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Abstract and Concrete

What do types, sets, universals, increases, theorems, species and governments have in common that distinguishes them from sticks, stones, mountains, molecules and cities? It's not that only the latter are causally efficacious: on many accounts (e.g. those of Lewis and Kim), events -- the paradigm examples of causal efficacy -- are sets; and why shouldn't one say that if a thing's being charged produces an effect, Charge (the universal) is just as much responsible for this as the thing itself? It's also not that only the latter are located in space or time: impure sets, species, Aristotelian universals and governments arguably are spatiotemporally located as well. And by the Helen Cartwright Theorem Theorem, theorems are sometimes written on blackboards. Indeed, I'm not sure whether anything at all clearly fails to be located in time, unless we require that something located in time must undergo intrinsic change or have a beginning or an end, which sounds ad hoc. Without such restrictions, I can't see a reason to deny that e.g. numbers exist at every time. (Oddly, I'm less inclined to say that numbers exist everywhere. But I might get used to it.)

Unhelpful Trees

Today I wondered about the connection between

Under certain ideal conditions, something is conceivable iff it is possible

and

Something is possible iff it is conceivable under certain ideal conditions.

So I asked my tree prover whether

1)  for all y(Iy then  for all x(Px iff Cxy)) then  for all x(Px iff  for all y(Iy then Cxy))
and
2)  for all x(Px iff  for all y(Iy then Cxy)) then  for all y(Iy then  for all x(Px iff Cxy)).
The answer to the first question is "not valid (1764 nodes, 84 open branches)". For the second question I manually stopped the prover at "79623 nodes, 727 unticked, 35844 open branches, 18 constants". Clearly, these results are not very helpful.

Strike Asylum

Entering the philosophy library of Humboldt University got rather unpleasant two weeks ago when a couple of students decided to occupy the building as a kind of protest against planned cuts and tuition fees and capitalism and whatever. I partly support their aims (though I think cuts in the philosophy department would be quite appropriate, given its quality, and I certainly don't want any more 'democratization' of the university), but I don't see how occupying the buildings and keeping me away from doing philosophy is a good way to achieve these aims. Anyway, I'm now in Bielefeld where there are no strikes. I'll probably return to Berlin on Saturday.

Modal Epistemology

Brute necessity is hard to accept, much harder than brute possibility. If someone claims that necessarily there are no purple cows, I expect an explanation. Perhaps he knows what kind of DNA is essential for cowhood and also that this kind of DNA can never produce purple beings, and he also believes that the laws of nature are necessary. This would make his claim understandable. But suppose he had no such explanation. Suppose in fact that we all know that only a minor mutation would be required to produce purple cows, a mutation perfectly compossible with the laws of nature. And still he claims that there could not be any purple cows. This would seem bizarre.

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.

Not many people believe in this account. That's surprising, because many people do believe that there are rigid designators -- terms denoting the same thing in every possible world --, and this seems to imply something that looks to me just like (an application of) the epistemic account of vagueness.

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.

No doubt there are other uses. For instance, "identity" and its cognates are often used to express sameness of kind, as in "this record is the same Jones bought last week". Sometimes, "identity" is used as a singular term for a thing's characteristc properties or individual essence, as in "the festival has lost its identity". The conceptual platitudes above do not apply to these other uses.

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.

Understood literally, this leads to a position one might call strong humeanism:

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?

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