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[1] based on ideas of Gottlob Frege[2][3] to resolve some paradoxes. The ontology is related to certain modal logics.

Paradox of the name relationship

If x=y and y=z, then substituting z for y, x=z.
(1) Mary believes that Pluto = the farthest planet from the sun.
(2) Neptune = the farthest planet from the sun.
Therefore, substituting ‘Neptune’ for ‘the farthest planet from the sun’ in (1), we get
(3) Mary believes that Pluto = Neptune.

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.[4]

References

  1. Church, Alonzo. "A Formulation of the Logic of Sense and Denotation." In Structure, Method and Meaning: Essays in Honor of Henry M. Sheffer, edited by P. Henle, H. Kallen and S. Langer, 3- 24. New York: Liberal Arts Press, 1951.
  2. Gottlob Frege. "Über Sinn und Bedeutung" in Zeitschrift für Philosophie und philosophische Kritik 100: 25-50. Translation: "On Sense and Reference" in Geach and Black (1980).
  3. Gottlob Frege. "Über Begriff und Gegenstand" in Vierteljahresschrift für wissenschaftliche Philosophie 16: 192-205. Translation: "Concept and Object" in Geach and Black (1980).
  4. Church, Alonzo. "A Formulation of the Logic of Sense and Denotation." In Structure, Method and Meaning: Essays in Honor of Henry M. Sheffer, edited by P. Henle, H. Kallen and S. Langer, 3- 24. New York: Liberal Arts Press, 1951.
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