According to John Locke, the traditional authority on primary and secondary qualities, the effects of secondary qualities wholly depend the operations of the primary. This is compatible with Reid's identity theory. However, Locke only hesitantly ascribes secondary qualities to physical objects, regarding them as ‘nothing in the objects themselves’, ‘powers barely’, ‘mere powers’ and ‘imputed’ powers. Why does Lock write as though these properties are unreal? Because qualities of physical objects and secondary quality sense experiences do not exhibit strong correlations or, as Descartes calls it, ‘exact correspondence’. Locke offers several examples of secondary quality ideas changing without variation in supposed physical objects of perception: looking at coloured objects in the light and in the dark, tasting crushed and uncrushed almonds, and placing hands of different temperatures into lukewarm water. This lack of correlation between objective property and subjective sensation or idea underlies the most prolific and important series of objections to the identity theory of secondary qualities, which is why this chapter considers five non-correspondence objections.

These five are variations on one theme: there is no single-valued function from perceiver-independent physical property to sensation type, and none from sensation type to property type. Four of the five involve non-correspondence in the first direction, from property to sensation. They make it apparent that one physical property in fact causes many different sensations. The fifth, the case of metamerism, demonstrates non-correspondence the other way. Each of several sensations is caused by many different physical properties. However, this non-correspondence, regardless of direction, does not warrant the rejection of the identity theory of secondary qualities. Those who have argued in this manner have assumed either that sensations are essential constituents of perceptions or that secondary quality perceptions commit human perceivers to more than they in fact do.

Others have tried to solve the non-correspondence objection in other ways. Michael Huemer, for example, when faced with the lack of correspondence between colour sensations and scientific physical properties, like spectral reflectance, offers a promissory note, that scientists will find a correspondence once they learn to think of the scientific properties in the relevant categories, whatever those happen to be.