102 ideas
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 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.] |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 19737 | A system can infer the structure of the world by making predictions about it [New Sci.] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 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.] |
| 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.] |
| 21152 | The strong force binds quarks tight, and the nucleus more weakly [New Sci.] |
| 21151 | Gluons, the particles carrying the strong force, interact because of their colour charge [New Sci.] |
| 21150 | Three different colours of quark (as in the proton) can cancel out to give no colour [New Sci.] |
| 21142 | Classifying hadrons revealed two symmetry patterns, produced by three basic elements [New Sci.] |
| 21143 | Quarks in threes can build hadrons with spin ½ or with spin 3/2 [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.] |
| 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.] |
| 21154 | Three particles enable the weak force: W+ and W- are charged, and Z° is not [New Sci.] |
| 21140 | Spin is a built-in ration of angular momentum [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.] |
| 21149 | Quarks have red, green or blue colour charge (akin to electric charge) [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.] |
| 21144 | Top, bottom, charm and strange quarks quickly decay into up and down [New Sci.] |
| 21138 | Neutrons are slightly heavier than protons, and decay into them by emitting an electron [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.] |
| 19953 | In string theory space-time has a grainy indivisible substructure [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.] |
| 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.] |
| 21178 | String theory is now part of 11-dimensional M-Theory, involving p-branes [New Sci.] |
| 21179 | Supersymmetric string theory can be expressed using loop quantum gravity [New Sci.] |
| 21159 | Supersymmetry has extra heavy bosons and heavy fermions [New Sci.] |
| 21162 | Only supersymmetry offers to incorporate gravity into the scheme [New Sci.] |
| 21172 | The evidence for supersymmetry keeps failing to appear [New Sci.] |
| 21173 | Supersymmetry says particles and superpartners were unities, but then split [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.] |
| 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.] |
| 21174 | Dark matter must have mass, to produce gravity, and no electric charge, to not reflect light [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.] |