Could there be 7/8 of a conscious subject, or 1.34 conscious subjects, or an entity indeterminate between being one conscious subject and seventeen? Such possibilities might seem absurd or inconceivable, but our ordinary assumptions on this matter might be radically mistaken. Taking inspiration from Dennett, we argue that, on a wide range of naturalistic views of consciousness, the processes underlying consciousness are sufficiently complex to render it implausible that conscious subjects must always arise in determinate whole numbers. Whole-number-countability might be an accident of typical vertebrate biology. We explore several versions of the inconceivability objection, suggesting that the fact that we cannot imagine what it's like to be 7/8 or 1.34 or an indeterminate number of conscious subjects is no evidence against the possibility of such subjects. Either the imaginative demand is implicitly self-contradictory (imagine the one, determinate thing it's like to be an entity there isn't one, determinate thing it's like to be) or imaginability in the relevant sense isn't an appropriate test of possibility (in the same way that the unimaginability, for humans, of bat echolocation experiences does not establish that bat echolocation experiences are impossible).

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