32 ideas
| 19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
| 19067 | A successful proof requires recognition of truth at every step [Dummett] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
| 19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
| 19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
| 19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
| 19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
| 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] |
| 22449 | When we say 'is red' we don't mean 'seems red to most people' [Foot] |
| 19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
| 19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
| 22451 | All people need affection, cooperation, community and help in trouble [Foot] |
| 22452 | Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot] |