89 ideas
| 9198 | It is no longer possible to be a sage, but we can practice the exercise of wisdom [Hadot] |
| 9197 | The logos represents a demand for universal rationality [Hadot] |
| 5728 | The concept of truth was originated by the senses [Lucretius] |
| 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] |
| 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] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [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] |
| 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] |
| 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] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [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] |
| 13141 | Negation: if σ ¬¬X then σ X [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] |
| 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] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [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] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [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] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [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] |
| 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] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 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] |
| 5729 | If the senses are deceptive, reason, which rests on them, is even worse [Lucretius] |
| 5702 | The senses are much the best way to distinguish true from false [Lucretius] |
| 5697 | The only possible standard for settling doubts is the foundation of the senses [Lucretius] |
| 5727 | Most supposed delusions of the senses are really misinterpretations by the mind [Lucretius] |
| 5714 | Even simple facts are hard to believe at first hearing [Lucretius] |
| 5718 | The mind is in the middle of the breast, because there we experience fear and joy [Lucretius] |
| 5717 | The mind is a part of a man, just like a hand or an eye [Lucretius] |
| 21387 | The separate elements and capacities of a mind cannot be distinguished [Lucretius] |
| 5709 | The actions of the mind are not determinate and passive, because atoms can swerve [Lucretius] |
| 5695 | Only bodies can touch one another [Lucretius] |
| 5711 | The earth is and always has been an insentient being [Lucretius] |
| 5712 | Particles may have sensation, but eggs turning into chicks suggests otherwise [Lucretius] |
| 5719 | The mind moves limbs, wakes the body up, changes facial expressions, which involve touch [Lucretius] |
| 5724 | Lions, foxes and deer have distinct characters because their minds share in their bodies [Lucretius] |
| 5713 | You needn't be made of laughing particles to laugh, so why not sensation from senseless seeds? [Lucretius] |
| 6611 | One man's meat is another man's poison [Lucretius] |
| 5730 | Our bodies weren't created to be used; on the contrary, their creation makes a use possible [Lucretius] |
| 5726 | The dead are no different from those who were never born [Lucretius] |
| 9196 | The pleasure of existing is the only genuine pleasure [Hadot] |
| 5705 | Nature only wants two things: freedom from pain, and pleasure [Lucretius] |
| 5716 | Nature runs the universe by herself without the aid of gods [Lucretius] |
| 5704 | There can be no centre in infinity [Lucretius] |
| 5703 | The universe must be limitless, since there could be nothing outside to limit it [Lucretius] |
| 5693 | Everything is created and fed by nature from atoms, and they return to atoms in death [Lucretius] |
| 5701 | If an object is infinitely subdivisible, it will be the same as the whole universe [Lucretius] |
| 5708 | In downward motion, atoms occasionally swerve slightly for no reason [Lucretius] |
| 17004 | Nothing can break the binding laws of eternity [Lucretius] |
| 5706 | Atoms move themselves [Lucretius] |
| 5696 | If there were no space there could be no movement, or even creation [Lucretius] |
| 5700 | It is quicker to break things up than to assemble them [Lucretius] |
| 5698 | We can only sense time by means of movement, or its absence [Lucretius] |
| 5715 | This earth is very unlikely to be the only one created [Lucretius] |
| 5694 | Nothing can be created by divine power out of nothing [Lucretius] |
| 5699 | If matter wasn't everlasting, everything would have disappeared by now [Lucretius] |
| 5707 | The universe can't have been created by gods, because it is too imperfect [Lucretius] |
| 5710 | Gods are tranquil and aloof, and have no need of or interest in us [Lucretius] |
| 5731 | Why does Jupiter never hurl lightning from a blue sky? [Lucretius] |
| 5720 | Spirit is mortal [Lucretius] |
| 5722 | For a separated spirit to remain sentient it would need sense organs attached to it [Lucretius] |
| 5725 | An immortal mind couldn't work harmoniously with a mortal body [Lucretius] |
| 5721 | The mind is very small smooth particles, which evaporate at death [Lucretius] |
| 5723 | If spirit is immortal and enters us at birth, why don't we remember a previous existence? [Lucretius] |