Perceptual-role theories of mental qualities hold that we can discover the nature of a being’s mental qualities by investigating that being’s capacity to make perceptual discriminations. Many advocates of perceptual-role theories hold that the best explanation of these capacities is that mental quality spaces are homomorphic to the spaces of the physical properties that they help to discriminate. This paper disputes this thesis on largely empirical grounds, and offers an alternative. The alternative explains interesting patterns in our perception of color (...) differences and similarities across edges, emphasizing the importance of visual discontinuities. Further, it provides a simple explanation of the intransitivity of indiscriminability. The homomorphism thesis can explain this intransitivity only with the addition of an independently unsupported empirical hypothesis. Also, in contrast to the homomorphism thesis, the alternative view is perfectly consistent with empirical data that suggest that the visual system uses the dynamic allocation of a limited range of responses in order to discriminate a wider range of physical stimuli and that we are much better at detecting changes in relative luminance than changes in absolute luminance. Moreover, it does all this while using a more efficient strategy for encoding sensory information. (shrink)