Self as Kuthastha/perpetually immovable

An Indian philosopher, no names, no pack drill, who referred to The Elusive Self of Advaita in a paper was probable speaking ironically, at least I hope so. On the other hand he might have been alluding to the impossibility of definition in the sense of setting the bounds to the concept of the self or demarcating it. Traditionally in Advaita the Self as one with Brahman would be anantam/boundless. Swami Satprakashananda in his book on the pramanas, Methods of Knowledge refers to the Self as kuthastha as an anvil. Kuthastha is also an epithet of Durga the consort of Shiva – perpetually immovable. Sankaracarya in his commentary on the Kena Upanisad (II.4) says that the Self is pratibodha videtam known with every moment of consciousness or each state of awareness. This he even extends to the state of deep dreamless sleep arguing (Upadesa Sahasri) that our knowledge on waking that we have been in that state is due to a bare or contentless self awareness which is never lost. Of course this goes against the chief tenet of empiricism which holds that we must have grounds for knowledge, or evidence of some sort. The Self does not require evidence, being, well, self-evident.

The search for wisdom is called atma vichara – inquiry into the Self. This resolves into an abiding with the Self as did the great modern sages Nisargadatta and Ramana Maharshi.

Superimposition / Adhyasa as manifest in ordinary Awareness. Upadesa Sahasri 8

54. The teacher said, Listen. It is true that the Self and the body are well-known, but they are not well-known to all people to be objects of different knowledge, like a human being and a trunk of tree. (Question): How are they known then? (Reply): (They are always known) to be the objects of an undifferentiated knowledge. For, no one knows them to be the objects of different knowledge saying, "This is the body" and "This is the Self". It is for this reason that people are deluded about the nature of the Self and of the non-Self and say, "The Self is of this nature" and "It is not of this nature". It was this peculiarity with reference to which I said that there was no such rule (viz., only well-known things could be superimposed on each other).

(from Chap.2 Upadesa Sahasri)

What Shankara is doing here is moving the concept of Superimposition to a new locus viz. to human self-awareness. The Self as encountered empirically is not known as separable from the physical entity through which it manifests. Consciousness is always manifested under some form or other. We can conceptually grasp the reality of the Self. However this apprehension is always in some state or other of manifest awareness. This is the basis of the pratibodha videtam (known with reference to each state of awareness) as delineated in Kena Up. II.4. cf. my previous remarks:
pratibodha videtam