Let's be very honest here about this sort of misrepresentation of Ajahn Brahm's teaching. As I mentioned here -Ñāṇa wrote:Ven. Brahmavamso's teachings on jhāna are either a non-apperceptive attainment (asaññasamāpatti) or dangerously close to being one. His understanding of mindfulness (sati), full awareness (sampajañña), and apperception (saññā) in the context of jhāna bear no resemblance to how these dhammas are defined and used in the canonical literature.
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the accusations have surreptitiously evolved from attacking Ajahn Brahm's kāmasaññanirodha teaching of 1st Jhana (as uncanonical) to become an insinuation that he teaches sabbasaññanirodha for the jhanas. Worse, you now say that he teaches asaññasamāpatti.
In the thread above cited, I have given ample canonical examples where the Buddha extolled the Jhanas as stages of successive cessations of different dhammas that make up our experiential "world". Specifically, in DN 9, the Buddha pointedly mentions that it is "with training one perception arises and with training another perception ceases". This is repeated for all the Jhanas, the Arupa attainments and Nirodha Samapatti.
I keep seeing this slippery misrepresentation of Ajahn Brahm. For the record, the perceptions that Ajahn Brahm mentions disappearing are kāmasañña in 1st Jhana, and that is explicitly sanctioned by the Anupubbanirodha Sutta, besides the standard "vivicc'eva kamehi" pericope. He describes the cessation of different factors through each progression through the Jhanas, which are then replaced by other dhammas. If you actually read his book, you'll find that it is nothing more than an expanded version of DN 9, with details being supplied by other suttas.
Unless, of course, you now reject these suttas' descriptions of the training to attain these successive cessations...