The Frege–Church ontology is an ontology, a theory of existence. Everything is considered as being in three categories, object (referent, denotation), name, or concept (sense). The ontology was developed by Alonzo Church based on ideas of Gottlob Frege to resolve some paradoxes. The ontology is related to certain modal logics.

Paradox of the name relationship

However, Mary does not believe that Pluto is Neptune, a paradox. The Frege–Church ontology resolves this by saying the belief introduces an "intensional context" whereby the terms following the words "believes that" are in a context whereby they refer not to the denotation of the words, but to the concept associated with the words for the believer. Each word has a name, a denotation, and a concept associated with it.

Terminology

Propositions, properties, and relationships

Object, name, concept

Resolution of the paradox of the name relationship using the Frege–Church ontology

Ambiguities in ordinary language lead to confusion

Intensional context

Resolution

“The farthest planet from the sun”, as it appears in proposition (1) is Mary’s concept of “the farthest planet from the sun”, not about the actual farthest planet from the sun as it appears in (2), so the substitution cannot be done. A more rigorous and formal treatment of this is given by Church.