The Frege–Church ontology is an

ontology In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities exi ...

, a

theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be ...

existence Existence is the ability of an entity to interact with reality. In philosophy, it refers to the ontological property of being. Etymology The term ''existence'' comes from Old French ''existence'', from Medieval Latin ''existentia/exsistentia' ...

. Everything is considered as being in three categories,

object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...

( referent, denotation), name, or

concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by ...

(

sense A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli. (For example, in the human body, the brain which is part of the central nervous system re ...

). The ontology was developed by

Alonzo Church Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scien ...

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. based on ideas of

Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic ph ...

Gottlob Frege. "Über Begriff und Gegenstand" in ''Vierteljahresschrift für wissenschaftliche Philosophie 16'': 192–205. Translation: "Concept and Object" in Geach and Black (1980). to resolve some

paradoxes A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

. The ontology is related to certain modal logics.

Paradox of the name relationship

*Suppose we are in the year 1995. Suppose Mary believes that Pluto (at the time still considered a planet) is the farthest planet from the sun. Because of Pluto’s irregular orbit, the orbit of Pluto crossed the orbit of Neptune, so that in 1995, the farthest planet from the sun is Neptune. Suppose Mary does not know this fact. : 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

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

*An object has properties. A banana has the property of being yellow. *A

proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

is a sentence that is either true or false. A proposition can be considered to be a

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

, with

objects Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...

in it considered as variables, and the value of the function being either

truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as belie ...

falsity Deception or falsehood is an act or statement that misleads, hides the truth, or promotes a belief, concept, or idea that is not true. It is often done for personal gain or advantage. Deception can involve dissimulation, propaganda and sleight o ...

, a

truth function In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly o ...

. For example, write “''x'' is yellow” as ''Y''(''x''), so that ''Y''(''x'') = Truth, if and only if “''x'' is yellow” is true, and ''Y''(''x'') = Falsity if and only if “''x'' is Yellow” is false. For example, ''Y''(banana) = Truth, since a banana is yellow. However, ''Y(''apple) = Truth also, since some apples are yellow. *Similarly a sentence expressing a relationship between two objects can be considered a truth function of two variables, that is, a relationship between two objects can be considered to be a truth function of two variables. For example, let ''S''(''x'', ''y'') = “''x'' is smaller than ''y''”. So S(mouse, elephant) = truth, since a mouse is smaller than an elephant, but S(mouse, ant) = Falsity, since a mouse is not smaller than an ant.

Object, name, concept

*An object (referent, denotation) has a name, the name of the object. The object has a concept (sense), the concept of the object, associated with the name of the object. A name or concept are themselves objects, and have names, the name of the name of the object, and the name of the concept of the object. Similarly they have concepts as any other object. A name is said to

denote In linguistics and philosophy, the denotation of an expression is its literal meaning. For instance, the English word "warm" denotes the property of being warm. Denotation is contrasted with other aspects of meaning including connotation. For in ...

the object for which it is the name.

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

Ambiguities in ordinary language lead to confusion

*The English

ordinary language Ordinary language philosophy (OLP) is a philosophical methodology that sees traditional philosophical problems as rooted in misunderstandings philosophers develop by distorting or forgetting how words are ordinarily used to convey meaning in ...

has ambiguities that need to be clarified as we sometimes refer to an object with a word, e.g., a cat. We refer to the name by using scare quotes, the name of the cat, e.g., the word “cat”. There is ambiguity in the language as regards referring to the cat as a concept, and cat as an object.

Intensional context

*An expression such as “believes that” is said to introduce an intensional context. In an intensional context, the names that occur denote the concepts of the objects for the believer. They do not denote the objects themselves.

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.

References

External links

* {{DEFAULTSORT:Frege-Church ontology Ontology Modal logic