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.
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.
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?
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".)
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.
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