36 ideas
| 15053 | If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K] |
| 15054 | 'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K] |
| 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] |
| 15007 | If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on Fine,K] |
| 15006 | Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider] |
| 15055 | Grounding relations are best expressed as relations between sentences [Fine,K] |
| 15050 | Reduction might be producing a sentence which gets closer to the logical form [Fine,K] |
| 15051 | Reduction might be semantic, where a reduced sentence is understood through its reduction [Fine,K] |
| 15052 | Reduction is modal, if the reductions necessarily entail the truth of the target sentence [Fine,K] |
| 15056 | The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K] |
| 15047 | What is real can only be settled in terms of 'ground' [Fine,K] |
| 15046 | Reality is a primitive metaphysical concept, which cannot be understood in other terms [Fine,K] |
| 15060 | Why should what is explanatorily basic be therefore more real? [Fine,K] |
| 15048 | In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 16614 | Matter and form give true unity; subject and accident is just unity 'per accidens' [Duns Scotus] |
| 15061 | Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K] |
| 15059 | Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K] |
| 15057 | Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K] |
| 15058 | A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K] |