2018 paper, J. Dmitri Gallow shows that it is difficult to combine
multiple deference principles. The argument is a little complicated,
but the basic idea is surprisingly simple.
Suppose A and B are two weather forecasters. Let r be the
proposition that it will rain tomorrow, let A=x be the proposition
that A assigns probability x to r; similarly for B=x. Here are two
deference principles you might like to follow:
(1) Cr(r / A=x) = x.
(2) Cr(r / B=x) = x.
Now conceivably, A and B might issue different forecasts. So what
should you believe on the assumption that A=x and B=y, where x and y
are different? One natural idea is to split the difference:
Consider a world where eating doughnuts is illegal and where everyone
thinks it is OK to torture animals for fun. Suppose Norman at w is
eating doughnuts while torturing his pet kittens. Is he violating the
laws? Is he doing something immoral?
In one sense, yes, in another, no. His doughnut eating violates the
laws of w, but not the laws of our world. Conversely,
his kitten torturing violates a moral code accepted at our world, but
not a code accepted at w.
In general, when we ask whether people at other worlds do what they
ought to do, we can evaluate their actions relative to their
norms, or we can evaluate them relative to our norms. Both
perspectives make sense. But they lead to different deontic logics.
I recently refereed Eliezer Yudkowsky and Nate Soares's "Functional Decision
Theory" for a philosophy journal. My recommendation was to accept
resubmission with major revisions, but since the article had already
undergone a previous round of revisions and still had serious
problems, the editors (understandably) decided to reject it. I normally don't publish
my referee reports, but this time I'll make an exception because the
authors are well-known figures from outside academia, and I want to
explain why their account has a hard time gaining traction in academic
philosophy. I also want to explain why I think their account is wrong,
which is a separate point.
On the modal analysis of belief, 'S believes that p' is true iff p is
true at all possible worlds compatible with S's belief state. So
'believes' is a necessity modal. One might expect there to be a dual
possibility modal, a verb V such that 'S Vs that p' is true iff p is
true at some worlds compatible with S's belief state. But there
doesn't seem to be any such verb in English (or German). Why not?
What do we use if we want to say that something is compatible with
someone's beliefs? Suppose at some worlds compatible with Betty's
belief state, it is currently snowing. We could express this by "Betty
does not believe that it is not snowing". But (for some reason) that's
really hard to parse.
Gibbard's 1981 paper "Two recent theories of conditionals" contains
a famous passage about a poker game on a riverboat.
Sly Pete and Mr. Stone are playing poker on a Mississippi
riverboat. It is now up to Pete to call or fold. My henchman Zack sees
Stone's hand, which is quite good, and signals its content to Pete. My
henchman Jack sees both hands, and sees that Pete's hand is rather
low, so that Stone's is the winning hand. At this point, the room is
cleared. A few minutes later, Zack slips me a note which says "If Pete
called, he won," and Jack slips me a note which says "If Pete called,
he lost." I know that these notes both come from my trusted henchmen,
but do not know which of them sent which note. I conclude that Pete
One puzzle raised by this scenario is that it seems perfectly
appropriate for Zack and Jack to assert the relevant conditionals, and
neither Zack nor Jack has any false information. So it seems that the
conditionals should both be true. But then we'd have to deny that 'if
p then q' and 'if p then not-q' are contrary.
I've been reading about objective consequentialism lately. It's
interesting how pervasive and natural the use of counterfactuals is in
this context: what an agent ought to do, people say, is whichever
available act would lead to the best outcome (if it were
chosen). Nobody thinks that an agent ought to choose whichever act
will lead to the best outcome (if it is chosen). The
reason is clear: the indicative conditional is information-relative,
but the 'ought' of objective consequentialism is not supposed to be
information-relative. (That's the point of objective
consequentialism.) The 'ought' of objective consequentialism is
supposed to take into account all facts, known and unknown. But while
it makes perfect sense to ask what would happen under condition
C given the totality of facts @, even if @ does not imply C, it
arguably makes no sense to ask what will happen under condition
C given @, if @ does not imply C.
It has often been pointed out that the probability of an indicative
conditional 'if A then B' seems to equal the corresponding conditional
probability P(B/A). Similarly, the probability of a subjunctive
conditional 'if A were the case then B would be the case' seems to
equal the corresponding subjunctive conditional probability
P(B//A). Trying to come up with a semantics of conditionals that
validates these equalities proves tricky. Nonetheless, people keep
trying, buying into all sorts of crazy ideas to make the equalities
come out true.
I am puzzled about these efforts, for two reasons.
Dutch Book arguments are often used to justify various epistemic
norms – in particular, that credences should obey the
probability axioms and that they should evolve by
condionalization. Roughly speaking, the argument is that if someone
were to violate these norms, then they would be prepared to accept
bets which amount to a guaranteed loss, and that seems
But it's hard to spell out how exactly the argument is meant to go. In
fact, I'm not aware of any satisfactory statement. Here's my
For concreteness, I'll focus on the argument for probabilism,
but the case of conditionalization is similar.
My paper "Imaginary
Foundations" has been accepted at Ergo (after rejections from
Phil Review, Mind, Phil Studies, PPR, Nous, AJP, and Phil
Imprint). The paper has been in the making since 2005, and I'm quite
fond of it.
The question I address is simple: how should we model the impact of
perceptual experience on rational belief? That is, consider a
particular type of experience – individuated either by its
phenomenology (what it's like to have the experience) or by its
physical features (excitation of receptor cells, or whatever). How
should an agent's beliefs change in response to this type of
According to the Principle of Indifference, alternative
propositions that are similar in a certain respect should be given
equal prior probability. The tricky part is to explain what should
count as similarity here.
Van Fraassen's cube factory nicely illustrates the problem. A
factory produces cubes with side lengths between 0 and 2 cm, and
consequently with volumes between 0 and 8 cm^3. Given this
information, what is the probability that the next cube that will be
produced has a side length between 0 and 1 cm? Is it 1/2, because the
interval from 0 to 1 is half of the interval from 0 to 2? Or is it
1/8, because a side length of 1 cm means a volume of 1 cm^3, which is
1/8 of the range from 0 to 8?