70 ideas
| 7846 | Nietzsche thinks philosophy makes us more profound, but not better [Nietzsche, by Ansell Pearson] |
| 20107 | How many mediocre thinkers are occupied with influential problems! [Nietzsche] |
| 20352 | Nietzsche has a metaphysics, as well as perspectives - the ontology is the perspectives [Nietzsche, by Richardson] |
| 20379 | Reason is just another organic drive, developing late, and fighting for equality [Nietzsche] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| 20123 | First see nature as non-human, then fit ourselves into this view of nature [Nietzsche] |
| 20105 | Storms are wonderful expressions of free powers! [Nietzsche] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 20376 | We begin with concepts of kinds, from individuals; but that is not the essence of individuals [Nietzsche] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| 22501 | Nietzsche classified actions by the nature of the agent, not the nature of the act [Nietzsche, by Foot] |
| 22500 | Nietzsche failed to see that moral actions can be voluntary without free will [Foot on Nietzsche] |
| 20128 | Each person has a fixed constitution, which makes them a particular type of person [Nietzsche, by Leiter] |
| 22503 | Nietzsche could only revalue human values for a different species [Nietzsche, by Foot] |
| 8041 | The superman is a monstrous oddity, not a serious idea [MacIntyre on Nietzsche] |
| 20135 | Nietzsche's higher type of man is much more important than the idealised 'superman' [Nietzsche, by Leiter] |
| 20353 | The 'will to power' is basically applied to drives and forces, not to people [Nietzsche, by Richardson] |
| 20113 | Friendly chats undermine my philosophy; wanting to be right at the expense of love is folly [Nietzsche] |
| 22475 | Moral generalisation is wrong, because we should evaluate individual acts [Nietzsche, by Foot] |
| 22476 | Nietzsche thought our psychology means there can't be universal human virtues [Nietzsche, by Foot] |
| 20104 | Nietzsche tried to lead a thought-provoking life [Safranski on Nietzsche] |
| 7847 | Initially nihilism was cosmic, but later Nietzsche saw it as a cultural matter [Nietzsche, by Ansell Pearson] |
| 9782 | Nietzsche urges that nihilism be active, and will nothing itself [Nietzsche, by Zizek] |
| 20102 | Flight from boredom leads to art [Nietzsche] |
| 20106 | Nietzsche was fascinated by a will that can turn against itself [Nietzsche, by Safranski] |
| 20124 | Reliving life countless times - this gives the value back to life which religion took away [Nietzsche] |
| 20367 | Individual development is more important than the state, but a community is necessary [Nietzsche] |
| 20371 | Nietzsche thinks we should join a society, in order to criticise, heal and renew it [Nietzsche, by Richardson] |
| 20108 | Every culture loses its identity and power if it lacks a major myth [Nietzsche] |