103 ideas
| 8093 | Seek wisdom rather than truth; it is easier [Joubert] |
| 8095 | We must think with our entire body and soul [Joubert] |
| 8107 | The love of certainty holds us back in metaphysics [Joubert] |
| 8099 | The truths of reason instruct, but they do not illuminate [Joubert] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 8098 | Truth consists of having the same idea about something that God has [Joubert] |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| 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.] |
| 8101 | To know is to see inside oneself [Joubert] |
| 19737 | A system can infer the structure of the world by making predictions about it [New Sci.] |
| 8094 | The imagination has made more discoveries than the eye [Joubert] |
| 19736 | Neural networks can extract the car-ness of a car, or the chair-ness of a chair [New Sci.] |
| 8103 | A thought is as real as a cannon ball [Joubert] |
| 16419 | No one has yet devised a rationality test [New Sci.] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 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.] |
| 8100 | Where does the bird's idea of a nest come from? [Joubert] |
| 8096 | He gives his body up to pleasure, but not his soul [Joubert] |
| 8104 | What will you think of pleasures when you no longer enjoy them? [Joubert] |
| 8097 | Virtue is hard if we are scorned; we need support [Joubert] |
| 8106 | In raising a child we must think of his old age [Joubert] |
| 21167 | Gravity is unusual, in that it always attracts and never repels [New Sci.] |
| 19950 | Entropy is the only time-asymmetric law, so time may be linked to entropy [New Sci.] |
| 21176 | In the Big Bang general relativity fails, because gravity is too powerful [New Sci.] |
| 21147 | Quantum electrodynamics incorporates special relativity and quantum mechanics [New Sci.] |
| 19478 | Light moves at a constant space-time speed, but its direction is in neither space nor time [New Sci.] |
| 21155 | Photons have zero rest mass, so virtual photons have infinite range [New Sci.] |
| 21161 | In the standard model all the fundamental force fields merge at extremely high energies [New Sci.] |
| 21146 | Electrons move fast, so are subject to special relativity [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.] |
| 21148 | The strong force is repulsive at short distances, strong at medium, and fades at long [New Sci.] |
| 21151 | Gluons, the particles carrying the strong force, interact because of their colour charge [New Sci.] |
| 21152 | The strong force binds quarks tight, and the nucleus more weakly [New Sci.] |
| 21143 | Quarks in threes can build hadrons with spin ½ or with spin 3/2 [New Sci.] |
| 21142 | Classifying hadrons revealed two symmetry patterns, produced by three basic elements [New Sci.] |
| 21150 | Three different colours of quark (as in the proton) can cancel out to give no colour [New Sci.] |
| 21145 | The four fundamental forces (gravity, electromagnetism, weak and strong) are the effects of particles [New Sci.] |
| 21153 | The weak force explains beta decay, and the change of type by quarks and leptons [New Sci.] |
| 21154 | Three particles enable the weak force: W+ and W- are charged, and Z° is not [New Sci.] |
| 21156 | The weak force particles are heavy, so the force has a short range [New Sci.] |
| 21164 | Why do the charges of the very different proton and electron perfectly match up? [New Sci.] |
| 21170 | The Standard Model cannot explain dark energy, survival of matter, gravity, or force strength [New Sci.] |
| 21140 | Spin is a built-in ration of angular momentum [New Sci.] |
| 21149 | Quarks have red, green or blue colour charge (akin to electric charge) [New Sci.] |
| 21158 | Fermions, with spin ½, are antisocial, and cannot share quantum states [New Sci.] |
| 21165 | Spin is akin to rotation, and is easily measured in a magnetic field [New Sci.] |
| 21157 | Particles are spread out, with wave-like properties, and higher energy shortens the wavelength [New Sci.] |
| 21163 | The mass of protons and neutrinos is mostly binding energy, not the quarks [New Sci.] |
| 21168 | Gravitional mass turns out to be the same as inertial mass [New Sci.] |
| 21138 | Neutrons are slightly heavier than protons, and decay into them by emitting an electron [New Sci.] |
| 21144 | Top, bottom, charm and strange quarks quickly decay into up and down [New Sci.] |
| 21141 | Neutrinos were proposed as the missing energy in neutron beta decay [New Sci.] |
| 21169 | Only neutrinos spin anticlockwise [New Sci.] |
| 21166 | Standard antineutrinos have opposite spin and opposite lepton number [New Sci.] |
| 21171 | The symmetry of unified electromagnetic and weak forces was broken by the Higgs field [New Sci.] |
| 19954 | It is impossible for find a model of actuality among the innumerable models in string theory [New Sci.] |
| 21178 | String theory is now part of 11-dimensional M-Theory, involving p-branes [New Sci.] |
| 19476 | String theory needs at least 10 space-time dimensions [New Sci.] |
| 21179 | Supersymmetric string theory can be expressed using loop quantum gravity [New Sci.] |
| 19953 | In string theory space-time has a grainy indivisible substructure [New Sci.] |
| 21175 | String theory might be tested by colliding strings to make bigger 'stringballs' [New Sci.] |
| 21177 | String theory offers a quantum theory of gravity, by describing the graviton [New Sci.] |
| 21162 | Only supersymmetry offers to incorporate gravity into the scheme [New Sci.] |
| 21159 | Supersymmetry has extra heavy bosons and heavy fermions [New Sci.] |
| 21173 | Supersymmetry says particles and superpartners were unities, but then split [New Sci.] |
| 21172 | The evidence for supersymmetry keeps failing to appear [New Sci.] |
| 19947 | Hilbert Space is an abstraction representing all possible states of a quantum system [New Sci.] |
| 21160 | The Higgs field means even low energy space is not empty [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.] |
| 21174 | Dark matter must have mass, to produce gravity, and no electric charge, to not reflect light [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.] |
| 8105 | We can't exactly conceive virtue without the idea of God [Joubert] |
| 8102 | We cannot speak against Christianity without anger, or speak for it without love [Joubert] |