'there is smoke implies there was fire' is what kind of pramāṇa (valid means of knowledge)

The statement "there is smoke implies there was fire" relates to the concept of inference, which is a key type of pramāṇa (valid means of knowledge) in Indian philosophy, particularly in the context of Nyaya philosophy.

1. Inference as a Valid Means of Knowledge (Anumana): This type of pramāṇa is based on the relationship between cause and effect. When we observe smoke, we infer the existence of fire because, traditionally, smoke is a sign that fire is present. This inference relies on a general rule: wherever there is smoke, there is fire.

2. Example of Anumana: In a more structured format, if we denote:

   • $S$ = Smoke
   • $F$ = Fire A typical argument in this context would be: If $S$ is present, then it can be inferred that $F$ is present as well.

3. Logical Structure: This follows a syllogism structure often seen in the reasoning process:

   • Major Premise: Wherever there is smoke, there is fire.
   • Minor Premise: There is smoke.
   • Conclusion: Therefore, there is fire.

4. Conclusion: Thus, the phrase "there is smoke implies there was fire" is an example of anumana (inference), which serves as a valid means of knowledge in understanding the relationship between observable signs and their underlying causes.