106 ideas
| 19608 | Wisdom is just the last gasp of a dying civilization [Cioran] |
| 23064 | So-called wisdom is just pondering things instead of acting [Cioran] |
| 19624 | Intelligence only fully flourishes at the end of a historical period [Cioran] |
| 19599 | Ideas are neutral, but people fill them with passion and weakness [Cioran] |
| 19631 | The history of ideas (and deeds) occurs in a meaningless environment [Cioran] |
| 19645 | Some thinkers would have been just as dynamic, no matter when they had lived [Cioran] |
| 19629 | A nation gives expression to its sum of values, and is then exhausted [Cioran] |
| 19618 | I abandoned philosophy because it didn't acknowledge melancholy and human weakness [Cioran] |
| 19621 | Originality in philosophy is just the invention of terms [Cioran] |
| 19607 | The mind is superficial, only concerned with the arrangement of events, not their significance [Cioran] |
| 19638 | Metaphysics is a universalisation of physical anguish [Cioran] |
| 19620 | Great systems of philosophy are just brilliant tautologies [Cioran] |
| 23072 | Systems are the worst despotism, in philosophy and in life [Cioran] |
| 23075 | A text explained ceases to be a text [Cioran] |
| 19630 | No great idea ever emerged from a dialogue [Cioran] |
| 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] |
| 19642 | Eventually every 'truth' is guaranteed by the police [Cioran] |
| 19636 | Truth is just an error insufficiently experienced [Cioran] |
| 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] |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 19632 | An axiom has no more authority than a frenzy [Cioran] |
| 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] |
| 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] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
| 23073 | Convictions are failures to study anything thoroughly [Cioran] |
| 3568 | Surely ALL truths are externally justified, by the facts? [Cross,A] |
| 19626 | Our instincts had to be blunted and diminished, to make way for consciousness! [Cioran] |
| 23076 | If people always acted without words we would take them for robots [Cioran] |
| 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] |
| 19633 | We use concepts to master our fears; saying 'death' releases us from confronting it [Cioran] |
| 23065 | If only we could write like a reptile, of endless sensations and no concepts! [Cioran] |
| 19615 | I want to suppress in myself the normal reasons people have for action [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] |
| 19628 | At a civilisation's peak values are all that matters, and people unconsciously live by them [Cioran] |
| 19646 | Values don't accumulate; they are ruthlessly replaced [Cioran] |
| 19614 | Lovers are hateful, apart from their hovering awareness of death [Cioran] |
| 19634 | Man is never himself; he always aims at less than life, or more than life [Cioran] |
| 19619 | To live authentically, we must see that philosophy is totally useless [Cioran] |
| 19622 | The pointlessness of our motives and irrelevance of our gestures reveals our vacuity [Cioran] |
| 19617 | Evidence suggests that humans do not have a purpose [Cioran] |
| 19612 | The universe is dirty and fragile, as if a scandal in nothingness had produced its matter [Cioran] |
| 19604 | Unlike other creatures, mankind seems lost in nature [Cioran] |
| 19606 | We can only live because our imagination and memory are poor [Cioran] |
| 19601 | Life is now more dreaded than death [Cioran] |
| 23074 | In anxiety people cling to what reinforces it, because it is a deep need [Cioran] |
| 19640 | No one is brave enough to say they don't want to do anything; we despise such a view [Cioran] |
| 19641 | If you lack beliefs, boredom is your martyrdom [Cioran] |
| 23062 | It is better to watch the hours pass, than trying to fill them [Cioran] |
| 23069 | Fear cures boredom, because it is stronger [Cioran] |
| 19644 | History is the bloody rejection of boredom [Cioran] |
| 19602 | You are stuck in the past if you don't know boredom [Cioran] |
| 19613 | It is pointless to refuse or accept the social order; we must endure it like the weather [Cioran] |
| 19627 | Opportunists can save a nation, and heroes can ruin it [Cioran] |
| 19625 | The ideal is to impose a religion by force, and then live in doubt about its beliefs [Cioran] |
| 19605 | Despite endless suggestions, no one has found a goal for history [Cioran] |
| 19637 | History is wonderfully devoid of meaning [Cioran] |
| 19610 | Religions see suicide as insubordination [Cioran] |
| 19611 | No one has ever found a good argument against suicide [Cioran] |
| 19609 | If you have not contemplated suicide, you are a miserable worm [Cioran] |
| 23067 | Suicide is pointless, because it always comes too late [Cioran] |
| 19639 | We all need sexual secrets! [Cioran] |
| 19603 | Why is God so boring, and why does God resemble humanity so little? [Cioran] |
| 19616 | As the perfect wisdom of detachment, philosophy offers no rivals to Taoism [Cioran] |
| 19600 | When man abandons religion, he then follows new fake gods and mythologies [Cioran] |
| 19643 | A religion needs to motivate killings, and cannot tolerate rivals [Cioran] |
| 23063 | The first man obviously found paradise unendurable [Cioran] |
| 19623 | Circles of hell are ridiculous; all that matters is to be there [Cioran] |