‘Sound is eternal because it is produced’ refers to which of the following Hetvabhasa?

The correct option is Asiddha.

In Classical Indian Philosophy (specifically Nyaya logic), Hetvabhasa refers to a fallacy of inference. An inference (Anumana) is fallacious when the reason (hetu) given to prove a claim is not valid.

Let us analyze the structure of the given statement: "Sound is eternal because it is produced."
- Paksha (Subject): Sound
- Sadhya (Object to be proven): Eternal (imperishable)
- Hetu (Reason): Produced (having a beginning/origin)

The fallacy here is Asiddha (also known as Sadhyasama), which translates to the "unproved middle." This fallacy occurs when the reason (hetu) is not present in the subject (paksha), or when the relation between the subject and the reason is not established. However, in this specific case, it illustrates the subtype of Asiddha where the middle term itself is unproved or does not exist in a way that can prove the major term (eternality), because what is "produced" is universally understood to be non-eternal (temporary). Since the character of being "produced" contradicts "eternality" directly and cannot coexist, the reason fails to establish the claim, making the argument fallacious under Asiddha (specifically, the reason given cannot prove the property of being eternal).