36 ideas
| 8820 | Rules of reasoning precede the concept of truth, and they are what characterize it [Pollock] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 8819 | We need the concept of truth for defeasible reasoning [Pollock] |
| 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] |
| 12066 | Aristotelian and Kripkean essentialism are very different theories [Witt] |
| 12067 | An Aristotelian essence is a nonlinguistic correlate of the definition [Witt] |
| 12082 | If unity is a matter of degree, then essence may also be a matter of degree [Witt] |
| 12089 | Essences mainly explain the existence of unified substance [Witt] |
| 12102 | Essential properties of origin are too radically individual for an Aristotelian essence [Witt] |
| 8822 | Statements about necessities need not be necessarily true [Pollock] |
| 8818 | Defeasible reasoning requires us to be able to think about our thoughts [Pollock] |
| 8811 | What we want to know is - when is it all right to believe something? [Pollock] |
| 8817 | Logical entailments are not always reasons for beliefs, because they may be irrelevant [Pollock] |
| 8814 | Epistemic norms are internalised procedural rules for reasoning [Pollock] |
| 8823 | Reasons are always for beliefs, but a perceptual state is a reason without itself being a belief [Pollock] |
| 8813 | If we have to appeal explicitly to epistemic norms, that will produce an infinite regress [Pollock] |
| 8812 | Norm Externalism says norms must be internal, but their selection is partly external [Pollock] |
| 8816 | Externalists tend to take a third-person point of view of epistemology [Pollock] |
| 8815 | Belief externalism is false, because external considerations cannot be internalized for actual use [Pollock] |
| 12085 | Reality is directional [Witt] |