Combining Texts

All the ideas for 'The New Organon', 'Knowledge and the Philosophy of Number' and 'Philosophical Fragments'

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13 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 / 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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
16007 I assume existence, rather than reasoning towards it [Kierkegaard]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
16639 Only individual bodies exist [Bacon]
9. Objects / C. Structure of Objects / 2. Hylomorphism / c. Form as causal
16033 There are only individual bodies containing law-based powers, and the Forms are these laws [Bacon]
10. Modality / A. Necessity / 2. Nature of Necessity
16013 Nothing necessary can come into existence, since it already 'is' [Kierkegaard]
14. Science / B. Scientific Theories / 2. Aim of Science
21950 Science must clear away the idols of the mind if they are ever going to find the truth [Bacon]