This paper defends the following principle: For any visually perceptible set of objects and any visual phenomenal character, there could be a veridical perception of exactly those objects with that character. This principle is rejected by almost all contemporary theories of perception, yet rarely addressed directly. Many have taken the apparent inconceivability of a certain sort of “shape inversion” — as compared to the more plausible, frequently discussed “color inversion” — as evidence that the spatial characters of our perceptions are (...) uniquely suited to and/or revelatory of the structure of their objects, such that alleged perceptions of those objects that differed radically in spatial character could not be veridical. I argue that these conclusions are unjustified: I claim that the difficulty involved in constructing coherent “shape inversion” scenarios is attributable to the complex relations among visual and tactile shape experiences, as opposed to relations between shape experiences and worldly shape properties. (shrink)