40 ideas
23064 | So-called wisdom is just pondering things instead of acting [Cioran] |
23072 | Systems are the worst despotism, in philosophy and in life [Cioran] |
23075 | A text explained ceases to be a text [Cioran] |
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] |
23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
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] |
13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
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] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
23077 | The word 'being' is very tempting, but in fact means nothing at all [Cioran] |
23068 | People who really believe anti-realism don't bother to prove it [Cioran] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
23073 | Convictions are failures to study anything thoroughly [Cioran] |
23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
23076 | If people always acted without words we would take them for robots [Cioran] |
23065 | If only we could write like a reptile, of endless sensations and no concepts! [Cioran] |
23071 | We could only be responsible if we had consented before birth to who we are [Cioran] |
23070 | We morally dissolve if we spend time with excessive beauty [Cioran] |
23074 | In anxiety people cling to what reinforces it, because it is a deep need [Cioran] |
23069 | Fear cures boredom, because it is stronger [Cioran] |
23062 | It is better to watch the hours pass, than trying to fill them [Cioran] |
23067 | Suicide is pointless, because it always comes too late [Cioran] |
23063 | The first man obviously found paradise unendurable [Cioran] |