100 ideas
| 224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
| 232 | Opposites are as unlike as possible [Plato] |
| 8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
| 18486 | We might define truth as arising from the truth-maker relation [MacBride] |
| 18484 | Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride] |
| 18466 | If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride] |
| 18481 | Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride] |
| 18473 | 'Maximalism' says every truth has an actual truthmaker [MacBride] |
| 18483 | The main idea of truth-making is that what a proposition is about is what matters [MacBride] |
| 18479 | There are different types of truthmakers for different types of negative truth [MacBride] |
| 18477 | There aren't enough positive states out there to support all the negative truths [MacBride] |
| 18482 | Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride] |
| 18485 | Even idealists could accept truthmakers, as mind-dependent [MacBride] |
| 18474 | Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride] |
| 18493 | Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride] |
| 18490 | Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride] |
| 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] |
| 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] |
| 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] |
| 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] |
| 18489 | Connectives link sentences without linking their meanings [MacBride] |
| 18476 | 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
| 14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| 229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
| 21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
| 18480 | Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride] |
| 18471 | Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride] |
| 18472 | Which has priority - 'grounding' or 'truth-making'? [MacBride] |
| 18475 | Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride] |
| 221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
| 223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
| 227 | You must always mean the same thing when you utter the same name [Plato] |
| 228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
| 211 | If admirable things have Forms, maybe everything else does as well [Plato] |
| 219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
| 16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
| 210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
| 220 | The concept of a master includes the concept of a slave [Plato] |
| 212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
| 216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
| 215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
| 218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
| 213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
| 214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
| 217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
| 15851 | Parts must belong to a created thing with a distinct form [Plato] |
| 15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
| 15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
| 15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
| 13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
| 15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 18478 | Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride] |
| 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] |
| 222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
| 225 | The unlimited has no shape and is endless [Plato] |
| 231 | Everything partakes of the One in some way [Plato] |
| 2062 | The only movement possible for the One is in space or in alteration [Plato] |
| 233 | Some things do not partake of the One [Plato] |
| 234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |