84 ideas
| 17016 | Philosophy must abstract from the senses [Newton] |
| 17266 | Using modal logic, philosophers tried to handle all metaphysics in modal terms [Correia/Schnieder] |
| 17263 | Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder] |
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| 18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
| 13152 | We can talk of 'innumerable number', about the infinite points on a line [Newton] |
| 13151 | Not all infinites are equal [Newton] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 17270 | Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder] |
| 17268 | Grounding is metaphysical and explanation epistemic, so keep them apart [Correia/Schnieder] |
| 17267 | The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder] |
| 17011 | I suspect that each particle of bodies has attractive or repelling forces [Newton] |
| 17028 | Particles mutually attract, and cohere at short distances [Newton] |
| 17014 | The place of a thing is the sum of the places of its parts [Newton] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 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] |
| 17022 | We should admit only enough causes to explain a phenomenon, and no more [Newton] |
| 17021 | Natural effects of the same kind should be assumed to have the same causes [Newton] |
| 17026 | From the phenomena, I can't deduce the reason for the properties of gravity [Newton] |
| 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] |
| 15863 | The principles of my treatise are designed to fit with a belief in God [Newton] |
| 16746 | Principles of things are not hidden features of forms, but the laws by which they were formed [Newton] |
| 8340 | I do not pretend to know the cause of gravity [Newton] |
| 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] |
| 17009 | I won't object if someone shows that gravity consistently arises from the action of matter [Newton] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| 13150 | The motions of the planets could only derive from an intelligent agent [Newton] |
| 12178 | That gravity should be innate and essential to matter is absurd [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] |
| 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] |
| 20968 | Newton's Third Law implies the conservation of momentum [Newton, by Papineau] |
| 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] |