39 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] |
| 13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 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] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 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] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 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] |
| 7607 | Nagarjuna and others pronounced the world of experience to be an illusion [Nagarjuna, by Armstrong,K] |