Wolfgang Schwarz

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

Evidentialism and time-slice epistemology

Time-slice epistemology is the idea that epistemic norms are history-independent: whether an agent at a time satisfies an epistemic norm is always determined by the agent's state at that time, irrespective of the agent's earlier states.

The broken duplication machine

Fred has bought a duplication machine at a discount from a series in which 50 percent of all machines are broken. If Fred's machine works, it will turn Fred into two identical copies of himself, one emerging on the left, the other on the right. If Fred's machine is broken, he will emerge unchanged and unduplicated either on the left or on the right, but he can't predict where. Fred enters his machine, briefly loses consciousness and then finds himself emerge on the left. In fact, his machine is broken and no duplication event has occurred, but Fred's experiences do not reveal this to him.

Evidentialism, conservatism, skepticism

An evil scientist might have built a brain in vat that has all the experiences you currently have. On the basis of your experiences, you cannot rule out being that brain in a vat. But you can rule out being that scientist. In fact, being that scientist is not a skeptical scenario at all. For example, if the scientist in question suspects that she is a scientist building a brain in a vat, then that would not constitute a skeptical attitude.

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