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Reference.org
Plural quantification
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Mathematical_logic/SaI7Y3wN">logic</a>, plural quantification is the theory that an individual <a href="/facts/Variable_(mathematics)/VbQlrvKz">variable</a> x may take on <i><a href="/facts/Plural/3VjXP7VF">plural</a></i>, as well as singular, values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London etc. for x, we may substitute both Alice and Bob, or all the numbers between 0 and 10, or all the buildings in London over 20 stories. </p><p>The point of the theory is to give <a href="/facts/First-order_predicate_calculus/lcISqWIg">first-order logic</a> the power of <a href="/facts/Set_theory/1ptfsvUP">set theory</a>, but without any "<a href="/facts/Existential_commitment/yx2vJfuE">existential commitment</a>" to such objects as sets. The classic expositions are Boolos 1984 and Lewis 1991. </p>