What abstract conditions concerning embodiment are necessary, together with formal conditions, for a specification of sufficient conditions for cognition? A material environment does more than realise one formal specification. There is no one base specification on which all the formal specifications that it realises supervene. Thus a relationship with a material environment may defy comprehensive formal analysis. Cognitive capacities are capacities to have relationships with material environments as such. Thus they are capacities which are not analysable in terms of any one formal model of the cogniser and its environment. An account of cognisers as autonomous intentional agents is developed. The question of whether a cogniser and its environment can be computational is explored.