By Vincent F. Hendricks
The major topic of this anthology is the original interplay among arithmetic, physics and philosophy in the course of the starting of the twentieth century. during this booklet, ten popular philosopher-historians probe insightfully into key conceptual questions of pre-quantum mathematical physics. the result's a various but thematically concentrated compilation of first-class papers on arithmetic, physics and philosophy, and a source-book at the interplay among them.
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Additional info for Interactions: Mathematics, physics and philosophy, 1860-1930
Thus actions must sum geometrically, and forces, which are the causes of the relative displacement of pairs, do so as well. This all assumes, however, that the frame of reference whose existence is postulated in the last step must exist. Furthermore, as I have already pointed out, it is not in general the case that the action of a point can always be decomposed into independent linear actions relative to the other points in the system. And these two demands, taken together, give a clear indication of what Kant wants, but cannot have.
But Helmholtz also appeals to logical determination in a second, “upward” sense: each concept must be determined, in that it should be seen as a specific case of a higher-order concept. The specific forces that causes changes in motion should be seen as positional determinations of a single force; furthermore, this single force should derive from a material point, and it should itself be a member of the family of “basic forces” that define the various kinds of matter. In my previous discussion, I have distinguished loosely between these two aspects of Helmholtz’s arguments by using the Kantian distinction between “regulative” and “constitutive” principles.
But that sense of determination is not sufficient to do the work required by Helmholtz’s definitions: the magnitude they determine must be congruent with another magnitude determined by those points at a second point in time. And Helmholtz, in contrast to Kant, is quite aware that there is a problem lurking here—that congruence is not the “complete similarity and identity” of two spatial magnitudes, to repeat Kant’s definition from the Phoronomy, but that every claim concerning the congruence of two spatial magnitudes contains an implicit reference to motion.
Interactions: Mathematics, physics and philosophy, 1860-1930 by Vincent F. Hendricks