Visuddhimagga CHAPTER XXI Purification by Knowledge and Vision of the Way
In short they are three gateways to nibbāna. You either take nibbāna as object by way of focusing on impermanence, which leads to the signless samādhi. By way of dukkha which leads to the Wishless/Desireless (basically not intending this way or that) samādhi or by way of anatta which leads to the Emptiness Samādhi.
Difficult to say, Commentary on this series of suttas does not say. Commentaries often doesn’t repeat what was pointed out somewhere else. Should be very carefully investigated.
But although stated in this way, insight knowledge is not literally signless because there is no abandoning of the sign of formations [as formed, here, as distinct from their sign as impermanent and so on]. It is however literally void and desireless. And it is at the moment of the noble path that the liberation is distinguished, and that is done according to insight knowledge’s way of arrival at the path. That, should be understood, is why only two liberations are stated [in the Abhidhamma], namely, the desireless and the void.
The long discussion on why signless path is inadmissable is very interesting (it’s quite long to post here), paraphrasing: It mentions how dukkha can give rise to desireless, anatta can give rise to emptiness, however, contemplation on impermanence is not self-consistent apparently.
It’s quite a thick section with interesting notes. It also quotes Patis II 68, which I’m not sure where in Patis it refers to, it’s not a cataloguing system I’m familiar with.
No friend, it is not a matter of being inadmissable or of any inconsistency. Rather the Abhidhamma(specifically, The Dhammasangani, ) does not mention the signless path.( Reasons are explained both in the Dhammasangani commentary and Visuddhimagga and may be other places also)
Its because the Abhidhamma and commentators don’t consider the signless to be able to transcend its object, since the focus is on impermanence (and so on the rise and fall of dhammas). The commentary though does say that according to the sutta method there is a signless path.
For example dukkhanupassana ñāṇa and anattanupassana ñāṇa also sees the rise and fall.
But aniccanupassana ñāṇa cannot be called ‘animitta’ in a nippariyāya sense. Hence the path that arises by way of aniccanupassana is not mentioned in the Abhidhamma. Which is the nippariyāya desana of the Blessed One.
‘Homage to you, O thoroughbred!
‘Namo te purisājañña,
Homage to you, supreme among men!
namo te purisuttama;
We don’t understand
Yassa te nābhijānāma,
the basis of your absorption.’”
yampi nissāya jhāyasī’”ti.