Combining Texts

Ideas for 'fragments/reports', 'On the Foundations of Logic and Arithmetic' and 'Must We Believe in Set Theory?'

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5 ideas

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

10491

Infinite natural numbers is as obvious as infinite sentences in English [Boolos]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

10483

Mathematics and science do not require very high orders of infinity [Boolos]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10490

Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]

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

17697

The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17698

Logic already contains some arithmetic, so the two must be developed together [Hilbert]