49 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 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.] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 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.] |
| 3986 | The 'intentional stance' is a way of interpreting an entity by assuming it is rational and self-aware [Dennett] |
| 3987 | Like the 'centre of gravity', desires and beliefs are abstract concepts with no actual existence [Dennett] |
| 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.] |
| 3984 | The nature of content is entirely based on its functional role [Dennett] |
| 3983 | Learning is evolution in the brain [Dennett] |
| 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.] |
| 19948 | Einstein's merging of time with space has left us confused about the nature of time [New Sci.] |
| 19955 | Space-time may be a geometrical manifestation of quantum entanglement [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.] |
| 3985 | Biology is a type of engineering, not a search for laws of nature [Dennett] |