According to classical Indian logicians (Naiyayikas), which of the following…

Concept. In Nyaya an inference is sound only when the reason (hetu) is invariably concomitant (vyapti) with the property to be proved (sadhya): wherever the reason is present, the sadhya must also be present. A reason that fails this test is a hetvabhasa, a fallacious middle.

The irregular middle. Savyabhichara (anaikantika) is the reason that does not lead uniformly to a single conclusion. It is sadharana (common) when the reason is present both where the sadhya is present and where it is absent, and asadharana (uncommon) when the reason belongs to the subject alone, so that there is neither a positive example (sapaksa) nor a negative example (vipaksa) through which vyapti could ever be established.

Application. Audibility (shravanatva) belongs to sound and to nothing else. No eternal thing other than sound is audible, and no non-eternal thing is audible either, so this reason has no positive example and no negative example; it can establish neither eternality nor non-eternality. The argument “Sound is eternal because it is audible” is therefore the standard illustration of the uncommon (asadharana) irregular middle.

Cross-check — the other three arguments fail in other ways:

• “Sound is a quality because it is visible” — visibility does not belong to sound at all, so the reason is unreal in the subject: the unproved middle, asiddha (svarupasiddha).

• “Sound is eternal because it is produced” — producedness is invariably concomitant with non-eternality, so the reason establishes the very opposite of what is claimed: the contradictory middle, viruddha.

• “Fire is cold because it is a substance” — the claim is set aside by perception itself, since fire is felt as hot: the non-inferentially contradicted middle, badhita (kalatita).

Result. The fallacy of the irregular middle is committed by the argument “Sound is eternal because it is audible”.