Here is Lewis's 1996 analysis of knowledge:
S knows proposition P iff P holds in every possibility left uneliminated by S's evidence. ("Elusive Knowledge", p.422 in Papers)
By evidence, Lewis explains, he means perceptual experiences and memories; a possibility W counts as eliminated iff the subject does not have the same evidence in W: "When perceptual experience E (or memory) eliminates a possibility W [...], W is a possibility in which the subject is not having experience E" (424). It follows that everyone trivially knows what perceptual experiences they have: In every possibility W in which I have experience E, I obviously have experience E.
Many versions of the recombination principle are floating
around in the literature. Most of them are principles for individuals,
saying, roughly, that you get a possible world by patching together
(copies of) arbitrary parts of other possible worlds. (I will have
more on principles for properties later.)
It is surprisingly difficult to make this precise. All attempts I
know of fail in one way or another. To illustrate some of the
pitfalls, let's begin with this classic version from Daniel Nolan's
"Recombination Unbound".
Hello, I've been away from philosophy and the internet for a while. Now I'm back in Canberra, where there's fortunately not much else to do.
I've been hiking in the Italian Alps for a week. We had great weather, even featuring snow. Will be back in Berlin soon, searching for a new flat and trying to catch up with my email.
Does the semantic value of expressions in a language sometimes depend on other things than their utterance context? That depends on what is meant by "semantic value", but for the most part, I think not.
It can appear otherwise if one identifies the content of an utterance with the main proposition it conveys to competent hearers.
Alice, Bob and Carol are searching for honey. Alice sees a bee hive on a tree near Bob and wants to inform both Bob and Carol about this. That is, she wants Bob to acquire the self-locating belief that there is a bee hive on the tree near him, and she wants Carol to acquire the belief that there is a bee hive on the tree over there near Bob. She achieves both goals simultaneously by pointing at the relevant tree and saying, "there's a bee hive on the tree over there".
Since Alice conveys two different (centered) propositions to Bob and Carol with her sentence, one might conclude that her sentence expresses two different contents, one relative to Bob's context of assessment and one relative to Carol's. Content, then, is relative to both an utterance context and an assessment context. However, it is quite implausible that Alice's utterance really has these two propositions as its literal semantic value. Instead, what she expressed was just the proposition that there is a bee hive on the tree she is pointing at, and Bob and Carol figured out the centered propositions they were meant to learn from this information.
After nine good months in Canberra (and a couple of conferences in Sydney and Armidale), I'm back in Berlin -- awaiting unemployment, homelessness and death. I'll probably be somewhat slow catching up with emails since I don't have electricity at home. (Nor gas or water, for that matter. At least I've been warned.)
Let F be a fundamental property, understood as a maximal class of possible things that are perfectly similar in one respect. (This is one of Lewis's four proposed definitions of fundamental properties, and I think the best one.) And suppose I have F. What would it take to know that I have F?
Given that F is some class { Wo, Fred, ... }, and given that having F means being a member of F, it might seem puzzling how I can be ignorant about whether or not I'm F: how could I fail to know that I am a member of { I, Fred, ... }? But here we are substituting corefering expressions in a (hyper)intensional context, which is illegitimate. If I knew that F = { I, Fred, ... }, then I probably ought to know that I am F. So if I don't know that I am F, that's because I don't know that F = { I, Fred, ... }.
Some properties are inherited from wholes to their parts: if x is (completely) made of steel, then its parts are also (completely) made of steel; if x is in the top drawer, then its parts are also in the top drawer. Other properties are upwards inherited from parts to wholes: if a part of x contains steel, then x contains steel; if a part of x touches the ground, then x touches the ground. Yet other properties are not inherited either way: if x is a hand, then x usually has non-hands as parts and is part of non-hands.
Following up on Weng-Hong (1, 2, 3), here are a few thoughts on thresholds for belief.
If beliefs come in different degrees or strength, what do we mean when we say not that Fred believes that P with strength x, but simply that Fred believes that P? Perhaps we mean that Fred believes that P with sufficient strength, where context may help determining what counts as sufficient. However, on this account, the following principles should be obviously invalid (both descriptively and normatively):
Let's call the class of counterfactual circumstances at which a sentence S is true the C-proposition expressed by S. This is more or less what Kaplan calls the "content" of S. Here are three reasons why the circumstances constituting a C-proposition should be understood as centered possible worlds rather than old-fashioned uncentered worlds.
First reason: centering is needed for modal embeddings. The standard use of C-propositions is the analysis of modal constructions: "it is possible that hummingbirds can fly backwards" is true iff there is at least one relevant circumstance w at which "hummingbirds can fly backwards" is true. Now take a sentence such as "it is early afternoon", or "it is starting to rain". It doesn't make much sense to say of an entire world that it is early afternoon there, or starting to rain. So on the standard view, on which the circumstances in C-propositions are uncentered worlds, we first have to fix a time and place, presumably by drawing on the utterance context: "necessarily, it is early afternoon" is true iff it is early afternoon at every possible world at the time and place of the utterance. So "necessarily, it is early afternoon" is true whenever it is uttered on an early afternoon. That seems wrong.
