32 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] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
13790 | A name-giver might misname something, then force other names to conform to it [Plato] |
13777 | A name is a sort of tool [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] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
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] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
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] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
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] |