40 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] |
| 22189 | Why abandon a theory if you don't have a better one? [Gorham] |
| 22190 | If a theory is more informative it is less probable [Gorham] |
| 22192 | Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham] |
| 22194 | Structural Realism says mathematical structures persist after theory rejection [Gorham] |
| 22195 | Structural Realists must show the mathematics is both crucial and separate [Gorham] |
| 22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
| 22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
| 22193 | Consilience makes the component sciences more likely [Gorham] |
| 22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |