40 ideas
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
7667 | There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin] |
20624 | Work degrades into heat, but not vice versa [Close] |
20623 | First Law: energy can change form, but is conserved overall [Close] |
20625 | Third Law: total order and minimum entropy only occurs at absolute zero [Close] |
20622 | All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close] |
20628 | The electric and magnetic are tightly linked, and viewed according to your own motion [Close] |
20635 | The general relativity equations relate curvature in space-time to density of energy-momentum [Close] |
20642 | Photon exchange drives the electro-magnetic force [Close] |
20627 | Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close] |
20630 | Light isn't just emitted in quanta called photons - light is photons [Close] |
20637 | In general relativity the energy and momentum of photons subjects them to gravity [Close] |
20629 | Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close] |
20632 | In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close] |
20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
20641 | Electrons get their mass by interaction with the Higgs field [Close] |
20631 | Dirac showed how electrons conform to special relativity [Close] |
20626 | Modern theories of matter are grounded in heat, work and energy [Close] |
20633 | The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close] |
20640 | Space-time is indeterminate foam over short distances [Close] |