30 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] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 23814 | Every human yearns for an unattainable transcendent good [Weil] |
| 23824 | Where human needs are satisfied we find happiness, friendship and beauty [Weil] |
| 23815 | We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil] |
| 23823 | Life needs risks to avoid sickly boredom [Weil] |
| 23822 | We all need to partipate in public tasks, and take some initiative [Weil] |
| 23817 | We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil] |
| 23819 | Deliberate public lying should be punished [Weil] |
| 23818 | We have liberty in the space between nature and accepted authority [Weil] |
| 23820 | People need personal and collective property, and a social class lacking property is shameful [Weil] |
| 23821 | Crime should be punished, to bring the perpetrator freely back to morality [Weil] |
| 20723 | Only when working people are poor do they remain obedient to God [Calvin, by Weber] |
| 23816 | Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil] |