Because ‘thickness’ always leaves room for dispute, this is one of those cases in philosophy in which one is at the mercy of the arguments philosophers happen to think up. The conceivability argument creates a prima facie case for thinking that mind has no more than causal ontological dependence on the body. Let us assume that one rejects analytical (behaviourist or functionalist) accounts of mental predicates. Then the above arguments show that any necessary dependence of mind on body does not