and intellectual nature of numbers in abstract has made them in esteem
with those philosophers who seem to have affected an uncommon fineness
and elevation of thought. It has set a price on the most trifling
numerical speculations which in practice are of no use, but serve only
for amusement; and has therefore so far infected the minds of some, that
they have dreamed of mighty mysteries involved in numbers, and attempted
the explication of natural things by them. But, if we inquire into our
own thoughts, and consider what has been premised, we may perhaps
entertain a low opinion of those high flights and abstractions, and look
on all inquiries, about numbers only as so many difficiles nugae, so far
as they are not subservient to practice, and promote the benefit of life.

120. Unity in abstract we have before considered in sect. 13, from which
and what has been said in the Introduction, it plainly follows there is
not any such idea. But, number being defined a "collection of units," we
may conclude that, if there be no such thing as unity or unit in
abstract, there are no ideas of number in abstract denoted by the numeral
names and figures. The theories therefore in Arithmetic. if they are
abstracted from the names and figures, as likewise from all use and
practice, as well as from the particular things numbered, can be supposed
to have nothing at all for their object; hence we may see how entirely
the science of numbers is subordinate to practice, and how jejune and
trifling it becomes when considered as a matter of mere speculation.

121. However, since there may be some who, deluded by the specious show
of discovering abstracted verities, waste their time in arithmetical
theorems and problems which have not any use, it will not be amiss if we
more fully consider and expose the vanity of that pretence; and this will
plainly appear by taking a view of Arithmetic in its infancy, and
observing what it was that originally put men on the study of that