31 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] |
| 15200 | How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin] |
| 14761 | Change is not just having two different qualities at different points in some series [McTaggart] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 15119 | Aristotelian explanation by essence may need to draw on knowledge of other essences [Aristotle, by Koslicki] |
| 2608 | For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer] |
| 22936 | A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin] |
| 4231 | Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe] |
| 8591 | There could be no time if nothing changed [McTaggart] |
| 22935 | The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin] |
| 7802 | A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle] |
| 4230 | A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe] |
| 15199 | The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin] |
| 23302 | Plants have far less life than animals, but more life than other corporeal entities [Aristotle] |
| 23301 | There is a gradual proceeding from the inanimate to animals, with no clear borderlines [Aristotle] |