Mathematical Expressibility, Perceptual Relativity, and Secondary Qualities

During the seventeenth century, several apparently very disparate reasons were advanced for a believing that there is an important distinction between primary and secondary qualities. The most prominent were (1) the overall explanatory success of a physical science which refers only to primary qualities (2) the mathematical expressibility of primary but not secondary qualities, and (3) the immunity of primary but not secondary qualities to perceptual relativity arguments. The first of these would find sympathy today; questions about which types of qualities are real are often taken to be decided by the scientific theory that provides the best explanation for all of the relevant phenomena. But the second and third of these reasons may seem odd. Why should perceptual relativity or mathematical expressibility mark an important distinction among qualities? I shall argue that mathematical expressibility and immunity from perceptual relativity indeed provide strong evidence for the reality of physical qualities. Furthermore, I shall contend that immunity from perceptual relativity and mathematical expressibility are intimately connected; what explains the plausibility of the perceptual relativity arguments also accounts for the power of the arguments from mathematical expressibility.