Krämer (2017) and Button and Trueman (Forthcoming) have argued that cumulative type theories are inconsistent with the existence of absolutely unrestricted domains of quantification. If their arguments are sound, then cumulative type theories’ expressive and deductive power is unavailable to generality absolutists. Starting with the construction of an independently motivated cumulative type-theoretic language with a complex-predicate forming operator, I show that, from the standpoint of typical higher-orderists, those arguments either: i) do not factor in the view that universal quantifiers of type-theoretic languages are sui generis rather than species of a single genus; ii) fail to appreciate the implications of variable-binding vis-à-vis the type of the properties that quantifiers apply to. I then argue that the best higher-orderist precisifications of the claims “there are unrestricted domains” and “everything is an entity” are theorems of attractive cumulative type theories.
Cumulativity and Absolute Generality
Organização: CFCUL & CFUL
Faculdade de Letras da Universidade de Lisboa, Sala Mattos Romão
29 / 06 / 2022