Combining Texts

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

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11 ideas

1. Philosophy / H. Continental Philosophy / 5. Critical Theory
Adorno and Horkheimer subjected the Enlightenment to 'critical theory' analysis [Adorno/Horkheimer, by Finlayson]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
De Sade said it was impossible to rationally argue against murder [Adorno/Horkheimer]
28. God / C. Attitudes to God / 3. Deism
Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]