I've heard it suggested that a major difference between the mind and the brain is that (only) the former is private, i.e. in principle inaccessible to others. But that just doesn't seem true. As our knowledge of cognitive neuro-psychology improves, we will gain the ability to know more and more about the contents of minds from brain scans and the like. Already experimenters can tell, from brain scans alone, whether subjects are seeing a face or a house. So doesn't that disprove the claim that the contents of our minds are 'private' in any deep sense?
At least qualia might plausibly be claimed to be irreducibly private/subjective. Sure, you can tell that the bat is receiving echolocation data of an object with such and such primary qualities. But, as Nagel points out, you can't know what it's like to be that bat! So the experiential qualities of consciousness may be 'private' in the sense that they cannot be grasped by just any old (sufficiently intelligent and well-equipped) being.
But qualia are notoriously tricky properties, so I'm happy to set them aside for now. So, what about the rest of our minds? Is there any good reason to accept the traditional view that they are deeply 'private' in either sense described above? (This strikes me as so obviously mistaken that I suspect I must be missing something...)