, in poetry, in fine art, and in the scheming
of business), it is useless to complain. We should rather recognise a
place for fools' hypotheses, as Darwin did for "fools' experiments." But
to complete the scientific character, there must be great patience,
accuracy, and impartiality in examining and testing these conjectures,
as well as great ingenuity in devising experiments to that end. The want
of these qualities leads to crude work and public failure and brings
hypotheses into derision. Not partially and hastily to believe in one's
own guesses, nor petulantly or timidly to reject them, but to consider
the matter, to suspend judgment, is the moral lesson of science:
difficult, distasteful, and rarely mastered.

Sec. 5. The word 'hypothesis' is often used also for the scientific device
of treating an Abstraction as, for the purposes of argument, equivalent
to the concrete facts. Thus, in Geometry, a line is treated as having no
breadth; in Mechanics, a bar may be supposed absolutely rigid, or a
machine to work without friction; in Economics, man is sometimes
regarded as actuated solely by love of gain and dislike of exertion. The
results reached by such reasoning may be made applicable to the concrete
facts, if allowance be made for the omitted circumstances or properties,
in the several cases of lines, bars, and men; but otherwise all
conclusions from abstract terms are limited by their definitions.
Abstract reasoning, then (that is, reasoning limited by definitions),
is often said to imply 'the hypothesis' that things exist as their names
are defined, having no properties but those enumerated in their
definitions. This seems, however, a needless and confusing extension of
the term; for an hypothesis proposes an agent, collocation, or law
hitherto unknown; whereas abstract reasoning proposes to exclude from
consideration a good deal that is well known. There seems no reason why
the latter device should not be plainly called an Abstraction.

Such abstractions are necessary to science; for no object is
comprehensible by us in all its properties at once. But if we forget the
limitations of our abstract data, we are liable to make strange blunders
by mistaking the character of the results: treating the results as
simply true of actual things, instead of as true of actual things only
so far as they are represented by the abstractions. In addressing
abstract reasoning, therefore, to those who are unfamiliar with
scientifi