29 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] |
4038 | Properties are sets of their possible instances (which separates 'renate' from 'cordate') [Lewis, by Mellor/Oliver] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
21075 | The state of nature always involves the threat of war [Kant] |
20569 | Kant made the social contract international and cosmopolitan [Kant, by Oksala] |
21079 | The a priori general will of a people shows what is right [Kant] |
21077 | Each nation should, from self-interest, join an international security constitution [Kant] |
21078 | A constitution must always be improved when necessary [Kant] |
21076 | Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant] |
20570 | There is now a growing universal community, and violations of rights are felt everywhere [Kant] |
20571 | There are political and inter-national rights, but also universal cosmopolitan rights [Kant] |
21073 | Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant] |
21074 | Some trust in the enemy is needed during wartime, or peace would be impossible [Kant] |