119 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] |
| 6575 | Philosophy may never find foundations, and may undermine our lives in the process [Fogelin] |
| 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] |
| 6585 | Rationality is threatened by fear of inconsistency, illusions of absolutes or relativism, and doubt [Fogelin] |
| 6557 | Humans may never be able to attain a world view which is both rich and consistent [Fogelin] |
| 6568 | A game can be played, despite having inconsistent rules [Fogelin] |
| 6560 | The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin] |
| 6565 | The law of noncontradiction makes the distinction between asserting something and denying it [Fogelin] |
| 19630 | No great idea ever emerged from a dialogue [Cioran] |
| 6574 | Legal reasoning is analogical, not deductive [Fogelin] |
| 19636 | Truth is just an error insufficiently experienced [Cioran] |
| 19642 | Eventually every 'truth' is guaranteed by the police [Cioran] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| 19632 | An axiom has no more authority than a frenzy [Cioran] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 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] |
| 6582 | Conventions can only work if they are based on something non-conventional [Fogelin] |
| 23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
| 23073 | Convictions are failures to study anything thoroughly [Cioran] |
| 6576 | My view is 'circumspect rationalism' - that only our intellect can comprehend the world [Fogelin] |
| 6589 | Knowledge is legitimate only if all relevant defeaters have been eliminated [Fogelin] |
| 6596 | For coherentists, circularity is acceptable if the circle is large, rich and coherent [Fogelin] |
| 6597 | A rule of justification might be: don't raise the level of scrutiny without a good reason [Fogelin] |
| 6588 | Scepticism is cartesian (sceptical scenarios), or Humean (future), or Pyrrhonian (suspend belief) [Fogelin] |
| 6590 | Scepticism deals in remote possibilities that are ineliminable and set the standard very high [Fogelin] |
| 6583 | Radical perspectivism replaces Kant's necessary scheme with many different schemes [Fogelin] |
| 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] |
| 6555 | We are also irrational, with a unique ability to believe in bizarre self-created fictions [Fogelin] |
| 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] |
| 6605 | Critics must be causally entangled with their subject matter [Fogelin] |
| 6607 | The word 'beautiful', when deprived of context, is nearly contentless [Fogelin] |
| 23070 | We morally dissolve if we spend time with excessive beauty [Cioran] |
| 6604 | Saying 'It's all a matter to taste' ignores the properties of the object discussed [Fogelin] |
| 19628 | At a civilisation's peak values are all that matters, and people unconsciously live by them [Cioran] |
| 6586 | Cynics are committed to morality, but disappointed or disgusted by human failings [Fogelin] |
| 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] |
| 19602 | You are stuck in the past if you don't know boredom [Cioran] |
| 23069 | Fear cures boredom, because it is stronger [Cioran] |
| 19644 | History is the bloody rejection of boredom [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] |
| 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] |
| 6572 | Deterrence, prevention, rehabilitation and retribution can come into conflict in punishments [Fogelin] |
| 6573 | Retributivists say a crime can be 'paid for'; deterrentists still worry about potential victims [Fogelin] |
| 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] |