Elements of Psychophysics, Vol. I

...considered written for non-mathematicians, and for mathematicians on behalf of non-mathematicians, in that my endeavor was directed toward being understandable to the former and satisfying the latter—an effort that did not proceed entirely without conflict. May the mathematicians, in particular, excuse many somewhat broad and popular explanations provided in the interest of the non-mathematicians; I kept in mind that this work might primarily interest physiologists, while it also desires to interest philosophers. To expect to find mathematicians among both groups, however, is not yet as permissible today as it really should be required. In the mid-19th century, the fields of physiology and philosophy were becoming increasingly specialized, and Fechner is lamenting the lack of mathematical training among these scholars.

On the other hand, may the non-mathematicians accept derivations they cannot follow—even though only those with very low demands on mathematical understanding occur—as mathematical facts, and here and there skip a chapter, an insertion, or an elaboration that delves a bit too deep. If I am not mistaken, everyone will find the course and content of this work generally graspable if they only know what a mathematical equation is and are familiar with the properties of logarithms, or are willing to follow the brief recapitulation A summary or review of previous principles of them given at the beginning of the following part. Of others, I would not wish that they concern themselves with this work, and least of all that they pass judgment upon it, which in no case could be an insightful one.

I intentionally refrain in this work from entering in any way into the contrast that the mathematical conception of psychological relations presented here will offer against that of Herbart. Johann Friedrich Herbart (1776–1841) was a German philosopher and psychologist who was the first to attempt to apply mathematics to the study of the mind, though his approach was purely theoretical rather than experimental. To Herbart will always remain the merit of having not only first voiced the possibility of a mathematical conception of these relations but also of having made the first ingenious attempt at carrying out such a conception; and everyone after him will, in this regard, remain only a second. In fact, however, the following...