What is Truth? [pp. 506-535]

What is Truth?
racy, and through the use of methods more precise the altitude
is established for all practical purposes, it is still not absolutely
correct. This process is like the asymptotes, where there is a perpetual approach of the two lines without ever meeting. Still it
is all the time plain that the facts in the case are not changed
by our ignorance or knowledge. Take an example more nearly
concerning practical life. Let it be proposed to establish the
latitude or longitude of a given place. It is determined approximately, so that geodesy can fix upon one point in a certain locality, and another at a short distance from the first, and assert
with full assurance that the desired meridian is between them,
without being able, however, to say precisely where. By a better compass and more accurate trigonometrical calculations,
the point may possibly be found and the absolute meridian
is fixed. So, in the early survey of a territory, the lines may
not, either through haste in the survey, or employment
of unskillful men, be correctly laid off, and prove fruitful
sources of dispute between contiguous owners. A strip of land
may be in litigation, while each proprietor willingly admits that
his neighbor rightfully possesses the greater part of what is
considered his estate. The boundary is somewhere between
the two lines claimed by the respective parties. The point is.
to determine where, so that the true amount of land may be
adjudged to each. In all these cases the matter in dispute is
not uncertain in itself, and is made plain provided the proper
appliances be employed for determining the facts.
It may be said that these are examples taken from concrete
mathematics, and that the uncertainty of the result arises from
the elements of imperfection introduced by instruments or their
manual application. But the like failures to obtain absolute accuracy is shown when the calculations are made from numerical data. For in the integral calculus there are multitudes
of cases where more than one answer will satisfy the requirements of the problem. Many equations again are interminate;
and there is as much room for ingenuity in fencing with the cabalistic signs of quaternions as there was with Barbara, Celarent,
etc, of the schoolmen. Besides, pure mathematics, like every
subject of investigation whose terms are, ex necessitate, postulates, must, as an independent science without applications, be
a nullity. For, if you dissever numbers from objects, you di
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