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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.
In a nice little paper, "The Non-Transitivity of the Contingent and Occasional Identity Relations", Ralf Bader argues that if identity is relative to times or worlds, then it becomes non-transitive and thus no longer qualifies as real identity.
Following Gallois, Bader assumes that a proponent of occasional identity must insist that identity statements are always relativised to a time. Now he considers a case where between times t1 and t2, two objects B and D simultaneously undergo fission in such a way that one fission product of B fuses with one fission product of D. Of the three resulting objects A, C and E, one (C) is a fission product of both B and D. Bader argues that at the initial time t1, it is then true that A=C and C=E, but not that A=E. So identity at t1 is not transitive.
In the (Northern) summer, I wrote a short survey article on contingent identity. The word limit did not allow me to go into many details. In particular, I ended up with only a brief paragraph on Andre Gallois's theory of occasional identity, although I would have liked to say a lot more. So here are some further thoughts and comments on Gallois's account.
In his 1998 monograph Occasions of Identity, Gallois defends the view that things can be identical at some times and worlds and non-identical at others. For simplicity, I'll focus only on the temporal dimension here. Gallois begins with a long list of scenarios where it is intuitive to say that things are identical at one time but not at others. For example, when an amoeba A fissions into two amoebae B and C, it is tempting to say that B and C were identical prior to the fission and non-identical afterwards.
To what extent are the beliefs and desires of rational agents determined by their actual and counterfactual choices? More precisely, suppose we are given a preference order that obtains between a possible act A and a possible act B iff the relevant agent is disposed to choose A over B. Say that a pair (C,V) of a credence function C and a utility (desirability) function V fits the preference order iff, whenever A is preferred over B, then A has higher expected utility than B by the lights of (C,V). Now, to what extent does a rational preference order constrain fitting credence-utility pairs?
Some recent papers:
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