30 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
15163 | The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
15158 | Indefinite descriptions are quantificational in subject position, but not in predicate position [Soames] |
15157 | Recognising the definite description 'the man' as a quantifier phrase, not a singular term, is a real insight [Soames] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
15156 | The universal and existential quantifiers were chosen to suit mathematics [Soames] |
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] |
15162 | We understand metaphysical necessity intuitively, from ordinary life [Soames] |
15161 | There are more metaphysically than logically necessary truths [Soames] |
22449 | When we say 'is red' we don't mean 'seems red to most people' [Foot] |
15152 | To study meaning, study truth conditions, on the basis of syntax, and representation by the parts [Soames] |
15153 | Tarski's account of truth-conditions is too weak to determine meanings [Soames] |
15154 | We should use cognitive states to explain representational propositions, not vice versa [Soames] |
22451 | All people need affection, cooperation, community and help in trouble [Foot] |
22452 | Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot] |