92 ideas
| 16000 | Fixed ideas should be tackled aggressively [Kierkegaard] |
| 7578 | I conceived it my task to create difficulties everywhere [Kierkegaard] |
| 22087 | Philosophy fails to articulate the continual becoming of existence [Kierkegaard, by Carlisle] |
| 22047 | Wherever there is painless contradiction there is also comedy [Kierkegaard] |
| 16012 | Philosophy can't be unbiased if it ignores language, as that is no more independent than individuals are [Kierkegaard] |
| 22092 | Kierkegaard's truth draws on authenticity, fidelity and honesty [Kierkegaard, by Carlisle] |
| 15999 | Pure truth is for infinite beings only; I prefer endless striving for truth [Kierkegaard] |
| 22094 | Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle] |
| 16005 | I recognise knowledge, but it is the truth by which I can live and die that really matters [Kierkegaard] |
| 5651 | Traditional views of truth are tautologies, and truth is empty without a subject [Kierkegaard, by Scruton] |
| 20313 | The highest truth we can get is uncertainty held fast by an inward passion [Kierkegaard] |
| 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] |
| 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] |
| 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] |
| 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] |
| 16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
| 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] |
| 20742 | The real subject is ethical, not cognitive [Kierkegaard] |
| 16002 | The self is a combination of pairs of attributes: freedom/necessity, infinite/finite, temporal/eternal [Kierkegaard] |
| 22098 | Socrates neglects the gap between knowing what is good and doing good [Kierkegaard, by Carlisle] |
| 22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |
| 15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
| 16003 | If people marry just because they are lonely, that is self-love, not love [Kierkegaard] |
| 7579 | While big metaphysics is complete without ethics, personal philosophy emphasises ethics [Kierkegaard] |
| 7581 | Speculative philosophy loses the individual in a vast vision of humanity [Kierkegaard] |
| 22090 | For me time stands still, and I with it [Kierkegaard, by Carlisle] |
| 22096 | Anxiety is not a passing mood, but a response to human freedom [Kierkegaard, by Carlisle] |
| 22097 | The ultimate in life is learning to be anxious in the right way [Kierkegaard] |
| 21909 | Ultimate knowledge is being anxious in the right way [Kierkegaard] |
| 20758 | Anxiety is staring into the yawning abyss of freedom [Kierkegaard] |
| 21910 | Our destiny is the highest pitch of world-weariness [Kierkegaard] |
| 9305 | The plebeians bore others; only the nobility bore themselves [Kierkegaard] |
| 5650 | Reason is just abstractions, so our essence needs a subjective 'leap of faith' [Kierkegaard, by Scruton] |
| 22095 | There are aesthetic, ethical and religious subjectivity [Kierkegaard, by Carlisle] |
| 20314 | People want to lose themselves in movements and history, instead of being individuals [Kierkegaard] |
| 7582 | Becoming what one is is a huge difficulty, because we strongly aspire to be something else [Kierkegaard] |
| 20747 | What matters is not right choice, but energy, earnestness and pathos in the choosing [Kierkegaard] |
| 16001 | Life may be understood backwards, but it has to be lived forwards [Kierkegaard] |
| 22093 | Life is a repetition when what has been now becomes [Kierkegaard] |
| 16009 | When we seek our own 'freedom' we are just trying to avoid responsibility [Kierkegaard] |
| 22091 | Kierkegaard prioritises the inward individual, rather than community [Kierkegaard, by Carlisle] |
| 7586 | God does not think or exist; God creates, and is eternal [Kierkegaard] |
| 16006 | Either Abraham rises higher than universal ethics, or he is a mere murderer [Kierkegaard] |
| 7577 | Abraham was willing to suspend ethics, for a higher idea [Kierkegaard] |
| 20312 | God cannot be demonstrated objectively, because God is a subject, only existing inwardly [Kierkegaard] |
| 7580 | Pantheism destroys the distinction between good and evil [Kierkegaard] |
| 16008 | The best way to be a Christian is without 'Christianity' [Kierkegaard] |
| 20735 | We need to see that Christianity cannot be understood [Kierkegaard] |
| 22088 | Faith is like a dancer's leap, going up to God, but also back to earth [Kierkegaard, by Carlisle] |
| 7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |
| 7584 | Without risk there is no faith [Kierkegaard] |