28 ideas
22087 | Philosophy fails to articulate the continual becoming of existence [Kierkegaard, by Carlisle] |
5651 | Traditional views of truth are tautologies, and truth is empty without a subject [Kierkegaard, by Scruton] |
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] |
22312 | Facts can be both positive and negative [Wittgenstein, by Potter] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
22090 | For me time stands still, and I with it [Kierkegaard, by Carlisle] |
9305 | The plebeians bore others; only the nobility bore themselves [Kierkegaard] |
5650 | Reason is just abstractions, so our essence needs a subjective 'leap of faith' [Kierkegaard, by Scruton] |
22095 | There are aesthetic, ethical and religious subjectivity [Kierkegaard, by Carlisle] |
20747 | What matters is not right choice, but energy, earnestness and pathos in the choosing [Kierkegaard] |
22091 | Kierkegaard prioritises the inward individual, rather than community [Kierkegaard, by Carlisle] |
22088 | Faith is like a dancer's leap, going up to God, but also back to earth [Kierkegaard, by Carlisle] |