display all the ideas for this combination of philosophers
2 ideas
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] |
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. |