Ideas from 'The Philosophy of Logic' by Hilary Putnam [1971], by Theme Structure

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6. Mathematics / A. Nature of Mathematics / 4. The Infinite / j. Large cardinals
Very large sets should be studied in an 'if-then' spirit
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Indispensability strongly supports predicative sets, and somewhat supports impredicative sets
We must quantify over numbers for science; but that commits us to their existence