Wednesday, December 3, 2008

Two problems for conspecificity as primitive

Here is something growing out of last night's neo-Aristotelian metaphysics class with Rob Koons. Suppose we take the relation of conspecificity as a primitive, in order to be a nominalist about species. (The context here is Aristotelian, so "species" may include "Northern leopard frog", but it may also include "electron".) Then we will have a hard time making sense of claims like:

1. Possibly, none of the actual members of x's species exist (in the timeless sense), but there is some member of x's species.
Suppose for instance x is an electron. Then, surely, there is a possible world where there are electrons, but none of the actual world's electrons exist. But to make sense of (1) on an account that takes conspecificity to be primitive would require a conspecificity relation between an electron in the actual world and an electron in the possible world. But how can there be a relation one of whose relata does not exist? (Intentional relations are like that, but I don't think we want conspecificity to be like that.) The realist about species doesn't have this particular problem. She just explains (1) by saying that if s is the species of x, then possibly none of the actual members of s exist but s nonetheless has a member. Also, if one takes conspecificity as primitive but allows the existence of non-actual individuals, the problem disappears, since then we can unproblematically relate a non-actual individual with an actual one.

The problem here is that of interworld conspecificity. What makes an individual a1 in a world w1 conspecific to an individual a2 in w2? If there is an individual a2 in w1 conspecific to a1 who also exists in w2 and is conspecific to a2, by transitivity of (Aristotelian) conspecificity this is not a problem. We can generalize this solution by saying that a1 in w1 is conspecific to a2 in w2 provided that there are chains of worlds W1,...,Wn and entities A1,...,An such that

• W1=w1, Wn=w2, A1=a1, and An=a2
• bi is in both Wi and in Wi+1 for i=1,...,n−1
• bi and bi+1 are conspecifics in Wi+1 for i=1,...,n−1.
For this approach to give a good account of interworld conspecificity it has to be the case that conspecificity is transitive and that species membership is essential. (But the approach can also work if species membership is not essential, as long as we have individual forms, and the membership of an individual form in a species is essential. For then we can give the story not in terms of chains of particulars, but chains of individual forms.)

The above account does, however, entail the following metaphysical principle:

1. Whenever worlds w1 and w2 contain individuals a1 and a2 who are members of species s (understood nominalistically), then there is a finite chain of possible worlds, starting at w1 and ending at w2, such that every pair of successive members of the chain has a common member of s.
Is (2) true? Well, it seems hard to come up with counterexamples to it, at least. If we could imagine a species whose possible members could be divided into two classes, A and B, such that no member of A could exist in a world that contains a member of B, then we would have a violation of (2). But I am not sure we have much reason to think such species exist.

But now consider a different problem for the account. Two photons can collide and produce an electron-positron pair. Suppose we are in a world where there are lots of photons, but only one collision has occurred, producing electron e (and a positron that I don't care about). We now want to be able to say this:

1. A pair of photons p1 and p2 jointly have the power of producing an electron.
Presumably this should reduce to some claim about how they have the power of producing a conspecific to e. But that is an extrinsic characterization of the power of the photons. Yet it is an intrinsic feature of the joint power of p1 and p2 that it is a power to produce an electron (and a positron). Moreover, supposing that no collisions occurred, and hence there was no e in sight, we would still want to be able to say this:
1. A pair of photons p1 and p2 jointly have the power of producing a conspecific to something that photons p3 and p4 jointly have the power of producing.
Tricky, tricky. Here is a suggestion. We slice powers, considered as particulars ("x's power to do A") finely enough that we can talk of a particular power that p1 and p2 jointly have (or maybe one has the power to operate on the other in some Aristotelian way), the power of producing an electron (this power can only be exercised together with a power to produce a positron). Now, we can talk of the primitive conspecificity not just of particles, but of productive powers, and we can characterize the conspecificity of two entities disjunctively:
1. e1 and e2 are conspecific (non-primitively) if and only if either e1 and e2 are primitively conspecific or e1 results from the exercise of a power primitively conspecific to a power the exercise of which results in e2 or e1 results from the exercise of a power which results from the exercise of a power primitively conspecific to a power the exercise of which results in a power the exercise of which results in e2 or ....
Assuming that powers are characterized by what they produce, any disjunct further down in the disjunction entails all the disjuncts further up in the disjunction. Now we can make sense of (3) and (4) in an intrinsic way, in terms of the conspecificity of the powers of producing electrons. Moreover, we can make the chain-of-worlds move as needed for non-primitive conspecificity. This will yield a very complicated analogue of (2), but that analogue will, if anything, be even more plausible than (2).

This is all too messy, but maybe mess is unavoidable.