59 ideas
17016 | Philosophy must abstract from the senses [Newton] |
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
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] |
17019 | 3: All actions of bodies have an equal and opposite reaction [Newton] |
17017 | 1: Bodies rest, or move in straight lines, unless acted on by forces [Newton] |
20968 | Newton's Third Law implies the conservation of momentum [Newton, by Papineau] |
17018 | 2: Change of motion is proportional to the force [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] |