 While Stevens’ classification of scales met with general approval in scientific and philosophical circles, its wider implications for measurement theory became the topic of considerable debate. Two issues were especially contested. The first was whether classification and ordering operations deserve to be called “measurement” operations, and accordingly whether the representation of magnitudes on nominal and ordinal scales should count as measurement. Several physicists, including Campbell, argued that classification and ordering operations did not provide a sufficiently rich structure to warrant the use of numbers, and hence should not count as measurement operations. The second contested issue was whether a concatenation operation had to be found for a magnitude before it could be fundamentally measured on a ratio scale. The debate became especially heated when it re-ignited a longer controversy surrounding the measurability of intensities of sensation. It is to this debate we now turn.