14 ideas
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
3644 | Two things being joined together doesn't prove they are the same [Descartes] |
3621 | Only judgement decides which of our senses are reliable [Descartes] |
3637 | Ideas in God's mind only have value if he makes it so [Descartes] |