Suppose that there were only four possible properties: heat, cold, dryness and moistness. Then the Platonic-sounding sentences that trouble nominalists could have their Platonic commitments reduced away. For instance, van Inwagen set the challenge of how to get rid of the commitment to properties (or features) in:
- Spiders and insects have a feature in common.
- Spiders and insects are both hot, or spiders and insects are both cold, or spiders and insects are both dry, or spiders and insects are both moist.
- All but one property are instantiated
- Something is hot and something is cold and something is dry but nothing is moist, or something is hot and something is cold and something is moist but nothing is dry, or something is hot and something is dry and something is moist but nothing is cold, or something is cold and something is dry and something is moist but nothing is hot.
And of course there are more than four properties. But as long as there is a finite list of all the possible properties, the above solution works. But in fact the solution works even if the list is infinite, as long as (a) we can form infinite conjunctions (or infinite disjunctions—they are interdefinable by de Morgan) and (b) the list of properties does not vary between possible worlds. Fortunately in regard to (b), the default view among Platonists seems to be that properties are necessary beings.