Physics says that it cannot deal with the mind-brain problem, because it does not deal in subjectivities, and mind is subjective. However, biologists (among others) still claim to seek a material basis for subjective mental processes, which would thereby render them objective. Something is clearly wrong here. I claim that what is wrong is the adoption of too narrow a view of what constitutes 'objectivity', especially in identifying it with what a 'machine' can do. I approach the problem in the light of two cognate circumstances: (a) the 'measurement problem' in quantum physics, and (b) the objectivity of standard mathematics, even though most of it is beyond the reach of 'machines'. I argue that the only resolution to such problems is in the recognition that closed loops of causation are 'objective'; i.e. legitimate objects of scientific scrutiny. These are explicitly forbidden in any machine or mechanism. A material system which contains such loops is called 'complex'. Such complex systems thus must possess non-simulable models; i.e. models which contain impredicativities or 'self-references' which cannot be removed, or faithfully mapped into a single coherent syntactic time-frame. I consider a few of the consequences of the above, in the context of thus redrawing the boundary between subject and object.