more from A.George / D.J.Velleman

Single Idea 10114

[catalogued under 6. Mathematics / C. Sources of Mathematics / 8. Finitism]

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


A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)

Book Reference

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.