of uniformities, it is, if exclusively or too habitually pursued, apt to produce perversions of general thought. Inevitably it generates a special bent of mind; and inevitably this special bent affects all the intellectual actions—causes a tendency to look in a mathematical way at questions beyond the range of Mathematics. The mathematician is ever dealing with phenomena of which the elements are relatively few and definite. His most involved problem is immeasurably less involved than are the problems of the Concrete Sciences. But he cannot help bringing with him his mathematical habits of thought; and, in dealing with questions which the Concrete Sciences present, he recognizes some few only of the factors, tacitly ascribes to these a definiteness which they have not, and proceeds after the mathematical manner to draw positive conclusions from these data, as though they were specific and adequate.
Hence the truth, so often illustrated, that mathematicians are bad reasoners on contingent matters. To previous illustrations may be added the recent one yielded by M. Michel Chasles, who proved himself incapable as a judge of evidence in the matter of the Newton-Pascal forgeries. Another was supplied by the late Prof. De Morgan, who, bringing his mental eye to bear with microscopic power on some small part of a question, ignored its main features.
By cultivation of the Abstract-Concrete Sciences, there is produced a further habit of thought, not otherwise produced, which is essential to right thinking in general, and by implication to right thinking in Sociology. Familiarity with the various orders of physical and chemical phenomena gives distinctness and strength to the consciousness of cause and effect. Experiences of things around do, indeed, yield conceptions of special forces and of force in general. The uncultured get from these experiences degrees of faith in causation such that, where they see some striking effect, they usually assume an adequate cause, and, where a cause of given amount is manifest, a proportionate effect is looked for. Especially is this so where the actions are simple mechanical actions. Still, these impressions which daily life furnishes, if unaided by those derived from physical science, leave the ordinary mind with but vague conceptions of causal relations. It needs but to remember the readiness with which people accept the alleged facts of the Spiritualists, many of which imply a direct negation of the mechanical axiom that action and reaction are equal and opposite, to see how much the ordinary thoughts of causation lack quantitativeness—lack the idea of proportion between amount of force expended and amount of change wrought. Very generally, too, the ordinary thoughts of causation are not even qualitatively valid; the most absurd notions as to what cause will produce what effect are frequently disclosed. Take, for instance, the popular belief that a goat kept in a stable will preserve the health of
