My apologies, I think I have not been sufficiently clear.
You are absolutely right when you say that the goal is to arrive at the perception “This is not mine, I am not this, This is not myself”. The ultimate aim is to become dispassionate towards all things, thereby transcending desire and achieving Nibbana.
What I have endeavored to describe is not the Buddha’s theory of Self… we all know he maintained silence on that front! Rather this is his tactic, the technique used by the Buddha (as recorded in the Suttas in allegedly his own words) to examine all objects of experience, as well as experience itself, so as to see it as it really is. In achieving that final Right View, one loses desire for all objects/ experience. At that point, one is freed from Samsara. The question of “Self” existing or not becomes a non issue at that point.
A good start point to use this technique of insight is the experience of Dukkha. In doing this, one proceeds inwards from the external world deeper and deeper within the mind till one reaches the very innermost level of experience. Sila and Samadhi assist in achieving the quiet mind that is a necessary pre requisite of such emotionally jarring investigation.
A short example: -
Let us say, I feel bad because my car got scratched. I realize, I am suffering (at this time my sense of Self is still strong… and that’s OK as we will see later). I examine this feeling and perception. Why do I feel this way about my car? Did I expect it to last forever, unsullied? Isn’t it rusting, falling apart as it stands, getting depreciated, soon to end up at the junkyard? Attachment to such an object is just going to cause me Suffering, so I should let it go. The car is not really mine, I am not the car, neither is it an extension of me, it’s not my Self, I can’t control or make it Be. I realize the Anicca, Dukkha and Anatta nature of the car. Realizing this, desire for the car fades.
Next day, I sweep my house. I see bits of head and body hair and nail clippings mixed in with the dust. Just yesterday these bits were part of my body. Should I hold onto them as “Me”? I investigate all the 31 parts of the body in this way. I realize, my body is just like the car, falling apart, eventually to end up as an inanimate log being burnt in the pyre or rotting in the ground, attachment to it is Dukkha…I have no power to preserve it… this is not mine, I am not this, this is not my Self. Letting the attachment to the body go, not having desire for it to be this way or that, I experience Freedom. (Note, this doesn’t mean the body disappears or changes its nature- its just the perception of it and my attitude to it that changes)
And so it goes ever inwards, to the examination of feelings, one’s own perceptions, thoughts… deeper still to the very deepest layer of Awareness. Even the Jhana experiences betray themselves as Impermanent, not under control, longing after them brings Dukkha, they too are seen as Anatta and let go of. Yes, even within the 8th Jhana there is still that Perception and ultimately letting go.
Finally the stage is reached where one has examined all objects as well as Experience itself, realized their Anicca, Dukkha, Anatta nature and so let go of them all. In this penultimate stage is the final duality… whatever is left within me // /observing/// all of Samsara. At this point, I realize that the question of Self itself is meaningless, it was all a tactic anyways… now that the aim of release from desire has been achieved, that too can be let go of. In that final letting go lies Nibbana. At this point, “I” and “Samsara” go over the event horizon, into a place where there are no words or descriptions… #UNDEFINED, zero divided by infinity … Does the Self still exist at that point? Does it not exist? Does it both exist and not exist? Does it neither exist nor not exist?
Well, the Buddha refused to answer that question. And neither have any of the Arahants since, ever commented on the matter. Best to leave it sub-judice till we all become Arahants - and then we will know!!