I am familiar with the Milinda-panna. But notice that the translator has interpolated the term 'no soul' throughout this passage. I don't agree with that interpolation. The word 'soul' has no counterpart in Pali or Sanskrit. The Sanskrit equivalent would be 'atma' which simply means 'self'. I understand the Buddhist opposition to the 'atmavada'. But I still don't agree with this interpolation 'no soul'. This doesn't imply the opposite, either - that there
is a soul. Remember the Buddha's response to Vachagotta on the question of whether there is a self - neither 'yes' nor 'no'. The 'no soul' phrase is a definite 'no'.
I think the point of Nagasena's argument is to demonstrate the falsehood of being attached to one's sense of identity. But this argument can also easily lead to a nihilist view.
On the other forum that I post to, the materialists also say there is no soul. Why? Because they say that human beings are a completely natural outcome of material interactions, formed by evolution and whatever physical processes have lead to living beings. At death, the elements disintegrate, and that is the end of it. There is no soul (which they think is just a superstition) and no life beyond this one. Accordingly, they think dharma is simply a social convention, and karma a myth to keep the masses in control. The atheist interpreters of Dharma, like Stephen Batchelor, dispute the notion of karma and rebirth for exactly this reason. They say it is interposed on the 'original teaching'. I say the opposite - that this materialist notion of 'no soul' is actually what is being interposed. It is not what the teaching means.
In the Buddhist tradition, it is understood that an individual life unfolds over many lifetimes (hence Dusko's original question). Remember the categorization of disciples in the Theravada tradition - never-returner, once returner, and stream-winner? This explicitly recognizes the process of re-birth, and the idea of karma playing itself out over lifetimes. What is the mechanism by which karma propagates through lifetimes? There is no easy answer to that question. In fact I don't think the Theravada tries to answer it, it simply assumes it. The Buddhist school that really worked out a detailed description of this whole process was the Yogācāra, who found it necessary to introduce concepts such as the ālaya-vijñāna in order to provide the basis for the process.
Philosophically, we can distinguish between a substance-view and a process-view. It is mistaken to think of 'soul' or 'atma' - whether you accept it or not - as a substance or an entity. In the Buddhist view of rebirth, there is a
process which plays itself out over many lifetimes. There is not
a substance which undergoes the process, there is only the process. We have become involved in this process, through craving and delusion, and therefore identify with the elements in the process, to the point that we think we
are the process. This is what Nagasena's argument is pointing to: he is trying to show us that we are identifying with all of these phenomena which are 'anatta', not-self.
Ultimately this argument leads to the doctrine of emptiness and all the Prajñāpāramitā teachings, such as the Diamond Sutra:
Buddha then asked, "What do you think, Subhuti, does one who has entered the stream which flows to Enlightenment, say 'I have entered the stream'?"
"No, Buddha", Subhuti replied. "A true disciple entering the stream would not think of themselves as a separate person that could be entering anything. Only that disciple who does not differentiate themselves from others, who has no regard for name, shape, sound, odor, taste, touch or for any quality can truly be called a disciple who has entered the stream."
Buddha continued, "Does a disciple who is subject to only one more rebirth say to himself, 'I am entitled to the honors and rewards of a Once-to-be-reborn.'?"
"No, Lord. 'Once-to-be-reborn' is only a name. There is no passing away, or coming into, existence. Only one who realizes this can really be called a disciple."
"Subhuti, does a venerable One who will never more be reborn as a mortal say to himself, 'I am entitled to the honor and rewards of a Non-returner.'?"
"No, Perfectly Enlightened One. A 'Non-returner' is merely a name. There is actually no one returning and no one not-returning."
"Tell me, Subhuti. Does a Buddha say to himself, 'I have obtained Perfect Enlightenment.'?"
"No, lord. There is no such thing as Perfect Enlightenment to obtain. If a Perfectly Enlightened Buddha were to say to himself, 'I am enlightened' he would be admitting there is an individual person, a separate self and personality, and would therefore not be a Perfectly Enlightened Buddha."
This is the 'great paradox' of the whole teaching: that awakening to the true identity is to go beyond all sense of myself, me, and mine, self and other, spirit and matter, and all of the other dualities that the 'phenomenal mind' clings to. From this viewpoint, there is indeed 'no soul' - but this is, if you like, viewed from above, from the transcendent realm, rather than from below, from the material realm. And within this material realm, if we say there is 'no soul', I still reckon we will end up falling back into materialism. We understand there is no soul by going beyond the realm of individuation, not by denying that it exists - and there is a world of difference between the two understandings.