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] |
17771 | How we evaluate evidence depends on our background beliefs [Bayne] |
17770 | Clifford's dictum seems to block our beliefs in morality, politics and philosophy [Bayne] |
17766 | Physicalism correlates brain and mind, explains causation by thought, and makes nature continuous [Bayne] |
17768 | Perception reveals what animals think, but humans can disengage thought from perception [Bayne] |
17769 | Some people centre space on themselves; others centre space on the earth [Bayne] |
17767 | The alternative to a language of thought is map-like or diagram-like thought [Bayne] |
23865 | Morality would improve if people could pursue private interests [Weil] |
23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
23871 | No central authority can initiate decentralisation [Weil] |
23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
23863 | Only individual people of good will can achieve social progress [Weil] |
23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |