Have you wondered how we learn things? How do we acquire knowledge about something? Rarely do we get an opportunity to reflect on how we learn because we are constantly learning and we are immersed in the process. This is what Patanjali Maharishi says “Vritti sarupyam itaratra” (all other times we are of the nature of the vrittis. We get identified with the vrittis and hence are not witness to the process).
Let us look at how a child learns things. A child looks at an object that we show and we provide the label for the object. The child does not have prior knowledge of the object and hence trusts our words. We say “Apple” and show an apple to the child. The child sees it for the very first time, remembers features of the fruit and learns its name. It is also stored in memory by repeated learning. We then show another fruit and say “Orange”, the child then makes sense of distinguishing factors and records this in memory. The child directly cognises the object and also relies on our words to know about it.
We as adults use other sources as well. We look at an object and directly cognise it. We also learn from experts (and may or may not experimentally verify) and we also draw a lot of inferences. We draw conclusions based on various pieces of information we may have. We see smoke and infer that there is fire. Inference is drawn based on a systematic process of reasoning. We may reach the right conclusion or may make an invalid conclusion based on how well we deducted things.
One of the key distinguishing features of Sanatana Dharma is that it gives equal importance to the words of experts and personal verification of the truth. The Bhagavad Gita says “श्रद्धावान् लभते ज्ञानं “. The one who has Shraddha (faith) gains knowledge. Not always do we need to have empirical or experimental evidence as we recognise that some aspects of knowledge go beyond the senses.
In our tradition, the sources of knowledge (Pramana) are different in different philosophical systems. The six sources include: Pratyakṣa (perception), Anumāṇa (inference), Upamāṇa (comparison and analogy), Arthāpatti (postulation, derivation from circumstances), Anupalabdhi (non-perception, negative/cognitive proof) and Śabda (word, testimony of past or present reliable experts) : source Wikipedia.

Let us look at Anumana or inference here. Leaving out the complexities, Anumana can be of 3 types:
Purvavat: This type of Anumana is based on the previous observation or knowledge. For example, if someone has seen smoke rising from a distant hill before, they can infer that there must be fire there now when they see smoke rising from the same hill.
Sheshavat: This type of Anumana is based on the observation of a residual effect. For example, if someone sees wet footprints on the floor, they can infer that someone has walked on the floor with wet feet.
Samanyato Dhrishti: This type of Anumana is based on the generalization of a particular observation. For example, if someone observes that all crows they have seen are black, they can infer that all crows must be black.
These frameworks are not only used in physical science but also in life science ‑Ayurveda. Inorder to diagnose a disease, the Vaidya may do it based on pre-symptoms, various signs and symptoms or various pathological activities that occur (the five fold process is described as Nidana Panchaka in Ayurveda). These inferences decide the kind of treatment given to the patient.
Inferential knowledge, also known as inferential reasoning, is an important aspect of scientific inquiry and discovery in modern science. It involves using evidence and logical reasoning to draw conclusions and make predictions about phenomena that are not directly observable or measurable.
In modern science, inferential knowledge is used in a variety of fields, including physics, chemistry, biology, and social sciences. Some examples of inferential reasoning in modern science include:
Inference from experiments: Scientists conduct experiments to test hypotheses and collect data. They then use inferential reasoning to draw conclusions and make predictions based on the data. For example, if a physicist measures the velocity of a moving object at different times, they can infer the acceleration of the object over time using mathematical equations.
Inference from observations: Scientists also use inferential reasoning to make predictions based on observations. For example, if a biologist observes a pattern in the distribution of a particular species of plant or animal in an ecosystem, they can infer the ecological factors that influence its distribution.
Inference from models: Scientists use mathematical models to represent complex systems or processes. They use inferential reasoning to test the models and make predictions about how the systems or processes will behave in the future. For example, climate scientists use models to infer the effects of greenhouse gas emissions on global temperatures.
Inference from data analysis: Scientists use inferential reasoning to analyze and interpret large datasets. They use statistical methods to identify patterns and relationships in the data, which they can use to make predictions or draw conclusions. For example, epidemiologists use inferential reasoning to analyze data on disease outbreaks to identify the factors that contribute to their spread.
Inference for oneself and others: When someone is deducing or making inferences in one’s own mind then it is swaartha anumana and when one is making inferences and conveying the same to others it is paraartha anumana. Five components are used while communicating the inference to others. This is called Panchaavayava Vakya. Panchaavayava is a term from the Indian philosophical system of Nyaya, which refers to the five components or parts of a syllogism. A syllogism is a logical argument in which a conclusion is drawn from two premises, which are propositions that are assumed or proven to be true. The five components of a syllogism in Nyaya philosophy are:
Pratijna: The first component is the proposition or statement that needs to be proved. This is called Pratijna, and it is the conclusion of the syllogism.
Hetu: The second component is the reason or evidence that supports the conclusion. This is called Hetu, and it is the premise of the syllogism.
Udaharana: The third component is the example or illustration that supports the Hetu or reason. This is called Udaharana, and it is an example that illustrates the relationship between the Hetu and the Pratijna.
Upanaya: The fourth component is the application or inclusion of the subject or term under consideration. This is called Upanaya, and it is the application of the Hetu and the Udaharana to the subject or term in question.
Nigamana: The fifth component is the conclusion or inference drawn from the Hetu and the Upanaya. This is called Nigamana, and it is the final inference or conclusion that is drawn from the syllogism.
Here is an example:
Pratijna (Conclusion): There is fire on the mountain.
Hetu (Reason): Because we see smoke coming from the mountain.
Udaharana (Example): Just as we see smoke coming from a kitchen when there is fire in the stove, we see smoke coming from the mountain, indicating the presence of fire.
Upanaya (Application): We see smoke coming from this mountain, so there must be fire on the mountain.
Nigamana (Conclusion): Therefore, there is fire on the mountain because we see smoke coming from it.