s to the figures made up "by putting together
many short straight lines." Correspondingly, the Proper Name may be
called the Limit of the class-name; since its attributes are infinite,
whereas any name whose attributes are less than infinite stands for a
possible class. In short, for logical purposes, a Limit may be defined
as any extreme case to which actual examples may approach without ever
reaching it. And in this sense 'Method of Limits' might be used as a
term including the Method of Abstractions; though it would be better to
speak of them generically as 'Methods of Approximation.'

We may also notice the Assumptions (as they may be called) that are
sometimes employed to facilitate an investigation, because some definite
ground must be taken and nothing better can be thought of: as in
estimating national wealth, that furniture is half the value of the
houses.

It is easy to conceive of an objector urging that such devices as the
above are merely ways of avoiding the actual problems, and that they
display more cunning than skill. But science, like good sense, puts up
with the best that can be had; and, like prudence, does not reject the
half-loaf. The position, that a conceivable case that can be dealt with
may, under certain conditions, be substituted for one that is
unworkable, is a touchstone of intelligence. To stand out for ideals
that are known to be impossible, is only an excuse for doing nothing at
all.

In another sense, again, the whole of science is sometimes said to be
hypothetical, because it takes for granted the Uniformity of Nature; for
this, in its various aspects, can only be directly ascertained by us as
far as our experience extends; whereas the whole value of the principle
of Uniformity consists in its furnishing a formula for the extension of
our other beliefs beyond our actual experience. Transcendentalists,
indeed, call it a form of Reason, just because it is presupposed in all
knowledge; and they and the Empiricists agree that to adduce material
evidence for it, in its full extent, is impossible. If, then, material
evidence is demanded by any one, he cannot regard the conclusions of
Mathematics and Physical Science as depending on what is itself
unproved; he must, with Mill, regard these conclusions as drawn "not
from but according to" the axioms of Equality and Causation. That is to
say, if the axioms are true, the conclusions are; the material evidence
for both the axioms and the concl