Probably not important

Consider this sentence:

            PN       PN is probably not true.

Sentences can be true even if they’re probably not, at least on some readings of ‘probably’. I’m intending ‘probably’ in one of those ways. It sounds Moore-paradoxical to say ‘P but probably not-P’, but Moore-paradoxicality isn’t inconsistency. So the instance of the sloppy T-schema for PN...

            T-PN   PN is true iff PN is probably not true.

...doesn’t entail a contradiction. Maybe it’s true but probably not true. Contrast the instance of the sloppy T-schema for L:

            L          L is not true.

            T-L      L is true iff L is not true.

T-L does entail a contradiction, so L is paradoxical. T-PN doesn’t, but that’s not the end of it. First, note that there’s another way PN could go: it could be untrue though not probably. This might be because it was probably true, or because its truth and untruth were equiprobable. So it might be true, and it might be untrue. Which is it?

A fairly reasonable-sounding principle of indifference might say its truth and untruth were equiprobable. In that case it isn’t probably untrue, which means it isn’t true. But if the equiprobability was itself probable, then its consequence that PN isn’t true would seem to be probable, which means PN is true, which is a contradiction. So the equiprobability isn’t probable. What are the other credible options?

Maybe PN is probably not true. But this means it’s true. So if PN is probably probably not true, then it’s probably true. That doesn’t sound a very delicious combination.

The other possibility is that PN is probably true. In that case it’s not true. So if it’s probably probably true then it’s probably not true. Yuk again.

Can this lot even be made consistent? Here are the entailments:

            Probably true → untrue

            Probably not true → true

            Equiprobable → untrue

If the disjunction of probably and equiprobable is probable, then PN is probably untrue, but this contradicts the disjunction being probable, since the options are exclusive. So the disjunction is not probable, so probably not must be at least 50% probable. But if it’s exactly 50% probable, then given the entailments, PN is equiprobably true and not true. But this makes equiprobable true, which we’ve established is not probable. So suppose probably not is probable. This means PN is probably true, which is a contradiction. So the improbable equiprobable must be true. But if something must be true, then it’s probable. So the disjunction is probable after all, and that led to a contradiction. So dialetheism must be true. But if dialetheism must be true, we can reject some of the above reductio reasoning. So some contradictions are true, but possibly not this one.

The Dalai Lama and me

Everyone knows you shouldn’t take internet personality tests seriously, but I don’t know any other easy way of measuring how rightwing I’m becoming, so every so often I take the Political Compass test. You answer a questionnaire and it rates you on two scales: libertarian-authoritarian and socialist-capitalist. Then it puts you on a graph with various other people like Stalin, Silvio Berlusconi and Nelson Mandela so you can see how you compare. I don’t think they got Stalin to take the test though, so putting him in the socialist/authoritarian quadrant must have been an educated guess. What puzzles me is that no matter how rightwing I feel like I’m becoming, it always plonks me firmly in the libertarian socialist corner next to the Dalai Lama. I’m not surprised about the libertarian thing but I’m puzzled about the socialism. It’s not like I want to collectivize the means of production or put a 99% income tax on the top 1% or anything like that anymore. I’ve got three explanations for why they still count me as such a leftie.

One is that the test is badly designed. They either ask unrevealing questions or have a lousy algorithm for turning the information into an assessment of how rightwing I am. I think the second is more likely: the questions look divisive enough to me.

The second is that you just can’t tell how rightwing someone is by getting them to fill in a questionnaire. When I first took Simon Baron-Cohen’s empathy test and landed deep in the autistic zone I was a bit taken aback, but then it was pointed out to me that asking people whether they can read minds isn’t a foolproof way of finding out if they can. Maybe political views are like that: people assess their views on the basis of slogans like ‘free trade is fair trade’ and shibboleths like abortion, but this assessment might not be borne out by the positions they take on specific issues when they arise.

The last explanation is that I’m really not that rightwing, and that’s because becoming more pragmatic with age just can’t make you that rightwing. I think there are three reasons to support economic liberty which are often conflated, although it’s not clear to me they even overlap. One advantage is that free markets are often the most efficient way of getting the people what they want and need. Another is that economic freedom is a kind of freedom. The third is that capitalism distributes more goods to the most productive people. It seems to me that only the third is particularly up for debate in terms of its factual basis, but the only one I place much value on is the first. I’m not much fussed about who is most deserving, and much as I like Robert Nozick I’m willing to restrict people’s economic freedom a fair bit if it gets the needy what they need. If banning me from paying you £2 an hour to serve fast food is what will raise most children out of poverty then I’m happy to take the hit. The arguments from efficiency, freedom and desert really are distinct, and as far as I can tell they’re quite independent of each other and only one is much good. So why do we keep voting for such rightwing people?

All quiet on the Curry front

Sorry if you've been looking for my posts about Curry's paradox from a while back. I've taken them down because I'm writing a paper about that sort of thing, and taking them down seemed a good idea.

Robo economicus

A common criticism of economists is that their theories work if people behave like perfectly rational preference-maximisers but not if they behave like people. My understanding is that this criticism is a load of baloney, because economists are well aware that people don’t always behave as homo economicus would, it’s still a useful idealisation with genuine predictive and explanatory power, and economists study how much and in what ways the idealisation differs from the reality. Perhaps I’m wrong about this. I doubt it though, because if the criticism was justified then the rational thing would be to write a paper pointing it out and scoop the Nobel prize, and nobody’s done that.

This said, economists do seem to be better at explaining things than they are at predicting them, and maybe if people behaved more like the idealisations then economic behaviour would be easier to predict. My suggestion is that we make a lot of artificially intelligent robots that really do behave like that, give them a bunch of money and release them into society.

Part of the beauty of this is that economies would become more predictable. The other part is that we could programme the robots to have the preferences we have but aren’t rational enough to maximise even when we have the means to do so. If we want more hospitals built, we could entrust their construction to corruptible, fallible humans, or to incorruptible, infallible, single-minded robots. The hospitals would be built as efficiently as possible, and as an added bonus the robot would be delighted.

I’ve long wondered why the government can’t stimulate the economy by pumping a load of money into international development, so the world gets developed by the invisible hands of the profit motive instead of by the sporadic largesse of the notoriously self-obsessed, myopic and capricious general public. I’m sure there’s a reason we can’t do this, or we’d have done it. But even if governments can’t create a market for that sort of thing, I don’t see why a rampaging rabble of rich rational robots couldn’t. It that pays the piper calls the tune.

The problem of transobject identity

Yesterday I finished reading the first volume of David Armstrong’s Universals and Scientific Realism for the first time. It’s fun, interesting and short. I recommend it, even though some of the arguments probably aren’t the kind of thing you can get away with nowadays. Armstrong is dealing with the problem of how different things can be the same in some respect, and he argues that nominalism, Platonism and trope-theory either don’t explain what needs explaining or lead to explanatory regresses. Since these are bad things, he adopts a theory of immanent universals, which are repeatable things which crop up in different objects. If two particulars are both negatively charged, that’s because there’s a thing, negative charge, which is in both of them. I wouldn’t say I was convinced, but he makes the case pretty well.

Now, when I was reading it, I noticed a parallel between the problem Armstrong is addressing and the problem of transworld identity. Armstrong wants to know how different things can share properties, and the problem of transworld identity is about how different possible worlds can share inhabitants. Some issues in one debate have corresponding issues in the other, and this gives rise to analogies between the positions. I think at one point Armstrong even calls the thing he’s trying to explain ‘generic identity’.

Transworld identity gets explained by the worlds having either strictly identical things in them, or suitably similar things in them. Generic identity gets explained by particulars having strictly identical universals in them or suitably similar tropes. The ‘no explanation needed’ positions are magical modal realism, which reifies worlds but not possibilia, and ostrich nominalism, which reifies objects but not properties. (Both were named by their opponents.) Another parallel is that people disagree about whether particulars are bundles of properties or something besides their properties, and they also disagree about whether worlds are fusions of their inhabitants or something besides their inhabitants. The bundle theory of particulars is typically most plausible to trope theorists, and the fusion theory of worlds is typically most plausible to counterpart theorists.

When you spot a parallel between two debates it can help you in at least two ways. One is that the analogy can help us understand the more mysterious debate better. Our thinking about time became clearer when we realised it was a bit like space, and our thinking about modality became clearer when we realised it was a bit like time. I’m not sure whether we’ll be helped much in this way here: space and time really are quite like each other, whereas the relationship between a world and its inhabitants seems quite unlike the relationship between a thing and its properties, at least if the bundle theory isn't right.

The other way analogies between debates can help is more promising though. There’s some pressure to hold analogous positions in analogous areas, because a good argument for one position will often correspond to a good argument for the other. This way of killing a large number of birds with a small number of stones is particularly useful for people like me who like to make their minds up about things. For example, shortly after I came round to counterpart theory about de re modality I came round to stage theory about persistence. I’ve never really had a view about property ontology before, but maybe now I should have another look at trope theory.

How can this possibly be legal?

One of the measures which is standardly used to prevent corruption is making people in positions of power declare their interests. For example, if a politician is deciding which company gets a government contract, and the politician works for one of the companies in the running, they have to declare it and the decision may be delegated to someone else. If they don’t declare it and get found out, they get into trouble. It is fairly obvious that a system lacking this feature would be open to abuse.

One thing which seems to be allowed, however, is for a politician to take a job with a company after having used the power entrusted to them by the electorate to benefit said company. Private Eye reports on this sort of thing all the time. They call it the Revolving Door. I can’t see any principled reason to think that undeclared future interests compromise the integrity of the politicians involved much less than undeclared present interests would.

It seems to me that it would be pretty easy to put a stop to it. You say that politicians giving contracts to companies have to declare an interest or either face trouble or not take a job with the company for, say, five years. And if people keep waiting out the time limit and then immediately taking jobs with companies they’ve helped, we smell a rat and extend the time limit. But perhaps I’m missing something and a rule like this would be impossible to put into practice.

Epistemic virtue

I watched Sherlock when the BBC repeated it recently. It’s a reimagining of Sherlock Holmes set in the present, and it’s a lot of fun, even for someone like me who’s ordinarily a bit of Holmosceptic. Anyway, two of Sherlock’s most striking traits are that he’s very good at gathering evidence and inferring what’s what, and that he’s a sociopath. I’ve lately been wondering about epistemic virtues, and it seems that there’s a case to be made against the obvious position, and that the obvious position entails that we should be just like Sherlock.

The obvious position is that we should proportion our credences in P to the probability of P given our evidence. The hard work is all in working out what this amounts to. You have to say where your prior probability distribution should come from, what counts as evidence, how to deal with apparently non-propositional evidence, and so on. There is also an issue about actively seeking out evidence. Maybe we should make exceptions when not proportioning our credences to the evidence will enable us to get more evidence, so our beliefs will better approximate the truth in the long run. A stock example is when the fount of all knowledge can only be reached by jumping a chasm which you’re more likely to clear if you believe you will. But it seems that the action in epistemic virtue theory is in finding out how to emulate Sherlock when it comes to gathering evidence and making proper inferences from it. We don’t expect to have to emulate his sociopathy.

Lately that’s what I’ve questioning. When a friend, spouse or what have you tells you something, you are in many circumstances supposed to believe what they say. Suppose your wife tells you she was stuck at the office until 3am and slipped in a large puddle of beer on her way home. You could add that she has said this and that she came home stinking of beer when it was already getting light to the rest of your evidence and update like a good Bayesian, but perhaps this is one thought too many. Sometimes there are conflicts between being a good husband and a good Bayesian, and skill at resolving such conflicts is one of the things distinguishing the epistemically virtuous from the rest of us.

I don’t know what people whose day job it is to think about this sort of thing have thought about it, but I can see three natural responses. One is to say that belief isn’t voluntary and all this talk about epistemic virtues is wrongheaded. I’ll put that to one side. Another response is that the epistemic virtues and the virtues of personal concern aren’t the same and can conflict. I’m quite sympathetic towards that, but if it’s true then parity of reasoning would suggest that favouring our friends isn’t any more morally virtuous than believing our wives is epistemically virtuous. The last natural response is to say we’re called upon to practise a kind of doublethink, where we separate our credences as rational inquirers from the credences which rationalise our behaviour and which we profess to have. We can’t do this with the conflicts between morality and friendship because we have only one set of actions, but with credences it seems almost feasible.