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Ideas for 'What is Logic?st1=Ian Hacking', 'On the Infinite' and 'Dialogue on human freedom and origin of evil'

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6. Mathematics / C. Sources of Mathematics / 7. Formalism
The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]