I've thought a bit about belief update recently. One thing I noticed is that it is often assumed in the literature (usually without argument) that if you know that there are two situations in your world that are evidentially indistinguishable from your current situation, then you should give them roughly the same credence. Although I agree with some of the applications, the principle in general strikes me as very implausible. Here is a somewhat roundabout counter-example that has a few other interesting features as well.
I'm away from the internet until January 15.
Sometimes, a property A entails a property B while B does not entail A, and yet there seems to be no interesting property C that is the remainder of A minus B. For instance, being red entails being coloured, but there is no interesting property C such that being red could be analysed as: being coloured & being C. In particular, there seems to be no such property C that doesn't itself entail being coloured.
This fact has occasionally been used to justify the claim that various other properties A entail a property B without being decomposable into B and something else. I will try to raise doubts about a certain class of such cases.
Daniel Nolan and I once suggested that talk about sets should be analyzed as talk about possibilia. For simplicity, assume we somehow simply replace quantification over sets by quantification over possible objects in our analysis. This appears to put a strong constraint on modal space: there must be as many possible objects as there are sets.
But does it really? "There are as many possible objects as there are sets." By our analysis, this reduces to, "there are as many possible objects as there are possible objects". Which is no constraint at all!
As a principle of plentitude, Recombination for Individuals is far too weak. If there happens to be nothing that is both red and dodecagonal, the recombination principle for individuals gives us no world where anything is. Likewise, if it happens that no red thing is on top of a blue thing, the principle gives us no world where this is different. But combinatorial reasoning seems to give us such worlds.
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.
