Philosophical Works, v. 1 (of 4): Including All the Essays, and Exhibiting the More Important Alterations and Corrections in the Successive Editions Published by the Author — David Hume — John Shaqi
Philosophical Works, v. 1 (of 4): Including All the Essays, and Exhibiting the More Important Alterations and Corrections in the Successive Editions Published by the Author
David Hume · en
'Tis true, mathematicians pretend they give an exact definition of
a right line when they say, _it is the shortest way betwixt two
points_. But in the first place I observe, that this is more properly
the discovery of one of the properties of a right line, than a just
definition of it. For I ask any one, if, upon mention of a right line,
he thinks not immediately on such a particular appearance, and if 'tis
not by accident only that he considers this property? A right line can
be comprehended alone; but this definition is unintelligible without a
comparison with other lines, which we conceive to be more extended. In
common life 'tis established as a maxim, that the straightest way is
always the shortest; which would be as absurd as to say, the shortest
way is always the shortest, if our idea of a right line was not
different from that of the shortest way betwixt two points.
Secondly, I repeat, what I have already established, that we have no
precise idea of equality and inequality, shorter and longer, more than
of a right line or a curve; and consequently that the one can never
afford us a perfect standard for the other. An exact idea can never be
built on such as are loose and undeterminate.
The idea of a _plain surface_ is as little susceptible of a precise
standard as that of a right line; nor have we any other means of
distinguishing such a surface, than its general appearance. 'Tis in
vain that mathematicians represent a plain surface as produced by the
flowing of a right line. 'Twill immediately be objected, that our idea
of a surface is as independent of this method of forming a surface, as
our idea of an ellipse is of that of a cone; that the idea of a right
line is no more precise than that of a plain surface; that a right line
may flow irregularly, and by that means form a figure quite different
from a plane; and that therefore we must suppose it to flow along two
right lines, parallel to each other, and on the same plane; which is a
description that explains a thing by itself, and returns in a circle.