Which of the arguments is fallacious because the middle term is pervaded by…

Concept: In Nyāya inference the hetu (middle term) is admissible only when it is pervaded by the sādhya (major term): wherever the hetu occurs, the sādhya must occur as well. When a hetu is instead invariably accompanied by the absence of the sādhya, the reason establishes the very contradictory of the thesis it was advanced to prove. That defect is the viruddha hetvābhāsa, the contradictory middle described in the question.

Application: Apply this to the argument whose sādhya is eternality and whose hetu is produced-ness (kṛtakatva):

1. The thesis advanced is that sound is eternal, so here the sādhya is eternality and the hetu offered in its support is produced-ness.

2. Every instance of produced-ness open to observation — a pot, a cloth, a lamp flame — is an instance in which eternality is absent, so produced-ness is invariably concomitant with non-eternality.

3. The hetu is therefore pervaded by the absence of the sādhya rather than by its presence, which is exactly the defect the question describes.

4. Carrying that pervasion through yields "sound is non-eternal", the contradictory of the very thesis the reason was advanced to support, so "Sound is eternal because it is produced" is the argument the question asks for.

Contrast: Each remaining argument is defective in a different way, and none of them has a middle pervaded by the absence of the major term:

• "The hill has fire because it is knowable" — knowability belongs to every object whatsoever, so the middle occurs both where fire is present and where fire is absent. A middle that strays to both sides is sādhāraṇa anaikāntika (savyabhicāra), the irregular or straying middle.

• "Sound is eternal because it is audible" — audibility belongs to sound and to nothing else, so the middle is available in no example on either side. This is asādhāraṇa anaikāntika, the uncommon straying middle.

• "Sound is quality because it is visible" — visibility (cākṣuṣatva), the property of being apprehended by the eye, does not reside in sound at all, so the middle is not even established in the minor term. This is svarūpāsiddha, the unproved middle.

Result: Only produced-ness both resides in the subject and is invariably concomitant with the absence of eternality, so "Sound is eternal because it is produced" is the viruddha (contradictory-middle) fallacy.