The Frege–Church ontology is an

ontology Ontology is the philosophical study of existence, being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of realit ...

, a

theory A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...

existence Existence is the state of having being or reality in contrast to nonexistence and nonbeing. Existence is often contrasted with essence: the essence of an entity is its essential features or qualities, which can be understood even if one does ...

. 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 a ...

(

referent A referent ( ) is a person or thing to which a name – a linguistic expression or other symbol – refers. For example, in the sentence ''Mary saw me'', the referent of the word ''Mary'' is the particular person called Mary who is being spoken o ...

denotation In linguistics and philosophy, the denotation of a word or expression is its strictly literal meaning. For instance, the English word "warm" denotes the property of having high temperature. Denotation is contrasted with other aspects of meaning in ...

name A name is a term used for identification by an external observer. They can identify a class or category of things, or a single thing, either uniquely, or within a given context. The entity identified by a name is called its referent. A person ...

, or

concept A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, ...

(

sense A sense is a biological system used by an organism for sensation, the process of gathering information about the surroundings through the detection of Stimulus (physiology), stimuli. Although, in some cultures, five human senses were traditio ...

). The ontology was developed by

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

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 philos ...

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 or apparently true premises, leads to a seemingly self-contradictor ...

. The ontology is related to certain

modal logic Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...

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 A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...

is a sentence that is either true or false. A proposition can be considered to be a function, with objects in it considered as variables, and the value of the function being either

truth Truth or verity is the Property (philosophy), property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth, 2005 In everyday language, it is typically ascribed to things that aim to represent reality or otherwise cor ...

or falsity, 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 ...

. 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 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 Philosophical categories Modal logic