82 ideas
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
18825 | S5 is the logic of logical necessity [Rumfitt] |
18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
21167 | Gravity is unusual, in that it always attracts and never repels [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.] |
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.] |
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.] |
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.] |
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.] |
21160 | The Higgs field means even low energy space is not empty [New Sci.] |
21174 | Dark matter must have mass, to produce gravity, and no electric charge, to not reflect light [New Sci.] |