58 ideas
| 13786 | Wisdom is called 'beautiful', because it performs fine works [Plato] |
| 13780 | Good people are no different from wise ones [Plato] |
| 12596 | Reasoning aims at increasing explanatory coherence [Harman] |
| 12599 | Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman] |
| 13778 | A dialectician is someone who knows how to ask and to answer questions [Plato] |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
| 12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
| 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] |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 2063 | How can beauty have identity if it changes? [Plato] |
| 12598 | Reality is the overlap of true complete theories [Harman] |
| 13775 | We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 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] |
| 12602 | There is no natural border between inner and outer [Harman] |
| 12603 | We can only describe mental attitudes in relation to the external world [Harman] |
| 12601 | The way things look is a relational matter, not an intrinsic matter [Harman] |
| 12592 | Concepts in thought have content, but not meaning, which requires communication [Harman] |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| 12590 | Take meaning to be use in calculation with concepts, rather than in communication [Harman] |
| 12593 | The use theory attaches meanings to words, not to sentences [Harman] |
| 12588 | Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman] |
| 12589 | Some regard conceptual role semantics as an entirely internal matter [Harman] |
| 12600 | The content of thought is relations, between mental states, things in the world, and contexts [Harman] |
| 12594 | If one proposition negates the other, which is the negative one? [Harman] |
| 12591 | Mastery of a language requires thinking, and not just communication [Harman] |
| 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] |