Combining Texts

Ideas for 'Causal Explanation', 'Continuity and Irrational Numbers' and 'Must We Believe in Set Theory?'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

17611

We want the essence of continuity, by showing its origin in arithmetic [Dedekind]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts

10572

A cut between rational numbers creates and defines an irrational number [Dedekind]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

17612

Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]

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 / A. Nature of Mathematics / 5. The Infinite / l. Limits

18087

If x changes by less and less, it must approach a limit [Dedekind]

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]