58 ideas
| 21960 | Ordinary language is the beginning of philosophy, but there is much more to it [Austin,JL] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 10835 | True sentences says the appropriate descriptive thing on the appropriate demonstrative occasion [Austin,JL] |
| 10836 | Correspondence theorists shouldn't think that a country has just one accurate map [Austin,JL] |
| 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] |
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13028 | Replacement was added when some advanced theorems seemed to need it [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] |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
| 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] |
| 16588 | I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine] |
| 22979 | Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine] |
| 21598 | Austin revealed many meanings for 'vague': rough, ambiguous, general, incomplete... [Austin,JL, by Williamson] |
| 3912 | I must exist in order to be mistaken, so that even if I am mistaken, I can't be wrong about my own existence [Augustine] |
| 22167 | Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas] |
| 22117 | Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews] |
| 22981 | Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine] |
| 22980 | Memory contains innumerable principles of maths, as well as past sense experiences [Augustine] |
| 22983 | We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine] |
| 22977 | I can distinguish different smells even when I am not experiencing them [Augustine] |
| 22982 | Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine] |
| 22978 | Memory is so vast that I cannot recognise it as part of my mind [Augustine] |
| 22984 | Without memory I could not even speak of myself [Augustine] |
| 5982 | If the future does not exist, how can prophets see it? [Augustine] |
| 6683 | The contact of spirit and body is utterly amazing, and incomprehensible [Augustine] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 22976 | Memories are preserved separately, according to category [Augustine] |
| 22118 | Augustine created the modern concept of the will [Augustine, by Matthews] |
| 4348 | Love, and do what you will [Augustine] |
| 7821 | Pagans produced three hundred definitions of the highest good [Augustine, by Grayling] |
| 22985 | Everyone wants happiness [Augustine] |
| 22119 | Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews] |
| 5984 | Maybe time is an extension of the mind [Augustine] |
| 22888 | To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon] |
| 5980 | How can ten days ahead be a short time, if it doesn't exist? [Augustine] |
| 5979 | If the past is no longer, and the future is not yet, how can they exist? [Augustine] |
| 5981 | The whole of the current year is not present, so how can it exist? [Augustine] |
| 5978 | I know what time is, until someone asks me to explain it [Augustine] |
| 5983 | I disagree with the idea that time is nothing but cosmic movement [Augustine] |
| 5977 | Heaven and earth must be created, because they are subject to change [Augustine] |
| 22887 | If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon] |
| 5976 | If God is outside time in eternity, can He hear prayers? [Augustine] |
| 16702 | All things are in the present time to God [Augustine] |
| 22116 | Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews] |
| 19338 | Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins] |