Combining Philosophers

Ideas for David O. Brink, Theodore Sider and ystein Linnebo

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2 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension

10779	A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]
	Full Idea: If φ contains no bound second-order variables, the corresponding comprehension axiom is said to be 'predicative'; otherwise it is 'impredicative'.
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §1)
	A reaction: ['Predicative' roughly means that a new predicate is created, and 'impredicative' means that it just uses existing predicates]

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

23445	Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
	Full Idea: Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical.
	From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.2)
	A reaction: The second principle is a standard axiom of ZFC. The first principle causes the trouble.