ations they interpolate and expunge; and this mutilated and
adulterated product they call a fact. And why? Because the real
phenomena, if admitted, would spoil the pleasant music of their
thoughts, and convert its factitious harmony into a discord. In
consequence of this many a system professing to be reared exclusively on
observation and fact, rests, in reality, mainly upon hypothesis and
fiction. A pretended experience is indeed the screen behind which every
illusive doctrine regularly retires. 'There are more false facts,' says
Cullen, 'current in the world than false theories.' Fact, observation,
induction, have always been the watchwords of those who have dealt most
extensively in fancy."[324] We propose, therefore, to show that, _I. The
students of the physical sciences have no such certain knowledge of
their facts and theories as Secularists pretend._

1. Mathematical science relating merely to abstract truth is supposed to
possess powers of demonstration, and capability of scientific certainty
superior to all other kinds of knowledge, but the moment we begin to
apply it to any existing facts we enter the domain of liability to
errors as numerous as our fallible observations of these facts; and when
we attempt to apply mathematical demonstration to the infinite, and to
enter the domain of faith, in which as immortals we are chiefly
concerned, it baffles, deceives, and insults our reason. Take the
following illustrations:

Let an infinite whole be divided into halves; the parts must be either
finite or infinite. But they can not be finite, else an infinite whole
would consist of a finite number of parts; neither can they be infinite,
being each less than the infinite whole.

Again: it is mathematically demonstrable, that any piece of matter is
infinitely divisible. A line therefore of half an inch long is
infinitely divisible, or divisible into an infinite number of parts.
Thus we have an infinite half inch. Further, for a moving body to pass a
given point requires some time; and to pass an infinite number of points
must require an infinite number of portions of time, or an eternity;
therefore, as half an inch contains an infinite number of points, it
will require eternity to pass half an inch.

Again: it is mathematically demonstrable, that a straight line, the
asymptote of a hyperbola, may _eternally approach_ the curve of the
hyperbola and _never meet_ it. But no axiom can be plainer than that if
two lines