The view that Baka has taken up is this:
Idañhi, mārisa, niccaṃ, idaṃ dhuvaṃ, idaṃ sassataṃ, idaṃ kevalaṃ, idaṃ acavanadhammaṃ, idañhi na jāyati na jīyati na mīyati na cavati na upapajjatī’ti; santañca panaññaṃ uttari nissaraṇaṃ ‘natthaññaṃ uttari nissaraṇa’nti vakkhatīti.Our first question is what does Baka mean by 'this', what is he referring to? And because the text moves swiftly on to another tack it is difficult to tell. However there is a clue in the passage I've cited, in the sequence: birth, aging, death, falling, rebirth. This is not a random sequence, nor are death (mīyati) and falling (cavati) simply synonyms as one might easily assume them to be, nor perhaps are birth (jāyati) and rebirth (upapajati).
This, sir, is permanent, this is enduring, this is eternal, this is everything, this is unending. This is not being born, is not aging, is not dying, is not falling, is not being reborn; and beyond this, there is no escaping.
I need to backtrack for a bit. In 2002 Gananath Obeyesekere published Imagining Karma: Ethical Transformation in Amerindian, Buddhist and Greek Rebirth, which took a broad view of the idea of rebirth. It seems that many cultures develop a theory of rebirth and in its most basic form it involves circulating between this world and another world - usually some form of heaven, often inhabited by one's own ancestors. It has been asserted for a long time that in the early Vedic period there is no evidence of a belief in rebirth, but more recently Joanna Jurewicz showed that the Ṛgvedic mantra 10.16.5 can be interpreted as a request for Agni to send the dead person back again to his descendants (this is discussed in Richard Gombrich's 2010 book What the Buddha Thought). This suggests that early Vedic people had a standard rebirth theory in which the person (actually the man) cycled between this world and the other world.
The 'other world' for the Vedic Brahmin was the world of the fathers (pitaraḥ). This idea is expressed in greater detail in the Bṛhadāranyaka and Chāndogya Upaniṣads which both tell the story of how one precesses through the cycles. However the simple binary persisted for some time and it is referred to in the Pāli texts (in the phrase 'this world and the next world'). The simplest expression of this cycle does not allow for escape.
Let us now reconsider the Brahmanimantanika Sutta. The sequence, again, is: birth, aging, death, falling, rebirth. The cycle involves being born (jāyati) and living in this world (jīyati); dying (mīyati) and arising (upapajti) in the heavenly realms. Having lived a long time in the heavenly realms, one falls (cavati) back down to earth to be once again born (jāyati). And so the cycle goes round.
This cycle is called saṃsāra which is a noun from the the verb sam+√sṛ 'flow' - and means to move about continuously, to come again and again. It is this that Baka is saying is "permanent, enduring, eternal, everything, unending". This is his deceit: the view he adopts is that saṃsāra is forever, and inescapable, that we are doomed to go around and around endlessly. The ethicization of the universe that occurred amongst the samaṇa movements meant that the model had to become more sophisticated, but I will leave that thread for now. But the idea that one could escape from the rounds of rebirth (or redeath as it is sometimes called) must have seemed extremely radical. Indeed the Upaniṣads the idea is introduced to Brahmins by a King or Kṣatriya, and although there is much speculation about what this might mean, at the very least it shows that the idea was new and from outside fold.
Māra steps into the sutta at this point and his contribution at first sight is puzzling. However Māra is sometimes called Namuci, which is a contraction of na muñcati 'does not release'. His role often relates to keeping beings in saṃsāra. Māra as an archetypal figure is often associated with our own doubts, he is the inner voice of doubt. So whereas Baka seems to represent the social pressure exerted on us to doubt the possibility of liberation; Māra represents our own doubts.
One of his warnings to Buddha is:
so... mā tvaṃ brahmano vacanaṃ upātivattittho... evaṃ sampadamidam bhikkhu, tuyham bhavissatiThis is reminiscent of the debate scene in BU 3.6 where Gārgī is questioning Yajñavalkya on what the various aspects of the universe are made; and finally asks on what brahman is woven. Yajñavalkya replies
He... do not overstep what Brahmā says... [or various evils] will befall you.
sa hovāca gargī mātiprākṣīḥGārgī desists, but later in the text another questioner's head does split apart.
mā te mūrdhā vyapaptat
Don't ask too many questions, Gārgī
your head will split apart.
Of course Māra also plays the role of Lord of saṃsāra - he thinks of the kāmaloka as his realm, where we dwell at his mercy, which is to say we dwell suffering. Māra is afraid that if the Buddha teaches that beings will go beyond his realm (te me visayaṃ upātivattissanti).
Then the Buddha and Baka have a discussion about the elements. Baka says
Sace kho tvaṃ, bhikkhu, pathaviṃ ajjhosissasi, opasāyiko me bhavissasi vatthusāyiko, yathākāmakaraṇīyo bāhiteyyoThis is repeated for a list of elements. Of course the Buddha is aware of this and says that he not attached to the elements. The list of elements is unusual: earth, water, fire, air, beings (bhūta), devas, Prajāpati and Brahmā. Once again I refer the reader to BU 3.6 and the discussion with Gārgī. It goes like this (I'll use Valerie Roebuck's translation, slightly modified)
If indeed you, bhikkhu, will be attached to earth, you will be in my domain, in my reach, at my mercy.
"Yajñāvalkya, she said, since all this earth (idaṃ sarvaṃ pārthivaṃ) is woven on the waters, as warp and weft, on what are the waters woven?And so on. The list begins the same: earth, water, air. Then we get 'the middle realm' (antarikṣaloka) which may well correspond to bhūta in the Pāli list. Then in BU a list of various devalokas - gandharvaloka, adityaloka, candraloka, nakṣatraloka, devaloka, indraloka - then prajāpatiloka and finally brahmaloka. If we collapse the list from gandharva to indraloka into 'devaloka' (which they are all varieties of) then the list from Brahmanimantanika Sutta and BU are very similar indeed. What's more the list makes more sense in the context of BU than it does in a Pāli sutta, because the Buddha was hardly likely to be attached to Prajāpati or Brahmā.
On what is air woven?"
There is one snafu here. And it is that one of the distinctive teachings of the BU, which we meet at the end of book 3 (3.9.28), is the idea of escape from rebirth:
jāta eva na jāyate ko nv enaṃ janayet punaḥ |It seems that in all of these kinds of references to Vedic ideas in Pāli texts, there is always an element of over-simplification, of parody. One gets the sense that the last thing a Buddhist wanted to do was debate a Brahmin on their own terms - and yet again so many of the converts seem to have been, at least nominally Brahmin.
vijñānam ānandaṃ brahma rātir dātuḥ parāyaṇaṃ ||
Born, only, not born again; who could beget him?
Consciousness, bliss, Brahman, grace; the gift to the giver.
In Brahmanimantanika Sutta we seem to have some quite clear references to Upaniṣadic ideas. However as I noted in Early Buddhists and Ātman/Brahman the references are to cosmology rather than to the more central details of the Upaniṣadic thought. It seems as though the cosmologically notions had been popularised, or perhaps more likely that the cosmology recorded in the Upaniṣads represents a popular tradition rather than a specifically Upaniṣadic tradition - I would make the contrast with the identification of ātman and brahman, which is not found in the Pāli texts.