85 ideas
| 21955 | My dogmatic slumber was first interrupted by David Hume [Kant] |
| 16931 | Metaphysics is generating a priori knowledge by intuition and concepts, leading to the synthetic [Kant] |
| 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] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
| 16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
| 16919 | Geometry rests on our intuition of space [Kant] |
| 16930 | Geometry is not analytic, because a line's being 'straight' is a quality [Kant] |
| 16920 | Numbers are formed by addition of units in time [Kant] |
| 16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
| 16910 | Mathematics can only start from an a priori intuition which is not empirical but pure [Kant] |
| 16917 | All necessary mathematical judgements are based on intuitions of space and time [Kant] |
| 16928 | Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant] |
| 11116 | Being a physical object is our most fundamental category [Jubien] |
| 11117 | Haecceities implausibly have no qualities [Jubien] |
| 11833 | The substance, once the predicates are removed, remains unknown to us [Kant] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 11119 | De re necessity is just de dicto necessity about object-essences [Jubien] |
| 11118 | Modal propositions transcend the concrete, but not the actual [Jubien] |
| 11108 | Your properties, not some other world, decide your possibilities [Jubien] |
| 11111 | Modal truths are facts about parts of this world, not about remote maximal entities [Jubien] |
| 11105 | We have no idea how many 'possible worlds' there might be [Jubien] |
| 11107 | If there are no other possible worlds, do we then exist necessarily? [Jubien] |
| 11106 | If all possible worlds just happened to include stars, their existence would be necessary [Jubien] |
| 11112 | Possible worlds just give parallel contingencies, with no explanation at all of necessity [Jubien] |
| 11109 | If other worlds exist, then they are scattered parts of the actual world [Jubien] |
| 11113 | Worlds don't explain necessity; we use necessity to decide on possible worlds [Jubien] |
| 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] |
| 11110 | We mustn't confuse a similar person with the same person [Jubien] |
| 21957 | 'Transcendental' concerns how we know, rather than what we know [Kant] |
| 16923 | I admit there are bodies outside us [Kant] |
| 21441 | 'Transcendental' is not beyond experience, but a prerequisite of experience [Kant] |
| 16916 | A priori synthetic knowledge is only of appearances, not of things in themselves [Kant] |
| 16915 | A priori intuitions can only concern the objects of our senses [Kant] |
| 16914 | A priori intuition of objects is only possible by containing the form of my sensibility [Kant] |
| 21447 | I can make no sense of the red experience being similar to the quality in the object [Kant] |
| 16924 | I count the primary features of things (as well as the secondary ones) as mere appearances [Kant] |
| 16913 | I can't intuit a present thing in itself, because the properties can't enter my representations [Kant] |
| 16925 | Appearance gives truth, as long as it is only used within experience [Kant] |
| 16911 | Intuition is a representation that depends on the presence of the object [Kant] |
| 16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause [Kant] |
| 16926 | Analytic judgements say clearly what was in the concept of the subject [Kant] |
| 16927 | Analytic judgement rests on contradiction, since the predicate cannot be denied of the subject [Kant] |
| 16922 | Space must have three dimensions, because only three lines can meet at right angles [Kant] |
| 16921 | If all empirical sensation of bodies is removed, space and time are still left [Kant] |