science for one that they find fit to live.  If this is how the mind works in scientific inquiry (as it certainly is, with most men, 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 scientific methods, pains should be taken to make it clear what the abstractions are, what are the consequent limitations upon the argument and its conclusions, and what corrections and allowances are necessary in order to turn the conclusions into an adequate account of the concrete facts.  The greater the number, variety, and subtlety of the properties possessed by any object (such as human nature), the greater are the qualifications required in the conclusions of abstract reasoning, before they can hold true of such an object in practical affairs.