Quantity in Principia Mathematica

Abstract

In the Introduction, I quoted the letter Whitehead wrote to Russell on 14 September 1909:

The importance of quantity grows upon further considerations — The modern arithmetization of mathematics is an entire mistake — of course a useful mistake, as turning attention upon the right points. It amounts to confining the proofs to the particular arithmetic cases whose deduction from logical premisses forms the existence theorem. But this limitation of proof leaves the whole theory of applied mathematics (measurement, etc.) unproved. Whereas with a true theory of quantity, analysis starts from the general idea, and the arithmetic entities fall into their place as providing the existence theorems. To consider them as the sole entities involves in fact complicated ideas by involving all sorts of irrelevancies — In short the old fashioned algebras which talked of ‘quantities’ were right, if they had only known what ‘quantities’ were — which they did not.