In decision theory, the available options are often glossed informally
as the acts the agent can perform, or the propositions she can make
true. But this yields implausible results in cases where an agent has
doubts about what she can do.
For example, assume Bob suspects that the button in front of him
functions as a light switch, as in fact it does. Then Bob can turn
on the light by pressing the button. But if he is not certain that
the button is a light switch, decision theory should consider the
consequences of pressing the button if it has some other function. So
turning on the light by pressing the button should not count as
an option.
It is tempting to think that there is nothing more to physical
quantities than their nomic role: that to have a certain mass just is
to behave in such-and-such a way under such-and-such conditions.
But it is also tempting to think that the "Galilean equivalence" of
inertial mass and gravitational mass is a true identity; i.e.,
that
Inertial mass = gravitational mass.
However, the role associated with "inertial mass" is completely
different from the role associated with "gravitational mass". So if
having such-and-such inertial mass is having the relevant
dispositions associated with "inertial mass", and likewise for
gravitational mass, then the Galilean equivalence could not be an
identity. It would rather state an empirical law, according to which
two distinct quantities always have the same value.
In chapter 8 of Doing Good Better, William MacAskill argues
that we should not make a great effort to reduce our carbon emissions,
to buy Fairtrade coffee, or to boycott sweatshops. The reason is that
these actions have at best a small impact on improving other people's
lives and so the cost and effort is better spent elsewhere.
From a strictly utilitarian perspective, there is nothing to
complain about this. But strict utilitarianism is a highly
counterintuitive position. In fact, MacAskill himself rejects it when
he says that it would not be OK to consume meat from factory farms and
"offset" by donating to animal welfare organisations, even if the net
result would be less animal suffering. I agree. Whether a course of
action is right or wrong is not just a matter of the net difference it
makes to the amount of suffering in the world. But then we also have
to reconsider MacAskill's conclusions about carbon offsetting,
fairtrade, and sweatshops.
You observe a process that generates two kinds of outcomes, 'heads'
and 'tails'. The outcomes appear in seemingly random order, with
roughly the same amount of heads as tails. These observations support
a probabilistic model of the process, according to which the
probability of heads and of tails on each trial is 1/2, independently
of the other outcomes.
How observations about frequencies confirm or disconfirm
probabilistic models is well understood in Bayesian epistemology. The
central assumption that does most of the work is the Principal
Principle, which states that if a model assigns (objective)
probability x to some outcomes, then conditional on the model, the
outcomes have (subjective) probability x. It follows that models that
assign higher probability to the observed outcomes receive a greater
boost of subjective probability than models that assign lower
probability to the outcomes.
In my recent post on Interventionist Decision Theory, I suggested that causal interventionists
should follow Stern and move from a Jeffrey-type definition
of expected utility to a Savage-Lewis-Skyrms type definition. In that case, I also suggested that they could avoid various problems arising from the concept of an intervention by construing the agent's
actions as ordinary events. In conversation,
Reuben Stern convinced me that things are not so easy.
The two-dimensionalist account of a posteriori (metaphysical)
necessity can be motivated by two observations.
First, all good examples of a posteriori necessities follow a priori
from non-modal truths. For example, as Kripke pointed out, that his
table could not have been made of ice follows a priori from the
contingent, non-modal truth that the table is made of wood. Simply
taking metaphysical modality as a primitive kind of modality would
make a mystery of this fact.
Imagine you and I are walking down a long path. You are ahead,
but we can communicate on the phone. If you say, "there are strawberries here" and I trust you, I should not come to believe that there
are strawberries where I am, but that there are strawberries wherever
you are. If I also know that you are 2 km ahead, I should come to
believe that there are strawberries 2 km down the path. But what's the
general rule for deferring to somebody with self-locating beliefs?
I used to agree with Lewis that classical mereology, including
mereological universalism, is "perfectly understood, unproblematic,
and certain". But then I fell into a dogmatic slumber in which it seemed
to me that the debate over mereology is
somehow non-substantive: that there is no fact of the
matter. I was recently awakened from this slumber by a footnote in
Ralf Busse's forthcoming article "The
Adequacy of Resemblance Nominalism" (you should read the whole
thing: it's terrific). So now I once again think that Lewis was right. Let
me describe the slumber and the awakening.
Causal models are a useful tool for reasoning about causal
relations. Meek
and Glymour 1994 suggested that they also provide new resources to
formulate causal decision theory. The suggestion has been endorsed by
Pearl
2009, Hitchcock
2016, and others. I will discuss three problems with this proposal
and suggest that fixing them leads us back to more or less the
decision theory of Lewis
1981 and Skyrms
1982.
What makes the Sleeping Beauty problem non-trivial is Beauty's
potential memory loss on Monday night. In my view, this means that
Sleeping Beauty should be modeled as a case of potential epistemic
fission: if the coin lands tails, any update Beauty makes to her
beliefs in the transition from Sunday to Monday will also fix her
beliefs on Tuesday, and so the Sunday state effectively has two
epistemic successors, one on Monday one on Tuesday. All accounts of
epistemic fission that I'm aware of then entail halfing.