Is the self the same as the bodily parts? Most probably, most readers will be inclined to answer that this is not the case. But the question becomes trickier if we ask whether the self is the same as the intellect.
Veṅkaṭanātha, like many others before him, replies (in Seśvaramīmāṃsā ad 1.1.4) that this is not the case and the intellect is only an instrument of the self, like the mind or the body. In fact, we do say “I understood it through my intellect”, don’t we? And is not this a proof of the fact that the intellect is different from the “I”?
An opponent promptly suggests that this common usage might be misleading. We do also say things like “The body of a pestle” or “Rāhu’s head”, although the pestle has nothing beyond its body and Rāhu’s body consists only of his head.*
Veṅkaṭanātha counter-reply is that this can only be done if there is no other way out (yadi gatyantaraṃ na syāt), whereas in the case of the self, it is much easier to assume that the body is its instrument, since it has no consciousness.
*The background of the metaphore of the śīlaputrakasya śarīram is exhaustively discussed in Anne McDonald’s In clear words, pp. 248–250, where previous translations and possible misunderstandings are also discussed.