132 ideas
| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
| 17016 | Philosophy must abstract from the senses [Newton] |
| 13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
| 10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 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] |
| 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
| 13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| 13151 | Not all infinites are equal [Newton] |
| 18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
| 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
| 13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
| 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
| 17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
| 17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
| 13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
| 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
| 8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
| 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
| 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
| 13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
| 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
| 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
| 13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| 17011 | I suspect that each particle of bodies has attractive or repelling forces [Newton] |
| 9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
| 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] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 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] |
| 13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| 13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
| 7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
| 13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
| 17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
| 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] |
| 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] |