30 ideas
| 20320 | Truth is what unites, and the profound truths create a community [Jaspers] |
| 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] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 20323 | Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers] |
| 20322 | I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers] |
| 20324 | My freedom increases as I broaden my vision of possiblities and motives [Jaspers] |
| 20321 | The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers] |
| 20318 | My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers] |
| 20325 | Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers] |
| 20315 | 'Existenz' is the potential being, which I could have, and ought to have [Jaspers] |
| 20317 | Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers] |
| 20319 | We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers] |
| 20316 | Every decision I make moves towards or away from fulfilled Existenz [Jaspers] |