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Full Idea
The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes.
Gist of Idea
Limitation of Size is a vague intuition that over-large sets may generate paradoxes
Source
Penelope Maddy (Believing the Axioms I [1988], §1.3)
Book Ref
-: 'Journal of Symbolic Logic' [-], p.485
A Reaction
This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system.
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |