Combining Texts

All the ideas for 'Science and Method', 'Knowledge and the Philosophy of Number' and 'The Meditations (To Himself)'

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15 ideas

1. Philosophy / A. Wisdom / 2. Wise People
A philosopher should have principles ready for understanding, like a surgeon with instruments [Aurelius]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
One geometry cannot be more true than another [Poincaré]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
7. Existence / B. Change in Existence / 1. Nature of Change
Everything is changing, including yourself and the whole universe [Aurelius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Nothing is evil which is according to nature [Aurelius]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Justice has no virtue opposed to it, but pleasure has temperance opposed to it [Aurelius]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / b. Living naturally
The art of life is more like the wrestler's than the dancer's [Aurelius]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
Humans are naturally made for co-operation [Aurelius]