32 ideas
7740 | There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner] |
19466 | The word 'true' seems to be unique and indefinable [Frege] |
19465 | There cannot be complete correspondence, because ideas and reality are quite different [Frege] |
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
19468 | The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege] |
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] |
19470 | Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege] |
19471 | A fact is a thought that is true [Frege] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
9877 | Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett] |
19469 | We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege] |
8162 | Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett] |
9818 | A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett] |
16379 | Thoughts about myself are understood one way to me, and another when communicated [Frege] |
19467 | A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege] |
19472 | A sentence is only a thought if it is complete, and has a time-specification [Frege] |
20695 | God's eternal power and deity are clearly seen in what has been created [Paul] |