31 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. |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| Full Idea: Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903. | |
| From: Wilfrid Hodges (Model Theory [2005], 2) | |
| A reaction: [compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together. |
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
| Full Idea: A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.1) | |
| A reaction: [Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming. |
| 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. |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| Full Idea: In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!). | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: [actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy! |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| Full Idea: If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'. | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians. |
| 10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
| Full Idea: To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) |
| 10284 | There are three different standard presentations of semantics [Hodges,W] |
| Full Idea: Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) | |
| A reaction: I haven't yet got the hang of the latter two, but I note them to map the territory. |
| 10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
| Full Idea: I |= φ means that the formula φ is true in the interpretation I. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.5) | |
| A reaction: [There should be no space between the vertical and the two horizontals!] This contrasts with |-, which means 'is proved in'. That is a syntactic or proof-theoretic symbol, whereas |= is a semantic symbol (involving truth). |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| Full Idea: The symbol in 'I |= S' reads that if the interpretation I (about word meaning) happens to make the sentence S state something true, then I 'is a model for' S, or I 'satisfies' S. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: Unfortunately this is not the only reading of the symbol |= [no space between | and =!], so care and familiarity are needed, but this is how to read it when dealing with models. See also Idea 10477. |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| Full Idea: Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Tarski's truth definition as a paradigm. | |
| From: Wilfrid Hodges (Model Theory [2005], Intro) | |
| A reaction: My attention is caught by the fact that natural languages are included. Might we say that science is model theory for English? That sounds like Quine's persistent message. |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| Full Idea: A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'. |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| Full Idea: The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it. | |
| From: Wilfrid Hodges (Model Theory [2005], 5) | |
| A reaction: Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things, |
| 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
| Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
| Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
| Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) | |
| A reaction: If entailment is possible, it can be done finitely. |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| Full Idea: First-order logic is hopeless for discriminating between one infinite cardinal and another. | |
| From: Wilfrid Hodges (Model Theory [2005], 4) | |
| A reaction: This seems rather significant, since mathematics largely relies on first-order logic for its metatheory. Personally I'm tempted to Ockham's Razor out all these super-infinities, but mathematicians seem to make use of them. |
| 10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
| Full Idea: A 'set' is a mathematically well-behaved class. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.6) |
| 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. |
| 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. |
| 21006 | If women share rights with men, they will exhibit similar virtues [Wollstonecraft] |
| Full Idea: Let woman share the rights and she will emulate the virtues of man; for she must grow more perfect when emancipated, or justify that authority that chains such a weak being to her duty. | |
| From: Mary Wollstonecraft (Vindication of the Rights of Women [1792], p.294), quoted by Amartya Sen - The Idea of Justice 18 'Wrath' | |
| A reaction: Presumably this implies that if emancipation led to women exceeding men in such virtues, there would be some justification for imposing the chains on the men rather than the women. Consider wars. Probably best to just abandon chains. |
| 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. |