112 ideas
| 19608 | Wisdom is just the last gasp of a dying civilization [Cioran] |
| Full Idea: Wisdom is the last word of an expiring civilization, the nimbus of historic twilights, fatigue transfigured into a vision of the world, the last tolerance before the advent of newer gods, and of barbarism. A vain attempt at melody among the death rattles. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Twilight') | |
| A reaction: I didn't quite get what he said there, but I picked up the tone all right. But I thought wisdom was something sought in the early stages of western civilization, and now relegated to the wings as an idle dream? |
| 23064 | So-called wisdom is just pondering things instead of acting [Cioran] |
| Full Idea: What is known as 'wisdom' is ultimately only a perpetual 'thinking it over', i.e. non-action as first impulse. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 01) | |
| A reaction: This may be how most people view wisdom. Wisdom is for the spectators, not the actors (perhaps). Wisdom needs a lot of thought, and I don't associate it with extremely active people. |
| 19624 | Intelligence only fully flourishes at the end of a historical period [Cioran] |
| Full Idea: Intelligence flourishes only in the ages when beliefs wither. ...Every period's ending is the mind's paradise, for the mind regains its play and its whims only within an organism in utter dissolution. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Felicity') | |
| A reaction: I wouldn't have thought that the facts of history supported this very well. The golden ages of philosophy are the Age of Pericles, the Aristotelian Renaissance, the Enlightenment, and the early twentieth century. |
| 19599 | Ideas are neutral, but people fill them with passion and weakness [Cioran] |
| Full Idea: In itself, every idea is neutral, or should be; but man animates ideas, projects his flames and flaws into them. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Genealogy') | |
| A reaction: If it isn't neutral (if, say, it expresses love or hatred) then presumably it doesn't qualify as an 'idea'. Are ideas as neutral as mathematical theorems. It's a nice remark, and a good epigraph for a book on the history of ideas. |
| 19631 | The history of ideas (and deeds) occurs in a meaningless environment [Cioran] |
| Full Idea: The history of ideas, like that of deeds, unfolds in a meaningless climate. | |
| From: E.M. Cioran (A Short History of Decay [1949], 3) | |
| A reaction: This is the 'Tory' view of the history of ideas (as opposed to the 'Whig' view of directedness - a distinction made by historians). I would say there are periods where a certain inevitable sequence is worked out, but then there are dislocations. |
| 19645 | Some thinkers would have been just as dynamic, no matter when they had lived [Cioran] |
| Full Idea: A Kierkegaard, a Nietzsche, had they appeared in the most anodyne age, would have had no less tremulous, no less incendiary an inspiration. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'Truths') | |
| A reaction: He is saying that some (only some) thinkers are independent of the age and culture in which they live. Personally I think of those two as distinctive products of a romantic age. Diogenes of Sinope seems a bit of a misfit! |
| 19629 | A nation gives expression to its sum of values, and is then exhausted [Cioran] |
| Full Idea: A nation cannot create indefinitely. It is called upon to give expression and meaning to a sum of values which are exhausted with the soul which has begotten them. | |
| From: E.M. Cioran (A Short History of Decay [1949], 3) | |
| A reaction: This phenomenon is obvious. Is it the people who run out of steam, or the ideas and values to which their nation is giving expression? Is this a reason to break up nations every few centuries, and re-form them differently? Break up the UK! |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 19618 | I abandoned philosophy because it didn't acknowledge melancholy and human weakness [Cioran] |
| Full Idea: I turned away from philosophy when it became impossible to discover in Kant any human weakness, any authentic accent of melancholy; in Kant and in all the philosophers. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Farewell') | |
| A reaction: An interesting challenge, but if I set out to develop a philosophy based on human weakness I'm not sure where I would start, once I had settled the 'akrasia' [weakness of will] problem. |
| 19621 | Originality in philosophy is just the invention of terms [Cioran] |
| Full Idea: The philosopher's originality comes down to inventing terms. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Farewell') | |
| A reaction: Analytic philosophers are just as obsessed with inventing terms as their continental rivals. Kit Fine, for example. It can't be wrong to invent terms. Scientists do it too. |
| 19607 | The mind is superficial, only concerned with the arrangement of events, not their significance [Cioran] |
| Full Idea: The mind in itself can be only superficial, its nature being uniquely concerned with the arrangement of conceptual events, and not with their implications in the spheres the signify. | |
| From: E.M. Cioran (A Short History of Decay [1949], 'The Abstract') | |
| A reaction: This may be excessively pessimistic, and any decent philosopher must partially concede the point. Thoughts about the significance of historical events just recede into the mist. |
| 19638 | Metaphysics is a universalisation of physical anguish [Cioran] |
| Full Idea: Every metaphysic begins with an anguish of the body, which then becomes universal. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'Underside') | |
| A reaction: Not sure if I understand this, but anyone who registers the physical aspect of abstract thought gets a nod of approval from me. |
| 19620 | Great systems of philosophy are just brilliant tautologies [Cioran] |
| Full Idea: The great philosophical systems are no more than brilliant tautologies. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Farewell') | |
| A reaction: This makes them sound pointless, but the terms used in the system all have some kind of reference, so the systems are in some way about the world, and not mere private games. At the very least, they are a wonderful branch of poetry. |
| 23072 | Systems are the worst despotism, in philosophy and in life [Cioran] |
| Full Idea: Aristotle, Aquinas, Hegel - three enslavers of the mind. The worst form of despotism is the system, in philosophy and in everything. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 07) | |
| A reaction: I'm not quite clear why intellectual 'despotism' is a dreadful crime. I revere Aristotle, partly because he is systematic, but I reject about 30% of what he says. Still, many people agree with this idea. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 23075 | A text explained ceases to be a text [Cioran] |
| Full Idea: Why embroider upon what excludes commentary? A text explained is not longer a text. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 09) | |
| A reaction: I like that. I'm not a great fan of explicating texts, especially if they are literary, where the whole point is the primary experience, of a novel, poem or play. Philosophy is different, because that is a dialogue between writer and reader. |
| 19630 | No great idea ever emerged from a dialogue [Cioran] |
| Full Idea: Nothing monumental has ever emerged from dialogue, nothing explosive, nothing 'great'. | |
| From: E.M. Cioran (A Short History of Decay [1949], 3) | |
| A reaction: This may be an argument in favour of dialogue! It smacks of the creepier side of Nietzsche's thinking. I suspect individuals have had many great ideas during dialogues, though not as part of them. Greek schools were all dialogue. |
| 19636 | Truth is just an error insufficiently experienced [Cioran] |
| Full Idea: What we call truth is an error insufficiently experienced. | |
| From: E.M. Cioran (A Short History of Decay [1949], 5) | |
| A reaction: I'm not sure how to go about refuting that claim! Turn the tables, I suppose. 'Tell me, Cioran, are you claiming that this idea is true?' |
| 19642 | Eventually every 'truth' is guaranteed by the police [Cioran] |
| Full Idea: Once a belief is established the police will guarantee its 'truth' sooner or later. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'Views') |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| Full Idea: Negation never proceeds from reasoning but from something much more obscure and old. Arguments come afterward, to justify and sustain it. Every no rises out of the blood. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: Music to my ears. In the Fregean era no one is allowed to talk about the origins of logical relations in the universal facts of physical existence. You can watch dogs saying no. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 19632 | An axiom has no more authority than a frenzy [Cioran] |
| Full Idea: This earth is a place where can confirm anything with an equal likelihood: here axioms and frenzies are interchangeable. | |
| From: E.M. Cioran (A Short History of Decay [1949], 3) | |
| A reaction: A perceptive and poetic expression of the modern anti-Euclidean and anti-Fregean view of axioms, as purely formal features of a model or system. |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 9117 | The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen] |
| Full Idea: Hart argues that the smallest heap consists of four objects: three on the bottom, one on the top. | |
| From: report of William D. Hart (Hat-Tricks and Heaps [1992]) by Roy Sorensen - Vagueness and Contradiction Intro | |
| A reaction: If the objects were rough bolders, you could get away with two on the bottom. He's wrong. No one would accept as a 'heap' four minute grains barely visible to the naked eye. No one would describe such a group of items in a supermarket as a heap. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 23077 | The word 'being' is very tempting, but in fact means nothing at all [Cioran] |
| Full Idea: Whether it is spoken by a grocer or a philosopher, the word 'being', apparently so rich, so tempting, so charged with significance, in fact means nothing at all; incredible that a man in his right mind can use it on any occasion whatever. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 12) | |
| A reaction: I entirely agree. It resembles the redundancy view of 'true' (with which I do not agree). |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 23068 | People who really believe anti-realism don't bother to prove it [Cioran] |
| Full Idea: When you know quite absolutely that everything is unreal, you then cannot see why you should take the trouble to prove it. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: Does the same apply to realists? There are at least genuine arguments in both directions. Presumably the thought is that realists have something they care about, but true anti-realists don't. |
| 23073 | Convictions are failures to study anything thoroughly [Cioran] |
| Full Idea: We have convictions only if we have studied nothing thoroughly. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 08) | |
| A reaction: Excellent! I cannot imagine studying anything at all in great depth without it resulting in a dwindling expectation of full understanding. Philosophy in spades, but also probably any topic in history. |
| 23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
| Full Idea: To have opinions is inevitable, is natural; to have convictions is less so. Each time I meet someone who has convictions, I wonder what intellectual vice, what flaw has caused him to acquire such a thing. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 12) | |
| A reaction: 'The best lack all conviction/ While the worst are full of passionate intensity' (Yeats). I agree with this. Convictions are so often accompanied by anger. |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 19626 | Our instincts had to be blunted and diminished, to make way for consciousness! [Cioran] |
| Full Idea: How much our instincts must have had to be blunted and their functioning slackened before consciousness extended its control over the sum of our actions and our thoughts! | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'The Coming') | |
| A reaction: Modern wisdom, founded in neuroscience, seems to tell us that the role of consciousness even now is far less than Cioran believed. Once you digest that wisdom, I believe introspection supports it. Still, instinct in animals is much stronger than ours. |
| 23076 | If people always acted without words we would take them for robots [Cioran] |
| Full Idea: It is because of speech that men give the illusion of being free. If they did - without a word - what they do, we would take them for robots. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 09) | |
| A reaction: Love this one. Though it might be said that the power of speech does add an extra dimension of freedom to an action, beyond what any animal could attain. I take the absolute idea of 'being free' to be nonsense. |
| 19633 | We use concepts to master our fears; saying 'death' releases us from confronting it [Cioran] |
| Full Idea: It is the use of concepts which makes us master of our fears. We say: Death - and this abstraction releases us from experiencing its infinity, its horror. By baptising events and things, we elude the inexplicable. | |
| From: E.M. Cioran (A Short History of Decay [1949], 3) | |
| A reaction: I like this idea. I'm struck by how weird our lives would become if people no longer had names. They are so deeply embedded in our experience that we don't notice them. Imagine if it were taboo to ever name death. |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 23065 | If only we could write like a reptile, of endless sensations and no concepts! [Cioran] |
| Full Idea: If only we could reach back before the concept, could write on a level with the senses, record the infinitesimal variations of what we touch, do what a reptile would do if it were to set about writing! | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: A lovely thought. It is a huge effort for us to try to imagine a mental life without concepts. And then to express that mental life in words…..! |
| 19615 | I want to suppress in myself the normal reasons people have for action [Cioran] |
| Full Idea: I want to suppress in myself the reasons men invoke in order to exist, in order to act. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Gamut') | |
| A reaction: So much of our inner and moral life concerns not what we think or feel, but what we want to think or feel. The theory of action (if there can be such a thing) must account for these metareasons, which hover over us while we act. |
| 23071 | We could only be responsible if we had consented before birth to who we are [Cioran] |
| Full Idea: The problem of responsibility would have a meaning only if we had been consulted before our birth and had consented to be precisely who we are. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 06) | |
| A reaction: The question could still be asked retrospectively, like agreeing to be in an army into which you have been conscripted. People gripped by deeply anti-social desires would probably welcome the chance to become different. |
| 23070 | We morally dissolve if we spend time with excessive beauty [Cioran] |
| Full Idea: Moral disintegration when we spend time in a place that is too beautiful: the self dissolves upon contact with paradise. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 06) | |
| A reaction: I'm not sure whether that is true, but it is worth thinking about the value of experiences which are overwhelming. |
| 19628 | At a civilisation's peak values are all that matters, and people unconsciously live by them [Cioran] |
| Full Idea: Epochs of apogee cultivate values for their own sake: life is only a means of realising them; the individual is not aware of living - he lives. | |
| From: E.M. Cioran (A Short History of Decay [1949], 3) | |
| A reaction: This is a very Nietzschean thought. Mind you, a crazed and dangerous crowd exhibits the same absorption in simple values. |
| 19646 | Values don't accumulate; they are ruthlessly replaced [Cioran] |
| Full Idea: Values do not accumulate: a generation contributes something new only by trampling on what was unique in the preceding generation. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'We') | |
| A reaction: That may seem true for a Frenchman or a Romanian, but it doesn't feel true of British culture, which seems to me to have accumulated values over the last five hundred years. Before 1500 it seems to me to be a foreign country. We may be near the end! |
| 19614 | Lovers are hateful, apart from their hovering awareness of death [Cioran] |
| Full Idea: As for lovers, they would be hateful if among their grimaces the presentiment of death did not hover. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Gamut') | |
| A reaction: A nice existential corrective, if you were planning to build an ethical system around a rather sentimental idea of love! If you are not gripped by a latent fear that your beloved may die, I doubt whether you are in love. |
| 19634 | Man is never himself; he always aims at less than life, or more than life [Cioran] |
| Full Idea: Able to live only beyond and short of life, man is a prey to two temptation: imbecility and sanctity: sub-man and superman, never himself. | |
| From: E.M. Cioran (A Short History of Decay [1949], 4 'Threat') | |
| A reaction: To me, Taoism embodies imbecility, and spiritual religions embody the superman idea. [This is not Nietzsche's übermensch]. |
| 19619 | To live authentically, we must see that philosophy is totally useless [Cioran] |
| Full Idea: We begin to live authentically only where philosophy ends, at its wreck, when we have understood its terrible nullity, when we have understood that it was futile to resort to it, that it is no help. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Farewell') | |
| A reaction: The existentialist dream of trying to find an 'authentic' way of life. That idea means nothing to me. You would need to be utterly immersed in the life of a community with which you identified to live authentically, and that life has almost vanished. |
| 19622 | The pointlessness of our motives and irrelevance of our gestures reveals our vacuity [Cioran] |
| Full Idea: When we realise that no human motive is compatible with infinity, and that no gesture is worth the trouble of making it, our heart, by its very beating, can no longer conceal its vacuity. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Disintoxication') | |
| A reaction: An interesting choice of reasons. Nihilism in comparison with infinity, and in comparison with the vastness of society? If you were immortal, and there were only fifty other humans, would that help? |
| 19617 | Evidence suggests that humans do not have a purpose [Cioran] |
| Full Idea: By all evidence, we are in the world to do nothing. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Militant') | |
| A reaction: I'm not clear what evidence there could be. Other animals are all enmeshed in a particular environment. As soon as homo sapiens left Africa, it became a baffling phenonomen. I'm not sure what an alligator is in the world for, either. |
| 19612 | The universe is dirty and fragile, as if a scandal in nothingness had produced its matter [Cioran] |
| Full Idea: Everything which is done and undone in the universe bears the stamp of a filthy fragility, as if matter were the fruit of a scandal at the core of nothingness. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'The Reactionary') | |
| A reaction: A gloriously imagined idea, worthy of Shakespeare. By 'scandal' I suppose he implies that the universe is the bastard child of a horrible relationship. A prize exhibit for my 'Nihilism' collection. True nihilists, of course, don't write books. |
| 19604 | Unlike other creatures, mankind seems lost in nature [Cioran] |
| Full Idea: Whereas all beings have their place in nature, man remains a metaphysically straying creature, lost in Life, a stranger to the Creation. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'The Indirect5') | |
| A reaction: Nice challenge to the Aristotelian idea that we can identify the nature and function of man, and derive an ethics from it. This idea seems to state the essence of existentialism, perhaps better than anything in Sartre. We should have stayed in Africa? |
| 19606 | We can only live because our imagination and memory are poor [Cioran] |
| Full Idea: Life is possible only by the deficiencies of our imagination and our memory | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'The Key') | |
| A reaction: Does this mean that we should actually aspire to limit our imaginations and memories? Or are we mercifully intrinsically limited, so that massive intellectual ambition will do no harm? We should be told these things, Cioran! |
| 19601 | Life is now more dreaded than death [Cioran] |
| Full Idea: By dint of accumulating non-mysteries and monopolizing non-meanings, life inspires more dread than death; it is life which is the Great Unknown. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Variations') | |
| A reaction: This is the sort of remark we pay continental philosophers to make. |
| 23074 | In anxiety people cling to what reinforces it, because it is a deep need [Cioran] |
| Full Idea: In anxiety, a man clings to whatever can reinforce, can stimulate his providential discomfort: to try to cure him of it is to destroy his equilibrium, anxiety being the basis of his existence and his prosperity. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 09) | |
| A reaction: A report from the front line of the age of anxiety, on which I am not qualified to comment. I assume that some anxiety can be a good thing, like nerves before a public performance. |
| 19640 | No one is brave enough to say they don't want to do anything; we despise such a view [Cioran] |
| Full Idea: No one has the audacity to exclaim: 'I don't want to do anything!' - we are more indulgent with a murderer than with a mind emancipated from actions. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'The Architect') | |
| A reaction: Perhaps this should be the anti-epigraph for this website. I've slogged away at this project for nineteen years, probably for no other reason than that inactivity appears to be wicked. If I abandoned it, I would invent another project. Sad. |
| 19602 | You are stuck in the past if you don't know boredom [Cioran] |
| Full Idea: The man who knows nothing of ennui is still in the world's childhood. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Dislocation') | |
| A reaction: Boredom well may be the central experience of existentialism, rather than angst, or nihilism, or the temptations of suicide. |
| 23069 | Fear cures boredom, because it is stronger [Cioran] |
| Full Idea: Fear is the antidote to boredom: the remedy must be stronger than the disease. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 05) | |
| A reaction: I suspect that this is the motivation of people who indulge in dangerous sports. Maybe all that is need is something daunting, rather than frightening. |
| 19644 | History is the bloody rejection of boredom [Cioran] |
| Full Idea: History is the bloody product of the rejection of boredom. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'Views') | |
| A reaction: How many absurd and horrible things have been done by people who could not stand being bored? But also, almost everything wonderful has the same source. How did Bach and Shakespeare and Rembrandt feel about boredom? |
| 19641 | If you lack beliefs, boredom is your martyrdom [Cioran] |
| Full Idea: Ennui is the martyrdom of those who live and die for no belief. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'Obsequies') |
| 23062 | It is better to watch the hours pass, than trying to fill them [Cioran] |
| Full Idea: I do nothing, granted. But I see the hours pass - which is better than trying to fill them. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 01) | |
| A reaction: As Nietzsche would have pointed out, this came from a man who regularly wrote books. It is, though, certainly worth asking whether the way we fill our time is better than doing nothing. |
| 19613 | It is pointless to refuse or accept the social order; we must endure it like the weather [Cioran] |
| Full Idea: It is equally futile to refuse or to accept the social order: we must endure its changes for the better or the worse with a despairing conformism, as we endure birth, love, the weather, and death. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'The Reactionary') |
| 19627 | Opportunists can save a nation, and heroes can ruin it [Cioran] |
| Full Idea: Opportunists have saved nations; heroes have ruined them. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Defense') | |
| A reaction: Siegfried smashes the staff of Wotan. Napoleon looks like a hero, but he increasingly looks like the single most disastrous figure ever to have emerged in Europe. It took the Germans till 1940 to avenge what he did. |
| 19625 | The ideal is to impose a religion by force, and then live in doubt about its beliefs [Cioran] |
| Full Idea: To belong to a church uncertain of its god - after once imposing that god by fire and sword - should be the ideal of every detached mind. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Felicity') | |
| A reaction: I'm trying hard to think of an adequate response to this. I'll get back to you.... |
| 19605 | Despite endless suggestions, no one has found a goal for history [Cioran] |
| Full Idea: No one has found a valid goal for history; but everyone has proposed one. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'The Indirect') | |
| A reaction: This seems to be an attack on the Hegelian idea of destiny that suffused both marxism and fascism in the 1930s. |
| 19637 | History is wonderfully devoid of meaning [Cioran] |
| Full Idea: That History has no meaning is what should delight our hearts. | |
| From: E.M. Cioran (A Short History of Decay [1949], 5) | |
| A reaction: I have just read a history of the Wars of the Roses, and I wholeheartedly endorse Cioran's view. |
| 19610 | Religions see suicide as insubordination [Cioran] |
| Full Idea: If the religions have forbidden us to die by our own hand, it is because they saw that such practices set an example of insubordination which humiliated temples and gods alike. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Resources') | |
| A reaction: Has anyone ever committed suicide in a cathedral (even during a service)? How many bishops, cardinals, rabbis etc have committed suicide? It is not uncommon among priests in the lower echelons. |
| 19611 | No one has ever found a good argument against suicide [Cioran] |
| Full Idea: No church, no civil institution has as yet invented a single argument valid against suicide. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Resources') | |
| A reaction: Suicide in young people usually looks like an error of judgement (in quiet moments of history). You need more inductive evidence that life is going to be irremediably awful. But if life is fine but they choose suicide anyway, what can you say? |
| 19609 | If you have not contemplated suicide, you are a miserable worm [Cioran] |
| Full Idea: The man who has never imagined his own annihilation, who has not anticipated recourse to the rope, the bullet, poison, or the sea, is a degraded galley slave or a worm crawling upon the cosmic carrion. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1'Resources') | |
| A reaction: I guess by this date everyone in Paris had read Camus' 'The Myth of Sisyphus', so suicide was the main topic in the cafés. I sort of agree with it. The possibility of suicide is part of the examined life. |
| 23067 | Suicide is pointless, because it always comes too late [Cioran] |
| Full Idea: It's not worth the bother of killing yourself, since you always kill yourself too late. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: A neat thought, but unlikely to be true for those who commit suicide, which presumably results from a sustained and apparently incurable situation. |
| 19639 | We all need sexual secrets! [Cioran] |
| Full Idea: Woe to those who have no sexual secrets! | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'Wonders') |
| 19603 | Why is God so boring, and why does God resemble humanity so little? [Cioran] |
| Full Idea: Why is God so dull, so feeble, so inadequately picturesque? Why does He lack interest, vigor, actuality and resemble us so little? Is there any image less anthropomorphic and more gratuitously remote? | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'The Devil') | |
| A reaction: This seems to be directed at those like Feuerbach who said that we had merely created God as a glorified image of humanity. |
| 19616 | As the perfect wisdom of detachment, philosophy offers no rivals to Taoism [Cioran] |
| Full Idea: China alone long since arrived at a refined wisdom superior to philosophy: Taoism surpasses all the mind has conceived by way of detachment. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Militant') | |
| A reaction: Personally I dislike Taoism, which seems to advocate a sort of suicide within life. But given Cioran's evident state of mind, I can see its attractions. If this country deteriorates any further [I write on 4th July 2016], I may turn to Taoism. |
| 19600 | When man abandons religion, he then follows new fake gods and mythologies [Cioran] |
| Full Idea: Even when he turns from religion, man remains subject to it; depleting himself to create fake gods, he then feverishly adopts them: his need for fiction, for mythology triumphs over evidence and absurdity alike. | |
| From: E.M. Cioran (A Short History of Decay [1949], 1 'Genealogy') | |
| A reaction: Cioran had just lived through the high water mark of communism and fascism. I don't think modern atheists fit this description very well. |
| 19643 | A religion needs to motivate killings, and cannot tolerate rivals [Cioran] |
| Full Idea: A religion dies when it tolerates truths which exclude it; and the god in whose name one no longer kills is dead indeed. | |
| From: E.M. Cioran (A Short History of Decay [1949], 6 'Views') | |
| A reaction: I fear that in our time we have people who are killing in the name of their religion as a last resort to try to convince themselves that their religion is not dying. It is startlingly how religion can now be publicly mocked. Unthinkable 50 years ago. |
| 23063 | The first man obviously found paradise unendurable [Cioran] |
| Full Idea: Paradise was unendurable, otherwise the first man would have adapted to it. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 01) | |
| A reaction: Seems a bit harsh. There was evidently one aspect that was missing (knowledge), and he was surprised to find himself ejected for wanting it. Like a holiday in a Mediterranean hotel, with good food. |
| 19623 | Circles of hell are ridiculous; all that matters is to be there [Cioran] |
| Full Idea: What a preposterous notion, to draw circles in hell, to make the intensity of the flames vary in its compartments, to hierarchise its torments! The important thing is to be there. | |
| From: E.M. Cioran (A Short History of Decay [1949], '1 'La Perduta') |