Much recent work in the philosophy of consciousness has centered around the Determinacy thesis: the thesis that for each , it is determinate whether  is conscious. Whether this thesis is true is a matter of considerable urgency, for it is widely taken to entail the falsehood of both physicalism about consciousness and gradualism about its evolution. Here we offer a new argument against the determinacy thesis. We first argue that if consciousness is multidimensional, the main argument in favour of determinacy—the No Borderline Case argument—is unsound. We then argue that multidimensionality makes it highly probable that Determinacy is false, because multidimensionality brings with it a distinctive and heretofore unrecognized form of indeterminacy. We then offer arguments that consciousness is in fact multidimensional, and accordingly, that the drastic consequences of Determinacy should not concern us.