Frege–Church ontology

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.

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.

“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.

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