The problem of one over many: Lewis vs Armstrong
The problem of one over many poses the challenge of explaining the Moorean fact of sameness of type: how can it be possible that two different particulars share something? For Armstrong, no nominalist theory can offer a correct resolution to this problem because it fails to fulfil a constraint of no-regress, which requires that each predicate should be analysed for any sentence. Armstrong thinks he can account for the Moorean facts while satisfying the constraint. According to him, two different particulars resemble each other because they both instantiate a common universal. Lewis is uncongenial with Armstrong’s answer to the one over many problem. To reach this result, Lewis says, Armstrong demands to satisfy an unreasonable constraint as no theory can yield an analysis of each predicate for any sentence.