| 9791 | Science is more accurate when it is prior and simpler, especially without magnitude or movement [Aristotle] |
| Full Idea: A scientific subject will possess more accuracy (i.e. simplicity) the more that it is about conceptually prior and simpler things, and so it will be more accurate without than with magnitude being involved, and above all being without movement. | |
| From: Aristotle (Metaphysics [c.324 BCE], 1078a10) | |
| A reaction: Aristotle is especially concerned to show how we can achieve accuracy, even while abstracting away from the details of the objects we are studying. Frege should have studied Aristotle more closely. |
| 22746 | If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus] |
| Full Idea: When we have gone so far as to deprive the length of its breadth altogether, we no longer conceive even the length, but along with the removal of the breadth the conception of the length is also removed. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.392) | |
| A reaction: The only explanation of our retaining an understanding of a line even after we have removed its breadth is that we have abandoned experience and conceptualised the line - by idealising it. |
| 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. |
| 19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
| Full Idea: An absolute drive toward perfection and completeness is an illness, as soon as it shows itself to be destructive and averse toward the imperfect, the incomplete. | |
| From: Novalis (General Draft [1799], 33) | |
| A reaction: Deep and true! Novalis seems to be a particularist - hanging on to the fine detail of life, rather than being immersed in the theory. These are the philosophers who also turn to literature. |
| 22591 | We know perfection when we see what is imperfect [Murdoch] |
| Full Idea: We know of perfection as we look upon what is imperfect. | |
| From: Iris Murdoch (Metaphysics as a Guide to Morals [1992], 13) | |
| A reaction: This is in the context of a discussion of the ontological argument for God's existence, but I seize on it as a nice expression of the idealisation capacity of our minds. The alternative is that perfection is innate idea, since we aren't seeing it. |
| 13600 | The point of models in theories is not to idealise, but to focus on what is essential [Ellis] |
| Full Idea: Most model theories abstract from reality in order to focus on the essential nature of some kind of process or system of relations. ... The point of idealizing in this case is not to simplify, but to eliminate what is not essential. | |
| From: Brian Ellis (Scientific Essentialism [2001], 4.03) | |
| A reaction: I like this idea a lot. It is where scientific essentialism cashes out in actual scientific practice. Ellis's example is the idealised Carnot heat engine, which never can exist, but which captures what is essential about the process. |
| 15868 | Idealisation idealises all of a thing's properties, but abstraction leaves some of them out [Harré] |
| Full Idea: An 'idealisation' preserves all the properties of the source but it possesses these properties in some ideal or perfect form. ...An 'abstraction', on the other hand, lacks certain features of its source. | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: Yet another example in contemporary philosophy of a clear understanding of the sort of abstraction which Geach and others have poured scorn on. |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man. |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| Full Idea: In science we treat the earth's surface as flat, we assume the ocean to be infinitely deep, we use continuous functions for what we know to be quantised, and we take liquids to be continuous despite atomic theory. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) | |
| A reaction: If fussy people like scientists do this all the time, how much more so must the confused multitude be doing the same thing all day? |