35 ideas
| 12596 | Reasoning aims at increasing explanatory coherence [Harman] |
| 12599 | Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman] |
| 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] |
| 12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
| 12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
| 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] |
| 12598 | Reality is the overlap of true complete theories [Harman] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 490 | Everything happens by reason and necessity [Leucippus] |
| 12602 | There is no natural border between inner and outer [Harman] |
| 12603 | We can only describe mental attitudes in relation to the external world [Harman] |
| 12601 | The way things look is a relational matter, not an intrinsic matter [Harman] |
| 12592 | Concepts in thought have content, but not meaning, which requires communication [Harman] |
| 12590 | Take meaning to be use in calculation with concepts, rather than in communication [Harman] |
| 12593 | The use theory attaches meanings to words, not to sentences [Harman] |
| 12588 | Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman] |
| 12589 | Some regard conceptual role semantics as an entirely internal matter [Harman] |
| 12600 | The content of thought is relations, between mental states, things in the world, and contexts [Harman] |
| 12594 | If one proposition negates the other, which is the negative one? [Harman] |
| 12591 | Mastery of a language requires thinking, and not just communication [Harman] |