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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.
Gist of Idea
A triangle diagram is about all triangles, if some features are ignored
Source
Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
Book Ref
Arnauld,A/Nicole,P: 'Logic, or the Art of Thinking (Port-Royal)', ed/tr. Buroker,J.V. [CUP 1996], p.38
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.
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |