38 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] |
21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
23623 | Predicativism says only predicated sets exist [Hossack] |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
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] |
21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
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] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
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] |
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] |
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] |