20 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] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
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] |
21110 | An understanding of the most basic physics should explain all of the subject's mysteries [Krauss] |
21105 | In 1676 it was discovered that water is teeming with life [Krauss] |
8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
21109 | Space itself can expand (and separate its contents) at faster than light speeds [Krauss] |
21104 | General Relativity: the density of energy and matter determines curvature and gravity [Krauss] |
21107 | Uncertainty says that energy can be very high over very short time periods [Krauss] |
21106 | Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss] |
21112 | Empty space contains a continual flux of brief virtual particles [Krauss] |
21108 | The universe is precisely 13.72 billion years old [Krauss] |
21111 | It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss] |