11 ideas
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 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. |
| 21093 | Friendship without community spirit misses out on the main part of virtue [Hume] |
| Full Idea: A man who is only susceptible of friendship, without public spirit or a regard to the community, is deficient in the most material part of virtue. | |
| From: David Hume (That Politics may be reduced to a Science [1750], p.21) | |
| A reaction: I think this is aimed at the epicureans. If the highest virtues are focused on one's friends that can easily lead to injustice, because it can tolerate prejudice against people who are very unlike one's friends. |
| 21091 | It would be absurd if even a free constitution did not impose restraints, for the public good [Hume] |
| Full Idea: A republican and free form of government would be an obvious absurdity, if the particular checks and controls, provided by the constitution, had really no influence, and made it not the interest, even of bad men, to act for the public good. | |
| From: David Hume (That Politics may be reduced to a Science [1750], p.14) | |
| A reaction: Presumably if you attain absolute power you can write any old constitution you like (Clause 1: the presidency is for life). But there does seem much point in doing it - unless it is to facilitate the use of the law for persecutions. |
| 21092 | Nobility either share in the power of the whole, or they compose the power of the whole [Hume] |
| Full Idea: A nobility may possess power in two different ways. Either every nobleman shares the power as part of the whole body, or the whole body enjoys the power as composed of parts, which each have a distinct power and authority. | |
| From: David Hume (That Politics may be reduced to a Science [1750], p.15) | |
| A reaction: He says the first type is found in Venice, and is preferable to the second type, which is found in Poland. Presumably in the shared version there is some restraint on depraved nobles. The danger is each noble being an autocrat. |
| 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! |