Wolfgang Schwarz

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Away

I'm away from the internet until January 15.

Property Subtraction

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.

Analytic constraints

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!

The Principle of Recombination for Properties

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.

Lewis on knowing one's evidence

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.

The Principle of Recombination for Individuals

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".

Back

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.

Bergell

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.

Assessment-relativity and pretended dialogs

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.