In this model the collection of all subsets of the set of natural numbers (represented by predicates) is of cardinality ω1 and is similar to the ramified hierarchy.
According to this notion, reductionism means that the properties expressed by the predicates of (say) a psychological theory are identical to the properties expressed by the predicates of (say) a neurological theory — in other words, this version of reductionism is in essence a version of type physicalism or the identity theory.
First-level probabilities involve infinite sequences; the ordered sets referred to by the predicates of probability implications.
It is thus doubtful that the inadequacy of Descartes' identification of body with extension can be overcome simply by predicating regions of extension with different "power".
In what Nishida alternatively called the logic of objects or subjective logic, objects of consciousness are made the grammatical subject of propositions or judgments, and are specified by predicating properties of the subject.
For instance, having learned how to use the term 'horse' by predicating it of the white horse and black horse owned by his family, a child might then "proceed" to further apply it to an unfamiliar brown horse passing by in the road.
If a wff of LPC is considered as a proposition form, instances of it are obtained by replacing all free variables in it by predicates or by names of individuals, as appropriate.
A version of underdetermination that might threaten realism would thus assert that our postulated complete global theory of the world will have empirically equivalent alternatives with no translation from one to the other being possible, i.e. that we cannot obtain one from the other by reconstruing the predicates of the theory.
In an epistemological sense, finally, as predicative concepts expressed by the predicate of a proposition that are connected with the concept expressed by the subject of the proposition into a thought expressed by the proposition itself, transcendentals are concepts that cannot be analyzed by taking recourse to a still higher genus and are, therefore, first known, self-evident, and primitive.
Such an extension faces problems analogous to those faced by truth-relativists about predicates of personal taste (cf. Beebe (2010) for a helpful discussion of truth-relativist semantics versus varieties of contextualist competitors).
