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If the tiles of a mosaic are arranged symmetrically, then the image those tiles constitute must be symmetric as well. This paper formulates and defends the general principle at work in this case: roughly, that a symmetry cannot ground an asymmetry. It is argued that the principle supports strong objections to four metaphysical views: qualitativism, relationalism, the tenseless or 'B' theory of time, and comparativism. A response to these objections is developed which appeals to fragmentalism, the view that reality contains facts which are incompatible with one another. But fragmentalism might be thought too bizarre to tolerate, and if it is, then the objections developed in this paper may well be fatal.
Martin Glazier (Mon,) studied this question.