If we assume that the essence of Buddhism is fundamentally based on dependent origination (pratîtyasamutpada) and no-self (J., muga; S., anâtman) as Hakamaya Noriaki and Matsumoto Shiro of Critical Buddhism (hereafter CB) assume, then Zen Buddhism is not Buddhism. And for that matter, Mahayana Buddhism is not Buddhism.

I don’t think there is any doubt that Hakamaya Noriaki and Matsumoto Shiro, in the book, Pruning the Bodhi Tree (http://goo.gl/sSsyyC), defend the thesis that Buddhism is the negation of the transcendent which lies beyond the sphere of temporality. Any idea of liberation by nirvana is not Buddhism because it implicitly accepts a self to be liberated which goes against no-self.

"In the next essay, on "Liberation and Nirvana: Some Non-Buddhist Ideas," Matsumoto carries his critique one step further to argue that there is no greater misunderstanding than to say that the final goal of Buddhism is "liberation" (gedatsu; vimukti). The reason is that the idea of liberation (vimukti) is based on the non-Buddhist idea that there is a self (âtmavâda) to be liberated, which is an anti-Buddhist idea. Not only liberation, but nirvana, a concentrated state of mind (jhâna, samâdhi), and even "mind" (citta), are all based on the non-Buddhist idea of a self” (Pruning the Bodhi Tree, p. 10).

On the other hand, if CB’s assertion cannot be sustained where the discourses of the Buddha do not regard dependent origination and no-self as primary teachings and, instead, regard transcendence of dependent origination and no-self as primary, then Zen is Buddhism along with Mahayana Buddhism.

If we turn our attention to the scholarly world of what dependent origination probably means, including no-self, these terms merely describe the world of conditionality, namely, samsara.

“The ultimate purpose of the teaching of dependent origination is to expose the conditions that sustain the round of rebirths, samsara, so as to show what must be done to gain release from the round. Existence within samsara is suffering and bondage (dukkha), and hence the ending of suffering requires deliverance from the round" (Bhikkhu Bodhi, The Connected Discourses of the Buddha, p. 517).

Dependent origination is usually explained by the twelve nidânas (ni-dâ = to bind down) or links. This linking process helps to explain rebirth beginning with avidya all the way to old age and death. Without the removal of avidya, there is no escape from the wheel of samsara. In contrast to samsara is, naturally, nirvana which is unconditioned; which is not dependently originated. Nirvana is the primary teaching of the Buddha, not samsara.

“Here, secluded from sensual pleasures ... a bhikkhus enters and dwells in the first jhâna ... He considers whatever phenomena exist there pertaining to form, feeling, perception, volitional activities, and consciousness as impermanent, suffering, an illness, a boil, a dart, misery, affliction, alien, disintegrating, empty, and non-self. He turns his mind away from these phenomena and directs it to the deathless element thus: ‘This is peaceful, this is sublime, that is, the stilling of all activities, the relinquishing of all acquisitions, the destruction of craving, dispassion, cessation, nibbana” (A. iv. 422–23).

Turning to no-self which refers to the Five Aggregates (they appear in the above passage) and the senses, including their respective sense fields, they are all conditioned, never unconditioned. The Buddha tells us in so many words to reject no-self (SN 22:68) and never once the self. It is our self that wins nirvana.