How does Nyāya philosophy define ‘Anumāna’ and ‘Vyāpti’ ? Write a note on the process of ‘Parārthānumāna’ illustrating it with the help of two appropriate examples.

1. Definition of Anumāna and Vyāpti in Nyāya Philosophy:

In Nyāya philosophy, Anumāna refers to inference, a method of knowledge acquisition distinct from perception and testimony. It involves drawing conclusions about unseen or unperceived objects based on observed facts or relations. Vyāpti, on the other hand, is the underlying universal relation or concomitance between the observed and inferred objects that serves as the basis for inference.

According to Nyāya, Vyāpti is a universal relation that holds between the hetu (reason) and the sādhya (probandum) in a valid inference. For example, in the inference "Where there is smoke, there is fire," the presence of smoke (hetu) invariably indicates the presence of fire (sādhya). Vyāpti establishes this connection as an invariable concomitance between the two.

2. Process of Parārthānumāna:

Parārthānumāna, or inference for others, is a type of inference where one person infers a conclusion for the benefit of another. It involves presenting a logical argument to persuade or convince someone of a particular conclusion based on shared premises and valid inference.

a. Example 1: Deductive Reasoning

Suppose a teacher wants to illustrate the concept of deductive reasoning to their students. They present the following syllogism:

Premise 1: All humans are mortal.
Premise 2: Socrates is a human.
Conclusion: Therefore, Socrates is mortal.

Here, the teacher guides the students through the process of deductive inference, showing how the universal premise about humans' mortality (hetu) applies to the specific case of Socrates (sādhya). The teacher helps the students recognize the Vyāpti, or universal relation, between the two.

b. Example 2: Scientific Induction

Consider a scientist conducting an experiment to test the hypothesis that increased exposure to sunlight leads to higher vitamin D levels in the body. The scientist collects data from participants who spend varying amounts of time in the sun and measures their vitamin D levels.

Upon analyzing the data, the scientist observes a consistent pattern: participants who spend more time in the sun tend to have higher vitamin D levels. This observation forms the basis for an inductive inference:

Observation: Increased exposure to sunlight (hetu) is consistently associated with higher vitamin D levels (sādhya).
Conclusion: Therefore, exposure to sunlight causes an increase in vitamin D levels.

In this example, the scientist engages in Parārthānumāna by presenting the inference to colleagues or the scientific community, providing evidence and reasoning to support the conclusion.

Conclusion:

In conclusion, Nyāya philosophy defines Anumāna as inference, a method of knowledge acquisition based on observed facts and relations. Vyāpti represents the underlying universal relation between the observed and inferred objects. Parārthānumāna involves making inferences for others, using logical reasoning to persuade or convince them of a particular conclusion. Through examples of deductive reasoning and scientific induction, the process of Parārthānumāna illustrates how individuals can use inference to convey knowledge and understanding to others, relying on shared premises and valid reasoning to establish convincing conclusions.