Combining Texts

All the ideas for 'fragments/reports', 'Knowledge and the Philosophy of Number' and '74: Reply to Colotes'

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16 ideas

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 / 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]
16. Persons / B. Nature of the Self / 7. Self and Body / c. Self as brain controller
Rather than being the whole soul, maybe I am its chief part? [Plutarch]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
If atoms have no qualities, they cannot possibly produce a mind [Plutarch]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
Action needs an affinity for a presentation, and an impulse toward the affinity [Plutarch]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The good life involves social participation, loyalty, temperance and honesty [Plutarch]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
If only atoms exist, how do qualities arise when the atoms come together? [Plutarch]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
No one will ever find a city that lacks religious practices [Plutarch]