| Summary: | "The paper of Herman von Helmholtz to the translation of which this work is devoted, stands historically in the midst of a stream of speculation which today has progressed far beyond its original mathematical bounds and has become an active force in some of the most fundamental thought of modern physics. It is fitting, therefore, as an introduction to the speculations of Helmholtz on "Counting and Measuring" to survey briefly the background of present-day mathematical and physical foundations and to indicate the measure of advance which philosophers in these sciences believe they have achieved. The subject of number and its relationship to the description of nature possesses both ontological and epistemological aspects. It is in part psychological and in part philosophical. Basic tenets may often be reduced to questions of preference in belief since there is frequently and perhaps always no categorical necessity for choice between the systems of postulates employed. If we seek to classify what might be called the psychological elements which underlie the definition of number given by the philosophers we find that these may be grouped into three types: those which seek to associate number with an a priori intuition of time; those which seek to coordinate the idea of number with space; those which affirm that number is a concept sui generis and is related only secondarily if at all to time and space"--Introduction. (PsycINFO Database Record (c) 2009 APA, all rights reserved).
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