122 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] |
| 19636 | Truth is just an error insufficiently experienced [Cioran] |
| 19642 | Eventually every 'truth' is guaranteed by the police [Cioran] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| 19632 | An axiom has no more authority than a frenzy [Cioran] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 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] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
| 23073 | Convictions are failures to study anything thoroughly [Cioran] |
| 19626 | Our instincts had to be blunted and diminished, to make way for consciousness! [Cioran] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 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] |
| 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] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| 23063 | The first man obviously found paradise unendurable [Cioran] |
| 19623 | Circles of hell are ridiculous; all that matters is to be there [Cioran] |