36 ideas
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
| 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] |
| 19482 | Current physics says matter and antimatter should have reduced to light at the big bang [New Sci.] |
| 19483 | CP violation shows a decay imbalance in matter and antimatter, leading to matter's dominance [New Sci.] |
| 19737 | A system can infer the structure of the world by making predictions about it [New Sci.] |
| 19736 | Neural networks can extract the car-ness of a car, or the chair-ness of a chair [New Sci.] |
| 16419 | No one has yet devised a rationality test [New Sci.] |
| 16418 | People can be highly intelligent, yet very stupid [New Sci.] |
| 16417 | About a third of variation in human intelligence is environmental [New Sci.] |
| 19484 | Psychologists measure personality along five dimensions [New Sci.] |
| 19950 | Entropy is the only time-asymmetric law, so time may be linked to entropy [New Sci.] |
| 19478 | Light moves at a constant space-time speed, but its direction is in neither space nor time [New Sci.] |
| 19474 | Quantum states are measured by external time, of unknown origin [New Sci.] |
| 19473 | The Schrödinger equation describes the evolution of an object's wave function in Hilbert space [New Sci.] |
| 19954 | It is impossible for find a model of actuality among the innumerable models in string theory [New Sci.] |
| 19476 | String theory needs at least 10 space-time dimensions [New Sci.] |
| 19953 | In string theory space-time has a grainy indivisible substructure [New Sci.] |
| 19947 | Hilbert Space is an abstraction representing all possible states of a quantum system [New Sci.] |
| 19955 | Space-time may be a geometrical manifestation of quantum entanglement [New Sci.] |
| 19948 | Einstein's merging of time with space has left us confused about the nature of time [New Sci.] |
| 19475 | Relativity makes time and space jointly basic; quantum theory splits them, and prioritises time [New Sci.] |
| 19949 | Quantum theory relies on a clock outside the system - but where is it located? [New Sci.] |
| 19951 | Entropy is puzzling, so we may need to build new laws which include time directionality [New Sci.] |
| 19952 | Black holes have entropy, but general relativity says they are unstructured, and lack entropy [New Sci.] |
| 19477 | General relativity predicts black holes, as former massive stars, and as galaxy centres [New Sci.] |
| 16420 | 84.5 percent of the universe is made of dark matter [New Sci.] |
| 17604 | We are halfway to synthesising any molecule we want [New Sci.] |
| 17603 | Chemistry just needs the periodic table, and protons, electrons and neutrinos [New Sci.] |