28 ideas
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] |
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] |
7630 | Ryle's dichotomy between knowing how and knowing that is too simplistic [Maund] |
7632 | Perception is sensation-then-concept, or direct-concepts, or sensation-saturated-in-concepts [Maund] |
7635 | Sense-data have an epistemological purpose (foundations) and a metaphysical purpose (explanation) [Maund] |
7638 | One thesis says we are not aware of qualia, but only of objects and their qualities [Maund] |
7642 | The Myth of the Given claims that thought is rationally supported by non-conceptual experiences [Maund] |
7640 | Mountains are adverbial modifications of the earth, but still have object-characteristics [Maund] |
7641 | Adverbialism tries to avoid sense-data and preserve direct realism [Maund] |
7637 | Thought content is either satisfaction conditions, or exercise of concepts [Maund, by PG] |
21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm] |
1421 | A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm] |
21245 | The word 'God' can be denied, but understanding shows God must exist [Anselm] |
21246 | Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm] |
21247 | Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm] |
21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
1420 | Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm] |