Combining Texts

All the ideas for 'Introduction to 'Properties'', 'Open Society and Its Enemies:Hegel and Marx' and 'Knowledge and the Philosophy of Number'

expand these ideas     |    start again     |     specify just one area for these texts

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13 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor

4037	Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver]

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]

8. Modes of Existence / B. Properties / 6. Categorical Properties

4027	Properties are respects in which particular objects may be alike or differ [Mellor/Oliver]

8. Modes of Existence / B. Properties / 12. Denial of Properties

4029	Nominalists ask why we should postulate properties at all [Mellor/Oliver]

9. Objects / D. Essence of Objects / 15. Against Essentialism

5451	Popper felt that ancient essentialism was a bar to progress [Popper, by Mautner]

18. Thought / E. Abstraction / 5. Abstracta by Negation

4039	Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver]