Full Idea
We wish to say that when two straight lines cross each other they have a point in common, but if the series of points on a line were similar to the series of ratios, the two lines might cross in a 'gap' and have no point in common.
Gist of Idea
If straight lines were like ratios they might intersect at a 'gap', and have no point in common
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], X)
Book Reference
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.101
A Reaction
You can make a Dedekind Cut in the line of ratios (the rationals), so there must be gaps. I love this idea. We take for granted intersection at a point, but physical lines may not coincide. That abstract lines might fail also is lovely!
Related Idea
Idea 18188 The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]