Which of the following statements is logically fallacious as per classical…

Concept

In Nyāya inference, the reason or middle term (hetu) must establish an invariable relation (vyāpti) with the property to be proved (sādhya). Its distribution across the subject (pakṣa), similar cases (sapakṣa), and dissimilar cases (vipakṣa) determines the kind of fallacy.

An anupasaṃhāri reason is non-exclusive: the subject covers the whole domain, so no separate positive or negative instance remains for testing the proposed relation.

Application

In “All things are non-eternal because they are knowable,” the pakṣa is all things and the hetu, knowability, is asserted over that same total domain. Since nothing is left outside the universal subject to serve as a sapakṣa or vipakṣa, the inference has the anupasaṃhāri form.

Contrast

• “The hill has fire because it is knowable” uses a reason found in both fiery and non-fiery cases; that is the too-wide or sādhāraṇa form.

• “Sound is eternal because it is audible” treats audibility as confined to sound, leaving no independent comparison case; that is the too-narrow or asādhāraṇa form.

• “Fire is cold because it is a substance” is defeated by direct perception of fire as hot; this is the bādhita form.

Result

Therefore, the statement “All things are non-eternal because they are knowable” exemplifies the fallacy of a non-exclusive middle term.