41 ideas
| 23853 | Truth is not a object we love - it is the radiant manifestation of reality [Weil] |
| Full Idea: Love of truth is not a correct form of expression. Truth is not an object of love. It is not an object at all. …Truth is the radiant manifestation of reality. | |
| From: Simone Weil (The Need for Roots [1943], III 'Growing') | |
| A reaction: Wow! Love that one! |
| 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. |
| 23855 | Creation produced a network or web of determinations [Weil] |
| Full Idea: What is sovereign in this world is determinateness, limit. Eternal Wisdom imprisons this universe in a network, a web of determinations. | |
| From: Simone Weil (The Need for Roots [1943], III 'Growth') | |
| A reaction: Love this, because I take 'determination' to be the defining relationship in ontology. It covers both physical causation and abstract necessities. |
| 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. |
| 23848 | The aesthete's treatment of beauty as amusement is sacreligious; beauty should nourish [Weil] |
| Full Idea: The aesthete's point of view is sacreligious, not only in matters of religion but even in those of art. It consists in amusing oneself with beauty by handling it and looking at it. Beauty is something to be eaten: it is a food. | |
| From: Simone Weil (The Need for Roots [1943], II 'Country') | |
| A reaction: She is endorsing the 'food' view against the 'handling' view. Beauty should nourish, she says. |
| 23854 | Beauty is the proof of what is good [Weil] |
| Full Idea: When the subject in question is the good, beauty is a rigorous and positive proof. | |
| From: Simone Weil (The Need for Roots [1943], III 'Growing') | |
| A reaction: Purest platonism! It is incomprehensible to say 'this thing is evil, but it is beautiful'. But there are plenty of things which strike me as beautiful, without connecting that in any way to moral goodness. |
| 23837 | Respect is our only obligation, which can only be expressed through deeds, not words [Weil] |
| Full Idea: Humans have only one obligation: respect. The obligation is only performed if the respect is effectively expressed in a real, not a fictitious, way; and this can only be done through the medium of Man's earthly needs. | |
| From: Simone Weil (The Need for Roots [1943], I 'Needs') | |
| A reaction: She says man's 'eternal destiny' imposes this obligation. I read this as saying that you should not imagine that you treat people respectfully if you are merely polite to them. Col. Pickering and Eliza Doolittle! Respect is the supreme virtue. |
| 23844 | The most important human need is to have multiple roots [Weil] |
| Full Idea: To be rooted is perhaps the most important and least recognised need of the human soul. …Every human being needs to have multiple roots. | |
| From: Simone Weil (The Need for Roots [1943], II 'Uprootedness') | |
| A reaction: Agree. I think we are just like trees, in that we need roots to grow well, and plenty of space to fully flourish. Identifying those roots is the main task of parents and teachers. |
| 23838 | The need for order stands above all others, and is understood via the other needs [Weil] |
| Full Idea: Order is the first need of all; it evens stands above all needs properly so-called. To be able to conceive it we must know what the other needs are. | |
| From: Simone Weil (The Need for Roots [1943], I 'Order') | |
| A reaction: This may be music to conservative ears, but you should examine Weil's other ideas to see what she has in mind. |
| 23836 | Obligations only bind individuals, not collectives [Weil] |
| Full Idea: Obligations are only binding on human beings. There are no obligations for collectivities, as such. | |
| From: Simone Weil (The Need for Roots [1943], I 'Needs') | |
| A reaction: I take it that 'as such' excludes the institutions created by collectivities, such as parliaments and courts. A nomadic tribe seems to have no duties, as a tribe, apart from mutual obligations among its members. Does this excuse crimes by the tribe? |
| 23840 | A citizen should be able to understand the whole of society [Weil] |
| Full Idea: A man needs to be able to encompass in thought the entire range of activity of the social organism to which he belongs. | |
| From: Simone Weil (The Need for Roots [1943], I 'Responsibility') | |
| A reaction: She is urging the active involvement of citizens in decision making - for which they need appropriate knowledge. |
| 23843 | Even the poorest should feel collective ownership, and participation in grand display [Weil] |
| Full Idea: Participation in collective possessions is important. Where real civic life exists, each feels he has a personal ownership in the public monuments, gardens, ceremonial pomp and circumstances; sumptuousness is thus place within the reach of the poorest. | |
| From: Simone Weil (The Need for Roots [1943], I 'Collective') | |
| A reaction: OK with gardens. Dubious about fobbing the poor off with pomp. Monuments are a modern controversy, when they turn out to commemorate slavery and colonial conquest. I agree with her basic thought. |
| 23846 | Culture is an instrument for creating an ongoing succession of teachers [Weil] |
| Full Idea: Culture - as we know it - is an instrument manipulated by teachers for manufacturing more teachers, who, in their turn, will manufacture still more teachers. | |
| From: Simone Weil (The Need for Roots [1943], II 'Towns') | |
| A reaction: Lot of truth in this. We tend to view our greatest successes in students who become academics and teachers. Culture is very much seen as something which must be 'transmitted' to each new generation. |
| 23839 | A lifelong head of society should only be a symbol, not a ruler [Weil] |
| Full Idea: Wherever a man is placed for life at the head of a social organism, he ought to be a symbol and not a ruler, as is the case with the King of England. | |
| From: Simone Weil (The Need for Roots [1943], I 'Obedience') | |
| A reaction: Nice to hear a radical French thinker endorsing an ancient British tradition! She may not be endorsing a lifelong head of state. Lifelong rulers are the main agents of totalitarianism. |
| 23842 | Party politics in a democracy can't avoid an anti-democratic party [Weil] |
| Full Idea: A democracy where public life is made up of strife between political parties is incapable of preventing the formation of a party whose avowed aim is the overthrow of that democracy. | |
| From: Simone Weil (The Need for Roots [1943], I 'Opinion') | |
| A reaction: We have seen this around 2020 in the USA and the UK. Freedom is compulsory? Weil hates political parties (as did Rousseau). |
| 22595 | Liberty is the triumph of the individual, over both despotic government and enslaving majorities [Constant] |
| Full Idea: Lliberty is the triumph of the individual, as much over a government which seeks to rule by despotic methods, as over the masses who seek to render the minority the slave of the majority. | |
| From: Benjamin Constant (Principles of Politics [1806]), quoted by Ian Dunt - How to be a Liberal 4 | |
| A reaction: [No page given] Dunt describes Constant's book as the first really systematic account of liberalism. Very important to have rights against the majority, as well as against government. |
| 22597 | Minority rights are everyone's rights, because we all have turns in the minority [Constant] |
| Full Idea: To defend the rights of minorities is to defend the rights of all. Everyone in turn finds himself in the minority. | |
| From: Benjamin Constant (Principles of Politics [1806]), quoted by Ian Dunt - How to be a Liberal 4 | |
| A reaction: Very conformist people, who are often the most oppressive, are rarely in the minority, and are unlikely to be impressed by this idea. |
| 23847 | Socialism tends to make a proletariat of the whole population [Weil] |
| Full Idea: What is called Socialism tends to force everybody without distinction into the proletarian condition. | |
| From: Simone Weil (The Need for Roots [1943], II 'Towns') | |
| A reaction: For example, Weil favours maximising private house ownership, rather than communally owned housing. She is describing wholesale nationalisation. I would incline towards nationalisation only of all basic central services. |
| 23845 | The capitalists neglect the people and the nation, and even their own interests [Weil] |
| Full Idea: The capitalists have betrayed their calling by criminally neglecting not only the interests of the people, not only those of the nation, but even their own. | |
| From: Simone Weil (The Need for Roots [1943], II 'Towns') | |
| A reaction: It is certainly true that the dedicated capitalist has little loyalty either to the people or to the nation. She doesn't spell out their failure of self-interest. I guess it produces a way of life they don't really want, deep down. |
| 23841 | By making money the sole human measure, inequality has become universal [Weil] |
| Full Idea: By making money the sole, or almost the sole, motive of all actions, the sole, or almost the sole, measure of all things, the poison of inequality has been introduced everywhere. | |
| From: Simone Weil (The Need for Roots [1943], I 'Equality') | |
| A reaction: Presumably this dates right back to the invention of money, and then increases with the endless rise of capitalism. |
| 23835 | People have duties, and only have rights because of the obligations of others to them [Weil] |
| Full Idea: A right is effectual only in relation to its corresponding obligation, springing not from the individual who possesses it, but from others who consider themselves under an obligation to him. In isolation a man only has duties, and only others have rights. | |
| From: Simone Weil (The Need for Roots [1943], I 'Needs') | |
| A reaction: This seems correct, and obviously refutes the idea that people have intrinsic natural rights. However, it may be our sense of what nature requires which gives rise to the obligations we feel towards others. |
| 23852 | To punish people we must ourselves be innocent - but that undermines the desire to punish [Weil] |
| Full Idea: In order to have the right to punish the guilty, we ought first of all to purify ourselves of their crimes. …But once this is accomplished we shall no longer feel the least desire to punish, or as little as possible and with extreme sorrow. | |
| From: Simone Weil (The Need for Roots [1943], III 'Growing') | |
| A reaction: Elsewhere she endorses punishment, as a social necessity, and a redemption for the wicked. This idea looks like a bit of a change of heart. She may be thinking of Jesus on the mote in someone's eye. |
| 23850 | The soldier-civilian distinction should be abolished; every citizen is committed to a war [Weil] |
| Full Idea: The distinction between soldiers and civilians, which the pressure of circumstances has already almost obliterated, should be entirely abolished. Every individual in the population owes his country the whole of his strength, resources and life itself. | |
| From: Simone Weil (The Need for Roots [1943], II 'Nation') | |
| A reaction: Written in London in 1943. The year carpet bombing seriously escalated. The facts of warfare can change the ethics. |
| 23851 | Education is essentially motivation [Weil] |
| Full Idea: Education - whether its object be children or adults, individuals or an entire people, or even oneself - consists in creating motives. | |
| From: Simone Weil (The Need for Roots [1943], III 'Growing') | |
| A reaction: I can't disagree. Intellectual motivation is simply what we find interesting, and there is no formula for that. A teacher can teach a good session, and only 5% of the pupils find it interesting. A bad session could be life-changing for one student. |
| 23849 | Religion should quietly suffuse all human life with its light [Weil] |
| Full Idea: The proper function of religion is to suffuse with its light all secular life, public or private, without in any way dominating it. | |
| From: Simone Weil (The Need for Roots [1943], II 'Nation') | |
| A reaction: Even for the non-religious there is something attractive about some view of the world which 'suffuses our lives with light'. It probably describes medieval Christendom, but that contained an awful lot of darkness. |