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Ideas for 'works (all lost)', 'The Mysterious Flame' and 'Knowledge and the Philosophy of Number'

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3 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets

23623	Predicativism says only predicated sets exist [Hossack]
	Full Idea: Predicativists doubt the existence of sets with no predicative definition.
	From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3)
	A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate?

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]
	Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory.
	From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9)
	A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job.

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]
	Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC.
	From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9)
	A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be.