Three theories of nominalized predicates (Q1073011)

This paper surveys some formal systems which can be used to model nominalization in natural language. (I.e., the process which turns predicates ('love', 'divine') into individual concepts for these ('to love', 'divinity').) The challenge is to do this while avoiding conflicts of cardinality between the sets of individuals and predicates - and at the same time, maintaining as strong Comprehension principles as possible. First, a Fregean logic with Quinean stratification is considered (due to Cocchiarella), then a three-valued Aczel-Feferman type-free logic, and finally - the author's favourite - a classical version of the latter in the Feferman-Gillmore format. It is shown that the latter has models by a domain construction similar to Scott's modelling of the type-free lambda calculus.