# Wolfgang Schwarz

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## Reduction and coordination

The following principles have something in common.

Conditional Coordination Principle.
A rational person's credence in a conditional A->B should equal the ratio of her credence in the corresponding propositions B and A&B; that is, Cr(A->B) = Cr(B/A) = Cr(B)/Cr(A&B).
Normative Coordination Principle.
On the supposition that A is what should be done, a rational agent should be motivated to do A; that is, very roughly, Des(A/Ought(A)) > 0.5.
Probability Coordination Principle.
On the supposition that the chance of A is x, a rational agent should assign credence x to A; that is, roughly, Cr(A/Ch(A)=x) = x.
Nomic Coordination Principle.
On the supposition that it is a law of nature that A, a rational agent should assign credence 1 to A; that is, Cr(A/L(A)) = 1.

All these principles claim that an agent's attitudes towards a certain kind of proposition rationally constrain their attitudes towards other propositions.

## Do laws explain regularities?

Humeans about laws of nature hold that the laws are nothing over and above the history of occurrent events in the world. Many anti-Humeans, by contrast, hold that the laws somehow "produce" or "govern" the occurrent events and thus must be metaphysically prior to those events. On this picture, the regularities we find in the world are explained by underlying facts about laws. A common argument against Humeanism is that Humeans can't account for the explanatory role of laws: if laws are just regularities, then then laws can't really explain the regularities — so the charge — since nothing can explain itself.

## Confirmation and singular propositions

In discussions of the raven paradox, it is generally assumed that the (relevant) information gathered from an observation of a black raven can be regimented into a statement of the form Ra & Ba ('a is a raven and a is black'). This is in line with what a lot of "anti-individualist" or "externalist" philosophers say about the information we acquire through experience: when we see a black raven, they claim, what we learn is not a descriptive or general proposition to the effect that whatever object satisfies such-and-such conditions is a black raven, but rather a "singular" proposition about a particular object -- we learn that this very object is black and a raven. It seems to me that this singularist doctrine makes it hard to account for many aspects of confirmation.

## Small formulas with large models

Take the usual language of first-order logic from introductory textbooks, without identity and function symbols. The vast majority of sentences in this language are satisfied in models with very few individuals. You even have to make an effort to come up with a sentence that requires three or four individuals. The task is harder if you want to come up with a fairly short sentence. So I wonder, for any given number n, what is the shortest sentences that requires n individuals?

## Belief update: shifting, pushing, and pulling

It is widely agreed that conditionalization is not an adequate norm for the dynamics of self-locating beliefs. There is no agreement on what the right norms should look like. Many hold that there are no dynamic norms on self-locating beliefs at all. On that view, an agent's self-locating beliefs at any time are determined on the basis of the agent's evidence at that time, irrespective of the earlier self-locating belief. I want to talk about an alternative approach that assumes a non-trivial dynamics for self-locating beliefs. The rough idea is that as time goes by, a belief that it is Sunday should somehow turn into a belief that it is Monday.

## Functionalism and the nature of propositions

Let's assume that propositional attitudes are not metaphysically fundamental: if someone has such-and-such beliefs and desires, that is always due to other, more basic, and ultimately non-intentional facts. In terms of supervenience: once all non-intentional facts are settled, all intentional facts are settled as well.

## Sleeping Beauty is testing a hypothesis

Let's look at the third type of case in which credences can come apart from known chances. Consider the following variation of the Sleeping Beauty problem (a.k.a. "The Absentminded Driver"):

## Undermining and confirmation

Next, undermining. Suppose we are testing a model H according to which the probability that a certain type of coin toss results in heads is 1/2. On some accounts of physical probability, including frequency accounts and "best system" accounts, the truth of H is incompatible with the hypothesis that all tosses of the relevant type in fact result in heads. So we get a counterexample to simple formulations of the Principal Principle: on the assumption that H is true, we know that the outcomes can't be all-heads, even though H assigns positive probability to all-heads. In such a case, we say that all-heads is undermining for H.

## Inadmissible evidence in Bayesian Confirmation Theory

Suppose we are testing statistical models of some physical process -- a certain type of coin toss, say. One of the models in question holds that the probability of heads on each toss is 1/2; another holds that the probability is 1/4. We set up a long run of trials and observe about 50 percent heads. One would hope that this confirms the model according to which the probability of heads is 1/2 over the alternative.

## Conditional expressions

Most programming languages have conditional operators that combine a (boolean) condition and two singular terms into a singular term. For example, in Python the expression

'hi' if 2 < 7 else 'hello'

is a singular term whose value is the string 'hi' (because 2 < 7). In general, the expression

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