The paper presents a paradoxical feature of computational systems that suggests that computationalism cannot explain symbol grounding. If the mind is a digital computer, as computationalism claims, then it can be computing either over meaningful symbols or over meaningless symbols. If it is computing over meaningful symbols its functioning presupposes the existence of meaningful symbols in the system, i.e. it implies semantic nativism. If the mind is computing over meaningless symbols, no intentional cognitive processes are available prior to symbol grounding. In this case, no symbol grounding could take place since any grounding presupposes intentional cognitive processes. So, whether computing in the mind is over meaningless or over meaningful symbols, computationalism implies semantic nativism.