Here is the general schema for a real definition:
- S ise an F.
(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.
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.
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.