13 ideas
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with. | |
| From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory. |
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer. |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
| Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6 | |
| A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea. |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example). | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology. |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power. |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
| Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives. |
| 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. |
| 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! |