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.
Here's something puzzling. Suppose sometime in 1869, Frege uttered
1) more people today die of tuberculosis than of cancer.
As far as I know, this was true in 1871, but it is no longer true now. Today, more people die of cancer than of tuberculosis. On the other hand, suppose Frege also uttered
2) I am not particularly well-known among philosophers.
This, too, is no longer true. Today, Frege is exceptionally well-known among philosophers.
Everyone who has taught Kripke and Putnam to undergraduates knows that philosophers nowadays use "truth at a world" in a special, technical sense that requires a lot of explaining. The most straightforward way to assign a sentence a truth value at another world w is to consider an utterance of the same words in w and ask whether or not that utterance is true. But this is not what we mean. Nor do we ask what truth value the sentence has conditional on the assumption that our world is w. (Lewis uses "truth at a world" in roughly this sense in "How to define theoretical terms"; the current convention appears to be really quite new.) What, then, do we mean? I find most introductions of the concept utterly obscure: I'm told to identify the 'proposition expressed' by a sentence in the actual world, and then to 'evaluate' this entity at another possible world. What on earth does that mean?
Apparently, there's a Chinese park charging people to have pictures with a Dretske-style fake zebra. The experiment reveals the underappreciated role of fun in epistemology:
"We saw right away that the zebra is fake, but we are here for fun, so it doesn't really matter," said a mother who had just paid for her child's picture.
According to the City Evening News, the park says it doesn't know if the horse is a zebra or not: "It's not that important. It is for fun," said a spokesman.
Somewhat related to the Most Certain Principle is the following constraint on semantic content:
Same-Saying Constraint: if A utters a sentence S1,
and B utters a sentence S2, then they say the same thing iff
S1 and S2 have the same content.
"Saying the same thing" is here obviously not meant as "saying something with the same content". That would make the constraint empty. Rather, it's supposed to be an intuitive, pre-theoretic notion.
Cresswell calls this the Most Certain Principle:
MCP: if we have two sentences A and B, and A is true and B is false, then A and B do not mean the same.
Last year, I thought that this principle was most certainly false: if I say something true that is false at another world w, and somebody in w says something with the same content, then our utterances mean the same while they differ in truth value. To quote myself,
I believe that there is such a property as being two meters away. -- Not two meters away from me, or from somebody else, or two meters away from something or other. Just two meters away.
Admittedly, there is a sense in which something can be two meters away only relative to some point of reference. But compare properties like being empty and being bent. There is a sense in which, strictly speaking, persisting things can be empty or bent only relative to a time: this cup here is empty at the present time while it was full 5 minutes ago. Likewise, at least prima facie many things are empty or bent only relative to worlds: the cup is empty at the actual world, but full at other possible worlds. That's why properties are often modeled as something like functions from worlds and times to sets of objects.