29 ideas
| 13941 | Are the truth-bearers sentences, utterances, ideas, beliefs, judgements, propositions or statements? [Cartwright,R] |
| 13942 | Logicians take sentences to be truth-bearers for rigour, rather than for philosophical reasons [Cartwright,R] |
| 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] |
| 13945 | A token isn't a unique occurrence, as the case of a word or a number shows [Cartwright,R] |
| 21507 | Scientific explanation aims at a unifying account of underlying structures and processes [Hempel] |
| 13948 | For any statement, there is no one meaning which any sentence asserting it must have [Cartwright,R] |
| 13950 | People don't assert the meaning of the words they utter [Cartwright,R] |
| 13944 | We can pull apart assertion from utterance, and the action, the event and the subject-matter for each [Cartwright,R] |
| 13947 | 'It's raining' makes a different assertion on different occasions, but its meaning remains the same [Cartwright,R] |
| 13943 | We can attribute 'true' and 'false' to whatever it was that was said [Cartwright,R] |
| 13946 | To assert that p, it is neither necessary nor sufficient to utter some particular words [Cartwright,R] |
| 13951 | Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R] |