more from Arnauld / Nicole

Single Idea 10500

[catalogued under 15. Nature of Minds / C. Capacities of Minds / 6. Idealisation]

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.

Gist of Idea

No one denies that a line has width, but we can just attend to its length


Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)

Book Reference

Arnauld,A/Nicole,P: 'Logic, or the Art of Thinking (Port-Royal)', ed/tr. Buroker,J.V. [CUP 1996], p.38

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.