61 ideas
17016 | Philosophy must abstract from the senses [Newton] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
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] |
6017 | Nomos is king [Pindar] |
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] |
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] |
20968 | Newton's Third Law implies the conservation of momentum [Newton, by Papineau] |
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] |