even if we grant that both properties are necessarily coextensive. (The atheist has an
easier time with this puzzle.)
A plausible account of the notion of priority explicates it in terms ofintensiveness
and naturalness. Say that property F is at least asintensiveas G if and only if the set of
possible and actual instances of G is a subset of the possible and actual instances of F.
(IV1): Property P obtainsin virtue ofproperty Q obtaining = df. P and Q both
obtain; P is at least as intensive as Q and Q is more natural than P.^18The tricky cases we’ve discussed are ones in which the relevant properties are at least
as intensive as each other, i.e., are necessarily co-extensional. In such cases, IV1 says
the sole factor that determines which property is prior is which is more natural. More
formally:
- If two properties P1 and P2 are necessarily co-extensional and P2 obtains in
virtue of P1 obtaining, then P1 is more natural than P2.
The properties that concern us here arenaturalnessanddegrees of beingand we are
considering the hypothesis that
- Naturalnessanddegrees of beingare necessarily co-extensional, but one of
them obtains in virtue of the other obtaining.^19
It follows from premise 1 and 2 that
- One ofnaturalnessanddegrees of beingis more natural than the other.
But which is more natural?
- If one ofnaturalnessanddegrees of beingis more natural than the other, then
naturalnessis more natural thandegrees of being.
I don’t have much to say in favor of premise 4, but isn’t naturalness just intuitively
more likely to be natural than any competitor to it?
∴ Sonaturalnessis more natural thandegrees of being.This argument is interesting. However, it can be resisted. Note that the champion of
degrees of being needn’t accept IV1. Instead, she should accept:
(IV2): Property P obtains in virtue of property Q obtaining = df. P and Q both
obtain; P is at least as intensive as Q; Q is more real than P.(^18) This is not to say that it is the best account of priority. Perhaps an electron does not have the property
being such that there are infinitely many prime numbers in virtue of being negatively charged. We’ll have
more to say about priority in chapter 8; for now, let this account of priority suffice to illustrate the point
here. And so much the worse for the argument that naturalness is prior to degrees of being if this kind of
account of priority fails. Thanks to Alex Skiles for discussion here. 19
Here I am using both“naturalness”and“degrees of being”to designate the relevant quantitative
properties. We could run similar arguments using specific amounts of these quantities as well.