How are the brain and our observation of it in neuroscientific investigation related to each other? I here distinguish between brain-based and observer-based concepts. Brain-based concepts mean that they are very much in accordance with the way the brain functions and processes neural activity independent of our observation of it. In contrast, observer-based concepts refer to the dependence of our observations on the observer and his or her particular experimental (and technological and other) requirements. Since in observer-based concepts the observer intrudes into the observations and ultimately into the brain itself, I also speak of ‘observer-related intrusions’. I distinguish between extrinsic and intrinsic observer-related intrusions: extrinsic observer-related intrusions can in principle be avoided and minimized while intrinsic ones cannot in principle be overcome. This is so because they concern, as I assume, intrinsic design features of the brain, and do therefore define the brain as brain. I conclude that the intrinsic observer-related intrusions pose ‘neuro-experimental and neuroepistemological constraints’ on our possible knowledge of the brain. Extrinsic observer-related intrusions pose methodological fallacies that are to be avoided, as, for instance, the projection of the concept of free will onto the brain.