Combining Texts

Ideas for 'Defending the Axioms', 'Sources of the Self' and 'Elements of Intuitionism'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite

15938

Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]

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

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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]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

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For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]