34 ideas
| 12780 | We can grasp the wisdom of God a priori [Leibniz] |
| 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] |
| 12774 | Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz] |
| 12777 | Monads do not make a unity unless a substantial chain is added to them [Leibniz] |
| 12782 | Monads control nothing outside of themselves [Leibniz] |
| 12778 | There is active and passive power in the substantial chain and in the essence of a composite [Leibniz] |
| 12783 | Primitive force is what gives a composite its reality [Leibniz] |
| 6900 | A prior understanding of beauty is needed to assert that the Form of the Beautiful is beautiful [Westaway] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 12775 | Things seem to be unified if we see duration, position, interaction and connection [Leibniz] |
| 12776 | Every substance is alive [Leibniz] |
| 6956 | At what point does an object become 'whole'? [Westaway] |
| 12753 | A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz] |
| 12781 | A composite substance is a mere aggregate if its essence is just its parts [Leibniz] |
| 12779 | There is a reason why not every possible thing exists [Leibniz] |
| 12785 | Truth is mutually agreed perception [Leibniz] |
| 7335 | The Chinese Room should be able to ask itself questions in Mandarin [Westaway] |
| 12784 | Allow no more miracles than are necessary [Leibniz] |