49 ideas
| 9247 | Life will be lived better if it has no meaning [Camus] |
| Full Idea: Life will be lived all the better if it has no meaning. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs free') | |
| A reaction: One image of the good life is that of a successful wild animal, for which existence is not a problem, merely a constant activity and pursuit. Maybe life begins to acquire meaning once we realise that meaning should not be sought directly. |
| 6707 | Suicide - whether life is worth living - is the one serious philosophical problem [Camus] |
| Full Idea: There is but one truly serious philosophical problem and that is suicide. Judgine whether life is or is not worth living amounts to answering the fundamental question of philosophy. | |
| From: Albert Camus (The Myth of Sisyphus [1942], p.11) | |
| A reaction: What a wonderful thesis for a book. In Idea 2682 there is the possibility of life being worth living, but not worth a huge amount of effort. It is better to call Camus' question the first question, rather than the only question. |
| 9245 | To an absurd mind reason is useless, and there is nothing beyond reason [Camus] |
| Full Idea: To an absurd mind reason is useless, and there is nothing beyond reason. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Phil Suic') | |
| A reaction: But there is, surely, intuition and instinct? Read Keats's Letters. There is good living through upbringing and habit. Read Aristotle. If you like Camus' thought, you will love Chuang Tzu. Personally I am a child of the Enlightenment. |
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| Full Idea: The problem with the Axiom of Choice is that it allows an initiate (by an ingenious train of reasoning) to cut a golf ball into a finite number of pieces and put them together again to make a globe as big as the sun. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 9) | |
| A reaction: I'm not sure how this works (and I think it was proposed by the young Tarski), but it sounds like a real problem to me, for all the modern assumptions that Choice is fine. |
| 10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
| Full Idea: The Axiom of Choice seems better treated as a non-logical principle of set-theory. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4 n8) | |
| A reaction: This reinforces the idea that set theory is not part of logic (and so pure logicism had better not depend on set theory). |
| 10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
| Full Idea: We cannot explicitly define one-one correspondence from the sets to the ordinals (because there is no explicit well-ordering of R). Nevertheless, the Axiom of Choice guarantees that a one-one correspondence does exist, even if we cannot define it. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| Full Idea: Predicativists doubt the existence of sets with no predicative definition. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3) | |
| A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate? |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job. |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be. |
| 10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
| Full Idea: We might reduce sets to ordinal numbers, thereby reversing the standard set-theoretical reduction of ordinals to sets. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) | |
| A reaction: He has demonstrated that there are as many ordinals as there are sets. |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
| Full Idea: Extensional mereology defs: 'distinct' things have no parts in common; a 'fusion' has some things all of which are parts, with no further parts. Axioms: (transitivity) a part of a part is part of the whole; (sums) any things have a unique fusion. | |
| From: Keith Hossack (Plurals and Complexes [2000], 5) |
| 9244 | Logic is easy, but what about logic to the point of death? [Camus] |
| Full Idea: It is always easy to be logical. It is almost impossible to be logical to the bitter end. The only problem that interests me is: is there a logic to the point of death? | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs and Suic') | |
| A reaction: This is a lovely hand grenade to lob into an analytical logic class! It is very hard to get logicians to actually ascribe a clear value to their activity. They tend to present it as a marginal private game, and yet it has high status. |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
| Full Idea: The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4) | |
| A reaction: This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point. |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| Full Idea: The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3) | |
| A reaction: This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him. |
| 10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
| Full Idea: If we extend the power of language with plural definite descriptions, these would pick out the largest class of things that fit the description. | |
| From: Keith Hossack (Plurals and Complexes [2000], 3) |
| 10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
| Full Idea: It may be that plural reference gives atomism the resources to state complex facts without needing to refer to complex things. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: This seems the most interesting metaphysical implication of the possibility of plural quantification. |
| 10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
| Full Idea: If all properties are distributive, plural reference is just a handy abbreviation to avoid repetition (as in 'A and B are hungry', to avoid 'A is hungry and B is hungry'), but not all properties are distributive (as in 'some people surround a table'). | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: The characteristic examples to support plural quantification involve collective activity and relations, which might be weeded out of our basic ontology, thus leaving singular quantification as sufficient. |
| 10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
| Full Idea: Singular comprehension principles have a bad reputation, but the plural comprehension principle says that given a condition on individuals, there are some things such that something is one of them iff it meets the condition. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
| Full Idea: In a plural language we can discuss without fear of inconsistency the things that are not members of themselves. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) | |
| A reaction: [see Hossack for details] |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| Full Idea: You have 1 and 0, something and nothing. Adding gives us the naturals. Subtracting brings the negatives into light; dividing, the rationals; only with a new operation, taking of roots, do the irrationals show themselves. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Mind') | |
| A reaction: The suggestion is constructivist, I suppose - that it is only operations that produce numbers. They go on to show that complex numbers don't quite fit the pattern. |
| 10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
| Full Idea: The theory of the transfinite needs the ordinal numbers. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| Full Idea: The rationals are everywhere - the irrationals are everywhere else. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Nameless') | |
| A reaction: Nice. That is, the rationals may be dense (you can always find another one in any gap), but the irrationals are continuous (no gaps). |
| 10684 | I take the real numbers to be just lengths [Hossack] |
| Full Idea: I take the real numbers to be just lengths. | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) | |
| A reaction: I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged. |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| Full Idea: The 'commutative' laws say the order in which you add or multiply two numbers makes no difference; ...the 'associative' laws declare that regrouping couldn't change a sum or product (e.g. a+(b+c)=(a+b)+c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: This seem utterly self-evident, but in more complex systems they can break down, so it is worth being conscious of them. |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| Full Idea: The 'distributive' law says you will get the same result if you first add two numbers, and then multiply them by a third, or first multiply each by the third and then add the results (i.e. a · (b+c) = a · b + a · c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: Obviously this will depend on getting the brackets right, to ensure you are indeed doing the same operations both ways. |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| Full Idea: The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1) | |
| A reaction: Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm. |
| 10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
| Full Idea: A language with plurals is better for arithmetic. Instead of a first-order fragment expressible by an induction schema, we have the complete truth with a plural induction axiom, beginning 'If there are some numbers...'. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
| Full Idea: In arithmetic singularists need sets as the instantiator of numeric properties. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 10685 | Set theory is the science of infinity [Hossack] |
| Full Idea: Set theory is the science of infinity. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| Full Idea: I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro) | |
| A reaction: Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude. |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| Full Idea: Numbers cannot be mental objects constructed by our own minds: there exists at most a potential infinity of mental constructions, whereas the axioms of mathematics require an actual infinity of numbers. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro 2) | |
| A reaction: Doubt this, but don't know enough to refute it. Actual infinities were a fairly late addition to maths, I think. I would think treating fictional complete infinities as real would be sufficient for the job. Like journeys which include imagined roads. |
| 10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
| Full Idea: By Quine's test of ontological commitment, if some children are sitting in a circle, no individual child can sit in a circle, so a singular paraphrase will have us committed to a 'group' of children. | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: Nice of why Quine is committed to the existence of sets. Hossack offers plural quantification as a way of avoiding commitment to sets. But is 'sitting in a circle' a real property (in the Shoemaker sense)? I can sit in a circle without realising it. |
| 10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
| Full Idea: Complex particulars are of at least three types: masses (which sum, of which we do not ask 'how many?' but 'how much?'); composite individuals (how many?, and summing usually fails); and sets (only divisible one way, unlike composites). | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: A composite pile of grains of sand gradually becomes a mass, and drops of water become 'water everywhere'. A set of people divides into individual humans, but redescribe the elements as the union of males and females? |
| 10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
| Full Idea: The relation of composition seems to be indispensable in a correct account of the part-whole relation for individuals. | |
| From: Keith Hossack (Plurals and Complexes [2000], 7) | |
| A reaction: This is the culmination of a critical discussion of mereology and ontological atomism. At first blush it doesn't look as if 'composition' has much chance of being a precise notion, and it will be plagued with vagueness. |
| 10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
| Full Idea: We can employ Leibniz's Law against mereological atomism. Water is wet, but no water molecule is wet. The set of infinite numbers is infinite, but no finite number is infinite. ..But with plural reference the atomist can resist this argument. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: The idea of plural reference is to state plural facts without referring to complex things, which is interesting. The general idea is that we have atomism, and then all the relations, unities, identities etc. are in the facts, not in the things. I like it. |
| 10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
| Full Idea: The fusion of five rectangles may have a decomposition into more than five parts that are rectangles. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| Full Idea: The claim that no number is greater than a million is confirmed by the first million test cases. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Intro') | |
| A reaction: Extrapolate from this, and you can have as large a number of cases as you could possibly think of failing to do the inductive job. Love it! Induction isn't about accumulations of cases. It is about explanation, which is about essence. Yes! |
| 9249 | Whether we are free is uninteresting; we can only experience our freedom [Camus] |
| Full Idea: Knowing whether or not a man is free doesn't interest me. I can only experience my own freedom. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs free') | |
| A reaction: Camus has the right idea. Personally I think you could drop the word 'freedom', and just say that I am confronted by the need to make decisions. |
| 9253 | The human heart has a tiresome tendency to label as fate only what crushes it [Camus] |
| Full Idea: The human heart has a tiresome tendency to label as fate only what crushes it. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Appendix') | |
| A reaction: Nice. It might just as much be fate that you live a happy bourgeois life, as that you inadvertently murder your own father at a crossroads. But you can't avoid the powerful awareness of fate when a road accident occurs. |
| 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
| Full Idea: A thought can refer to a particular or a universal or a state of affairs, but it can predicate only a universal and it can affirm only a state of affairs. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: Hossack is summarising Armstrong's view, which he is accepting. To me, 'thought' must allow for animals, unlike language. I think Hossack's picture is much too clear-cut. Do animals grasp universals? Doubtful. Can they predicate? Yes. |
| 9250 | Discussing ethics is pointless; moral people behave badly, and integrity doesn't need rules [Camus] |
| Full Idea: There can be no question of holding forth on ethics. I have seen people behave badly with great morality and I note every day that integrity has no need of rules. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs Man') | |
| A reaction: I don't agree. If someone 'behaves badly with great morality' there is something wrong with their morality, and I want to know what it is. The last part is more plausible, and could be a motto for Particularism. Rules dangerously over-simplify life. |
| 9252 | The more one loves the stronger the absurd grows [Camus] |
| Full Idea: The more one loves the stronger the absurd grows. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Don Juan') | |
| A reaction: A penetrating remark, to be placed as a contrary to the remarks of Harry Frankfurt on love. But if the absurd increases the intensity of life, as Camus thinks, then they both make love the great life-affirmation, but in different ways. |
| 9251 | One can be virtuous through a whim [Camus] |
| Full Idea: One can be virtuous through a whim. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs Man') | |
| A reaction: A nice remark. Obviously neither Aristotle nor Kant would be too impressed by someone who did this, and Aristotle would certainly say that it is not really virtue, but merely right behaviour. I agree with Aristotle. |
| 9243 | If we believe existence is absurd, this should dictate our conduct [Camus] |
| Full Idea: What a man believes to be true must determine his action. Belief in the absurdity of existence must then dictate his conduct. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs and Suic') | |
| A reaction: It is intriguing to speculate what the appropriate conduct is. Presumably it is wild existential gestures, like sticking a knife through your hand. Suicide will be an obvious temptation. But bourgeois life might be equally appropriate. |
| 6708 | Happiness and the absurd go together, each leading to the other [Camus] |
| Full Idea: Happiness and the absurd are two sons of the same earth; they are inseparable; it would be a mistake to say that happiness necessarily springs from the absurd discovery; it happens as well that the feeling of the absurd springs from happiness. | |
| From: Albert Camus (The Myth of Sisyphus [1942], p.110) | |
| A reaction: I'm not sure that I understand this, but I understand the experience of absurdity, and I can see that somehow one feels a bit more alive when one acknowledges the absurdity of it all. Meta-meta-thought is the highest form of human life, I say. |
| 9242 | Essential problems either risk death, or intensify the passion of life [Camus] |
| Full Idea: The essential problems are those that run the risk of leading to death, or those that intensify the passion of living. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs and Suic') | |
| A reaction: This seems to be distinctively existentialist, in a way that a cool concern for great truths are not ranked as so important. Ranking dangerous problems as crucial seems somehow trivial for a philosopher. Intensity of life is more impressive. |
| 9246 | Danger and integrity are not in the leap of faith, but in remaining poised just before the leap [Camus] |
| Full Idea: The leap of faith does not represent an extreme danger as Kierkegaard would like it to do. The danger, on the contrary, lies in the subtle instant that precedes the leap. Being able to remain on the dizzying crest - that is integrity. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Phil Suic') | |
| A reaction: I have always found that a thrilling thought. It perfectly distinguishes atheist existentialism from religious existentialism. It is Camus' best image for how the Absurd can be a life affirming idea, rather than a sort of nihilism. Life gains intensity. |
| 9248 | It is essential to die unreconciled and not of one's own free will [Camus] |
| Full Idea: It is essential to die unreconciled and not of one's own free will. Suicide is a repudiation. | |
| From: Albert Camus (The Myth of Sisyphus [1942], 'Abs free') | |
| A reaction: Camus' whole book addresses the question of suicide. He suggests that life can be redeemed and become livable if you squarely face up to the absurdity of it, and the gap between what we hope for and what we get. |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
| Full Idea: We might dispense with substantival space, and say that if the distribution of matter in space could have been different, that just means the matter of the Universe could have been shaped differently (with geometry as the science of shapes). | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) |