In this paper I offer an account of the meaning of ‘must’ and ‘can’ within the framework of possible worlds semantics. The paper consists of two parts: the first argues for a relative concept of modality underlying modal words like ‘must’ and ‘can’ in natural language. I give preliminary definitions of the meaning of these words which are formulated in terms of logical consequence and compatibility, respectively. The second part discusses one kind of insufficiency in the meaning definitions given in the first part, which arise from the ‘ex falso quodlibet’ paradox of logical consequence. In stepwise fashion, I make an attempt to avoid most of the consequences of this paradox for the meaning definitions of ‘must’ and ‘can’.