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Full Idea
In formal logic, quantifiers are operators that turn an open sentence into a sentence to which a truth-value can be assigned.
Clarification
An 'open sentence' is one with a free variable, like a general formula in physics
Gist of Idea
Quantifiers turn an open sentence into one to which a truth-value can be assigned
Source
Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.464)
Book Ref
Mautner,Thomas: 'Dictionary of Philosophy' [Penguin 1997], p.464
A Reaction
The standard quantifiers are 'all' and 'at least one'. The controversy is whether quantifiers actually assert existence, or whether (as McGinn says) they merely specify the subject matter of the sentence. I prefer the latter.