So here’s an Aristotelian puzzle that I do not know how to sort out. It has apparently been reinstated, or a version of it, by Fine. I believe he did not even present it as a puzzle. Anyway, take a look at it, and help me solve it. Otherwise, I’m lost (and so is my paper).
Suppose you believe that properties are the set of their instances. Suppose, furthermore, that you are a modal realist. Aristotle was not, but he does believe in potential and actual bearers of properties, and he does think these are within the extension of a property [Meta, V.26].
In any case, there is a familiar problem with this view: coextensive properties. ‘renate’ and ‘chordate’ have the same actual extension, yet they are different properties. The solution is easy and well known: ‘renate’ and ‘chordate’ are not coextensive because they have different extensions in other possible worlds. Aristotle’s reply would be similar: ‘renate’ and ‘chordate’ are not coextensive because they have different potential instances.
The problem comes with a twisted version of this objection. Suppose you have necessarily coextensive properties, and yet distinct ones. (This is what Fine presents in his ‘famous’ paper against modal accounts of ‘essence’, where he claims ‘essential property’ is not synoymous with ‘necessary property’, I think, however, that Aristotle’s example is better). Aristotle talks about ‘Grammarian’ and ‘Human’. According to Aristotle, this much is true:x is human iff x is a grammarian (or has knowledge of grammar). Yet, ‘Human’ reveals the essence of its instances, and ‘grammarian’ does not.
My question is this: is there any way in which one can sort this case out, and still be extensionalist about properties? Do you know of any extensionalist reply to this? Or should we simply claim that ‘grammarian’ and ‘human’ have the same meaning?