28 ideas
16123 | Whenever you perceive a community of things, you should also hunt out differences in the group [Plato] |
16125 | To reveal a nature, divide down, and strip away what it has in common with other things [Plato] |
16124 | No one wants to define 'weaving' just for the sake of weaving [Plato] |
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] |
19393 | What is not active is nothing [Leibniz] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
5961 | The soul gets its goodness from god, and its evil from previous existence. [Plato] |
283 | The question of whether or not to persuade comes before the science of persuasion [Plato] |
282 | Non-physical beauty can only be shown clearly by speech [Plato] |
281 | The arts produce good and beautiful things by preserving the mean [Plato] |
22559 | Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle] |
279 | Only divine things can always stay the same, and bodies are not like that [Plato] |