35 ideas
14052 | Begin philosophy when you are young, and keep going when you are old [Epicurus] |
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] |
7639 | The Homunculus Fallacy explains a subject perceiving objects by repeating the problem internally [Evans] |
14062 | Sooner follow mythology, than accept the 'fate' of natural philosophers [Epicurus] |
1837 | We should not refer things to irresponsible necessity, but either to fortune or to our own will [Epicurus] |
1836 | Prudence is more valuable than philosophy, because it avoids confusions of the soul [Epicurus] |
14061 | Our own choices are autonomous, and the basis for praise and blame [Epicurus] |
14054 | Fearing death is absurd, because we are not present when it occurs [Epicurus] |
14053 | It is absurd to fear the pain of death when you are not even facing it [Epicurus] |
14055 | The wisdom that produces a good life also produces a good death [Epicurus] |
14057 | All pleasures are good, but it is not always right to choose them [Epicurus] |
14058 | Pleasure is the goal, but as lack of pain and calm mind, not as depraved or greedy pleasure [Epicurus] |
1833 | Pleasure is the first good in life [Epicurus] |
14063 | Sooner a good decision going wrong, than a bad one turning out for the good [Epicurus] |
14059 | The best life is not sensuality, but rational choice and healthy opinion [Epicurus] |
1835 | True pleasure is not debauchery, but freedom from physical and mental pain [Epicurus] |
14056 | We only need pleasure when we have the pain of desire [Epicurus] |
14060 | Prudence is the greatest good, and more valuable than philosophy, because it produces virtue [Epicurus] |