Wolfgang Schwarz

Rigidity and Hyper-Essentialism

According to the epistemic account of vagueness, there aren't really any vague statements: When we're uncertain whether to call somebody bald that's not because he is a borderline case of baldness. There are no borderline cases. The border between being bald and not being bald is perfectly precise. It's only that we don't quite know were it runs.

Identity, Quantum Vagueness and E.J. Lowe

Everything is identical to itself, and nothing is identical to anything except itself. No two things are ever identical. If A and B are identical then "they" are one, not two.

These are platitudes about identity, or rather about a somewhat technical use of "identity" common in mathematics and philosophy.

Strong and Weak Humeanism

Humeans distinguish between how things are in themselves and how they are related to other things. The latter, they say, is always a contingent matter: Even though this cup of tea is about 20m away from a book and stands on a table, it could very well not be 20m away from the book and not stand on the table. In slogan form, there are no necessary connections between distinct entities.

What's the Problem With Meinongianism?

Meinongians say that some things do not exist. In other words, existence is a property that befalls only some of the things there are. It follows that by 'existence' these Meinongians do not mean the trivial property that every thing whatever has. What else do they mean? Maybe they mean by 'existence' being in space or time, as Meinong sometimes does. Or maybe they mean an alleged primitive property of certain things. At any rate, I have no objection to this except that I'd rather not use the word 'existence' for that. But I can't really say that ordinary usage is on my side, given that a) ordinary quantification is almost always restricted (though not always in the same way), and b) there is hardly an ordinary usage of 'existence' at all. So far, Meinongianism is utterly trivial. It merely holds that some objects lack a certain property.

Intensions, Referents and Counterparts

Yesterday, I said that it doesn't really matter whether we regard identity simpliciter as identity-at-our world -- individuationg referents extensionally -- or as identity-at-every-world -- individuating referents intensionally. Suppose we want to do the latter, so that the referent of "the amazon" determines a function from worlds to world-bound individuals, that is, an intension. So on the present account, we identify the amazon with something that completely determines the intension of "the amazon". The intension? What if, as two-dimensionalists argue, "the amazon" has two intensions? Which one is the one we want extensions to determine?

Restricted Identity III: Too Many Solutions?

So there are several ways to make sense of restricted identities. Which is the right one? Maybe there is no fact of the matter.

The difference depends on which contexts are regarded as referentially transparent and which as opaque. And that in turn depends on how the referents are individuated. For instance, (de re) ascriptions of modal properties will be transparent iff the referents of singular terms are such that they determine the truth value of all such ascriptions, perhaps because they (the referents) are fusions of world-bound individuals with their counterparts, or because they are Carnapian individual concepts, or because they simply contain some hidden tag that determinately settles all their modal properties. At any rate, for de re modal contexts to be referentially transparent, the referents have to provide us with a function from worlds to world-bound individuals, as that's what we need to determine the the truth value of those ascriptions. Alternatively, if we hold that those contexts are referentially opaque, we decide that the referents do not contain that information. Instead, we put the information into another aspect of meaning, which we call the terms' intension. Is the difference really more than just a relabeling of semantic vocabulary?

Restricted Identity II: Analyses

Now restricted identities threaten to violate Leibniz's Law: If R1 is identical with R2, then how can they differ in their courses? If AD1 is AD2, how can they differ in their history? If A1 is A2, how can they differ in their modal properties?

Restricted Identity I: Examples

If you follow the Rhine upstream, you'll reach Reichenau in Switzerland, where its two tributaries, the Vorderrhein and the Hinterrhein, meet. As far as I know, it is undefined which of them, if any, is the Rhine. Obviously that's not a mystery but just a matter of stipulation. So let's stipulate that 'R1' is to denote the continuation of the Rhine through the Vorderrhein, and 'R2' its continuation through the Hinterrhein.

Substitutional Quantification

What's the difference between substitutional and objectual quantification? I'll use the old-fashioned round brackets for objectual quantifiers and square brackets for substitutional quantifiers. The standard interpretations are

Gödel's Ontological Proof

Let K be a class of sets such that whenever x is in K and x is a subset of y, then y is also in K. It follows that if the empty set is in K, then every set is in K. Let's rule this out by stipulating that some set is not in K. Thus every set that is in K is not empty. So instead of saying outright that some set is not empty we can instead say that it is in K, which sounds less controversial but really comes down to the same thing.