist you’ve got an answer to this. David Lewis had a bunch of spatiotemporally connected mereological sums representing ways things could have been. Yagisawa had the same things as Lewis but let you cut them up however you like, pretty much making the accessibility relation a counterpart relation. Ersatzists had abstract possible worlds. Once you’ve got ways things could have been you’re up and running and can give your counterpart-theoretic account of who could have been a chef. This keeps the reductive isthmus small, just like Mark Schroeder tells us to.

But what about me? I don’t want to sound like a maniac and I don’t see how ersatz worlds could bear much explanatory weight, so I’ve got nothing to reduce ways things could have been to. I need to take them as primitive, and that means I can’t be a counterpart theorist all the way down.

Perhaps this isn’t so bad. It’s pretty much what Ted Sider does in ‘the ersatz pluriverse’, taking overall possibilities as primitive and doing the rest with counterparts. What intrigues me is whether we’ve any reason to think, after letting in primitive possibilities and necessities for the world, that there aren’t primitive possibilities and necessities for me as well. I guess what I’m pushing is a kind of essentialism: there are some context-independent facts about possibility given by the essences of things, and the rest is counterparts. It’s inspired by a footnote to Naming and Necessity, though I suppose Kripke would be upset if he knew.

Hello world

This is the first post from Michael Bench-Capon's Blog, and you may be the first reader. I'm Michael Bench-Capon, and most of the content will probably be posted by me. So you'll know what to expect, I'll say a little about myself. I'm a philosophy PhD student, so I'll probably be writing about philosophy a bit. I'm quite into middlebrow culture (Seinfeld, Philip Roth etc) so I might write about some of that. I sometimes go through poetry-writing phases, so there may be some poetry on here too. I also take an interest in current affairs and sometimes form an opinion about something, so I won't promise to keep the blog wholly apolitical. I don't have any children or a usable camera so I won't be posting any boring baby photos. It'll probably be mostly philosophy.