39 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] |
| 4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
| 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] |
| 17000 | We might fix identities for small particulars, but it is utopian to hope for such things [Kripke] |
| 11868 | A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke] |
| 17044 | A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke] |
| 16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke] |
| 17058 | What many people consider merely physically necessary I consider completely necessary [Kripke] |
| 4970 | What is often held to be mere physical necessity is actually metaphysical necessity [Kripke] |
| 17059 | Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke] |
| 4950 | Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke] |
| 17003 | Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke] |
| 9221 | The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider] |
| 17052 | The a priori analytic truths involving fixing of reference are contingent [Kripke] |
| 4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
| 4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
| 4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
| 4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
| 4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
| 4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |
| 4969 | I regard the mind-body problem as wide open, and extremely confusing [Kripke] |
| 4956 | A description may fix a reference even when it is not true of its object [Kripke] |
| 17032 | Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke] |