34 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] |
| 21059 | General rules of action also need a judgement about when to apply them [Kant] |
| 21061 | Duty does not aim at an end, but gives rise to universal happiness as aim of the will [Kant] |
| 21060 | It can't be a duty to strive after the impossible [Kant] |
| 21062 | The will's motive is the absolute law itself, and moral feeling is receptivity to law [Kant] |
| 21071 | There can be no restraints on freedom if reason does not reveal some basic rights [Kant] |
| 21063 | Personal contracts are for some end, but a civil state contract involves a duty to share [Kant] |
| 21068 | There must be a unanimous contract that citizens accept majority decisions [Kant] |
| 21069 | A contract is theoretical, but it can guide rulers to make laws which the whole people will accept [Kant] |
| 21070 | A law is unjust if the whole people could not possibly agree to it [Kant] |
| 21067 | A citizen must control his own life, and possess property or an important skill [Kant] |
| 21064 | A lawful civil state must embody freedom, equality and independence for its members [Kant] |
| 21066 | Citizens can rise to any rank that talent, effort and luck can achieve [Kant] |
| 21065 | You can't make a contract renouncing your right to make contracts! [Kant] |
| 21072 | The people (who have to fight) and not the head of state should declare a war [Kant] |
| 9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
| 9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |