Combining Texts

All the ideas for 'Abstract of 'The Fourfold Root'', 'fragments/reports' and 'Logicism, Some Considerations (PhD)'

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11 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
An adequate account of a number must relate it to its series [Benacerraf]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer]
11. Knowledge Aims / A. Knowledge / 2. Understanding
All understanding is an immediate apprehension of the causal relation [Schopenhauer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
What we know in ourselves is not a knower but a will [Schopenhauer]
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer]
23. Ethics / A. Egoism / 2. Hedonism
All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer]