Wolfgang Schwarz

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.

Unique centers

Continuing the topic of the last post, suppose I'm certain that no-one else in the history of the universe ever had (or will have) exactly the experiences that I have now. Then I can 'translate' any centered proposition into an uncentered propositions in such a way that the translation is certain to preserve truth-values. For instance, "it is raining" gets translated into "it is raining at all times and places where someone has such-and-such experiences". In this case, one might think, purely centered information can never affect my uncentered beliefs. For purely centered information only distinguishes between multiple centers within a single world; but if no world has multiple possible centers, then there is nothing to learn from such information. (This line of reasoning is related to what Mike Titelbaum says in his forthcoming paper "The Relevance of Self-Locating Beliefs", though I don't think Mike would endorse the argument I present here.)

When centering matters

Darks clouds are gathering. Soon it will be raining. When it does, I will believe that it is raining. I do not yet believe that it is raining even though I do believe that my well-informed future self will believe that it is raining. I thereby violate the 'Principle of Reflection'. Once we allow for centered propositions that change their truth-value between times and places, Reflection, like its close cousin Conditioning, become very implausible norms of rationality.

OPP update

The OPP feed has been a bit bumpy recently because I made a few changes to the code. Things should be running smoothly again from today. The biggest changes are a bit of OCR to parse scanned documents (about 25% of all PDFs) and an improved algorithm to detect authors and co-authors. If you have contacted me about anything else: that has also been fixed.

How to change one's mind again

I've finally finished rewriting my paper on self-locating belief dynamics. Here is the new version. The presentation is quite different from before. In particular, I no longer use transition probabilities in modeling Cartesian agents, which allows me to be more specific about what these probabilities are. There's also a new section where I try to show that traditional arguments in support of conditioning turn into arguments for my revised rule when self-locating beliefs are considered.

Quantified counterfactuals, strict conditionals and escaping animals

Speaking of chapter six, Williamson here argues that the sentence

1) if an animal escaped from the zoo, it would be a monkey

is not adequately formalized as

1')

on the grounds that according to (1'), even the elephants are such that they would be monkeys if they escaped from the zoo. Williamson suggests that an adequate formalization might rather go like this: