39 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
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.] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
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.] |
16417 | About a third of variation in human intelligence is environmental [New Sci.] |
16418 | People can be highly intelligent, yet very stupid [New Sci.] |
19484 | Psychologists measure personality along five dimensions [New Sci.] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
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.] |
19953 | In string theory space-time has a grainy indivisible substructure [New Sci.] |
19476 | String theory needs at least 10 space-time dimensions [New Sci.] |
19954 | It is impossible for find a model of actuality among the innumerable models in string theory [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.] |
19477 | General relativity predicts black holes, as former massive stars, and as galaxy centres [New Sci.] |
19952 | Black holes have entropy, but general relativity says they are unstructured, and lack entropy [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.] |