variable

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variable
(logic) A fundamental notion of modern logic. Intuitively, suppose we have a class of objects about which we might be interested (a domain), and we start with a simple sentence ‘Jane is hungry’. We then strike out mention of Jane, leaving a gap that we mark with the letter x : ‘ x is hungry’. This represents something short of a sentence (it is called an open sentence, or predicate). We can ‘point’ the letter x at members of the domain in turn, giving successive sentences like the one with which we started. In such a process the letter x is said to function as a variable taking as values each member of the domain successively. We might conclude the procedure with information like this: somewhere in this process one of the sentences is true, or everywhere such a sentence is true. Such information does not tell us who is hungry, but tells us the quantity of times the predicate is satisfied. The information that somewhere the predicate F applies to the value is represented as (∃x )Fx ; the information that it always applies as (∀x )Fx . The expressions (∃…) and (∀…) are the existential and universal quantifiers . The power of the idea only becomes apparent when we consider multiple quantifications. If we start with a relational sentence, ‘Fred loves Jane’ and strike out both names, marking the spaces with different variables, we obtain ‘ x loves y ’. We can now build very different kinds of information: everyone loves someone: (∀x )(∃y ) x loves y ; someone loves everyone: (∃x )(∀y ) x loves y, and so on. The study of these forms and the relations between them is quantification theory. The basic calculus that formalizes their logic is the predicate calculus.

Philosophy dictionary. . 2011.

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• variable — [ varjabl ] adj. et n. • fin XII e; lat. variabilis 1 ♦ Qui est susceptible de se modifier, de changer souvent au cours d une durée. ⇒ changeant, 1. incertain, instable. Temps variable. N. m. Météor. L aiguille du baromètre est au variable, sur… …   Encyclopédie Universelle

• Variable — Va ri*a*ble, a. [L. variabilis: cf. F. variable.] [1913 Webster] 1. Having the capacity of varying or changing; capable of alternation in any manner; changeable; as, variable winds or seasons; a variable quantity. [1913 Webster] 2. Liable to… …   The Collaborative International Dictionary of English

• Variable — Variable, dt. Veränderliche bezeichnet: Variable (Philosophie), ein in der Philosophie mit unterschiedlichen Interpretationen belegter Begriff Variable (Programmierung), in der Informationstechnik ein Speicherplatz abhängige und unabhängige… …   Deutsch Wikipedia

• Variable — Va ri*a*ble, n. 1. That which is variable; that which varies, or is subject to change. [1913 Webster] 2. (Math.) A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable …   The Collaborative International Dictionary of English

• variable — adj. de tout genre. Sujet à varier, qui change souvent. En ce climat les saisons sont fort variables. temps variable. vent variable. la fortune est variable. c est un esprit variable. il est variable dans ses opinions, dans ses resolutions …   Dictionnaire de l'Académie française

• variable — (Del lat. variabĭlis). 1. adj. Que varía o puede variar. 2. Inestable, inconstante y mudable. 3. f. Mat. Magnitud que puede tener un valor cualquiera de los comprendidos en un conjunto. variable estadística. f. Mat. Magnitud cuyos valores están… …   Diccionario de la lengua española

• variable — Variable, Versutus, Inconstans, Mobilis, Desultorius. Estre variable et legier, Fidem mutare. Amitié variable, Desultoria amicitia, id est, identidem euarians, non constans …   Thresor de la langue françoyse

• variable — ► ADJECTIVE 1) not consistent or having a fixed pattern; liable to vary. 2) able to be changed or adapted. 3) Mathematics (of a quantity) able to assume different numerical values. ► NOUN 1) a variable element, feature, or quantity. 2) Astronomy… …   English terms dictionary

• variable — sujeto a variación. Inestable, inconstante y mudable. Valor numérico sobre el que puede establecerse una curva de variabilidad Diccionario ilustrado de Términos Médicos.. Alvaro Galiano. 2010. variable Factor de un experimento científico que… …   Diccionario médico

• variable — [ver′ē ə bəl, var′ē ə bəl] adj. [ME < MFr < L variabilis] 1. apt or likely to change or vary; changeable, inconstant, fickle, fluctuating, etc. 2. that can be changed or varied 3. Biol. tending to deviate in some way from the type; aberrant …   English World dictionary

• variable — I adjective aberrant, alterable, capricious, changeable, changeful, erratic, faithless, fanciful, fast and loose, fickle, fitful, fluctuating, inconstant, irregular, irresponsible, mercurial, modifiable, oscillating, protean, shifting, spasmodic …   Law dictionary