Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Human Personality' and 'Believing the Axioms I'

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30 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
Genius and love of truth are always accompanied by great humility [Weil]
     Full Idea: Love of truth is always accompanied by humility, and real genius is nothing else but the supernatural virtue of humility in the domain of thought.
     From: Simone Weil (Human Personality [1943], p.87)
     A reaction: A striking and attractive thought, true of all the lovers of truth I have ever encountered. Socrates is the role model. She likens truth to an inarticulate plaintiff stammering before a judge who fluently manipulates opinions.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
New axioms are being sought, to determine the size of the continuum [Maddy]
     Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum.
     From: Penelope Maddy (Believing the Axioms I [1988], §0)
     A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
The Axiom of Extensionality seems to be analytic [Maddy]
     Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.1)
     A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size.
Extensional sets are clearer, simpler, unique and expressive [Maddy]
     Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.1)
     A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
     Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.5)
     A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art.
Infinite sets are essential for giving an account of the real numbers [Maddy]
     Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.5)
     A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
     Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.6)
     A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one?
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Efforts to prove the Axiom of Choice have failed [Maddy]
     Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.7)
     A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof.
Modern views say the Choice set exists, even if it can't be constructed [Maddy]
     Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.7)
     A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence?
A large array of theorems depend on the Axiom of Choice [Maddy]
     Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.7)
     A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
     Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.3)
     A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story?
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
     Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.3)
     A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system.
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
What is sacred is not a person, but the whole physical human being [Weil]
     Full Idea: There is something sacred in every man, but it is not his person. Nor yet is it the human personality. It is this man; no more and no less. …It is he. The whole of him. The arms, they eyes, the thoughts, everything.
     From: Simone Weil (Human Personality [1943], p,70)
     A reaction: I take her to be referring to exactly the concept of a 'person' which Locke introduced. It is important to remember that his concept is mainly forensic - as a concept of ownership and contracts. A person is an abstraction. Even a corpse is a human.
18. Thought / A. Modes of Thought / 1. Thought
The mind is imprisoned and limited by language, restricting our awareness of wider thoughts [Weil]
     Full Idea: At the very best, a mind is enclosed in language as in a prison. It is limited to the number of relations which words can make simultaneously present to it; and remains in ignorance of thoughts which involve the combination of a greater number.
     From: Simone Weil (Human Personality [1943], p.89)
     A reaction: This seems to be a germ of the type of view of language which blossoms in Derrida. But she is on to something. None of us grasp fully, I think, the non-linguistic nature of good thinking.
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
Beauty is an attractive mystery, leaving nothing to be desired [Weil]
     Full Idea: Beauty is the supreme mystery of the world. It is a gleam which attracts the attention and yet does nothing to sustain it. …While exciting desire, it makes clear that there is nothing in it to be desired, because what we want is that it should not change.
     From: Simone Weil (Human Personality [1943], p.92)
     A reaction: She attributes beauty to a supernatural source. I catalogue this idea under 'the sublime', rather than 'beauty'. It may be better to say that beauty inspires love, rather than desire.
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
All we need are the unity of justice, truth and beauty [Weil]
     Full Idea: Justice, truth, and beauty are sisters and comrades. With three such beautiful words we have no need to look for any others.
     From: Simone Weil (Human Personality [1943], p.93)
     A reaction: The embodiment of platonist values. Without the platonist ontology, I like the identification of a few core values, and have always thought that Beauty, Goodness and Truth were a well chosen trio. Swapping 'justice' for 'goodness' is interesting.
22. Metaethics / B. Value / 2. Values / c. Life
The sacred in every human is their expectation of good rather than evil [Weil]
     Full Idea: At the bottom of every human heart …there is something that goes on indomitably expecting, in the teeth of all crimes committed, suffered and witnessed, that good and not evil will be done to him. It is this above all that is sacred in every human being.
     From: Simone Weil (Human Personality [1943], p.71)
     A reaction: I'm thinking that this expectation may come from having at least one loving parent, and failing that there are people who have no such expectation as adults. Simone obviously thinks the hope runs deeper than that.
22. Metaethics / B. Value / 2. Values / g. Love
Everything which originates in love is beautiful [Weil]
     Full Idea: Everything which originates from pure love is lit with the radiance of beauty.
     From: Simone Weil (Human Personality [1943], p.93)
     A reaction: I suppose if I found a counterexample, she would say that is not 'pure' love. This sentence leaves open the possibility of beauty in the absence of love (such as a beautiful face noticed in the street). In her case, can beauty and love be separated?
22. Metaethics / B. Value / 2. Values / j. Evil
Evil is transmitted by comforts and pleasures, but mostly by doing harm to people [Weil]
     Full Idea: One may transmit evil to a human being by flattering him or giving him comforts and pleasures; but most often men transmit evil to other men by doing them harm.
     From: Simone Weil (Human Personality [1943], p.94)
     A reaction: Some people receive harm very passively, especially if it is normal. What of tough love, which is erroneously seen as harm?
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
24. Political Theory / D. Ideologies / 8. Socialism
It is not more money which the wretched members of society need [Weil]
     Full Idea: Suppose the devil were bargaining for the soul of some wretch, and some pitying person said to the devil 'Shame on you, that commodity is worth twice as much'. Such is the sinister farce played by the working class unions, parties and intellectuals.
     From: Simone Weil (Human Personality [1943], p.80)
     A reaction: A striking thought. It is paradoxical when the working classes despise the middle classes, and yet aspire to be like them. It's hard to know what a mystic like Weil has in mind. An obvious thought is that the aspiration should be freedom, not money.
24. Political Theory / D. Ideologies / 9. Communism
The problem of the collective is not suppression of persons, but persons erasing themselves [Weil]
     Full Idea: The chief danger does not lie in the collectivity's tendency to circumscribe the person, but in the person's tendency to immolate himself in the collective.
     From: Simone Weil (Human Personality [1943], p.78)
     A reaction: I'm guessing that in 1943 she had in mind both Nazis and Communists. She seems to articulate a strong form of liberalism in an interesting way. It sounds like a form of Bad Faith.
25. Social Practice / B. Equalities / 1. Grounds of equality
People absurdly claim an equal share of things which are essentially privileged [Weil]
     Full Idea: To the dimmed understanding of our age there seems nothing odd in claiming an equal share of privilege for everybody - an equal share in things whose essence is privilege.
     From: Simone Weil (Human Personality [1943], p.84)
     A reaction: Not sure what she has in mind. Probably not the finest food and drink. I suppose she is attacking the modern egalitarian view of democratic society. What things have privilege as their 'essence'? Being a 'winner'? Interesting, though.
25. Social Practice / C. Rights / 1. Basis of Rights
Rights are asserted contentiously, and need the backing of force [Weil]
     Full Idea: Rights are always asserted in a tone of contention; and when this tone is adopted, it must rely upon force in the background, or else it will be laughed at.
     From: Simone Weil (Human Personality [1943], p.81)
     A reaction: This is the sort of observation which leads on to Foucault's account of all-pervasive power. Her observation may not be so sinister. It is obvious that introductions of new rights go against the grain of a conservative society - and so need a push.
Giving centrality to rights stifles all impulses of charity [Weil]
     Full Idea: To place the notion of rights at the centre of social conflicts is to inhibit any possible impulse of charity on both sides.
     From: Simone Weil (Human Personality [1943], p.83)
     A reaction: I think she exaggerates. To place personal charity at the centre of social conflicts strikes me as extremely conservative, and unlikely to improve the situation very much. I'm unsure how to reconcile this with Idea 23750. What sort of charity?
25. Social Practice / D. Justice / 1. Basis of justice
The spirit of justice needs the full attention of truth, and that attention is love [Weil]
     Full Idea: Because affliction and truth need the same kind of attention …the spirit of justice and the spirit of truth are one. The spirit of justice and truth is nothing else be a certain kind of attention, which is pure love.
     From: Simone Weil (Human Personality [1943], p.92)
     A reaction: I'm not sure about this as an observation, but as an inspiration it is very appealing, and (as so often with Weil) strikingly and attractively independent. I prefer love to arise naturally, rather than be a product of exhortation.
Justice (concerning harm) is distinct from rights (concerning inequality) [Weil]
     Full Idea: Justice is seeing that no harm is done to men. When a man cries inwardly 'Why am I being hurt?' he is being harmed. The other cry of 'Why have others got more than me?' refers to rights. We must distinguish them, and hush the second with law.
     From: Simone Weil (Human Personality [1943], p.93)
     A reaction: Her great passion is for justice, and so she downplays rights. The simple 'why am I being hurt?' has a horrible resonance in 1943. What of the hurts of disease? Are they unjust?
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
The only thing in society worse than crime is repressive justice [Weil]
     Full Idea: There is one, and only one, thing in society more hideous than crime - namely, repressive justice.
     From: Simone Weil (Human Personality [1943], p.95)
     A reaction: Presumably fans of 'repressive' justice would describe it as 'reformative' justice. In general, one of the most hideous parts of historical human societies has been the punishments they dished out (simply because they had the power to do it).
Punishment aims at the good for men who don't desire it [Weil]
     Full Idea: Punishment is solely a method of procuring pure good for men who do not desire it. The art of punishing is the art of awakening in a criminal, by pain or even death, the desire for pure good.
     From: Simone Weil (Human Personality [1943], p.95)
     A reaction: I know Weil is seen as some sort of saint, but this remark could have come from the Inquisition. I'm always alarmed by talk of 'pure' good and 'pure' evil, which seem to need a superior insight the rest of us lack. But see Idea 23764.
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
The only choice is between supernatural good, or evil [Weil]
     Full Idea: In all the crucial problems of human existence the only choice is between supernatural good on the one hand and evil on the other.
     From: Simone Weil (Human Personality [1943], p.86)
     A reaction: This idea strikes me as absurd, but I include it for a fuller picture of Simone Weil. Aristotle (my hero) is referred to, and labelled as more stupid than a village idiot.