29 ideas
19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
19583 | Philosophy only begins when it studies itself [Novalis] |
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] |
19581 | A problem is a solid mass, which the mind must break up [Novalis] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
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] |
22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
21799 | We just use the word 'faculty' when we don't know the psychological cause [Galen] |
19585 | Every person has his own language [Novalis] |
19582 | Morality and philosophy are mutually dependent [Novalis] |
22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |