In Hindu philosophy there are three main Pramanas or valid means of knowledge: Pratyaksha or sensory perception, Anumana or inference, and Shabda or revelation/scripture. And there is a hierarchy of these Pramanas: Anumana is only applicable to those things which cannot be known through Pratyaksha, and Shabda is only applicable to those things which cannot be known through either Pratyaksha or Anumana.
Now in the first section of his commentary on the Brihadaranyaka Upanishad, the Advaita philosopher Adi Shankaracharya argues that the existence of a soul which transcends the body cannot be established by either Pratyaksha or Anumana Pramana, and thus we must rely on Shabda Pramana, specifically the Vedas, to know that the soul transcends he body.
Now, unless a person is aware of the existence of the self in a future life, he will not be induced to attain what is good and avoid what is evil in that life. For we have the example of the materialists. Therefore the scriptures proceed to discuss the existence of the self in a future life and the particular means of attaining the good and avoiding the evil in that life. For we see one of the Upaniṣads starts with the words, ‘There is a doubt among men regarding the life after death, some saying that the self exists, and others that it does not’ (Ka. I. 20), and concludes, ‘It is to be realised as existing indeed’ (Ka. VI. 13), and so on. Also, beginning with, ‘How (the self remains) after death’ (Ka. V. 6), it ends with, ‘Some souls enter the womb to get a new body, while others are born, as stationary objects (plants etc.), all according to their past work and knowledge’ (Ka. V. 7). Elsewhere beginning with, ‘The man (self) himself becomes the light’ (IV. iii. 9), it ends with, ‘It is followed by knowledge, work’ (IV. iv. 2). Also, ‘One becomes good through good work and evil through evil work’ (III. ii. 13). Again beginning with, ‘I will instruct you’ (II. i. 15), the existence of the extracorporeal self is established in the passage, ‘Full of consciousness (i.e. identified with the mind),’ etc. (II. i. 16-17).
Objection: "Is it not a matter of perception?"
Reply: No, for we see the divergence of opinion among different schools. Were the existence of the self in a future body a matter of perception, the materialists and Buddhists would not stand opposed to us, saying that there is no self. For nobody disputes regarding an object of perception such as a jar, saying it does not exist.
Objection: "You are wrong, since a stump, for instance, is looked upon as a man and so on."
Reply: No, for it vanishes when the truth is known. There are no more contradictory views when the stump, for instance, has been definitely known as such through perception. The Buddhists, however, in spite of the fact that there is the ego-consciousness, persistently deny the existence of the self other than the subtle body. Therefore, being different from objects of perception, the existence of the self cannot be proved by this means. Similarly inference too is powerless.
Objection: "No, since the Śruti (Veda) points out certain grounds of inference for the existence of the self, and these depend on perception, (these two are also efficient means of the knowledge of the self)."
Reply: Not so, for the self cannot be perceived as having any relation to another life. But when its existence has been known from the Śruti and from certain empirical grounds of inference cited by it, the Mīmāṃsakas and logicians, who follow in its footsteps, fancy that those Vedic grounds of inference such as the ego-consciousness are the products of their own mind, and declare that the self is knowable through perception and inference.
I'm interested in Adi Shankaracharya's claim that the existence of a soul which transcends the body cannot be known through Anumana or inference. The thing is, in his commentary on Adhyaya 3 Pada 3 Sutra 54 of the Brahma Sutras, Adi Shankaracharya refutes the view of Charvakas or materialists that the soul is the same as the body, and presents a logical argument that the soul must transcend the body:
The assertion that the Self is not separate from the body cannot be maintained. The Self rather must be something separate from the body, 'because the existence (of the Self) does not depend on the existence of that (i.e. the body).' For if from the circumstance that they are where the body is you conclude that the qualities of the Self are qualities of the body, you also must conclude from the fact that they are not where the body is that they are not qualities of the body, because thereby they show themselves to be different in character from the qualities of the body. Now the (real) qualities of the body, such as form and so on, may be viewed as existing as long as the body exists; life, movement, &c., on the other hand, do not exist even when the body exists, viz. in the state of death. The qualities of the body, again, such as form and so on, are perceived by others; not so the qualities of the Self, such as consciousness, remembrance, and so on. Moreover, we can indeed ascertain the presence of those latter qualities as long as the body exists in the state of life, but we cannot ascertain their non-existence when the body does not exist; for it is possible that even after this body has died the qualities of the Self should continue to exist by passing over into another body. The opposite opinion is thus precluded also for the reason of its being a mere hypothesis.--We further must question our opponent as to the nature of that consciousness which he assumes to spring from the elements; for the materialists do not admit the existence of anything but the four elements. Should he say that consciousness is the perception of the elements and what springs from the elements, we remark that in that case the elements and their products are objects of consciousness and that hence the latter cannot be a quality of them, as it is contradictory that anything should act on itself. Fire is hot indeed but does not burn itself, and the acrobat, well trained as he may be, cannot mount on his own shoulders. As little could consciousness, if it were a mere quality of the elements and their products, render them objects of itself. For form and other (undoubted) qualities do not make their own colour or the colour of something else their objects; the elements and their products, on the other hand, whether external or belonging to the Self (the organism) are rendered objects by consciousness. Hence in the same way as we admit the existence of that perceptive consciousness which has the material elements and their products for its objects, we also must admit the separateness of that consciousness from the elements. And as consciousness constitutes the character of our Self, the Self must be distinct from the body. That consciousness is permanent, follows from the uniformity of its character (and we therefore may conclude that the conscious Self is permanent also; as also follows) from the fact that the Self, although connected with a different state, recognises itself as the conscious agent--a recognition expressed in judgments such as 'I saw this,'--and from the fact of remembrance and so on being possible.
That sounds like he is using Anumana to establish the existence of a soul which transcends the body. So my question is, does Adi Shankaracharya believe that Anumana is able to establish the existence of a soul which transcends the body, or does he believe that it can only be established through the Vedas? Is there any way to reconcile his statements in these two works?
On a side note, Ramanujacharya and other commentators do not think that Adhyaya 3 Pada 3 Sutra 54 of the Brahma Sutas is about refutation of Charvakas and the existence of the soul; see my question here.