[uchetrip]

... an Atman for a reincarnation scheme.

Seems to me the Atman problem also exists in the passage which Ajahn Buddhadhasa quoted. What is this "individuality" in which kamma ripens, and within which one experiences the fruit?

Here is the passage again:

Any action that one has carried out with greed, arising with greed as its cause, and having greed as its
origin; that action bears fruit within the aggregates that are the basis for ones individuality. In whichever
individuality that kamma bears fruit, one experiences that karmic fruit within that very individuality,
either immediately, soon after, or some time later.

Friends, this is comparable with plant seeds that have not broken, rotted, or been destroyed by wind
and sun, that have been chosen for their soundness, carefully stored, and planted by someone in a well
prepared plot with good top soil. Further, the rain falls according to the season. Those seeds will sprout,
develop, and thrive most certainly. In the same way, any action that someone has carried out with greed
… hatred … delusion, arising with greed … hatred … delusion as its cause, and having greed … hatred
… delusion as its origin; that action bears fruit within the aggregates that are the basis for his
individuality. In whichever individuality that kamma bears fruit, he experiences that karmic fruit within
that very individuality, either immediately, a moment later, or some time later. Aside from rebirth/reincarnation, my understanding is that the alaya model was put forward (by Vasubandhu, actually, not his brother Asanga) in order to address a more fundamental issue: how, in the absence of an atman, can kamma produce a vipaka? And more generally, how can a thought-moment at one time affect a thought moment at a later time?

We see from the passage above that kamma arises in connection with mental behaviors: greed, hatred and delusion. So it is essentially something that happens within the conscious mind. And the conscious mind is where vipaka is experienced as well. But without an atman, what connects the two experiences?

The problem comes up regardless of whether we are speculating about multiple lives or limiting the discussion to continuity across a present life.