60 ideas
| 13786 | Wisdom is called 'beautiful', because it performs fine works [Plato] |
| 13780 | Good people are no different from wise ones [Plato] |
| 13778 | A dialectician is someone who knows how to ask and to answer questions [Plato] |
| 13252 | Some truths have true negations [Beall/Restall] |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| 13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| 13253 | There are several different consequence relations [Beall/Restall] |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 13777 | A name is a sort of tool [Plato] |
| 13790 | A name-giver might misname something, then force other names to conform to it [Plato] |
| 13791 | Things must be known before they are named, so it can't be the names that give us knowledge [Plato] |
| 13789 | Anyone who knows a thing's name also knows the thing [Plato] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 2063 | How can beauty have identity if it changes? [Plato] |
| 13775 | We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato] |
| 13787 | Doesn't each thing have an essence, just as it has other qualities? [Plato] |
| 13774 | Things don't have every attribute, and essence isn't private, so each thing has an essence [Plato] |
| 13772 | Is the being or essence of each thing private to each person? [Plato] |
| 13788 | If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato] |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| 13792 | There can't be any knowledge if things are constantly changing [Plato] |
| 13781 | Soul causes the body to live, and gives it power to breathe and to be revitalized [Plato] |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| 13785 | 'Arete' signifies lack of complexity and a free-flowing soul [Plato] |
| 13779 | The natural offspring of a lion is called a 'lion' (but what about the offspring of a king?) [Plato] |
| 13783 | Even the gods love play [Plato] |