Modern brain research related to consciousness has resulted in many interesting in- sights, for example into the neurobiological basis of attention and of language. In biological terms, human consciousness appears as a system’s feature of our brain, with neural processes strictly following the laws of physics. This does not necessarily imply, however, that there can be a general and comprehensive scientific theory of consciousness. Predictions of the extent to which such a theory may become possi- ble vary widely in the scientific community. There are reasons - not only practical but also epistemological - why the brain-mind relation may not be fully decodable by finite procedures. In particular, analogies with mathematical theorems of un- decidability suggest that self-referential features of consciousness, such as multiple self-representations like those involved in strategic thought, may not be fully resolv- able by brain analysis. Assuming such limitations exist, this implies that ob jective analysis cannot exhaust sub jective experience in principle. A person’s consciousness and will are accessible to external observation only within limits. In some respects, we do not even learn to know ourselves except by our actions. It thus appears that a scientific look at consciousness and the human mind, combining universal physi- calism with epistemological scepticism, is not inconsistent with certain concepts of sub jectivity that are current in the humanities, despite all the differences in the style and terminology of discourse.