36 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] |
12132 | Indiscernibility is a necessary and sufficient condition for identity [Brody] |
15834 | Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P] |
12140 | Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody] |
11895 | A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P] |
12141 | Maybe essential properties are those which determine a natural kind? [Brody] |
12137 | De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody] |
12142 | Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody] |
12143 | An object having a property essentially is equivalent to its having it necessarily [Brody] |
12144 | Essentialism is justified if the essential properties of things explain their other properties [Brody] |
12139 | Mereological essentialism says that every part that ensures the existence is essential [Brody] |
12135 | Interrupted objects have two first moments of existence, which could be two beginnings [Brody] |
12130 | a and b share all properties; so they share being-identical-with-a; so a = b [Brody] |
12138 | Identity across possible worlds is prior to rigid designation [Brody] |
7257 | All modern social systems seem to be conspiracies of the rich [More,T] |
7254 | If you try to get elected, you should be permanently barred from seeking office [More,T] |
7255 | Only Utopians fail to see glory in warfare [More,T] |
7253 | In Utopia, legal euthanasia is considered honourable [More,T] |
7256 | In Utopia, the Supreme Being is identical with Nature [More,T] |