84 ideas
23064 | So-called wisdom is just pondering things instead of acting [Cioran] |
19608 | Wisdom is just the last gasp of a dying civilization [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] |
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] |
19629 | A nation gives expression to its sum of values, and is then exhausted [Cioran] |
19621 | Originality in philosophy is just the invention of terms [Cioran] |
19618 | I abandoned philosophy because it didn't acknowledge melancholy and human weakness [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] |
19636 | Truth is just an error insufficiently experienced [Cioran] |
19642 | Eventually every 'truth' is guaranteed by the police [Cioran] |
13520 | A 'tautology' must include connectives [Wolf,RS] |
13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
19632 | An axiom has no more authority than a frenzy [Cioran] |
13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
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] |
23073 | Convictions are failures to study anything thoroughly [Cioran] |
23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
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] |
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] |
19612 | The universe is dirty and fragile, as if a scandal in nothingness had produced its matter [Cioran] |
19617 | Evidence suggests that humans do not have a purpose [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] |
23062 | It is better to watch the hours pass, than trying to fill them [Cioran] |
19602 | You are stuck in the past if you don't know boredom [Cioran] |
19641 | If you lack beliefs, boredom is your martyrdom [Cioran] |
19644 | History is the bloody rejection of boredom [Cioran] |
19640 | No one is brave enough to say they don't want to do anything; we despise such a view [Cioran] |
23069 | Fear cures boredom, because it is stronger [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] |
19637 | History is wonderfully devoid of meaning [Cioran] |
19605 | Despite endless suggestions, no one has found a goal for history [Cioran] |
23067 | Suicide is pointless, because it always comes too late [Cioran] |
19610 | Religions see suicide as insubordination [Cioran] |
19609 | If you have not contemplated suicide, you are a miserable worm [Cioran] |
19611 | No one has ever found a good argument against suicide [Cioran] |
19639 | We all need sexual secrets! [Cioran] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
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] |