"It has long been a subject of remark, that while the science of mathematics, which discusses the properties and relations of space and number, is accompanied by the most conclusive evidence, and bears conviction with it at every step of its progress, the philosophy of the mind still remains enveloped in comparative darkness and uncertainty, after the intellect of ages has been expended in its investigation. The question arises, Are not both similar in their nature, and alike susceptible of demonstrative discussion? It seems evident, that they are not precisely alike, and yet much of the obscurity enveloping mental science, doubtless arises from the unphilosophical manner in which its investigations have been conducted and the inappropriate style in which the result of them has generally been recorded. The superior force of mathematical reasoning, arises from three sources. First, from an intrinsic difference in the nature of the subjects discussed. Secondly, from the more rigidly analytic method of investigation, pursued in the mathematics. And, thirdly, from a less elegant, indeed, but more precise and perspicuous method of conveying to others the knowledge we have acquired. The first of these causes, namely the intrinsic difference between the subjects discussed in these sciences, is derived from the Author of our being. We are so constituted that the properties and especially the relations of space and number, are more clearly apprehended by us than those of mind. Yet this difference is not so great as might, at first view, be supposed. The second source of superior clearness has been stated to be a more rigidly analytic method of investigation. This has led to greater improvements in these sciences, and hence the evidence attending their discussion is also greater. The fact that a better method of philosophizing has usually been pursued in the mathematical sciences is not altogether adventitious. The third source of the superior lucidness of mathematical discussions, is the simple, literal, concise style, in which they are recorded for the instruction of others, and the specific numeric notation of every item of knowledge obtained. It will hereafter appear more clearly, we trust, that one of the most prolific sources of error in human knowledge, is the use of language which does not express our ideas with entire, specific exactness. But mathematical language, consisting of a few figures, letters, and signs, and a small stock of well-defined words, the same idea is almost universally designated by one and the same term. The question here arises, What is the exact nature of the demonstration and proof in mathematics, and what in mental science?"--Introduction. (PsycINFO Database Record (c) 2008 APA, all rights reserved).