41 ideas
| 9766 | Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K] |
| 12442 | 'Mickey Mouse is a fictional mouse' is true without a truthmaker [Azzouni] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 12439 | Truth is dispensable, by replacing truth claims with the sentence itself [Azzouni] |
| 12437 | Truth lets us assent to sentences we can't explicitly exhibit [Azzouni] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 9775 | Excluded Middle, and classical logic, may fail for vague predicates [Fine,K] |
| 12446 | Names function the same way, even if there is no object [Azzouni] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 9771 | Logic holding between indefinite sentences is the core of all language [Fine,K] |
| 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] |
| 12447 | That all existents have causal powers is unknowable; the claim is simply an epistemic one [Azzouni] |
| 12445 | If fictional objects really don't exist, then they aren't abstract objects [Azzouni] |
| 9768 | Vagueness is semantic, a deficiency of meaning [Fine,K] |
| 9776 | A thing might be vaguely vague, giving us higher-order vagueness [Fine,K] |
| 9767 | A vague sentence is only true for all ways of making it completely precise [Fine,K] |
| 9770 | Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K] |
| 9772 | Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K] |
| 9773 | With the super-truth approach, the classical connectives continue to work [Fine,K] |
| 9774 | Borderline cases must be under our control, as capable of greater precision [Fine,K] |
| 12449 | Modern metaphysics often derives ontology from the logical forms of sentences [Azzouni] |
| 12440 | If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni] |
| 12438 | In the vernacular there is no unequivocal ontological commitment [Azzouni] |
| 12441 | We only get ontology from semantics if we have already smuggled it in [Azzouni] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 12448 | Things that don't exist don't have any properties [Azzouni] |
| 9769 | Vagueness can be in predicates, names or quantifiers [Fine,K] |
| 12450 | The periodic table not only defines the elements, but also excludes other possible elements [Azzouni] |