49 ideas
| 2056 | Philosophers are always switching direction to something more interesting [Plato] |
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| 2086 | Understanding mainly involves knowing the elements, not their combinations [Plato] |
| 2083 | Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato] |
| 2082 | A rational account is essentially a weaving together of things with names [Plato] |
| 2052 | Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato] |
| 15854 | A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| 10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
| 2060 | There seem to be two sorts of change: alteration and motion [Plato] |
| 2084 | If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato] |
| 15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
| 15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
| 2080 | Things are only knowable if a rational account (logos) is possible [Plato] |
| 16126 | Expertise is knowledge of the whole by means of the parts [Plato] |
| 2050 | It is impossible to believe something which is held to be false [Plato] |
| 2076 | How can a belief exist if its object doesn't exist? [Plato] |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| 2045 | Perception is infallible, suggesting that it is knowledge [Plato] |
| 2067 | Our senses could have been separate, but they converge on one mind [Plato] |
| 2068 | With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato] |
| 2078 | You might mistake eleven for twelve in your senses, but not in your mind [Plato] |
| 2069 | Thought must grasp being itself before truth becomes possible [Plato] |
| 2089 | An inadequate rational account would still not justify knowledge [Plato] |
| 2085 | Parts and wholes are either equally knowable or equally unknowable [Plato] |
| 2091 | Without distinguishing marks, how do I know what my beliefs are about? [Plato] |
| 2087 | A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato] |
| 2090 | A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato] |
| 2081 | Maybe primary elements can be named, but not receive a rational account [Plato] |
| 2088 | A rational account of a wagon would mean knowledge of its hundred parts [Plato] |
| 2047 | What evidence can be brought to show whether we are dreaming or not? [Plato] |
| 2053 | If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato] |
| 2059 | How can a relativist form opinions about what will happen in the future? [Plato] |
| 2054 | Clearly some people are superior to others when it comes to medicine [Plato] |
| 2058 | God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato] |
| 2057 | There must always be some force of evil ranged against good [Plato] |