21 ideas
9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [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] |
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] |
9984 | We can have a series with identical members [Tait] |
2614 | Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer] |
2615 | The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer] |
9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |