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Full Idea
Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical.
Gist of Idea
Naïve set theory says any formula defines a set, and coextensive sets are identical
Source
Øystein Linnebo (Philosophy of Mathematics [2017], 4.2)
Book Ref
Linnebo,Øystein: 'Philosophy of Mathematics' [Princeton 2017], p.62
A Reaction
The second principle is a standard axiom of ZFC. The first principle causes the trouble.
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |