27 ideas
| 20768 | Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius] |
| 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] |
| 411 | If we succeed in speaking the truth, we cannot know we have done it [Xenophanes] |
| 412 | If God had not created honey, men would say figs are sweeter [Xenophanes] |
| 3049 | The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius] |
| 3549 | Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas] |
| 1640 | The basic Eleatic belief was that all things are one [Xenophanes, by Plato] |
| 3055 | Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius] |
| 407 | Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes] |
| 408 | Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes] |