Wolfgang Schwarz

Lewis book

I forgot to mention that my book on Lewis has been released a couple of weeks ago. It's a distant descendant of my PhD thesis, and in German.

Values and consequences in economics and quantum mechanics

One of the novelties in Richard Jeffrey's "Logic of Decision" (1965) was to unify the space over which probabilities and values are defined: both probability and desirability are distributed over the space of possible worlds, of ways things might be. By contrast, in earlier theories like that of Savage, probabilities were defined over states (or events) and utilities over consequences, which were taken to be distinct kinds of things. Technically, this difference between Savage and Jeffrey isn't terribly important as long as anything an agent may care about can be found in the set of 'consequences'. However, the distinction and the labeling in Savage's treatment carries a danger to overlook the complexity of human values. This has, I believe, led to a number of serious mistakes.

Chance, credence, and centers

Rational credence should match the expectation of objective chance. Here I will have a brief look at what happens to this connection between credence and chance on the assumption that credence is centered and chance is not.

1. Fixing the time. Both credences and chances evolve over time. When a coin is tossed twice, the chance of two heads may initially be 1/4; after the first toss has come up heads, it is 1/2. So when your beliefs should match the assumed chance, it can only match the chance you assume to obtain at some particular time. At what time?

Can evidence be inadmissible?

First, a quick reminder of history. David Lewis once proposed a principle (the 'Principal Principle') linking rational credence and objective chance. It says (or rather, entails) that your rational credence in any proposition A, on the assumption that the objective chance of A is x, should also be x, no matter what (further) evidence E you have:

OP: P(A | ch(A)=x & E) = x.

This principle, the 'Old Principle', is widely taken to suffer from two defects. First, suppose your evidence E includes ~A. Then probability theory ensures that P(A | ch(A)=x & E) = 0, irrespective of x. Lewis responded by restricting OP to cases where E is 'admissible'. He suggested that a (true) proposition is admissible iff it is entailed by the history of the world up to now together with the laws of nature.

Are cartoon characters persons?

A judge in the New South Wales Supreme Court has decided that Bart and Lisa Simpson are persons under the age of 16.

This is odd. According to The Simpsons, Bart and Lisa are certainly persons under the age of 16; but 'according to The Simpsons, P' does not entail P, I would have thought. Indeed, according to the Simpsons, Bart and Lisa exist, while in reality they don't. And since Bart doesn't exist, no-one is Bart Simpson; so in particular, every person under the age of 16 is not Bart Simpson; therefore Bart Simpson is not a person under the age of 16.

Mike Titelbaum on Shifting and Sleeping Beauty

In the last entry, I have suggested that

EEP) P_2(A) = P_1(+A|+E)

is a sensible rule for updating self-locating beliefs. Here, E is the total evidence received at time 2 (the time of P_2), and '+' denotes a function that shifts the evaluation index of propositions, much like 'in 5 minutes': '+A' is true at a centered world w iff A is true at the next point from w where new information is received. (EEP) therefore says that upon learning E, your new credence in any proposition A should equal your previous conditional credence that A will obtain at the next point when information comes in, given that this information is E.

Terry Horgan on Sleeping Beauty

I've been participating in a couple of workshops here at ANU lately, and I thought I'd share some notes. First, we had a little Sleeping Beauty workshop where Terry Horgan and Mike Titlebaum defended thirding, and me halfing. Unfortunately, I think we didn't quite get to the heart of our disagreement. Each of us said their own thing, without saying enough about what's wrong with the reasoning of the other sides. So I'll do that here. I start with Terry's account.

Truth-conduciveness and rational priors

We Bayesians are sometimes bugged about ultimate priors: what probability function would suit a rational agent before the incorporation of any evidence? The question matters not because anyone cares about what someone should believe if they popped into existence in a state of ideal rationality and complete empirical ignorance. It matters because the answer also determines what conclusions rational agents should draw from their evidence at any later point in their life. Take the total evidence you have had up to now. Given this evidence, is it more likely that Obama won the 2008 election or that McCain won it? There are distributions of priors on which your evidence is a strong indicator that McCain won. Nevertheless, this doesn't seem like it's a rational conclusion to draw. So there must be something wrong with those priors.

Stalnaker on self-location

Here are some notes on Stalnaker's account of self-locating beliefs, in chapter 3 of Our Knowledge of the Internal World. I find the discussion there slightly intransparent, so I'll start with a presentation of what I take to be Stalnaker's account, but in my own words. This will lead to a few objections further down.

We start with extreme haecceitism. Every material object and every moment in time has, in addition to its normal, qualitative properties also a non-qualitative property, its 'haecceity', that distinguishes it from everything else. My haecceity belongs to me with metaphysical necessity, and could not belong to anyone else. Moreover, it is my only (non-trivial) essential property. (This is the 'extreme' part in extreme haecceitism.) In this world, I am a human being, but in other worlds, I am a cockatoo, or a poached egg. My haecceity is freely combinable with any qualitative property.

Stalnaker against internalism

Stalnaker holds a combination of views that seem independent to me, but closely connected to him. One is a kind of reductive naturalism about intentionality. On this view, the point of attributing beliefs and desires is to give a high-level characterisation of the subject's behavioural dispositions, their functional architecture and their causal relations to the environment. Another of Stalnaker's views is externalism about mental content. This says that intentional characterisations are relational: even when two subjects are perfect intrinsic and functional duplicates, they may still differ in their beliefs and desires, depending on what objects and properties they are causally related to.