This paper starts from the familiar premise that psychological anti-individualism is incompatible with materialism. It attempts to state more clearly what this incompatibility consists in, and — rather than arguing in detail for any particular resolution — to inquire whether this incompatibility admits any resolution. However, the paper does offer a conditional argument concerning the possibility that the incompatibility is genuine and cannot be resolved. Provided that anti-individualism and materialism cannot be squared, and anti-individualism is correct, it follows that materialism has to be abandoned. If so, the situation is not as disastrous as it might at first seem. We need not, in consequence of our inability to construe a coherent metaphysics of mind, give up on intentional vocabulary any more than we must stop, in consequence of our inability to make sense of induction, anticipating the future.