'Fire is cold because it is a substance' represents which of the following…

Concept

A hetvabhasa is a reason that appears to support an inference but fails a condition of valid reasoning. In a badhita inference, a stronger source of knowledge, such as direct perception, contradicts the proposition to be proved.

Application

Here the proposition is “fire is cold,” the subject is fire, and the reason is “because it is a substance.” Direct perception establishes that fire is hot, so perception cancels the proposition before the stated reason can support it.

Contrast

• Viruddha applies when the reason itself establishes the opposite of the proposition; the relevant defect here is the stronger perceptual contradiction to the proposition.

• Asiddha applies when the reason is not established in the subject; fire being a substance is not the unestablished part here.

• Savyabhichara applies when the reason is inconclusive because it occurs both where the proposition holds and where it does not; that is not the decisive defect here.

Therefore, the inference is an instance of Badhita hetvabhasa.