9 ideas
9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
Full Idea: An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'. | |
From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX | |
A reaction: The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate. |
10856 | A truly infinite quantity does not need to be a variable [Bolzano] |
Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable. | |
From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10 | |
A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity. |
22384 | A 'double effect' is a foreseen but not desired side-effect, which may be forgivable [Foot] |
Full Idea: 'Double effect' refers to action having an effect aimed at, and also one foreseen but in now way desired. The 'doctrine' is that it is sometimes permissible to bring about by oblique intention what one may not directly intend. | |
From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.20) | |
A reaction: Presumably this can only be justified by a trade-off. The unfortunate side effect must be rated as a price worth paying. If the side effect is not foreseen, that is presumably either understandable, or wickedly negligent. No clear rule is possible. |
22385 | The doctrine of double effect can excuse an outcome because it wasn't directly intended [Foot] |
Full Idea: Supporters of double effect say that sometimes it makes a difference to the permissibility of an action involving harm to others that this harm, although foreseen, is not part of the agent's intention. | |
From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.22) | |
A reaction: The obvious major case is the direction of wartime bombing raids. Controversial, because how can someone foresee a side effect and yet claim to have no intention to cause it? Isn't it wickedly self-deluding? |
22386 | Double effect says foreseeing you will kill someone is not the same as intending it [Foot] |
Full Idea: The doctrine of double effect offers us a way out [of the trolley problem], insisting that it is one thing to steer towards someone foreseeing that you will kill him, and another to aim at his death as part of your plan. | |
From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.23) | |
A reaction: [She has just created her famous Trolley Problem]. Utilitarians must constantly rely on the doctrine of double effect, as they calculate their trade-offs. |
22387 | Without double effect, bad men can make us do evil by threatening something worse [Foot] |
Full Idea: Rejection of the doctrine of double effect puts us hopelessly in the power of bad men. Anyone who wants us to do something we think is wrong has only to threaten that otherwise he himself will do something we think worse. | |
From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.25) | |
A reaction: Her example is they will torture five if you don't torture one. Bernard Williams's famous Jim and the Indians is they will shoot twenty if you don't shoot one. Williams aims it at utilitarian calculations. Double effect is highly relevant. |
22388 | Double effect seems to rely on a distinction between what we do and what we allow [Foot] |
Full Idea: The strength of the doctrine of double effect seems to lie in the distinction it makes between what we do (equated with direct intention) and what we allow (thought of as obliquely intended). | |
From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.25) | |
A reaction: She objects (nicely), saying her trolley driver 'does' the side-effect killing, and someone might 'allow' an obvious criminal death. There is also an intermediate class of 'brought about', where you set up a killing, but don't do it. |
7903 | 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'). |
22383 | Abortion is puzzling because we do and don't want the unborn child to have rights [Foot] |
Full Idea: One reason why most of us feel puzzled about the problem of abortion is that we want, and do not want, to allow to the unborn child the rights that belong to adults and children. | |
From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.19) | |
A reaction: We also do and don't want children to have the same rights as adults. Rights should accrue with development and maturity, it seems. No one thinks sperm and egg have rights. Why stop at 'adult'? Superior adults deserve more rights! |