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((Short description|Concept in logic))
((refimprove|date=January 2017))

In [[logic]], the '''scope''' of a [[Quantifier (logic)|quantifier]] or a quantification is the range in the [[Well-formed formula#Predicate logic|formula]] where the quantifier "engages in". It is put right after the quantifier, often in parentheses. Some authors describe this as including the variable put right after the forall or exists symbol. In the formula ((math|∀''xP'')), for example, ((math|''P'')) (or ((math|''xP''))<ref>((cite book|last1=Bell|first1=John L.|authorlink1=John Lane Bell|last2=Machover|first2=Moshé|authorlink2=Moshé Machover|title=A Course in Mathematical Logic|date=April 15, 2007|publisher=Elsevier Science Ltd|isbn=978-0-7204-2844-5|page=[https://archive.org/details/courseinmathemat0000bell/page/17 17]|chapter=Chapter 1. Beginning mathematical logic|chapter-url=https://archive.org/details/courseinmathemat0000bell/page/17))</ref>) is the scope of the quantifier ((math|∀''x'')) (or ((math|∀))).

A variable in the formula is [[free variable|free]], if and only if it does not occur in the scope of any quantifier for that variable. A [[term (logic)|term]] is free for a variable in the formula (i.e. free to substitute that variable that occurs free), if and only if that variable does not occur free in the scope of any quantifier for any variable in the term.

== See also ==
* [[Modal scope fallacy]]

== Notes ==
((reflist))

[[Category:Quantifier (logic)]]
[[Category:Predicate logic]]
[[Category:Mathematical terminology]]

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