We are therefore to understand by extension in abstract
an idea of extension, for instance, a line or surface entirely stripped
of all other sensible qualities and circumstances that might determine it
to any particular existence; it is neither black nor white, nor red, nor
hath it any colour at all, or any tangible quality whatsoever and
consequently it is of no finite determinate magnitude: for that which
bounds or distinguishes one extension from another is some quality or
circumstance wherein they disagree.
123. Now I do not find that I can perceive, imagine, or any wise frame in
my mind such an abstract idea as is here spoken of. A line or surface
which is neither black, nor white, nor blue, nor yellow, etc., nor long,
nor short, nor rough, nor smooth, nor square, nor round, etc., is
perfectly incomprehensible. This I am sure of as to myself: how far the
faculties of other men may reach they best can tell.
124. It is commonly said that the object of geometry is abstract
extension: but geometry contemplates figures: now, figure is the
termination of magnitude: but we have shown that extension in abstract
hath no finite determinate magnitude. Whence it clearly follows that it
can have no figure, and consequently is not the object of geometry. It is
indeed a tenet as well of the modern as of the ancient philosophers that
all general truths are concerning universal abstract ideas; without
which, we are told, there could be no science, no demonstration of any
general proposition in geometry.
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