Advaita seeks Atman, Buddhism seeks anatman, right?

[Coëmgenu]

That's okay. We can take it up via PM if you want.

I think I said everything I can

You're like clockwork, I'll give you that.

Something tells me you'll be saying more soon. Until then, I'll bid you a formal adieu, since we both agree that we've nothing left to say to each other regarding this.

[cappuccino]

Until then, I'll bid you a formal adieu, since we both agree that we've nothing left to say to each other regarding this.

[Rambutan]

Buddha wrote:
If I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, that would be conforming with those brahmans & contemplatives who are exponents of annihilationism.


Ananda Sutta

…but only because those exponents of the two extremes identify a soul with consciousness itself.

All that the Buddha is saying here is that the statement “not-self” is incorrect if it implies (as he perceived Vacchagotta to mean it) that no consciousness continues after the death of the body. He was silent because Vacchagotta‘s question, as he understood it, was not valid.
Vacchagotta is asking about “self” but what does he mean by “self”? According to eternalists and annihilationists, “self” is synonymous with consciousness (because of the question about what happens to it when we die).

It’s like asking if a winged cat can meow. The answer is neither yes or no, because there are no winged cats.

The view that no self can be found to exist in any composite phenomena (int the case of the body, this refers to the concept of atman) is basic premise of Buddhism. This doesn’t mean that consciousness ceases.

[Coëmgenu]

It will be very hard for you to defend the idea that consciousness does not "cease." You might want to rephrase your proposal.

[Rambutan]

It will be very hard for you to defend the idea that consciousness does not "cease." You might want to rephrase your proposal.

Let’s put it this way: while consciousness isn’t a continuous entity, but rather a self-triggering series of moments (each one caused immediately by the previous one), if we refer to that as a stream, then it can be said that this stream, one moment followed by the next, doesn’t cease at the time of death. Otherwise, no karmic cause for birth in samsara.

[Coëmgenu]

Yeah, I'd say that's better-phrased. Sorry for the unsolicited correction. I'm a consummate pedant. "Ceasing" is one of the main things that the Buddha specified that consciousness does, other than arise.