Ordinal numbers: Not superlatives, but modifiers of superlatives

The few existing accounts of the semantics of ordinal numbers attribute to them all or almost all of the semantic properties of superlatives. This work discusses a construction problematic for existing theories of ordinals: the ordinal superlative construction (e.g. Joel climbed the third highest mountain). Existing theories give ordinals and superlatives such similar semantics that they struggle to explain how an ordinal and a superlative could join together and form a complex modifier. As an alternative, I propose a semantics according to which ordinals are exceptive modifiers of superlatives. For example, the n-th highest mountain is the mountain that, with n - 1 exceptions, is the highest. When an ordinal does not co-occur with an overt superlative (e.g. the second train), I posit a covert superlative adjective that represents the contextual ordering. Not only does this approach account for the ordinal superlative construction, but it lends itself to a principled explanation of differences between ordinals and superlatives with respect to plurality.