In his section on Knowledge and Illusion he discusses what he calls The Advaita View of the Inexplicability of the Appearance. I would be very happy to be able to say that his treatment of the topic of what he calls illusion reflected his undoubted scholarship and his lifelong immersion in Sanscritic culture but on the contrary it seems slack and unfocussed. To begin with a petty point, it has always seemed to me that instead of illusion in the snake/rope example or nacre/silver in the other canonical example we ought to be speaking of confusion. To take one thing for another thing I.e. Taking Young Jack for Old Jack from a distance is not an illusion. We may speak of the Myer-Lyer illusion or the illusion of the meeting rail lines and so forth. Not to labour the point there is illusion, delusion and confusion each perfectly distinct from the other in the precise discourse which is the wont of philosophers when they do not want to get lost.
His introduction is questionable:
The first well-known non-Buddhist view, which is in a way derivable also from the Buddhist position, is called the anirvacanayakhyati which says that the object-form, the silver form or the snake-form, in sensory illusion (expressible as 'this silver' or 'this a snake') must belong to a third realm of objects which is neither existent nor non-existent. This view resolves the problematic character of the object-form which is sometimes called (wrongly, I think) in modern interpretations as the 'transcendental' realm.
To characterise something as an object is to say that it exists. If you can't say whether it exists or not then you a fortiori cannot say that it is an object. One of the definitions of purely mental existence as a mental modification (a vritti) is that it does not have the capacity to be an unknown object. It exists only during the time that it is experienced I.e. during the time that the mind has taken that form.
He goes on to say something which while it reflects much of the loose talk of the traditional advaitins who are without the philosophical background that he has, does not correspond to the core teaching.
Rather the model of sensory illusion is used as an argument to show that the world of experience is neither characterisable as real or existent nor as unreal or non-existent.
An analogy is not an argument. It may be a helpful way to orient oneself towards a truth which is ineffable but it does not in any way establish or demonstrate that truth. When the status of creation is likened to that of the snake that is seen in the rope, the point that being stressed in a focused way is that as the appearance of the snake has its reality grace of the substratum of the rope so too does creation as an appearance (vivarta) have its reality from the substratum of Brahman.
Matilal does make the point that the use of ‘reality’ in the case of the snake/rope does not have the same import as ‘reality’ in the case of Brahman/creation. The one is a straightforward illusion (confusion) and the other has a metaphysical background of contingency, necessity, mutability, a priori demands and so forth.
Or the world we experience behaves strangely enough to enable us to say that it contradicts or a priori notions of real and unreal. The snake that I experienced in my sensory illusion had, with all its peculiarities and generalities, the unmistakable mark of being real and existent but now it has vanished, and a thing as real as a snake cannot do this. Therefore, how else could we classify that snake-form in our illusion except as neither real nor unreal? This theory in fact tends more towards realism that phenomenalism or idealism. For it accepts the external world more seriously as real and existent. It is only in the context of the ultimate Brahman awareness that the reality-status of this world becomes questionable.
That is a fair summary. It is cheeky of me to incarnadine the notes of The Spalding Professor but the impression remains that he could do better.