Individual variable

This article or section needs to be revised. Details should be given on the talk page. Please help to improve it , and then remove this flag.

The individual variable denotes a variable that stands as a placeholder for an individual constant , an individual name.

Synonyms are "object variable" or "individual variable".

Individual variables are mostly symbolized by the Latin lower case letters x, y, z.

Related sub-terms of the common generic term variable ( cohyponyms ) include predicate variables and proposition variables .

The opposite term ( antonym ) is the individual constant (the individual name).

Individual variables make it possible to speak about individuals in the underlying individual domain in statements about the universe or existence , without naming specific individuals.

One then says

"X is true for every individual: ...." (symbolically ) ${\displaystyle \forall (x)....}$

or

“There is at least one individual x for whom: ...” (symbolic:) . ${\displaystyle \exists (x)}$

If individual variables appear as the only free variable in a proposition function and the individual variable is replaced by an individual constant, an individual proposition or a singular proposition is obtained.

Individual evidence

1. ↑ Essler / Martínez, Grundzüge der Logic I, 4th edition (1991), p. 174
2. ^ Copi, Introduction to Logic (1998), p. 172; Wunderlich, Arbeitsbuch Semantik, 2nd edition (1991), p. 345