Thursday, April 16, 2015

Essence and Hyperintensionality

The essence of something is the truthmaker of the real definition of the thing. So, to know what the essence of something is is to know its real definition. For instance, to know the essence of man is to know the proposition that man is a rational animal. This is traditionally thought to be the real definition of 'man'.

Here is the general schema for a real definition:
  • S ise an F.
'S' is replaced by some kind-term (or maybe even individual-term?), the thing to be defined, and 'F' with some predicate, the definiens. The 'is' here is a special kind of 'is': the 'is' of real definition or essence. The conditions that have to be met for something to bee F are much more strict than for something to be F in other senses of 'be' (such as the more general sense of 'is', the 'is' of predication).

(Side-note: In some contexts is this a schema for reduction too? Interesting...)

Real definitions are 'fine-grained'. You cannot always substitute extensional equivalents into the predicate position to get the same truth value. For instance, suppose all and only the actually existing rational animals are animals which evolved by a certain evolutionary process P on earth. Even if this so, the following is not true:
  • Man ise an animal which evolved by process P on earth.
After all, man could have evolved in some other way, or even not at all. Man could have randomly popped into existence. So it's certainly not part of the very definition of man that he evolved by a certain evolutionary process.

So real definitions are fine-grained. In fact, real definitions are very fine-grained; you cannot even substitute intensional equivalents into the predicate position and always retain the same truth value. Suppose for instance that, necessarily, any animal which is rational is the type of thing which can speak a language. This actually seems pretty plausible. (If not, think of some other necessary consequence of being rational. You could even use some fancy disjunctive, conjunctive, or conditional properties, though I try to avoid these.) Even if this is so, the following is not true:
  • Man ise an language-capable animal.
At least, it's not true when we're talking about the 'is' of real definition. For this doesn't get to the heart of what man is; it's not what he is at the most fundamental level, but rather something he happens to be.

So, the predicate position in real definitions is a hyperintensional position, in the sense that substitution of intensional equivalents will not always preserve the same truth value. I take it these points cohere well with what has been said about real definition and essence up to now by others, such as Fine.

In the next post, I'll try to say something about how the hyperintensionality in real definitions means that counterpossibles will be very closely related to real definitions. Maybe this will help, at least a little, with the epistemology of essence.

Lately I have been suspecting that hyperintensionality, counterpossibles, essence, explanation, grounding, reduction, fundamentality, naturalness, intrinsicality, and lots of other things are very closely related. In the future I'd like to try to bring out some of these relationships. I'm not sure how successful this will be, but my metaphysical nose is leading me in this direction.

Friday, April 10, 2015

Modal Realism and the Serviceability Argument

Here's a quote from David Lewis: "Why believe in a plurality of worlds? -- Because the hypothesis is serviceable, and that is a reason to think that it is true."

Question for David Lewis and other modal realists: Lots of worlds are serviceable, not just the metaphysically possible ones. Many times when we do semantics, discuss language, give thought experiments, etc., worlds which are strictly logically possible but not metaphysically possible are helpful. For example, one of the ways that intensional semantics deals with oblique transitive verbs, control verbs, etc. is by invoking worlds where, for instance, water is not H2O, or where Hesperus is not Phosphorus. Presumably these are not metaphysically possible worlds, but rather 'logically' possible worlds. (Sometimes metaphysically possible worlds are called 'broadly' logically possible worlds; by 'logically' possible worlds I mean what are sometimes called 'strictly' logically possible worlds.)

Do these exist too, in exactly the same way as the metaphysically possible ones? If yes, then we run into problems. After all, isn't it only the metaphysically possible worlds which can exist? If not, then what is the distinction between metaphysical possibility and mere logical possibility supposed to mean? In fact, if merely logically possible worlds exist just like the metaphysically possible ones then there is no distinction. But there is, of course, a distinction.

At the very least, aren't the metaphysically possible worlds the only ones which could be actual? But if 'actual' is indexical as Lewis thinks, and the logically possible worlds exist on a par with the metaphysically possible ones, then any of these worlds could be actual.

Personally, I think there's just as good reason to admit the existence of logically impossible worlds as there is to admit the existence of possible worlds (though I don't think there's much reason to admit the existence of either).  If we really needed possible worlds, I think we'd need impossible ones too. But if logically impossible worlds are serviceable too then that makes things even worse for the modal realist. After all, what would it mean to say that a logical contradiction actually holds true in a concrete world just like ours? Clearly there are no such concrete worlds, since whatever concretely exists must at least be possible. But even if one resists the need for impossible worlds, the metaphysically possible worlds are a proper subset of the strictly logically possible ones, and it should be clear that these latter are "serviceable" too.

In sum, if Lewis's argument works for the existence of concrete metaphysically possible worlds, then it works for the existence of metaphysically impossible worlds too. But these can't exist concretely; that's the whole point of making some metaphysically possible and others not. Hence, Lewis's argument does not work. This can be taken as either reason to abandon the 'serviceability' criterion of existence, or as reason for rejecting concrete possible worlds. I'm inclined to reject both.