Yes, that's what I more or less expected. However, that something is outside the range of our senses does not mean that it is not physical – each and every example in Medhus' argument is a physical phenomenon. Furthermore, while you may argue (as you did in one of the previous replies) that soul / spirit / consciousness may prove to be physical, when you investigate that “something more”, you realize that it is without attributes or forms, hence spatiotemporary uniform (i.e. not individual) and also not a phenomenon (thus, “beyond” time, space, and any physical substance), yet still the true nature of our personhood. (Hence, the persistent illusion of individual immaterial soul, but also the Vedic “great saying” that Atman, i.e. the notion of individual self or soul, is actually Brahman, i.e. the “universal” Self, which is all there is).
So yes, there simply cannot be a proof for “something more”, human beings are “meat talking to itself”, and “thinking is […] generated by the brain and when we die, [it] dies with us,” indeed. At the same time, we are in fact singular (or non-dual) immaterial conscious existence that predates life and death. We are literally one (immaterial and unindividual) person simultaneously knowing trillions of physical individual entities whose bodies, minds, memories, etc. come and go.
As you can see, the only problem with physicalism and materialism is when they try to generate consciousness from within Universe. That's where they hit the walls of hard problem of consciousness, qualia, etc. Similarly, the problem of spirituality is when it tries to introduce non-physical and imperceptible (but interacting thus somehow perceptible!) entities into a clearly physical system of manifested Universe just because it cannot accept the cessation of individual (mind). In other words, our deceased ancestors don't echo trough Universe as disembodied agents, but as physical causes of their lives which human can detect for “I” to know.
So yes, I am immortal but Sender Spike is not. Simple as that.