 There is, then, no very compelling argument for Geach’s sortal relativity thesis to be based on such examples, given the variety of responses available, some of which will be returned to below. On the other hand, no alternative solution to the puzzle of the cat on the mat stands out as clearly superior to the rest, or clearly superior to the sortal relativity thesis as a solution. We should conclude that this component of Geach’s position, though not proven, is not refuted either, and, possibly, that the linguistic data provide no basis for a decision for or against.