69 ideas
| 17016 | Philosophy must abstract from the senses [Newton] |
| 8952 | We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
| 8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher] |
| 8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
| 18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |
| 17011 | I suspect that each particle of bodies has attractive or repelling forces [Newton] |
| 17028 | Particles mutually attract, and cohere at short distances [Newton] |
| 8944 | Vagueness can involve components (like baldness), or not (like boredom) [Fisher] |
| 17014 | The place of a thing is the sum of the places of its parts [Newton] |
| 8941 | We can't explain 'possibility' in terms of 'possible' worlds [Fisher] |
| 8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher] |
| 8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |
| 17546 | If you changed one of Newton's concepts you would destroy his whole system [Heisenberg on Newton] |
| 17027 | Science deduces propositions from phenomena, and generalises them by induction [Newton] |
| 17021 | Natural effects of the same kind should be assumed to have the same causes [Newton] |
| 17022 | We should admit only enough causes to explain a phenomenon, and no more [Newton] |
| 17026 | From the phenomena, I can't deduce the reason for the properties of gravity [Newton] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 6421 | Newton's four fundamentals are: space, time, matter and force [Newton, by Russell] |
| 13470 | Mass is central to matter [Newton, by Hart,WD] |
| 17020 | An attraction of a body is the sum of the forces of their particles [Newton] |
| 23012 | Newtonian causation is changes of motion resulting from collisions [Newton, by Baron/Miller] |
| 17008 | You have discovered that elliptical orbits result just from gravitation and planetary movement [Newton, by Leibniz] |
| 17010 | We have given up substantial forms, and now aim for mathematical laws [Newton] |
| 17023 | I am not saying gravity is essential to bodies [Newton] |
| 15866 | Newton reclassified vertical motion as violent, and unconstrained horizontal motion as natural [Newton, by Harré] |
| 15958 | Inertia rejects the Aristotelian idea of things having natural states, to which they return [Newton, by Alexander,P] |
| 20968 | Newton's Third Law implies the conservation of momentum [Newton, by Papineau] |
| 17017 | 1: Bodies rest, or move in straight lines, unless acted on by forces [Newton] |
| 17018 | 2: Change of motion is proportional to the force [Newton] |
| 17019 | 3: All actions of bodies have an equal and opposite reaction [Newton] |
| 17547 | Newton's idea of force acting over a long distance was very strange [Heisenberg on Newton] |
| 20966 | Newton introduced forces other than by contact [Newton, by Papineau] |
| 20967 | Newton's laws cover the effects of forces, but not their causes [Newton, by Papineau] |
| 16708 | Newton's forces were accused of being the scholastics' real qualities [Pasnau on Newton] |
| 13153 | I am studying the quantities and mathematics of forces, not their species or qualities [Newton] |
| 12724 | The aim is to discover forces from motions, and use forces to demonstrate other phenomena [Newton] |
| 13593 | Newton showed that falling to earth and orbiting the sun are essentially the same [Newton, by Ellis] |
| 20969 | Early Newtonians could not formulate conservation of energy, having no concept of potential energy [Newton, by Papineau] |
| 17013 | Absolute space is independent, homogeneous and immovable [Newton] |
| 22915 | Newton needs intervals of time, to define velocity and acceleration [Newton, by Le Poidevin] |
| 22893 | Newton thought his laws of motion needed absolute time [Newton, by Bardon] |
| 17012 | Time exists independently, and flows uniformly [Newton] |
| 14012 | Absolute time, from its own nature, flows equably, without relation to anything external [Newton] |
| 22954 | Newtonian mechanics does not distinguish negative from positive values of time [Newton, by Coveney/Highfield] |
| 17015 | If there is no uniform motion, we cannot exactly measure time [Newton] |
| 17025 | If a perfect being does not rule the cosmos, it is not God [Newton] |
| 17024 | The elegance of the solar system requires a powerful intellect as designer [Newton] |