36 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
21812 | Being is the product of pure intellect [Plotinus] |
21817 | The One does not exist, but is the source of all existence [Plotinus] |
21824 | The One is a principle which transcends Being [Plotinus] |
21813 | Number determines individual being [Plotinus] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
21828 | A person is the whole of their soul [Plotinus] |
21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
21814 | How can multiple existence arise from the unified One? [Plotinus] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |