Dilip Ninan has also argued on a number of occasions that attitude
contents cannot in general be modelled by sets of qualitative centred
worlds; see especially his "Counterfactual
attitudes and multi-centered worlds" (2012). The argument is
based on an alleged problem for the centred-worlds account applied to what he
calls "counterfactual attitudes", the prime example being imagination.
Since the problem concerns the analysis of attitudes de re,
we first have to briefly review what the centred-worlds account might
say about this. Consider a de re belief report "x believes that y is
F". Whether this is true depends on what x believes about y, but if
belief contents are qualitative, we cannot simply check whether y is F
in x's belief worlds. We first have to locate y in these
qualitative scenarios. A standard idea, going back to Quine, Kaplan
and Lewis, is that the belief report is true iff there is some
"acquaintance relation" Q such that (i) x is Q-related uniquely to y
and (ii) in x's belief worlds, the individual at the centre is
Q-related to an individual that is F. For example, if Ralph sees
Ortcutt sneaking around the waterfront, and believes that the guy
sneaking around the waterfront is a spy, then Ralph believes de re of
Ortcutt that he is a spy.
If we want to model rational degrees of belief as probabilities,
the objects of belief should form a Boolean algebra. Let's call the
elements of this algebra propositions and its atoms (or
ultrafilters) worlds. Every proposition can be represented as a
set of worlds. But what are these worlds? For many applications, they
can't be qualitative possibilities about the universe as a whole, since
this would not allow us to model de se beliefs. A popular
response is to identify the worlds with triples of a possible universe,
a time and an individual. I prefer to say that they are maximally
specific properties, or ways a thing might be. David Chalmers (in
discussion, and in various papers, e.g. here and there) objects that
these accounts are not fine-grained enough, as revealed by David
Austin's "two tubes" scenario. Let's see.
Luc Bovens and Wlodek Rabinowicz (2010
and 2011)
present the following puzzle:
Three people are each given a hat to put on in the
dark. The hats' colours, either black or white, has been decided by
three independent tosses of a fair coin. Then the light goes on and
everyone can see the hats of the two others, but not their own. All of
this is common knowledge in the group.
Let's call the three players X, Y and Z. There are eight possible
distributions of hat colours, each with probability 1/8:
I had to move to a new server, hence the recent downtime. If you notice something that's broken, please let me know.
Allen Hazen (1979, pp.328-330)
pointed out a problem for Lewis's counterpart-theoretic interpretation
of modal discourse: the fact that x is essentially R-related to y
should be compatible with the fact that both x and y have multiple
counterparts at some world, without all counterparts of x being
R-related to all counterparts of y. But the latter is what Lewis's
semantics requires for the truth of `necessarily xRy'.
I'll begin with a strange consequence of the best system
account. Imagine that the basic laws of quantum physics are
stochastic: for each state of the universe, the laws assign
probabilities to possible future states. What do these probability
statements mean?
The best system account identifies chance with the probability
function that figures in whatever fundamental physical theory best
combines the virtues of simplicity, strength and fit, where fit is a
matter of assigning high probability to actual events. So when we say
that the chance of some radium atom decaying within the next 1600
years is 1/2, what we claim is true iff whatever fundamental theory
best combines the virtues of simplicity, strength and fit assigns
probability 1/2 to the mentioned outcome. As a piece of ordinary
language philosophy, this is not very plausible. For one thing, people
speak of chances even when it is assumed that the fundamental dynamics
is deterministic. Moreover, by ordinary usage, chances are logically
independent of actual frequencies, which is incompatible with the best
system account. Nevertheless, the account may be plausible as a
somewhat revisionary explication of one strand in the mess that is our
ordinary conception of chance.
It is well-known that humans don't conform to the model of rational
choice theory, as standardly conceived in economics. For example, the
minimal price at which people are willing to sell a good is often much
higher than the maximal price at which they would previously have been
willing to buy it. According to rational choice theory, the two prices
should coincide, since the outcome of selling the good is the same as
that of not buying it in the first place. What we philosophers call
'decision theory' (the kind of theory you find in Jeffrey's Logic
of Decision or Joyce's Foundations of Causal Decision
Theory) makes no such prediction. It does not assume that the
value of an act in a given state of the world is a simple function of
the agent's wealth after carrying out the act. Among other things, the
value of an act can depend on historical aspects of the relevant
state. A state in which you are giving up a good is not at all
the same as a state in which you aren't buying it in the first place,
and decision theory does not tell you that you must assign equal
value to the two results.
In The Metaphysics within Physics, Tim Maudlin raises a
puzzling objection to Humean accounts of laws. (Possibly the same
objection is raised by John Halpin in several earlier papers such as
"Scientific law: A perspectival account".)
Scientists often consider very different models of putative
laws. Such models can be understood as miniature worlds or scenarios
in which the relevant laws obtain. On Humean accounts, the laws at a
world are determined by the occurrent events at that world. The
problem is that rival systems of laws often have models with the very
same occurrent events. Whether this is a problem depends on what we
mean by "the relevant laws obtain". Maudlin:
For every way things might have been there is a possible world where
they are that way. What does that tell us about the number of worlds?
If we identify ways things might have been ("propositions") with
sentences of a particular language, or with semantic values of such
sentences, the answer will depend on the language and will generally
be small (countable). But that's not what I have in mind. It might
have been that a dart is thrown at a spatially continuous dartboard,
and each point on the board is a location where the dart's centre
might have landed. These are continuum many possibilities, although
they cannot be expressed, one by one, in English.
Many of our best scientific theories make only probabilistic
predications. How can such theories be confirmed or disconfirmed by
empirical tests?
The answer depends on how we interpret the
probabilistic predictions. If a theory T says 'P(A)=x', and we
interpret this as meaning that Heidi Klum is disposed to bet on A at
odds x : 1-x, then the best way to test T is by offering bets to Heidi
Klum.
Nobody thinks this is the right interpretation of probabilistic
statements in physical theories. Some hold that these statements are
rather statements about a fundamental physical quantity called
chance. Unlike other quantities such as volume, mass or charge,
chance pertains not to physical systems, but to pairs of a time and a
proposition (or perhaps to pairs of two propositions, or to triples of
a physical system and two propositions). The chance quantity is
independent of other quantities. So if T says that in a certain type
of experiment there's a 90 percent probability of finding a particle
in such-and-such region, then T entails nothing at all about particle
positions. Instead it says that whenever the experiment is carried
out, then some entirely different quantity has value 0.9 for a certain
proposition. In general, on this interpretation our best theories say
nothing about the dynamics of physical systems. They only make
speculative claims about a hidden magnitude independent of the
observable physical world.