31 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
10816 | We can use mereology to simulate quantification over relations [Lewis] |
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] |
10808 | Mathematics is generalisations about singleton functions [Lewis] |
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] |
10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
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] |
10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |