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:
- Possibly, none of the actual members of x's species exist (in the timeless sense), but there is some member of x's species.
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.
The above account does, however, entail the following metaphysical principle:
- 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.
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:
- A pair of photons p1 and p2 jointly have the power of producing an electron.
- 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.
- 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 ....
This is all too messy, but maybe mess is unavoidable.