My argument towards equivalence between cognition (or any other
physical process) is emulation.
I.e. if we consider cognition to be a large-scale behaviour of a given
physical structure (ion channels, lipid bilayers, cytoskeleton, etc.),
then by simulating the low-level processes sufficiently accurately I
would be able to reproduce also the high-level behaviour, in this
particular case, cognition.
In fact I am doing exactly this, investigating intricacies of
biomolecules: proteins and lipid bilayers on a vanilla PC, and not
even resorting to quantum weirdness: newtonian paradigm sufficies
here. In fact there are researchers who use compartmental neuron
models with some success, which shows that the molecular level is
actually not relevant -- you can do it at a much higher level.
Before you say that simulation of a thing and the thing itself are not
equivalent: very true, but cognition is one of the cases where
emulation and the process itself are equivalent. A computer simulating
playing chess, _plays chess_, after all.
Regards,
Eugene