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] |
| 9216 | Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K] |
| 9214 | Unsupported testimony may still be believable [Fine,K] |
| 8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
| 8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
| 8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
| 8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
| 8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
| 8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
| 8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
| 8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
| 8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |
| 9215 | Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K] |