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.

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
irrational.

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.

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.

Sometimes, when we say that someone can (or cannot, or must, or
must not) do P, we really mean that they can (cannot, must, must not)
do Q, where Q is logically stronger than P. By what linguistic
mechanism does this strengthening come about?

Why maximize expected utility? One supporting consideration that is
occasionally mentioned (although rarely spelled out or properly
discussed) is that maximizing expected utility tends to produce
desirable results in the long run. More specifically, the claim is
something like this:

According to realist structuralism, mathematics is the study of
structures. Structures are understood to be special kinds of complex
properties that can be instantiated by particulars together with
relations between these particulars. For example, the field of complex
numbers is assumed to be instantiated by any suitably large collection
of particulars in combination with four operations that satisfy certain
logical constraints. (The four operations correspond to addition,
subtraction, multiplication, and division.)

A might counterfactual is a statement of the form 'if so-and-so were
the case then such-and-such might be the case'. I used to think that
there are different kinds of might counterfactuals: that sometimes
the 'might' takes scope over the entire conditional, and other times
it does not.

I stumbled across a few interesting free books in the last few days.

1. Tony Roy has a 1051 page introduction
to logic on his homepage, which slowly and evenly proceeds from
formalising ordinary-language arguments all the way to proving
Gödel's second incompleteness theorem. All entirely mainstream
and classical, but it looks nicely presented, with lots of exercises.