28 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] |
23438 | Full rationality must include morality [Foot] |
23437 | Practical reason is goodness in choosing actions [Foot] |
23436 | It is an odd Humean view to think a reason to act must always involve caring [Foot] |
23431 | Human defects are just like plant or animal defects [Foot] |
23433 | Humans need courage like a plant needs roots [Foot] |
23432 | Concepts such as function, welfare, flourishing and interests only apply to living things [Foot] |
23434 | There is no fact-value gap in 'owls should see in the dark' [Foot] |
23439 | Principles are not ultimate, but arise from the necessities of human life [Foot] |
23435 | If you demonstrate the reason to act, there is no further question of 'why should I?' [Foot] |
21906 | Political theory should not focus on the state or economy, but on the small scale of power [Deleuze/Guattari, by May] |