29 ideas
| 23825 | We seek truth only because it is good [Weil] |
| Full Idea: Truth is sought not because it is truth but because it is good. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.233) | |
| A reaction: A perfect instance of modern platonism. A few weird people seem to enjoy lying. Personally I cannot find enough content in the word 'good' in such claims. |
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| Full Idea: In the Gödelian realistic view of set theory the statement that there is a null set as the assertion of the existence in the real world of a set that has no members. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It seems to me obvious that such a claim is nonsense on stilts. 'In the beginning there was the null set'? |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| Full Idea: Everything we know about the empty set is relational; we know that nothing is the membership relation to it. But what do we know about its 'intrinsic properties'? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: Set theory seems to depend on the concept of the empty set. Modern theorists seem over-influenced by the Quine-Putnam view, that if science needs it, we must commit ourselves to its existence. |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| Full Idea: In simple type theory, there is a null set of type 1, a null set of type 2, a null set of type 3..... (Quine has expressed his distaste for this). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.4) | |
| A reaction: It is bad enough trying to individuate the unique null set, without whole gangs of them drifting indistinguishably through the logical fog. All rational beings should share Quine's distaste, even if Quine is wrong. |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| Full Idea: In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set. |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| Full Idea: What is it about the intrinsic properties of just that one unit set in virtue of which Bill Clinton is related to just it and not to any other unit sets in the set-theoretical universe? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If we all kept pet woodlice, we had better not hold a wood louse rally, or we might go home with the wrong one. My singleton seems seems remarkably like yours. Could we, perhaps, swap, just for a change? |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| Full Idea: The set theorist cannot tell us anything about the true relationship of membership. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If three unrelated objects suddenly became members of a set, it is hard to see how the world would have changed, except in the minds of those thinking about it. |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| Full Idea: ZFU set theory talks about physical objects (the urelements), and hence is in some way about the physical world. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.5) | |
| A reaction: This sounds a bit surprising, given that the whole theory would appear to be quite unaffected if God announced that idealism is true and there are no physical objects. |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| Full Idea: A pack of wolves is not thought to go out of existence just because some member of the pack is killed. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.5) | |
| A reaction: The point is that the formal extensional notion of a set doesn't correspond to our common sense notion of a group or class. Even a highly scientific theory about wolves needs a loose notion of a wolf pack. |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| Full Idea: Everything one needs to do with relations in mathematics can be done by taking a relation to be a set of ordered pairs. (Ordered triples etc. can be defined as order pairs, so that <x,y,z> is <x,<y,z>>). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.2) | |
| A reaction: How do we distinguish 'I own my cat' from 'I love my cat'? Or 'I quite like my cat' from 'I adore my cat'? Nevertheless, this is an interesting starting point for a discussion of relations. |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| Full Idea: In first-order logic a set of sentences is 'consistent' iff there is an interpretation (or structure) in which the set of sentences is true. ..For Frege, though, a set of sentences is consistent if it is not possible to deduce a contradiction from it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.1) | |
| A reaction: The first approach seems positive, the second negative. Frege seems to have a higher standard, which is appealing, but the first one seems intuitively right. There is a possible world where this could work. |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| Full Idea: With the invention of analytic geometry (by Fermat and then Descartes) physical space could be represented as having a mathematical structure, which could eventually lead to its axiomatization (by Hilbert). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.3) | |
| A reaction: The idea that space might have axioms seems to be pythagoreanism run riot. I wonder if there is some flaw at the heart of Einstein's General Theory because of this? |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| Full Idea: Chihara's 'constructability theory' is nominalist - mathematics is reducible to a simple theory of types. Instead of talk of sets {x:x is F}, we talk of open sentences Fx defining them. Existence claims become constructability of sentence tokens. | |
| From: report of Charles Chihara (A Structural Account of Mathematics [2004]) by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.81 | |
| A reaction: This seems to be approaching the problem in a Fregean way, by giving an account of the semantics. Chihara is trying to evade the Quinean idea that assertion is ontological commitment. But has Chihara retreated too far? How does he assert existence? |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| Full Idea: If mathematics shares whatever confirmation accrues to the theories using it, would it not be reasonable to suppose that mathematics shares whatever disconfirmation accrues to the theories using it? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 05.8) | |
| A reaction: Presumably Quine would bite the bullet here, although maths is much closer to the centre of his web of belief, and so far less likely to require adjustment. In practice, though, mathematics is not challenged whenever an experiment fails. |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| Full Idea: Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.1) | |
| A reaction: It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either. |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| Full Idea: What I refer to as an 'equivalence class' (of line segments of a particular length) is an open sentence in my Constructibility Theory. I just use this terminology of the Platonist for didactic purposes. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.10) | |
| A reaction: This is because 'equivalence classes' is committed to the existence of classes, which is Quinean Platonism. I am with Chihara in wanting a story that avoids such things. Kit Fine is investigating similar notions of rules of construction. |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| Full Idea: Causal theories of reference seem doomed to failure for the case of reference to mathematical entities, since such entities are evidently causally inert. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.3) | |
| A reaction: Presumably you could baptise a fictional entity such as 'Polonius', and initiate a social causal chain, with a tradition of reference. You could baptise a baby in absentia. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 23826 | Beauty, goodness and truth are only achieved by applying full attention [Weil] |
| Full Idea: The authentic and pure values - truth, beauty and goodness - in the activity of a human being are the result of one and same act, a certain application of the full attention to the object. Teaching should only aim to train the attention for such an act. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.234) | |
| A reaction: A distinctive Weil idea, that absorbed 'attention' produces almost mystical results. I am not convinced that a great still life painter (than which there is no higher criterion of attention) achieves contact with goodness thereby. But attention is good! |
| 23833 | The good is a nothingness, and yet real [Weil] |
| Full Idea: The good seems to us a nothingness, since there is no thing that is good. But this nothingness is not unreal. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.278) | |
| A reaction: A neat move in the notoriously difficult platonic problem of specifying the actual nature of the good. |
| 23808 | There are two goods - the absolute good we want, and the reachable opposite of evil [Weil] |
| Full Idea: There are two goods - one which is the opposite of evil, and one which is the absolute. …That which we want is the absolute good. That which is within our reach is the good which is correlated with evil. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.142) | |
| A reaction: Elsewhere she seems in tune with the thought of Nietzsche (whom she despised) that good and evil are false social constructs which are quite different from healthy values. Weil, of course, sees the absolute as transcendent. |
| 23831 | The essence of power is illusory prestige [Weil] |
| Full Idea: Prestige, which is an illusion, is the very essence of power. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.255) | |
| A reaction: It is hard to maintain illusory prestige if there is no actual power behind it. |
| 23830 | A group is only dangerous if it endorses an abstract entity [Weil] |
| Full Idea: Any group which has not secreted an abstract entity will probably not be dangerous. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.255) | |
| A reaction: Written in the 1930s, the era of many political -isms. No group can be united if it lacks a clear label, and a few simple slogans. |
| 23809 | Our only social duty is to try to limit evil [Weil] |
| Full Idea: Our only duty with regard to the social is to try to limit the evil of it. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.143) | |
| A reaction: This is one of Weil's occasional remarks that have an anarchist flavour. I increasingly sympathise with this less idealistic view as I get older. |
| 23807 | The collective is the one and only object of false idolatry [Weil] |
| Full Idea: The Great Beast is the great object of idolatry, the only ersatz of God. …Only one thing can be taken as an end, for in relation to the human person it possesses a kind of transcendence: this is the collective. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.140) | |
| A reaction: [Society as the Great Beast is in Republic Bk 6] She is referring to both fascist and communist states. Weil seems to be a left-wing liberal, with a tendency towards anarchism, because her priority is the individual, not the group. |
| 23810 | Charity is the only love, and you can feel that for a country (a place with traditions), but not a nation [Weil] |
| Full Idea: We must not have any other love than charity. A nation cannot be an object of charity. But a country can be one - as an environment bearing traditions which are eternal. Every country can be that. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.146) | |
| A reaction: This definitely strikes a chord with me. I am English and British to the core, but don't feel any love at all for the current central institutions of the state. But I love my island, and its history, and its culture, and its style. |
| 23811 | If effort is from necessity rather than for a good, it is slavery [Weil] |
| Full Idea: To strive from necessity and not for some good - ...that is always slavery. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.180) | |
| A reaction: It is usual to see the possibility of anarchism as the starting point for political thinking, but I think for Weil the state of slavery has that role. |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
| Full Idea: An 'atomless gunk' is defined to be an individual possessing no parts that are atoms. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], App A) | |
| A reaction: [Lewis coined it] If you ask what are a-toms made of and what are ideas made of, the only answer we can offer is that the a-toms are made of gunk, and the ideas aren't made of anything, which is still bad news for the existence of ideas. |
| 23765 | The soul is the intrinsic value of a human [Weil] |
| Full Idea: The soul is the human being considered as having a value in itself. | |
| From: Simone Weil (Gravity and Grace (9 extracts) [1943], p.294) | |
| A reaction: [from 'Gravity and Grace'] A rather modern view, treating the soul as an abstraction, rather than as an entity. |