Whose nirvana is it anyway?

He claims that "my death" is inalienably mine: that no one can die my death for me.

Yes, but what is the phenomenology of "me" and "my". It is an experience that arises and passes away. In fact no experience is inalienably yours. The experience of "mine" (a sense of ownership over the object of experience) arises and passes away. "Mine" is an illusion. It certainly true that you have a first person perspective while you are conscious. But you don't have it when you are asleep for example. Nor when in deep samādhi. If there is no first person perspective then there is no sense of "mine".

So, in order to argue that death is "yours" you would have to argue that the first person perspective is a constant. In fact it is dependent on functioning senses - the five physical senses and the mind. If we are referencing Heidegger then we must admit that the brain and the senses stop working at death. So one can never experience death. At best one might experience the moment immediately preceding death, though I could not say that this moment is different in any way from other moments, but one could not experience death per se because experience ceases with death.

Now orthodox Theravādins say that after the final moment of mental activity in one body, a new moment of mental activity arises in another body. If we take this to mean experience arises, then the experience is of the moment before death, and then the moment of rebirth. With no gap. There is no experience of death. Sarvāstivādins in particular critiqued the idea that the transition was instantaneous - they argued that the transition involved travelling in space and thus must involve an appreciable time. For them there was an interim realm between death and rebirth called an antarābhava (Tibetan "bardo"). But the nature of experience in a mind that has no sense organs or brain is moot. It cannot possibly be experience in the sense that we normally use the word.

So it seems that you are right that "your" death never arrives, at least from your point of view, because your point of view is contingent on being alive. At best it can involve a shift in perspective: from one first perspective to another, either via a mysterious interim or instantaneously.

From a buddhist point of view, i think the question is flawed already from the beginning by assuming that there exists a "self or person" by using the words "whose nirvana, my death, person, his or her nirvana".

By using these words it is implied that a self exists which it do not. There exist a physical and a mental stream and nowhere is there a self to be found. A self is not even needed in the equation. Things work just fine without the need for a self.

If you try to search for this self by either using the method of analysis where you break things up into the constituent parts and look at them you will not find a self anywhere.

If you use the method of synthesis by looking at things in a relational/interdependent way by using the doctrine of dependent origination you will also not find a self anywhere. Why? Because according to dependent origination things only exist as a part/reflection of other things. Therefore no real self can be found.

The false idea of a self arises when the 5 aggregates work together as a physio-psychological machine. The false idea of a self is really just one of the 52 mental formations belonging to the 4th aggreate and all the aggregates are subject to the 3 signs of existence; anicca, dukkha, anatta. This is said by Dr. Walpola Rahula on p. 18 in his book "What The Buddha Taught".

So in order to answer your question i would say that you should take out the aforementioned words and then you have your answer which is that no "self or person" achieves nibbana. Assuming that a "self or person" exists is not refering to ultimate reality - paramattha sacca. Instead you are dealing with concepts which is not real.

Lanka

Don't look at it that way; look at it as the extinction of suffering.

The problem is that Buddhism is dealing with the ineffable, so any attempt to define these phenomena will be imperfect at best and a disaster at worst. Unfortunately, people have felt compelled to add details and in the process... well, your question is a classic example of the kinds of illusory problems people face.

First, you're obviously going to gain something out of Buddhism, otherwise why practice? If someone came to me, said that my finances were a wreck, but if I worked an extra job, someone ELSE would improve their finances, I wouldn't waste my time. So why is it different with Buddhism?

It isn't. However, the problem is that there are two different definitions of "self" that are being used in discourse, and it's not always clear which definition is in use. Thus semantic confusion reigns, creating illusory problems out of thin air -- nonsensical, utterly unimportant problems that prevent you from doing what Buddhism teaches you to do -- PRACTICE.

One "self" is raw consciousness. If you stub your toe, you will feel it. In that sense, that you does and will continue to exist.

The other "self" is the bundle of concepts that you identify with, the history and attributes that you think define "you". It's that you that won't exist and that's the source of your suffering.

Confusing the issue is the fact that the experience of the first kind of self's experiences can be transformed by one's conceptual filter (it's amazing how our perceptions are shaped by concepts), so that even that self -- while not vanishing -- also seems to be transformed. That stubbed toe that hurts may involve a lot more conceptualizations in the "physical pain" than you may think. This means that this first type of self would still feel the stubbed toe, but may not feel the pain of the stubbed toe, given how much of that pain is really conceptualization.

Does your head hurt yet?

A classic saying is "there is suffering, but none who suffers". On the surface, it seems to almost be a claim that suffering is a purely impersonal phenomena. In a way it is, but in a way it isn't. There's experiences that make up suffering, but it's those experiences when conceptualized with respect to the illusory (second type of) self turn those experiences into suffering. Which means there really is no suffering until we actually believe there is one who suffers (curiously circular, no?) so by eliminating the one who suffers, we eliminate suffering or the suffering of the one who suffered, who actually doesn't really exist, but does in a way.

Ok, NOW does your head hurt?

That's the thing; when we run into so many difficulties that half our time is spent trying to duct tape the holes in our conceptual edifice, it's a sign that we are thinking about the problem in a fundamentally wrong way.

Buddhism itself seemed to notice this and in (what I take) to be a rare moment of lucid self-criticism, it offered the Fetters of Views and Parable of the Poison Arrow teachings. The idea is to avoid the temptation to conceptualize and instead practice. If things get better, don't over-think it. Just do what works.