31 ideas
| 17070 | Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart] |
| 17072 | We need comprehensiveness, as well as self-coherence [Smart] |
| 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] |
| 12694 | Essence is the distinct thinkability of anything [Leibniz] |
| 17073 | I simply reject evidence, if it is totally contrary to my web of belief [Smart] |
| 17077 | The height of a flagpole could be fixed by its angle of shadow, but that would be very unusual [Smart] |
| 17078 | Universe expansion explains the red shift, but not vice versa [Smart] |
| 17074 | Explanations are bad by fitting badly with a web of beliefs, or fitting well into a bad web [Smart] |
| 17076 | Deducing from laws is one possible way to achieve a coherent explanation [Smart] |
| 17061 | Explanation of a fact is fitting it into a system of beliefs [Smart] |
| 17071 | An explanation is better if it also explains phenomena from a different field [Smart] |
| 17062 | If scientific explanation is causal, that rules out mathematical explanation [Smart] |
| 17075 | Scientific explanation tends to reduce things to the unfamiliar (not the familiar) [Smart] |
| 17063 | Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart] |