In his “New Work for a Theory of Universals”, David Lewis discusses Michael Devitt’s defense of Ostrich Nominalism in his article “‘Ostrich Nominalism’ or ‘Mirage Realism’?”, specifically as a response to the One Over Many argument. Devitt had proposed to paraphrase such sentences as
“a and b have the same property, F-ness”
“a and b are both F”
which itself can be analyzed as
“a is F”
“b is F”.
Lewis thinks that this is not satisfactory. He says:
But Devitt has set himself too easy a problem. If we attend to the modest, untransformed One over Many problem, which is no mirage, we will ask about a different analysandum:
a and b have some common property (are somehow of the same type)
in which it is not said what a and b have in common. This less definite analysandum is not covered by what Devitt has said.
I think there is an obvious paraphrase of Lewis’ example which, though not explicitly covered by what Devitt had said, is in perfect harmony with its spirit. Indeed, I think it’s obvious enough that it's probable someone else has already thought of it, which for a while made me hesitant to make this post. Nevertheless, I’m interested to see if others think the paraphrase works, so I’m posting this anyway, even if I can’t claim originality for it. The paraphrase goes like this (where F, G, H, etc., are all the predicates expressible in the language):
((Fa & Fb) v [(Ga &Gb) v (Ha &Hb)])…
Or, in English:
Either a and b are both F or a and b are both G or a and b are both H…
So my question is: Do you think the paraphrase works? And if not, why not?