28 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] |
| 18890 | Putnam smuggles essentialism about liquids into his proof that water must be H2O [Salmon,N on Putnam] |
| 7705 | The Twin Earth theory suggests that intentionality is independent of qualia [Jacquette on Putnam] |
| 4099 | If Twins talking about 'water' and 'XYZ' have different thoughts but identical heads, then thoughts aren't in the head [Putnam, by Crane] |
| 12026 | We say ice and steam are different forms of water, but not that they are different forms of H2O [Forbes,G on Putnam] |
| 3208 | Does 'water' mean a particular substance that was 'dubbed'? [Putnam, by Rey] |
| 3893 | Often reference determines sense, and not (as Frege thought) vice versa [Putnam, by Scruton] |
| 11191 | The hidden structure of a natural kind determines membership in all possible worlds [Putnam] |
| 8409 | Probabilistic causal concepts are widely used in everyday life and in science [Salmon] |
| 11192 | If causes are the essence of diseases, then disease is an example of a relational essence [Putnam, by Williams,NE] |
| 11190 | Archimedes meant by 'gold' the hidden structure or essence of the stuff [Putnam] |