Consider the following (slightly complicated) situation.

The agent does not know the truth value of either p or q. Indeed, each of the four combinations of truth values (p & q, p & ~q, ~p & q, ~p & ~q) have probability ¼. 

The agent has 7 possible options, with payouts affected by which of p and q are true.

O1 has a payout of 8 no matter what.

O2 has a payout of 9 if p is true, and 0 if p is false.

O3 has a payout of 10 if p&q is true, and 0 if p&q is false.

O4 has a payout of 10 if p&~q is true, and 0 if p&~q is false.

O5 has a payout of 9 if p is false, and 0 if p is true.

O6 has a payout of 10 if ~p&q is true, and 0 if ~p&q is false.

O7 has a payout of 10 if ~p&~q is true, and 0 if ~p&~q is false.

The following claims all seem to have clearly true readings.

(1) She should take O1.

(3) If p&q, she should take O3.

(4) If p&~q, she should take O4.

(6) If ~p&q, she should take O6.

(7) If ~p&~q, she should take O7.

But do the following have true readings?

(2) If p, she should take O2.

(5) If ~p, she should take O5.

They both sound true to me, or at least just as true as the other conditionals. But I wonder if they sound true to others as well.

Last week, FiveThirtyEight had an excellent post on segregation in US cities. It used data collected by researchers at Brown to answer the following two questions about a bunch of US cities.

1. If you pick two people at random from a city, what is the probability they are from different ‘groups’?
   
2. If you pick a census tract at random from a city, and then pick two people at random from within that tract, what is the probability that they are from different 'groups’?
   

The groups here are, as is always the case in discussion of segregation in the US, somewhat arbitrary. The ones used are:

• Non-hispanic whites;
  
• Non-hispanic blacks;
  
• Hispanics
  
• Asians
  
• Others (primarily, Native Americans)
  

The nice idea was that we can use the difference between the answer to question 1 and the answer to question 2 to get a rough idea of how segregated a city is. In the post FiveThirtyEight included values for that for a bunch of large cities. But they didn’t include mid sized cities like Ann Arbor. And I was interested in how the data looked for cities like mine. So I’ve made a spreadsheet with all the data for 3800 large cities.

• Diversity and Segregation Spreadsheet
  

The first column, labelled city diversity, is the answer to question 1. In Ann Arbor, the answer is 47%. That’s much higher than I think a lot of people would have expected given Ann Arbor’s reputation for a lack of diversity. At 47%, we’re right around the midpoint of diversity for large American cities.

The second column, labelled neighborhood diversity, is the answer to question 2. Note that the census tracts are about 4000 people large, so this is saying roughly, how diverse is each of the mid-sized neighborhoods in your town. At 43%, Ann Arbor is again around the midpoint for midsized American cities.

The third column is about the relationship between those numbers. More precisely, it shows how much the second number is above (or below) the line of best fit between the two. 

That’s a measure of segregation, but a fairly crude one. For small cities, it isn’t too surprising that the diversity by census tracts equals the diversity by city, since there are only a handful of census tracts in the city. And indeed there was a very strong negative correlation between city size and the third column. So the fourth column corrects for that, by drawing a line of best fit between the third column and the log of the city population. And this isn’t a bad measure of how segregated a city is. Ann Arbor looks a little better by this measure, but not wonderful.

The 'methodology’ I’ve used is pretty crude, and surely a good researcher could do better. But the data is a little crude to start with as well, and it probably isn’t worth getting any more accurate.

For one thing, the Brown researchers didn’t report numbers for the spread of people from the 'Other’ group throughout a city. So I had to delete from the spreadsheet the 60 or so towns where 'Other’ was more than 5% of the population, because I couldn’t think of a good way to account for them.

For another, these groups are really very arbitrary. I would have thought a town that consisted of equal numbers of Lebanese, Afghanis, Indians, Chinese and Vietnamese, all spread throughout the city, was incredibly diverse. But it would count as maximally un-diverse by this measure. 

From the other direction, a city can count as very diverse in virtue of having lots of light-skinned, middle-to-upper-class immigrants (and children of immigrants) from South America and East Asia. Is this what we intuitively mean by diversity? I suspect for some people it is not. This matters a lot in Ann Arbor; there are plenty of immigrants from South America, and from East and South Asia, on faculty. It is a little arbitrary to treat Argentinian and, say, Georgian, immigrants differently, but any grouping will involve some arbitrariness.

In any case, the main point of this was that if you read that FiveThirtyEight post and were wondering what the data looked like for 3700 other mid-sized American cities, here is the data!

In her entry on Elizabeth in the Stanford Encyclopaedia, Lisa Shapiro writes

[Elizabeth’s] criticisms of Descartes take up three distinct philosophical positions. First, she takes up the position of Aristotelian virtue ethics, in objecting that Descartes’s very liberal account of virtue, which requires only the intention to do good, does not require that one’s good intentions are realized in actions that are actually good. That is, she notes that Descartes makes virtue impervious to fortune or moral luck. She, however, goes beyond the canonical Aristotelian position to maintain that even our ability to reason is subject to luck. (This position helps to illuminate her view on the nature of the human mind. See the discussion in section 3.2 above.) Elisabeth also takes up a classically Stoic position, insofar as she objects to the way in which Descartes’s account of virtue separates virtue from contentment. She objects that Descartes’s account of virtue allows for the virtuous agent to make mistakes, and she does not see how an agent can avoid regret in the face of those mistakes. Insofar we regret when even our best intentions go awry, we can be virtuous and fail to be content. While it is unclear whether her objection is a psychological one or a normative one, she does maintain that achieving contentment requires an ‘infinite science’ (4:289) so that we might know all of the impact of our actions, and so properly evaluate them. Without a faculty of reason that is already perfected, on her view, we cannot only not achieve virtue, we also cannot rest content. (See Shapiro 2013 for an interpretation of these remarks.) In the context of this exchange, in the same letter of 13 September 1645, Elisabeth asks Descartes to “define the passions, in order to know them better” (AT 4: 289). It is this request that leads Descartes to draft a treatise on the passions, on which Elisabeth comments in her letter of 25 April 1646, and which is ultimately published in 1649 as The Passions of the Soul. Elisabeth’s concerns about our ability to properly evaluate our actions lead her to express a further concern, this time about the possibility of measuring value objectively, given that we each have personal biases, whether by temperament or by matters of self-interest. Without a proper measure of value, she implies, Descartes’s account of virtue cannot even get off the ground, for it is not clear what should constitute our best judgement of what is the best course of action. Behind Elisabeth’s objection here is a view of ethics akin to that of Hobbes and other contractarians, which takes the good to be a matter of balancing of competing self-interests.

Descartes is offering a very strong form of what I’ve called normative internalism. Descartes thinks the overriding moral imperative is to do what one thinks is right. This is an idea that you can see echoing down the ages, with it’s most famous instantiation being in the collection of cliches Shakespeare has Polonius string together, “This above all else: to thine own self be true”. Modern versions tend to be probabilistic, but probably even Shakespeare would have a hard time making “Maximise credally expected goodness” poetic.

I offer four families of criticisms of this view in the book manuscript I’m preparing, and you can see Elizabeth here as offering two of them. (One of the other two relies on some machinery from the probability calculus that Elizabeth and Descartes didn’t have access to, and the other is that the view is too solipsistic and narcissistic. Even if Elizabeth thought that, it isn’t something that one would naturally write to Descartes; it’s hard to believe it would move the author of the Meditations.)

The first she offers is that the view can’t explain why change in moral outlook should occasion regret at our past actions. We shouldn’t regret doing the right thing, but we do regret our actions that were in accord with past moral views after a change of view. Indeed, we might even feel guilt and shame at those actions. That’s hard to explain if we were, as Descartes says, doing the right thing all along.

And the other she offers is a kind of regress argument. If virtue is doing what one thinks is right, what is even the content of our thoughts when we are wondering what to do? If X thinks that it is right to push the large man onto the trolley tracks, not only does Descartes’s view imply that he should push the large man, but that he is right to think that. The only way for Descartes to avoid this problem is to think that there is some notion of objective value, but that it makes no difference to how we should act, or how we should evaluate others’ actions. And these seem bad.

So I should credit my royal predecessor, and include Descartes, alongside Polonius, as predecessors of my contemporary opponents.

I only found out about this because I was looking up things to include in my intro philosophy course, and looking through the Descartes-Elizabeth correspondence for material. Now I’m worried that if I looked deeper into the historical record, I’d find even more people I should credit.

Causal decision theories (CDTs) typically have, at their centre, a clause for right action in which the term ‘cause’ appears. Perhaps surprisingly, this isn’t universally true. The decision theory endorsed by Gibbard and Harper (1981) is a causal decision theory, but it has a counterfactual roughly where you’d expect to find 'cause’. But it is true of most causal decision theories.

And we can make a stronger generalisation than that. Consider an agent choosing between A and B, and choosing B will cause a better outcome, but the agent believes, perfectly reasonably, that choosing A will cause a better outcome. Causal decision theories will say the agent should choose A. They’d be better off if they chose B, but they should choose A. It’s bad luck to be in such a situation. But that’s the price of having a decision theory that is sensitive to one’s evidence. (There might be other senses of 'should’ that make the sentence 'They should to B’ come out true. Ignore those. They aren’t our concern.)

The way this is implemented is that 'cause’ doesn’t just appear in the middle of the theory, it appears inside the scope of a belief operator. The belief operator in question will usually be a quantitative operator (i.e., it will be expressly about credences) but it’s still a belief operator. That raises an interesting theoretical possibility.

Consider a case where there are two philosophically plausible theories of causation, C1 and C2. In fact, C1 is correct, and C2 false, but this isn’t obvious. In fact, a perfectly reasonable philosopher could hold C2, defend C2 in a series of papers, and so on. Now imagine that our philosopher has a choice between A and B, and she knows the following is true. If you plug C1 into where the causal decision theory says 'cause’, you get a clear recommendation to choose A. If you plug C2 into where the causal decision theory says 'cause’, you get a clear recommendation to choose B. What should our imagined philosopher do? Or, I hope equivalently, what should a causal decision theorist say that she should do?

You might worry that such a case is incoherent; it’s impossible to have reasonable competing theories of causation that have the characteristics decsribed in the previous paragraph. That’s a fair worry; I felt the same way until recently. But I’ve been convinced by the discussion in chapter 6 of Arif Ahmed’s recent book Evidence, Decision and Causality (2014) that it is possible. The details don’t really matter here, but the basic idea is embed our decision maker in an EPR quantum entanglement experiment. Remember the basic idea is that even though the two detectors are space-like separated, the output probabilities at the far detector are correlated with the settings at the near detector. This correlation is robust enough to support counterfactuals, but it does not permit superluminal signalling between the two detectors. (I’m aiming to follow Maudlin (2002) in this quick summary of the case, but I’m not an expert on the details.)

Question: Does changing the settings at the near detector cause the measurements at the far detector to be different?

Good question! It sure seems like it does; there is a nomologically grounded, counterfactual supporting correlation between frequencies that seem to be tracking chances. At least as I understand counterfactuals, there is counterfactual dependence between the settings at the near detector, and the measurements at the far detector, and so there is causation on a counterfactual dependence picture of causation. And on many other pictures besides; all that matters is that counterfactual dependence is sufficient for causation, not that causation should be understood or analysed in terms of it. On the other hand, there is no process that runs between the two detectors, there is no mark that is, or even could be, transmitted between the two. So it’s very hard to see how any kind of causal process theorist could say there is causation between the two detectors.

Now imagine the following setup:

• The agent knows the current angle between the detectors, and knows the probability that the two detectors will produce the same measurement given this angle.
  
• The agent is offered a bet at completely fair odds on whether the results of the two measurements will be the same.
  
• The agent knows that after they place the bet, and after the particles are discharged, they will have the opportunity to change the angle of the near detector in such a way that, were the angle that way to start with, their bet would have a very positive expected payout (even after the fee).
  
• The difference in win probabilities that would ensue after such a change is one that could not be classically explained.
  

Should they ever pay the fee? Intuitively, the answer is yes. Ahmed first argues that CDT can’t explain this. But the argument assumes that there is no causal link between one detector and the other, so set that aside. There is a more interesting, for my purposes, argument he has.

Imagine the agent believes, or at least gives high credence to, a theory of causation in which it is impossible for changing the settings at one detector to cause a change in the measurement at the other detector. This theory may well be false; that won’t matter. What will matter is that the agent give it high credence, and indeed reasonably give it high credence. Then, says Ahmed, CDT will still say that the fee shouldn’t be paid, and that’s still wrong.

There are a couple of moves the CDT believer could make at this point. First, they could say that we should expect people with false beliefs, as the agent has in this case about causation, will miss opportunities to make lots of money. That seems like a reasonable response to me, but set it aside. Because I think there’s a much better response.

At the heart of an version of CDT will be a formula for assigning values to actions. It will be of the form V(A) = …Cr(A causes X)…, where the X is a bound variable ranging over possible outcomes. Now the issue here is how to interpret Cr(A causes X) when the agent has a false belief, or at least non-zero credence in a false proposition, about what causation is. There are, basically, two options.

1. Cr(A causes X) = the credence has that A C’s X, where C is the actual causal relation.
   
2. Cr(A causes X) = the credence has that A and X stand in the causal relation, whatever it turns out to be.
   

And I think CDT should use the first. The kind of constitutive mistake that’s involved in having the wrong theory of causation, or constitutive uncertainty that’s involved in being unsure about what the right theory of causation is, shouldn’t be relevant to decision making. So if the CDT defender can defend a theory of causation on which counterfactual dependence is sufficient for causation, however that dependence is sustained, they will be able to get the intuitively right response in Ahmed’s example. Ahmed has a response to this argument, which runs like this.

The … objection to CDT is not that it gives bad advice, but that what advice it gives depends not on the observable statistics but on … whether or not there is any causal influence between the receivers. …[S]ome philosophical analyses of causation [say there is, others say there is not.] For now, what matters is not which analysis is correct, but that what advice CDT gives depends on settling this philosophical question.  
    
For it should seem strange that the answer to a practical question ('Which bet?’) should turn on abstruse theoretical matters. After all, nothing about the theoretical situation has any impact upon the facts that will actually settle your pay-offs. We know in advance what these are…    
    
This complaint against CDT goes to the heart of what distinguishes causalism from evidentialism. Causalism makes a practical question about what to do depend upon recondite metaphysical issues on which maybe nothing observable turns. That involves it in a complete misconception of what practical reasoning is and why it matters. To give non-trivially different practical advice in practically indistinguishable situations is to fail to understand that you are giving practical advice. (Ahmed, 2014, 156)

Ahmed goes on to try and cash out this objection, but he does so in a way that assumes the CDT defender will use reading 2, rather than reading 1, of Cr(A causes X). Still, there is an objection here to reading 1. Why should our practical decision theory turn on 'recondite metaphysical issues’?

Well, because there isn’t any alternative. Ahmed’s preferred theory turns on what the agent’s credence in various propositions is, and what the value of various payoffs is. But the metaphysics of credence and of value are just as hard as the metaphysics of causation. There are all sorts of cases where it is far from obvious just what the agent’s credence really is, and what the agent’s values really are. Yet still, what they should do in non-Newcomb-like cases is simply maximise expected utility. Saying just which choice maximises expected utility requires settling these hard, even perhaps recondite, metaphysical issues. But there’s no getting away from metaphysics.

I used to worry that my views on normative uncertainty faced the following dilemma. I say that what’s right to do for an agent turns on their evidence about factual questions (fairly broadly construed), but on what’s really true about normative questions (fairly broadly construed). That makes it look like my theory relies on the existence of a nice clean factual-normative distinction. And the history of philosophy suggests that that’s not something you want to rely on.

In partial response, I want to stress that cases like these show that I don’t really need a distinction between normative and non-normative questions. What I need, or at least a closer approximation to what I need, is a distinction between constitutive and non-constitutive questions. Uncertainty about what goodness really is, or about what rationality really is, don’t matter to decision making. Nor does uncertainty about what causation really is, and for just the same reason. This doesn’t eliminate the worry that I’m positing a dualism that might be thought untenable for various, broadly Quinean, reasons. But it does change the issue of which dualism I’m committed to.

Philosophy Bites had a recent episode compiling answers to the question “Who is the most impressive philosopher you’ve met?” Almost everyone answered with a philosopher older than them, usually someone they knew in graduate school. And when I thought about the question, I was the same. My first instinctive answers were Frank Jackson and Phillip Pettit.

Now there isn’t necessarily anything wrong with being impressed with your graduate school teachers. Frank and Phillip are genuinely impressive. But it’s a bit surprising if these are the only impressive philosophers you’ve ever met. I don’t know if it is just hard to be impressed by younger philosophers, or hard to reveal that one is so impressed, but either way, people don’t seem to volunteer many names of people younger than themselves when asked.

So that prompts a natural follow up to Philosophy Bites’s question

Who is the most impressive philosopher you’ve met who is younger than you?

After thinking about a number of candidates (almost all women, it turned out) my answer is Elizabeth Barnes. Probably because I grew up in Australia, my paradigm of a great philosopher is someone who works (and work well) on a bunch of different areas, and is active outside their writing in making the world a better place. And obviously Elizabeth fits that description. To do as much as she’s done, at such a young age is, well, impressive.

So, which young(er) philosophers have impressed you?

Like philosophy, economics has a terrible gender imbalance. Also like philosophy, folks in economics are starting to do something about it. Here are a sample of recent interesting posts.

• What can be done about the gender problem in economics?
• Economics Is a Dismal Science for Women
• How big is the sexism problem in economics? This article’s co-author is anonymous because of it

Reading through those feels a bit like reading philosophy blog posts from a few years ago, when the top priority (online at least) was often to draw attention to the problem. I don’t know whether that has any implications for what the debate will look like going forward.

One big difference between economics and philosophy is that because of their size, and political importance, their debates tend to play out on a much bigger stage. So we could be about to see a re-run of what has happened in philosophy over the last few years, except the horror stories in the NY Times instead of the Chronicle of Higher Education.

Two recent blogs that are worth following

• Being a Philosopher of Color
• What is it like to be a Foreigner in Academia?

Most of what I believe about testimony and learning from others, I believe because of this passage from Frank Jackson’s Conditionals:

Why should you ever accept what I say, unless you already did so before I spoke – in which case speech is a luxury? What is wrong with your always either saying ‘I already believe that’ or saying 'How interesting, here’s a point on which we disagree’. The answer cannot be that you are taking me to be sincere. Sincerity relates to whether my words mirror my beliefs, whereas we are wondering why your discovery of my beliefs, perhaps your presuming sincerity on my part, should ever make you alter your beliefs. Sincerity relates to whether you should infer prior agreement or disagreement in beliefs, not to whether posterior adjustment of belief is in order.

The reason posterior adjustment in belief may be in order is that hearers (readers) sometimes have justified opinions about the evidence that lies behind speakers’ (writers’) assertions. You assert that P. I know enough about you, and your recent situation, to know (i) that you have evidence for P, for you would not otherwise have said it, and (ii) that your evidence is such that had I had it, I would have believed P. I borrow your evidence, so to speak. Typically, I won’t know exactly what your evidence is. Perhaps you visited a factory and came back and said 'The factory is well run’. I don’t know just what experiences you had there – just what you saw, heard, smelt and so on – but I know enough to know that had I had these experiences – whatever exactly they were – I too would have come to believe the factory well run. So I do.

This is what goes on when we acquire beliefs from books. A history bok says that Captain Cook landed first at Botainy Bay. I may not know just what evidence the writer had for writing this, but I believe that had I had it – whatever exactly it is – I too [93] would have believed that Cook landed first at Botany Bay. I borrow this evidence, without knowing exactly what it is, and in this way an epistemological division of labour is achieved. Imagine the work (and invasion of privacy) involved if we all had to duplicate each other’s evidence.

Of course, I may not come to believe exactly what the speaker or writer believes. A friend returning from overseas may say to me of a certain country 'It is very well run’. I may know enough of my friend to know that experiences that would make him say that, are the kind that would make me say 'Dissent is suppressed’. In this case, I will borrow his evidence to arrive, not at what he believes, but at what I would have, had I had his experiences. (Jackson, Conditionals, 92-3).

Evidence about others’ beliefs is relevant to our beliefs because it is evidence of evidence. Sometimes that means we end up believing what the other person believes. Sometimes, as in the authoritarian-friendly friend’s travel report, we believe something else.

This last case is the one that convinces me that something like Jackson’s view is right. Every theory of testimony has to explain why inferring that dissent is suppressed is rational given the testimony. The theory that testimony is evidence of evidence does so very smoothly, and also explains more normal cases of testimony. (That’s the point of the factory example.) Most other theories of testimony will have to add some epicycles or special clauses to get the 'dissent’ case right. It’s better to avoid epicycles and add hoc clauses. So I think the view that testimony provides evidence of evidence, and that’s its epistemological significance, is in general the right view.

But note one special case. Assume we know that we have exactly the same evidence as the friend. Then learning what they believe should have no effect, because it does not provide us with evidence of evidence. So in that case we need not change our belief merely by learning of the friend’s beliefs.

So in the very odd case that has become central to debates about disagreement, the case where the parties are known to have the same evidence, the right response to disagreement as such is to do nothing.

This is, fundamentally, why I’m a staunch anti-conciliationist about disagreement. Conciliationism of any kind is inconsistent with this Jacksonian view of testimony, and the Jacksonian view is correct, so conciliationism is false.