110 ideas
| 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] |
| 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] |
| 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] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 20146 | 'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes] |
| 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] |
| 23101 | Intuitions don't prove things; they just receptivity to interpretations [Kekes] |
| 20169 | An action may be intended under one description, but not under another [Kekes] |
| 20149 | To control our actions better, make them result from our attitudes, not from circumstances [Kekes] |
| 23086 | Liberals say we are only responsible for fully autonomous actions [Kekes] |
| 23100 | Collective responsibility conflicts with responsibility's requirement of authonomy [Kekes] |
| 19738 | Values are an attempt to achieve well-being by bringing contingencies under control [Kekes] |
| 20145 | Values help us to control life, by connecting it to what is stable and manageable [Kekes] |
| 20170 | Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes] |
| 23093 | Moral and causal responsibility are not clearly distinct [Kekes] |
| 23096 | Morality should aim to prevent all evil actions, not just autonomous ones [Kekes] |
| 23087 | Much human evil is not autonomous, so moral responsibility need not be autonomous [Kekes] |
| 23098 | Effects show the existence of moral responsibility, and mental states show the degree [Kekes] |
| 23089 | Evil people may not be autonomously aware, if they misjudge the situation [Kekes] |
| 23094 | Ought implies can means moral responsibility needs autonomy [Kekes] |
| 23095 | Why should moral responsibility depend on autonomy, rather than social role or experience? [Kekes] |
| 20165 | Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes] |
| 20171 | Practical reason is not universal and impersonal, because it depends on what success is [Kekes] |
| 20175 | If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes] |
| 23090 | Liberals assume people are naturally free, equal, rational, and morally good [Kekes] |
| 20174 | Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes] |
| 20159 | Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes] |
| 20161 | The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes] |
| 20156 | We are bound to regret some values we never aspired to [Kekes] |
| 20150 | There are far more values than we can pursue, so they are optional possibilities [Kekes] |
| 20158 | Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes] |
| 20151 | Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes] |
| 20152 | Unconditional commitments are our most basic convictions, saying what must never be done [Kekes] |
| 20153 | Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes] |
| 23117 | Love should be partial, and discriminate in favour of its object [Kekes] |
| 23119 | Sentimental love distorts its object [Kekes] |
| 23088 | Evil is not deviation from the good, any more than good is a deviation from evil [Kekes] |
| 20162 | Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes] |
| 23097 | What matters for morality is the effects of action, not the psychological causes [Kekes] |
| 20157 | Well-being needs correct attitudes and well-ordered commitments to local values [Kekes] |
| 20154 | Control is the key to well-being [Kekes] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |
| 23099 | It is said that if an agent is not autonomous then their evil actions don't reflect on their character [Kekes] |
| 23118 | Awareness of others' suffering doesn't create an obligation to help [Kekes] |
| 20172 | Boredom destroys our ability to evaluate [Kekes] |
| 20173 | Boredom is apathy and restlessness, yearning for something interesting [Kekes] |
| 20155 | Society is alienating if it lacks our values, and its values repel us [Kekes] |
| 23109 | The veil of ignorance is only needed because people have bad motivations [Kekes] |
| 23114 | The chief function of the state is to arbitrate between contending visions of the good life [Kekes] |
| 20164 | The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes] |
| 20163 | Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes] |
| 23116 | Citizenship is easier than parenthood [Kekes] |
| 23103 | Power is meant to be confined to representatives, and subsequent delegation [Kekes] |
| 23107 | Prosperity is a higher social virtue than justice [Kekes] |
| 23081 | Liberal basics are pluralism, freedom, rights, equality, and distributive justice - for autonomy [Kekes] |
| 23085 | The key liberal values are explained by the one core value, which is autonomy [Kekes] |
| 23092 | Agents have little control over the capacities needed for liberal autonomy [Kekes] |
| 23102 | Liberals are egalitarians, but in varying degrees [Kekes] |
| 23084 | Are egalitarians too coercive, or not egalitarian enough, or lax over morality? [Kekes] |
| 23079 | Liberal justice ignores desert, which is the essence of justice [Kekes] |
| 23091 | Why do liberals not see a much wider range of values as basic? [Kekes] |
| 23112 | Liberals ignore contingency, and think people are good and equal, and institutions cause evil [Kekes] |
| 23082 | Liberal distribution cares more about recipients than donors [Kekes] |
| 23106 | To rectify the undeserved equality, we should give men longer and women shorter lives [Kekes] |
| 23121 | It is just a fact that some people are morally better than others [Kekes] |
| 23105 | It is not deplorable that billionaires have more than millionaires [Kekes] |
| 23120 | The problem is basic insufficiency of resources, not their inequality [Kekes] |
| 20148 | Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes] |
| 23108 | Justice combines consistency and desert; treat likes alike, judging likeness by desert [Kekes] |
| 23083 | Liberal welfare focuses on need rather than desert [Kekes] |
| 23113 | Sexual morality doesn't require monogamy, but it needs a group of sensible regulations [Kekes] |