Combining Texts

All the ideas for 'New System and Explanation of New System', 'Structuralism' and 'Grundlagen (Foundations of Theory of Manifolds)'

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8 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]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
8921 Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8922 Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
5044 Reality must be made of basic unities, which will be animated, substantial points [Leibniz]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
5045 No machine or mere organised matter could have a unified self [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
5046 The soul does know bodies, although they do not influence one another [Leibniz]
27. Natural Reality / G. Biology / 2. Life
5043 To regard animals as mere machines may be possible, but seems improbable [Leibniz]