There are several things that might be called ‘computationalism’. The one most central to the philosophy of mind is a theory that attempts to answer what Chalmers calls the ‘hard problem’ of consciousness: how can it be that brute material processes can give rise to phenomenal experience? The existing literature has addressed metaphysical challenges for computationalism piecemeal. In this thesis, I begin the work of assessing them as an interconnected whole. I analyse six key problems faced by the computationalist, showing how they mutually complicate each other in ways the existing literature does not appreciate. In mapping this problem space, I draw on and expand upon the work of thinkers including John Searle, Hilary Putnam, ...