30 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] |
23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
7440 | Secondary qualities are microscopic primary qualities of physical things [Armstrong] |
7437 | Consciousness and experience of qualities are not the same [Armstrong] |
7434 | Behaviourism is false, but mind is definable as the cause of behaviour [Armstrong] |
7436 | The manifestations of a disposition need never actually exist [Armstrong] |
7429 | Causal Functionalism says mental states are apt for producing behaviour [Armstrong] |
7438 | A causal theory of mentality would be improved by a teleological element [Armstrong] |
7431 | The identity of mental states with physical properties is contingent, because the laws of nature are contingent [Armstrong] |
7432 | One mental role might be filled by a variety of physical types [Armstrong] |
23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |