Proposition
The simplest expression of a language. It is a concatenation of words that has an independent meaning, i.e. expresses a complete statement. In formalized languages a proposition is a formula without free variables, i.e. parameters. In formalized languages a proposition is also called a closed formula. E.g., in a first-order language (the language of the narrow predicate calculus) the formulas
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are closed (the first is false, the second and third are true in the domain of natural numbers). The formulas
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are not closed, i.e. contain parameters ( and
in the first,
in the second).
References
[1] | A. Church, "Introduction to mathematical logic" , 1 , Princeton Univ. Press (1956) |
Comments
In Western parlance, the term "proposition" tends to be reserved for formulas in a language not involving variables at all (cf. Propositional calculus). The term "sentence" is used for a formula whose variables are all quantified, as in the examples above.
Proposition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Proposition&oldid=29861