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6. Mathematics / C. Sources of Mathematics / 8. Finitism

[true mathematics only concerns finite quantities]

5 ideas
Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [George/Velleman on Hilbert]
If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman]
Much infinite mathematics can still be justified finitely [George/Velleman]