"Fire is cold because it is a substance" - is an instance of which one of the hetvabhasas (fallacy of inference):

"Fire is cold because it is a substance" - is an instance of which one of the hetvabhasas (fallacy of inference): Correct Answer Badhita (non-inferential contradicted middle)

In Indian logic, a fallacy is technically called hetvabhasa, a word that means hetu or reason that appears as a valid reason but is not. Since the fallacies of inference are due to such fallacious reasons, the Naiyayikas consider these only as ones that may infect the constituent propositions of the syllogism.

According to Naiyayikas, there are five kinds of fallacies:

1. Savyabhicara (the irregular middle): It leads to no one single conclusion, but different opposite conclusions. This fallacy occurs when the middle term violates the general rule of inference, that it must be universally related to the major term or that the major term must be present in all cases in which the middle is present.
2. Viruddha (the contradictory middle): It is the one which disproves the very proposition which it is meant to prove. This happens when the ostensible middle term, instead of proving the existence of the major in the minor, which is intended by it, proves its nonexistence therein. The distinction between the savyabhicara and the viruddha is that while the former only fails to prove the conclusion, the latter disproves it or proves the contradictory proposition.
3. Satpratipaksa (the inferentially contradicted middle): This fallacy arises when the middle term of inference is validly contradicted by some other middle term which proves the non-existence of the major term of the first inference.
4. Asiddha (the unproved middle): It is one which is not yet proved, but requires to be proved. This fallacy occurs when the middle term is wrongly assumed in any of the premises and so cannot be taken to prove the truth of the conclusion.
5. Badhita (the non- inferentially contradicted middle):

• It is the ostensible middle term of inference, the non-existence of whose major is ascertained through some other source of knowledge.
• This fallacy consists in being contradicted by a stronger source which directly prevents inference.
• In the example, "Fire is cold because it is a substance", the reason ‘Substance’ is contradicted by factual perception (a stronger source which shows that fire is not cold but hot).
• According to Nyaya, the relation between a word and its meaning may be direct (Abhidha) or indirect (Abhidha). The former has the direct power to convey the sense intended, while in the latter this power is derived from the primary sense.

Hence, the given statement, "Fire is cold because it is a substance", is an instance of Badhita (non-inferential contradicted middle).