Concept
Predicate variable
Overview
In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predicate variables include capital roman letters such as
P
{\displaystyle P}
,
Q
{\displaystyle Q}
and
R
{\displaystyle R}
, or lower case roman letters, e.g.,
x
{\displaystyle x}
. In first-order logic, they can be more properly called metalinguistic variables. In higher-order logic, predicate variables correspond to propositional variables which can stand for well-formed formulas of the same logic, and such variables can be quantified by means of (at least) second-order quantifiers.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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An example of this is, when the simple propositions are connected by the particle _or_; as, Either A is B or C is D; or by the particle _if_; as, A is B if C is D. In the former case, the proposition is called _disjunctive_, in the latter, _conditional_: the name _hypothetical_ was originally common to both. As has been well remarked by Archbishop Whately and others, the disjunctive form is resolvable into the…
John Stuart Mill, A System of Logic
States what Predicate variable is.
Then follows in the second stage of expression in speech, an analysis of that total idea into its parts, in which these parts are always put into close relations with each other. Such relations are called by grammarians subject and predicate, noun and adjective, verb and adverb, &c. The grammatical meaning of these categories shows clearly that this analysis consists of a system of primary and secondary relations…
Wilhelm Max Wundt, An Introduction to Psychology Translated from the Second German Edition
States what Predicate variable is.
From the proposition, Some A is not B, we can not even infer that some B is not A; though some men are not Englishmen, it does not follow that some Englishmen are not men. The only mode usually recognized of converting a particular negative proposition, is in the form, Some A is not B, therefore something which is not B is A; and this is termed conversion by contraposition. In this case, however, the predicate and…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Predicate variable is.
Related ideas
- First-order logic
- Propositional variable
- Propositional logic
- Mathematical logic
- Predicate (logic)
- Second-order logic
- Well-formed formula
- Arity
- Quantifier (logic)
- Higher-order logic
- Latin script
Opposing perspectives
Place in the tradition
Part of Outline of logic.