88 ideas
| 16227 | Philosophers are good at denying the obvious [Hawley] |
| 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] |
| 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] |
| 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] |
| 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] |
| 16216 | Part of the sense of a proper name is a criterion of the thing's identity [Hawley] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 16211 | A homogeneous rotating disc should be undetectable according to Humean supervenience [Hawley] |
| 16219 | Non-linguistic things cannot be indeterminate, because they don't have truth-values at all [Hawley] |
| 16223 | Maybe for the world to be vague, it must be vague in its foundations? [Hawley] |
| 16226 | Epistemic vagueness seems right in the case of persons [Hawley] |
| 16208 | Supervaluation refers to one vaguely specified thing, through satisfaction by everything in some range [Hawley] |
| 16221 | Supervaluationism takes what the truth-value would have been if indecision was resolved [Hawley] |
| 16230 | Maybe the only properties are basic ones like charge, mass and spin [Hawley] |
| 16232 | An object is 'natural' if its stages are linked by certain non-supervenient relations [Hawley] |
| 16200 | Are sortals spatially maximal - so no cat part is allowed to be a cat? [Hawley] |
| 16237 | The modal features of statue and lump are disputed; when does it stop being that statue? [Hawley] |
| 16238 | Perdurantists can adopt counterpart theory, to explain modal differences of identical part-sums [Hawley] |
| 16220 | Vagueness is either in our knowledge, in our talk, or in reality [Hawley] |
| 16222 | Indeterminacy in objects and in properties are not distinct cases [Hawley] |
| 16228 | The constitution theory is endurantism plus more than one object in a place [Hawley] |
| 16229 | Constitution theory needs sortal properties like 'being a sweater' to distinguish it from its thread [Hawley] |
| 14492 | If the constitution view says thread and sweater are two things, why do we talk of one thing? [Hawley] |
| 16193 | 'Adverbialism' explains change by saying an object has-at-some-time a given property [Hawley] |
| 16195 | Presentism solves the change problem: the green banana ceases, so can't 'relate' to the yellow one [Hawley] |
| 16202 | The problem of change arises if there must be 'identity' of a thing over time [Hawley] |
| 16192 | Endurance theory can relate properties to times, or timed instantiations to properties [Hawley] |
| 16196 | Endurance is a sophisticated theory, covering properties, instantiation and time [Hawley] |
| 16197 | How does perdurance theory explain our concern for our own future selves? [Hawley] |
| 16191 | Perdurance needs an atemporal perspective, to say that the object 'has' different temporal parts [Hawley] |
| 16199 | If an object is the sum of all of its temporal parts, its mass is staggeringly large! [Hawley] |
| 16201 | Perdurance says things are sums of stages; Stage Theory says each stage is the thing [Hawley] |
| 16240 | If a life is essentially the sum of its temporal parts, it couldn't be shorter or longer than it was? [Hawley] |
| 16203 | Stage Theory seems to miss out the link between stages of the same object [Hawley] |
| 16204 | Stage Theory says every stage is a distinct object, which gives too many objects [Hawley] |
| 16212 | An isolated stage can't be a banana (which involves suitable relations to other stages) [Hawley] |
| 16213 | Stages of one thing are related by extrinsic counterfactual and causal relations [Hawley] |
| 16206 | Stages must be as fine-grained in length as change itself, so any change is a new stage [Hawley] |
| 16205 | The stages of Stage Theory seem too thin to populate the world, or to be referred to [Hawley] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 16225 | If two things might be identical, there can't be something true of one and false of the other [Hawley] |
| 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] |
| 16239 | To decide whether something is a counterpart, we need to specify a relevant sortal concept [Hawley] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 1457 | Morality requires a minimum commitment to the self [Rashdall] |
| 16218 | On any theory of self, it is hard to explain why we should care about our future selves [Hawley] |
| 6674 | All moral judgements ultimately concern the value of ends [Rashdall] |
| 6673 | Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall] |
| 16215 | Causation is nothing more than the counterfactuals it grounds? [Hawley] |
| 16207 | Time could be discrete (like integers) or dense (rationals) or continuous (reals) [Hawley] |
| 1458 | Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall] |
| 1459 | Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG] |