Combining Texts

All the ideas for 'Explanation in Mathematics', 'Explanation: the state of play' and 'Grundlagen (Foundations of Theory of Manifolds)'

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6 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

15946

Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

15911

Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]

9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities

13166

Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]

14. Science / D. Explanation / 1. Explanation / b. Aims of explanation

12313

Explanation is for curiosity, control, understanding, to make meaningful, or to give authority [Stanford]

12314

Audience-relative explanation, or metaphysical explanation based on information? [Stanford]

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

12315

We can explain by showing constitution, as well as showing causes [Stanford]