Wolfgang Schwarz

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Is it ever rational to calculate expected utilities?

Decision theory says that faced with a number of options, one should choose an option that maximizes expected utility. It does not say that before making one's choice, one should calculate and compare the expected utility of each option. In fact, if calculations are costly, decision theory seems to say that one should never calculate expected utilities.

New server

I've moved all my websites to a new server. Let me know if you notice anything that stopped working. (Philosophy blogging will resume shortly as well.)

Overlapping acts

I'm currently teaching a course on decision theory. Today we discussed chapter 2 of Jim Joyce's Foundations of Causal Decision Theory, which is excellent. But there's one part I don't really get.

Philosophical models and ordinary language

A lot of what I do in philosophy is develop models: models of rational choice, of belief update, of semantics, of communication, etc. Such models are supposed to shed light on real-world phenomena, but the connection between model and reality is not completely straightforward.

Beliefs, degrees of belief, and earthquakes

There has been a lively debate in recent years about the relationship between graded belief and ungraded belief. The debate presupposes something we should regard with suspicion: that there is such a thing as ungraded belief.

Validity judgments

Philosophers (and linguists) often appeal to judgments about the validity of general principles or arguments. For example, they judge that if C entails D, then 'if A then C' entails 'if A then D'; that 'it is not the case that it will be that P' is equivalent to 'it will be the case that not P'; that the principles of S5 are valid for metaphysical modality; that 'there could have been some person x such that actually x sits and actually x doesn't sit' is an unsatisfiable contradiction; and so on. In my view, such judgments are almost worthless: they carry very little evidential weight.

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?

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