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"):
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.
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.
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
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.
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.
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.
Decision theoretic representation theorems show that one can read off an agent's probability and utility functions from their preferences, provided the latter satisfy certain minimal rationality constraints. More substantive rationality constraints should therefore translate into further constraints on preference. What do these constraints look like?
In On the Plurality or Worlds, Lewis argues that any account of what possible worlds are should explain why possible worlds represent what they represent. I am never quite sure what to make of this point. On the one hand, I have sympathy for the response that possible worlds are ways things might be; they are not things that somehow need to encode or represent how things might be. On the other hand, I can (dimly) see Lewis's point: if we have in our ontology an entity called 'the possibility that there are talking donkeys', surely the entity must have certain features that make it deserve that name. In other words, there should be an answer to the question why this particular entity X, rather than that other entity Y, is the possibility that there are talking donkeys.
Noam Chomsky's New Horizons in the Study of Language and Mind contains a famous passage about London.
Referring to London, we can be talking about a location or area, people who sometimes live there, the air above it (but not too high), buildings, institutions, etc., in various combinations (as in 'London is so unhappy, ugly, and polluted that it should be destroyed and rebuilt 100 miles away', still being the same city). Such terms as 'London' are used to talk about the actual world, but there neither are nor are believed to be things-in-the-world with the properties of the intricate modes of reference that a city name encapsulates. (p.37)
I don't know what Chomsky is trying to say here, but there is something in the vicinity of his remark that strikes me as true and important. The point is that the reference of 'London' is a complex and subtle matter that is completely obscured when we say that 'London' refers to London.
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