Wolfgang Schwarz

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Practical irrationality or epistemic irrationality?

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.

Models of laws

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".)

On the cardinality of worlds

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.

Humean Everettian chances

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.

Bader against contingent and occasional identity

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.

Gallois on occasional identity

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.

Representation theorems and the indeterminacy of mental content

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?

Paper jam

Some recent papers:

Counterexamples to Stalnaker's Thesis

I like a broadly Kratzerian account of conditionals. On this account, the function of if-clauses is to restrict the space of possibilities on which the rest of the sentence is evaluated. For example, in a sentence of the form 'the probability that if A then B is x', the if-clause restricts the space of possibilities to those where A is true; the probability of B relative to this restricted space is x iff the unrestricted conditional probability of B given A is x. This account therefore valides something that sounds exactly like "Stalnaker's Thesis" for indicative conditionals:

Possible worlds and non-principal ultrafilters

It is natural to think of a possible world as something like an extremely specific story or theory. Unlike an ordinary story or theory, a possible world leaves no question open. If we identify a theory with a set of propositions, a possible world could be defined as a theory T which is

  1. maximally specific: T contains either P or ~P, for every proposition P;
  2. consistent: T does not contain P and ~P, for any proposition P;
  3. closed under conjunction and logical consequence: if T contains both P and Q, then it contains their conjunction P & Q, and if T contains P, and P entails Q, then T contains Q.

It is often useful to go in the other direction and identify propositions with sets of possible worlds. We can then analyse entailment as the subset relation, negation as complement and conjunction as intersection. Of course, we may not want to say that a world is a (non-empty) set of (consistent) propositions and also that a consistent proposition is a non-empty set of worlds, since these sets should eventually bottom out. But that doesn't seem very problematic, and it is easily fixed as long as there is a simple 1-1 correspondence between worlds and logically closed, consistent and maximally specific theories. In particular, one might suspect that on the present definitions, every logically closed, consistent and maximally specific theory uniquely corresponds to a possible world, namely the sole member of the intersection of the theory's members.

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