38 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] |
| 19393 | What is not active is nothing [Leibniz] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 14703 | Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter] |
| 14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |
| 14704 | 2D semantics gives us apriori knowledge of our own meanings [Schroeter] |
| 14706 | Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter] |
| 14711 | Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter] |
| 14717 | Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter] |
| 14720 | Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter] |
| 14695 | Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter] |
| 14696 | Simple semantics assigns extensions to names and to predicates [Schroeter] |
| 14697 | 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter] |
| 14698 | Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter] |
| 14699 | Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter] |
| 14709 | Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter] |
| 14719 | In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter] |
| 14701 | Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter] |
| 14702 | If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter] |
| 14705 | Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter] |
| 14715 | 2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter] |
| 14716 | 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter] |