Combining Texts

Ideas for 'Defending the Axioms', 'Creating Capabilities' and 'Letters to Bentley'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

13152

We can talk of 'innumerable number', about the infinite points on a line [Newton]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

13151

Not all infinites are equal [Newton]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17615

Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

17618

Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17614

The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]