Chance and credence 
In his paper at the SEP, Alan Hajek argued for this analogy: One's degree of belief in P being equal to the objective chance of P is like one's categorical belief that P being true. That is, a degree of belief getting the world right consists in it matching the objective chances.

This position requires that there be objective chances, he argued that there are, and I'll presume it for now.

A problem for his position arose in various forms during the question and answer period. Consider a fair coin.* The chance that it will come up heads is .5. I flip it, and it does in fact come up heads. Before flipping it, I have degree of belief .5 that it will come up heads on that flip. After flipping it, I can either change to degree of belief to 1 or continue with degree of belief .5. Neither option seems very good. The former has me believing the truth about the flip, but I no longer acknowledge the fact that the coin flip was a chancy event. The objective chance that the flip would come up heads is still .5, even after it did actually come up heads. The latter would leave me ignoring evidence about how events actually turn out, in favor of intermediate degrees of belief which are presumed to preserve information about how they might have gone.

It seems to me, however, that this is not especially a problem with Alan's account. Rather, it is an artifact of representing his account in terms of the usual probabilist framework. The framework treats agents' degrees of belief as probabilities assigned to propositions in first-order logic, with probabilistic judgments represented as intermediate degrees of belief. That is clearly inadequate in this case. I do believe that the chance that the coin would come up heads is one-half, and I also do believe that it did come up heads.

There is a difference between a degree of belief which is meant to correspond to an objective chance and a degree of belief that is merely an intermediate belief about a matter that does not admit of degrees.

There are formal ways of representing this difference, but notice that it will not help to consider belief to be a probability distribution over probability assignments. If I am less than certain that the coin is fair, then there will be a distribution around .5. If I am less than certain that the coin came up heads, then there will be a distribution close to 1. A bimodal distribution with peaks at .5 and 1 would not represent either situation.

We might instead introduce an operator Ch(P,p), meaning that the chance that P is p. After the coin toss, my degrees of belief are DoB(H)=1 and DoB(Ch(H,.5))=1. This handles the distinction, but it also means that the probabilist story about degree of belief is doing no work here. We might just as well represent my beliefs as H and Ch(H,.5).

Although we might try other expedients, representing degrees of belief as probabilities is de rigeur. Philosophers often do it presumptively nowadays, just as it was usual to write sentences in first-order logic in the 1960s. Why? Here are a few possible explanations:

1. The usual probabilist framework works for many purposes. There is no need to use a more complicated formalism if you don't need to.

2. Subjective Bayesians deny that there are any such things as objective chances, except insofar as they can be recovered from convergence in subjective degrees of belief. They have no incentive to try and represent beliefs about things that don't exist. (I am not sure whether the Subjective Bayesian should say that no one actually has beliefs in objective chances or just that beliefs in objective chances are wrong-headed.)

3. There is no clearly correct way to accommodate the distinction. This is a problem, because many probabilists say that probability just is the logic of confirmation. This imperialism requires that there is one specific formal system and that it captures the relevant structure. Once we admit that belief involves structures that cannot be readily represented in the usual probabilist idiom, then we must admit that there is more to the logic of science.


* If determinism makes you think that you can't attribute objective chances to coins, suppose instead that it is a radioactive atom and that the event is it decaying during a period equal to its half-life.

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Sentry duty and a three-word vocabulary 
There were many good talks at the SEP last week, and I am still mulling over some of them.

I'll mention Brian Skyrms' talk briefly, because I am still mulling it over but don't have anything deep to say about it.

Brian offered simple evolutionary models of animal signalling. As an example, he pointed to Dorothy Cheney and Robert Seyfarth's work on meerkat and monkey signaling; see especially their paper on meerkats [pdf]. Meerkats take turns standing sentry, and call out if they seeing anything worth mentioning. They have (roughly) a three word vocabulary: raptor, jackal, and snake.

I was curious about meerkats in contrast with his other examples, because the meerkat signaling system can't be wholly separated from their taking turns on sentry duty. Even if one behavior predated the other, each is more valuable when accompanied by the other. So it's too simple to treat selection for the signaling behavior in isolation.

Also: If we learned meerkat vocabulary, we could play roshambo with it:

-- 1... 2... 3... jackal!

-- My snake bites your jackal.

-- How about best two out of three?


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Rumor Volat 
Tonight was the opening session of the Society for Exact Philosophy. Walking past Brian Skyrms, I said hi and congratulated him on his new position. He was somewhat taken aback, because he only just agreed to it-- not that it is secret, but there hasn't been a public announcement yet.

News travels fast these days.

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An angsty tableaux 
Yesterday was the last class meeting for my Existentialism course. During the discussion, one of the students drew a doodle in her notes. She showed it to me; with her permission, I've pasted it in below. It summarizes the course, more or less. The philosophers we studied are on the left. She and several of her fellow students are on the right. There I am in the upper corner.



Although I am depicted as being above Kierkegaard's God, this was only because she was running out of space. I don't think any sacrilege was intended.

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Another quaff of realism 
In a recent entry, I discussed the possibilities for realist pluralism. This is the position that there are many real kinds out in nature, not just the priveleged short list of kinds that appears in our fundamental science. I asked how promiscuous this position ought to be: Should we say that silly, toy-example kinds like 'liz' and 'ard' are as real as important-to-us kinds like 'electron', 'gene', and 'seasoning'?

In the comments, Matt suggests a way that a realist pluralist could deny kinds toy-example kinds. Here is what he said:
[R]eal kinds are the ones that we get as a product of actual inquiries. Useless dreams [like liz and ard] may be hypothetical but not real kinds. This still allows for some promiscuity (because biologists, cooks, common sense, etc. may have different purposes/problems and come to different conclusions) without allowing in all the useless stuff.
Something similar was suggested to me by Dick Boyd at the last PSA. I think it faces a dilemma.

Either the kinds must appear in inquiry that we have actually done, or it need only appear in enquiry that we could do. Consider each horn of the dilemma:

Real kinds are ones that appear in inquiry that some person has actually conducted. A consequence of this would be that a kind like 'electron' was not a real kind in 1800; it became a real kind only when electrons were discovered. This is at least an odd way of speaking. The fact that they could be discovered suggests that they were already real. One could say that electrons were real in 1800, but that the kind electron was not real until it was first formulated.

Matt explicitly aligns himself with Dewey, and I suspect that Dewey would just accept this oddity. He says that America changed when Vikings discovered it, just by virtue of being known to the Vikings. So, he might also say, there is a change in electrons when scientists first discover them-- they first constitute a real kind.

Real kinds are ones that appear in inquiry that could be conducted. Suppose there were rich patrons of science who adored the front ends of lizards but loathed their back ends, and imagine the science they would fund. This is a counter-factual inquiry in which 'liz' and 'ard' appear as kinds.

As a philosopher, I have cultivated the talent of imagining bizarre counter-factual scenarios. There is no kind so trivial that I cannot imagine a science in which it appears. So the second horn of the dilemma reduces the criterion to triviality, and every kind counts as real.

So: Oddity or triviality? Which will it be?

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