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Autonymy

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An expression (a word) used as its own proper name. Such a use of an expression is said to be autonymous (as distinct from its use in the ordinary sense). For instance, if one says "x forms part of the equation x+ 3= 2" , then one is using $x$ as the name of the letter $x$, and is using "x+ 3= 2" as the name of the expression $x+3=2$. If one says "12 is divisible by 2" , then the term "12" is used in a non-autonymous manner (as the designation of an integer), while if one says "12 consists of two digits" one says the term "12" is used autonymously (as the name of itself).

In natural languages the context and the syntax are usually sufficiently reliable indicators for distinguishing between the autonymous and non-autonymous use of an expression. However, such a differentiation may be difficult in certain cases. Special care is then required to avoid ambiguity: the object itself must be distinguished from its name (its denotation); a difference must be made between a given linguistic term used as a name, and the term used for the object denoted by the name. The differentiation between the denotation and the object denoted may be achieved by using terms specially created for the purpose, or by using quotation marks; the term between quotation marks is then assumed to differ from the same term used without the quotation marks. Autonymous use of a term merges the meaning of the term with the term itself: it is both the object itself and the name by which it is denoted.

References

[1] A. Church, "Introduction to mathematical logic" , 1 , Princeton Univ. Press (1956)
[2] S.C. Kleene, "Introduction to metamathematics" , North-Holland (1951)
[3] H.B. Curry, "Foundations of mathematical logic" , McGraw-Hill (1963)
How to Cite This Entry:
Autonymy. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Autonymy&oldid=31498
This article was adapted from an original article by A.S. Kuzichev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article