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Full Idea
In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions.
Gist of Idea
Bounded quantification is originally finitary, as conjunctions and disjunctions
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.149
A Reaction
This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities.