40 ideas
| 14519 | It is a great good to show reverence for a wise man [Epicurus] |
| Full Idea: To show reverence for a wise man is itself a great good for him who reveres [the wise man]. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 32) | |
| A reaction: It is characteristic of Epicurus to move up a level in his thinking, and not merely respect wisdom, but ask after the value of his own respect. Compare Idea 14517. Nice. |
| 9307 | Modern Western culture suddenly appeared in Jena in the 1790s [Svendsen] |
| Full Idea: Foucault was right to say that Jena in the 1790s was the arena where the fundamental interests in modern Western culture suddenly had their breakthrough. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.2) | |
| A reaction: [Hölderlin, Novalis, Tieck, Schlegel, based on Kant and Fichte] Romanticism seems to have been born then. Is that the essence of modernism? Foucault and his pals are hoping to destroy the Enlightenment by ignoring it, but that is modern too. |
| 14518 | In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus] |
| Full Idea: In philosophy the pleasure accompanies the knowledge. For the enjoyment does not come after the learning but the learning and the enjoyment are simultaneous. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 27) |
| 9297 | You can't understand love in terms of 'if and only if...' [Svendsen] |
| Full Idea: I once began reading a philosophical article on love. The following statement soon came up: 'Bob loves Kate if and only if...' At that point I stopped reading. Such a formalized approach was unsuitable, because the actual phenomenon would be lost. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Pref) | |
| A reaction: It is hard to disagree! However, if your best friend comes to you and says, 'I can't decide whether I am really in love with Kate; what do you think?', how are you going to respond. You offer 'if and only if..', but in a warm and sympathetic way! |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 14524 | Bodies are combinations of shape, size, resistance and weight [Epicurus] |
| Full Idea: Epicurus said that body was conceived as an aggregate of shape and size and resistance and weight. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE]) | |
| A reaction: [Source Sextus 'Adversus Mathematicos' 10.257] Note that this is how we 'conceive' them. They might be intrinsically different, except that Epicurus is pretty much a phenomenalist. |
| 9308 | If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen] |
| Full Idea: It is doubtful whether the traditional dichotomy between the strictly subjective and the strictly objective can still be maintained; if not, we must also revise the distinction between primary and secondary qualities. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.3) | |
| A reaction: Very perceptive. The reason why I am so keen to hang onto the primary/secondary distinction is because I want to preserve objectivity (and realism). I much prefer Locke to Hume, as empiricist spokesmen. |
| 14521 | If everything is by necessity, then even denials of necessity are by necessity [Epicurus] |
| Full Idea: He who claims that everything occurs by necessity has no complaint against him who claims that everything does not occur by necessity. For he makes the very claim in question by necessity. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 40) |
| 9309 | Emotions have intentional objects, while a mood is objectless [Svendsen] |
| Full Idea: An emotion normally has an intentional object, while a mood is objectless. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.3) | |
| A reaction: It doesn't follow that the object of the emotion is clearly understood, or even that it is conscious. One may experience rising anger while struggling to see what its object is. Artistic symbolism seems to involve objects that create moods. |
| 9304 | Death appears to be more frightening the less one has lived [Svendsen] |
| Full Idea: Death appears to be more frightening the less one has lived. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.2) | |
| A reaction: [He credits Adorno with this] A good thought, which should be immediately emailed to Epicurus for comment. Which is worse - to die when you have barely started your great work (Ramsey), or dying in full flow (Schubert)? |
| 14522 | What happens to me if I obtain all my desires, and what if I fail? [Epicurus] |
| Full Idea: One should bring this question to bear on all one's desires: what will happen to me if what is sought by desire is achieved, and what will happen if it is not? | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 71) | |
| A reaction: Yet another example of Epicurus moving up a level in his thinking about ethical issues, as in Idea 14517 and Idea 14519. The mark of a true philosopher. This seems to be a key idea for wisdom - to think further ahead than merely what you desire. |
| 3563 | Pleasure and virtue entail one another [Epicurus] |
| Full Idea: It is not possible to live pleasantly without living intelligently and finely and justly, nor to live intelligently and finely and justly without living pleasantly. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 5), quoted by Julia Annas - The Morality of Happiness Ch.16 | |
| A reaction: A person with all these virtues might still suffer from depression. And I don't see why having limited intelligence should stop someone from living pleasantly. Just be warm-hearted. |
| 3560 | Justice is merely a contract about not harming or being harmed [Epicurus] |
| Full Idea: There is no such things as justice in itself; in people's relations with one another in any place and at any time it is a contract about not harming or being harmed. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 33), quoted by Julia Annas - The Morality of Happiness 13.2 |
| 14517 | We value our own character, whatever it is, and we should respect the characters of others [Epicurus] |
| Full Idea: We value our characters as our own personal possessions, whether they are good and envied by men or not. We must regard our neighbours' characters thus too, if they are respectable. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 15) | |
| A reaction: I like this because it introduces a metaethical dimension to the whole problem of virtue. We should value our own character - so should we try to improve it? Should we improve so much as to become unrecognisable? |
| 14513 | Justice is a pledge of mutual protection [Epicurus] |
| Full Idea: The justice of nature is a pledge of reciprocal usefulness, neither to harm one another nor to be harmed. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 31) | |
| A reaction: Notice that justice is not just reciprocal usefulness, but a 'pledge' to that effect. This implies a metaethical value of trust and honesty in keeping the pledge. Is it better to live by the pledge, or to be always spontaneously useful? |
| 9298 | We can be unaware that we are bored [Svendsen] |
| Full Idea: It is perfectly possible to be bored without being aware of the fact. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.1) | |
| A reaction: True. Also, I sometimes mistake indecision for boredom. It becomes very hard to say for certain whether you are bored. I am certain that I am bored if I am forced to do something which has no interest for me. The big one is free-but-bored. |
| 9301 | Boredom is so radical that suicide could not overcome it; only never having existed would do it [Svendsen] |
| Full Idea: Boredom is so radical that it cannot even be overcome by suicide, only by something completely impossible - not to have existed at all. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.1) | |
| A reaction: [he cites Fernando Pessoa for this] The actor George Sanders left a suicide note saying that he was just bored. A cloud of boredom is left hanging in the air where he was. |
| 9302 | We are bored because everything comes to us fully encoded, and we want personal meaning [Svendsen] |
| Full Idea: Boredom results from a lack of personal meaning, which is due to the fact that all objects and actions come to us fully encoded, while we (as descendants of Romanticism) insist on a personal meaning. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.2) | |
| A reaction: This idea justifies me categorising Boredom under Existentialism. This is an excellent idea, and perfectly captures the experience of most teenagers, for whom it is impossible to impose a personal meaning on such a vast cultural reality. |
| 9310 | The profoundest boredom is boredom with boredom [Svendsen] |
| Full Idea: In the profound form of boredom, I am bored by boredom itself. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.3) | |
| A reaction: Boredom is boring, which is why I try to avoid it. Third-level boredom is a rather enchanting idea. It sounds remarkably similar to the Buddha experiencing enlightenment. |
| 9311 | We have achieved a sort of utopia, and it is boring, so that is the end of utopias [Svendsen] |
| Full Idea: There can hardly be any new utopias. To the extent that we can imagine a utopia, it must already have been realised. A utopia cannot, by definition, include boredom, but the 'utopia' we are living in is boring. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.4) | |
| A reaction: Compare Idea 8989. Lots of people (including me) think that we have achieved a kind of liberal, democratic, individualistic 'utopia', but the community needs of people are not being met, so we still have a way to go. |
| 14515 | A law is not just if it is not useful in mutual associations [Epicurus] |
| Full Idea: If someone passes a law and it does not turn out to be in accord with what is useful in mutual associations, this no longer possesses the nature of justice. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 37) |
| 9303 | The concept of 'alienation' seems no longer applicable [Svendsen] |
| Full Idea: I do not believe that the concept of 'alienation' is all that applicable any more. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.1) | |
| A reaction: Interesting but puzzling. If alienation is the key existential phenomenon of a capitalist society, why should it fade away if we remain capitalist? He is proposing that it has metamorphosed into boredom, which may be a different sort of alienation. |
| 14520 | It is small-minded to find many good reasons for suicide [Epicurus] |
| Full Idea: He is utterly small-minded for whom there are many plausible reasons for committing suicide. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 38) | |
| A reaction: It is a pity that the insult of 'small-minded' has slipped out of philosophy. The Greeks use it all the time, and know exactly what it means. We all recognise small-mindedness, and it is a great (and subtle) vice. |