29 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] |
| 15091 | Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker] |
| 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] |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| 15095 | A property's causal features are essential, and only they fix its identity [Shoemaker] |
| 15097 | I claim that a property has its causal features in all possible worlds [Shoemaker] |
| 15094 | I now deny that properties are cluster of powers, and take causal properties as basic [Shoemaker] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 15099 | If something is possible, but not nomologically possible, we need metaphysical possibility [Shoemaker] |
| 15101 | Once you give up necessity as a priori, causal necessity becomes the main type of necessity [Shoemaker] |
| 15098 | Empirical evidence shows that imagining a phenomenon can show it is possible [Shoemaker] |
| 15100 | Imagination reveals conceptual possibility, where descriptions avoid contradiction or incoherence [Shoemaker] |
| 15096 | 'Grue' only has causal features because of its relation to green [Shoemaker] |
| 15093 | We might say laws are necessary by combining causal properties with Armstrong-Dretske-Tooley laws [Shoemaker] |