87 ideas
| 17016 | Philosophy must abstract from the senses [Newton] |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| 13711 | System B introduces iterated modalities [Sider] |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| 13714 | We can treat modal worlds as different times [Sider] |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| 18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
| 18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 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] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| 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] |
| 20761 | If existence is absurd it can never have a meaning [Beauvoir] |
| 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] |
| 17010 | We have given up substantial forms, and now aim for mathematical laws [Newton] |
| 17008 | You have discovered that elliptical orbits result just from gravitation and planetary movement [Newton, by Leibniz] |
| 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] |
| 20968 | Newton's Third Law implies the conservation of momentum [Newton, by Papineau] |
| 17018 | 2: Change of motion is proportional to the force [Newton] |
| 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] |
| 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] |