Helmholtz's Zählen und Messen16 October 2017
When I first encountered mention of Zählen und Messen, erkenntnisstheoretisch betrachtet [Numbering and Measuring, Epistemologically Considered] by Hermann [Ludwig Ferdinand] von Helmholtz, which sought to construct arithmetic on an empiricist foundation, I was interested. But for a very long while I did not act on that interest.
A few years ago, I learned of Zahl und Mass in der Ökonomik: Eine kritische Untersuchung der mathematischen Methode und der mathematischen Preistheorie (1893), by Andreas Heinrich Voigt, a early work on the mathematics of utility, and that it drew upon Helmholtz's Zählen und Messen, which impelled me to seek a copy of the latter to read. To my annoyance, I found that there was no English-language version of it freely available on-line. I decided to create one, but was distracted from the project by other matters. A few days ago, I recognized that my immediate circumstances were such that it might be a good time to return to the task.
I have produced a translation, Numbering and Measuring, Epistemologically Considered by Hermann von Helmholtz It is not much better than serviceable. I don't plan to return to the work, to refine the translation, except perhaps where some reader has suggested a clear improvement and I effect a transcription.
I have not inserted what criticisms I might make of this work into the document. Nor have I presented my thoughts on how Helmholtz's ostensible empiricism and Frege's logicism are not as far apart as might be thought.