Indeed. But since we do not identify people as merely their physical bodies (I have seen none of your physical bodies yet I surmise that I am speaking to humans, for your minds, your language, etc. displays itself), we can’t say that when someone’s physical bodies dies, that they altogether die, for it is quite obvious that the physical body is but one aspect of their total being (which includes mind), and that their mind cannot be tasted, touched, smelled, heard, nor seen.
So it is clear, via our senses, that the material aspect of the being, the body (including of course, the brain) rots away and dies. But we can’t say the same about mind, aka, that which see’s but can not be seen. That which tastes but cannot be tasted. This isn’t mere semantics, it’s quite real. We are talking about the exterior on one hand (the body) and the interior on the other hand (mind, or soul). We cannot say what happens to the interior of an organism that dies, only the exterior. But we can say, via logic, that non existence can not be seen, nor comprehended, and therefore, is logically unsound, in the same way that “God” is logically unsound.
The counter argument to this is that the mind and brain are one and the same. That everything can be reduced to matter, and therefore when we see that matter is dead, we can say that the mind is dead. I find this view to be reductionistic to the point of absurdity. For again, we can never reduce matter to that which observes matter, for we cannot see, cannot touch, cannot hear, cannot smell, and cannot taste what we call “mind” or “consciousness”.
One more thing, I find (or rather, suspect) that there is a pathological aspect to the belief that when you die, that you will cease to exist forever and ever more, or that you will be unconscious for ever and ever more. And that can be called the UTOPIA of the once-and-for-all end of suffering, of pain, of aversion, and so on. I find (or rather, suspect) that the pathology that rules the materialist is in many cases the same as the pathology that rules the Christian, the Islamist, and so forth. The desire for an eternity of everlasting non-suffering. Existence has shown us no such thing, and we ought not presume such a thing if we take this question seriously.