27 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] |
5953 | For the Cyrenaics experience was not enough to give certainty about reality [Aristippus young, by Plutarch] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
3023 | Even the foolish may have some virtues [Aristippus young, by Diog. Laertius] |
3026 | Actions are influenced by circumstances, so Cyrenaics say felons should be reformed, not hated [Aristippus young, by Diog. Laertius] |
3024 | Cyrenaics teach that honour, justice and shame are all based on custom and fashion [Aristippus young, by Diog. Laertius] |
3025 | For a Cyrenaic no one is of equal importance to himself [Aristippus young, by Diog. Laertius] |
3019 | No one pleasure is different from or more pleasant than another [Aristippus young, by Diog. Laertius] |
3021 | The Cyrenaics asserted that corporeal pleasures were superior to mental ones [Aristippus young, by Diog. Laertius] |
7844 | The Golden Rule is accepted everywhere, and gives a fixed target for morality [Voltaire] |
3027 | Cyrenaics say wise men are self-sufficient, needing no friends [Aristippus young, by Diog. Laertius] |