Combining Texts

All the ideas for 'fragments/reports', 'works' and 'Knowledge and the Philosophy of Number'

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17 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 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
23625 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
23628 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
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
13445 Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 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
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
16774 Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau]
12. Knowledge Sources / B. Perception / 3. Representation
7400 Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck]
16. Persons / F. Free Will / 4. For Free Will
4310 We have inner awareness of our freedom [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
6553 Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan]
26. Natural Theory / A. Speculations on Nature / 1. Nature
19676 Nature is devoid of thought [Descartes, by Meillassoux]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
6518 Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]