Posts Tagged ‘arithmetic’

Helmholtz's Zählen und Messen

Monday, 16 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.

Oh, you can't help that.

Sunday, 24 February 2013

When I went for dinner, I encountered someone slipping into madness. He was polite and pleasant, but going mad.

He was fixated upon improving the world globally. I don't know whether he were going mad because he wanted somehow to improve the world globally, or were obsessively focussed upon improving the world globally because he was going mad; my guess would be that the aspiration and the madness were each feeding upon the other. In any case, he was writing and drawing chaotically with bright marker on loose sheets of paper, and trying to engage random people in his efforts to figure-out How to Save the World. I was a random person.

I sometimes talk to madmen. No less or more comes out of my conversations with them than those with most other people. In this case, I wasn't much occupied at the time with anything else but eating.

He found talking with me to be discouraging. It's not that I don't think that the world might be saved, or that I might do something towards that end. It's that I think that most people, mad or otherwise and including him, fundamentally misconceive the nature of the problem and the potential methods of solution. The Good isn't subject to arithmetic; concern for others is no guarantee against actions that produce horrific outcomes; the meek are capable of over-estimating what can typically be done and thence what they can do; and any attempt to call a convention of the best-and-brightest in each field would attract a different sort (or none at all).

He took his madness to a different table.


Saturday, 21 May 2011

A previous entry quotes a foot-note from Austrian Marginalism and Mathematical Economics by Karl Menger; that foot-note is tied to a sentence that I found particularly striking.

(musings on the relationship of mathematics to economics)