Bertrand Russell's 1897 critique of the traditional theory of measurement (Q1293026)

The subject of attention here is the paper ``On the relations of number and quantity'', Mind, New Ser. 6, 326-341 (1897), written by the young Russell when still in his phase of the neo-Hegelian philosophy which held great sway in Britain. He adopted a version of the ``representational approach'' to measurement, as the author calls it, according to which a measurement pertains to facts about entities rather than the operations involved in making it or conditions under which it may be effected. It was an intrinsic theory in tune with his philosophical stance, but was abandoned when he switched in 1899-1900 to the empirical position proposed by his friend G. E. Moore. The author also compares Russell's account with a more formal one put forward by Otto Hölder in 1901, and notes comparable theories among some modern writers.