Nominator (logic)
A nominator (m., From Latin nominare ' to name' ), also a singular term or proper name, is an expression in the philosophy of language and in predicate logic that describes exactly one object . For example, the expression “1” denotes exactly one object, the number 1. In contrast to this, a predicate or a predicator , conceptual word or general term is an expression that stands for a concept that includes several objects (or none) can. An example would be the term “human”, which includes several people.
The proper name or name in the traditional, linguistic sense, on the one hand, does not always refer to just one object (e.g. Müller , Meier , etc.). B. the markings , is also too narrow at the same time. In logic , therefore, the made-up word singular term is preferred, in language philosophy one speaks of proper names , but in a restricted, technical sense. The terms nominator and predicator are mostly used in the context of Erlangen constructivism .
Examples
In the sentence “Peter is happy”, “Peter” is a nominator, the object corresponding to him, Peter himself, is assigned the quality of being happy (by means of the predicator “is happy”).
A nominator can appear in different forms:
- as a proper name ("Peter") or as an individual constant (formally usually represented by lowercase letters: "a", "b" etc.)
- as an indicator or deictic reference ("this chair here")
- as a label ("the currently incumbent Federal Chancellor").
- as a function expression, d. H. as the application of a functor on its part to a nominator ("the father of Hans", application of "the father of ..." to "Hans").
- as a class expression, therefore, as an application of the class abstract to an “open sentence”, d. H. a set with free variables ("the class of people", formally {x | x is a person}).
What all these expressions have in common is that they designate exactly one object (be they concrete like people, chairs or abstract like classes). (However, this "uniqueness condition" is not always met with the labeling expressions; the so-called labeling theories deal with this problem, see the article Labeling .)
history
The difference between general and singular terms (terms) was already known to traditional logic , but it played a lesser role there, since in the syllogistics statements about individual individuals were treated like general statements (ie “Socrates is a person” was treated like “all Greeks” are people").
Gottlob Frege , the founder of modern logic, distinguished (among other things in his essay Function and Concept ) between saturated and unsaturated expressions. Proper names were saturated for him, if one detects from a statement , e.g. B. "Peter is happy", a proper name, you get an unsaturated expression, "... is happy", which, according to Frege, denotes a term, and with today's terminology would be called a predicate or predicator .
Saturated expressions , i.e. the nominators, always have a denotation according to Frege , i. H. an object they designate. Since whole statements are also saturated, they must also designate an object, for Frege this is the truth value .
In addition to the denotation, proper names also have a meaning in Frege, which he identified with the way in which the object was given . The number 3 in the expression “2 + 1” is given differently than in the expression “4 - 1”. In contrast, Carnap later ascribes individual terms to individual terms as intension .
In the further development of formal logic , for example with David Hilbert , the difference between saturated and unsaturated expressions was partly abandoned, and the terms and their functional role in the formal calculus were identified (see also formal grammar ).
The question of how the meaning of proper names is fixed, i.e. how it can be ensured that they refer to exactly one object, is a topic in contemporary philosophy of language , for example with Donald Davidson , Ruth Barcan Marcus or Saul Kripke (especially in his work Name and need ).
literature
- Wilhelm Kamlah and Paul Lorenzen : Logical Propaedeutics. § 3: Proper names. Bibliographical Institute, Mannheim 1967.
- Ernst Tugendhat , Ursula Wolf : Logical-Semantic Propaedeutics. Reclam, Stuttgart 1986.
- Ursula Wolf (Ed.): Proper names, documentation of a controversy. Suhrkamp, Frankfurt am Main 1985.
Web links
Individual evidence
- ^ Rudolf Carnap: Introduction to Symbolic Logic. 3. Edition. Springer, Wien / New York 1968, p. 40: The meaning of an individual constant can be called "individual concept".