10 ideas
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. |
8499 | Nominalists cannot translate 'red resembles pink more than blue' into particulars [Jackson] |
Full Idea: It is not always possible for nominalists to translate all statements putatively about universals as statements about particulars. It is not possible for 'red is a colour' and 'red resembles pink more than blue' | |
From: Frank Jackson (Statements about Universals [1977], p.89) | |
A reaction: His second example strikes me as the biggest challenge facing nominalism. I wish they wouldn't use secondary qualities as examples. I am unconvinced that the existence of universals will improve the explanation. It's a mystery. |
8500 | Colour resemblance isn't just resemblance between things; 'colour' must be mentioned [Jackson] |
Full Idea: Some red things resemble some blue things more than some pink things because of factors other than colour. Nominalists must offer 'anything red colour-resembles anything pink', but that may contain a universal in disguise. | |
From: Frank Jackson (Statements about Universals [1977], p.90) | |
A reaction: Hume and Quine are probably right that we spot resemblances instantly, and only articulate the respect of the resemblance at a later stage. |
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. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |