In
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
, the scope of a
quantifier or a quantification is the range in the
formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwe ...
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 , for example, (or
) is the scope of the quantifier (or ).
A variable in the formula is
free
Free may refer to:
Concept
* Freedom, having the ability to do something, without having to obey anyone/anything
* Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism
* Emancipate, to procure ...
, if and only if it does not occur in the scope of any quantifier for that variable. A
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
A fallacy of necessity is a fallacy in the logic of a syllogism whereby a degree of unwarranted necessity is placed in the conclusion.
Example
:a) ''Bachelors are necessarily unmarried.''
:b) ''John is a bachelor.''
:Therefore, c) ''John cannot m ...
Notes
{{reflist
Quantifier (logic)
Predicate logic
Mathematical terminology