422 THE POPULAR SCIENCE MONTHLY. 



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 him- 

 self 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 chem- 

 ical phenomena gives distinctness and strength to the consciousness 

 of cause and effect. 



Experiences of things around do, indeed, yield conceptions of spe- 

 cial forces and of force in general. The uncultured get from these ex- 

 periences 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 propor- 

 tion 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 



