The Nyaya-Vaiseshika school was founded by two ancient Indian philosophers, Gautama and Kanada. Gautama is known for his work on the Nyaya Sutras, while Kanada is known for his work on the Vaiseshika Sutras. These two texts are considered the foundational texts of the Nyaya-Vaiseshika school.

The Nyaya-Vaiseshika school is primarily focused on logic and epistemology. It seeks to establish a rigorous system of logic and reasoning, and to investigate the nature and sources of knowledge. The school's emphasis on logic and epistemology is evident in its extensive use of syllogistic reasoning and its analysis of various types of knowledge.

The central concept of the Nyaya-Vaiseshika school's theory of knowledge is perception. The school holds that perception is the primary and most reliable source of knowledge. Perception is defined as the direct and immediate awareness of an object through the senses. The Nyaya-Vaiseshika school distinguishes between two types of perception: external perception and internal perception.

The Nyaya-Vaiseshika school recognizes four types of inference: categorical, hypothetical, disjunctive, and conjunctive. Categorical inference is a type of deductive inference in which the conclusion is necessarily true if the premises are true. Hypothetical inference is a type of deductive inference in which the conclusion is true if the premises are true, but the converse is not necessarily true. Disjunctive inference is a type of deductive inference in which the conclusion is true if at least one of the premises is true. Conjunctive inference is a type of deductive inference in which the conclusion is true if all of the premises are true.

The Nyaya-Vaiseshika school's theory of categories is known as the theory of six categories. The six categories are substance, quality, action, generality, particularity, and inherence. These categories are used to analyze the world into its basic constituents and to understand the relationships between different entities.

The Nyaya-Vaiseshika school holds that reality is composed of atoms and void. Atoms are the ultimate constituents of matter, while void is the space in which atoms move and interact. The school argues that atoms are eternal and indestructible, and that they combine in various ways to form different substances.

The Nyaya-Vaiseshika school holds that the soul is an immaterial substance. The soul is distinct from the body and is the seat of consciousness and agency. The school argues that the soul is eternal and indestructible, and that it transmigrates from one body to another after death.

The Nyaya-Vaiseshika school holds that God is a personal being. God is the creator, sustainer, and destroyer of the universe. The school argues that God is omniscient, omnipotent, and omnibenevolent. God is also the source of moral values and the ultimate goal of human life.

The Nyaya-Vaiseshika school holds that liberation is the attainment of moksha. Moksha is a state of liberation from the cycle of birth, death, and rebirth. It is a state of perfect happiness, peace, and knowledge. The school argues that moksha can be attained through the cultivation of knowledge, virtue, and detachment.

The Nyaya-Vaiseshika school has made significant contributions to Indian philosophy in various areas. These contributions include the development of a rigorous system of logic and epistemology, the analysis of reality into categories, the theory of atomism, and the theory of the soul. The school's emphasis on logic and epistemology has had a profound influence on the development of Indian philosophy, and its theories of categories, atomism, and the soul have been widely discussed and debated by philosophers throughout history.

The Nyaya-Vaiseshika school recognizes four valid sources of knowledge: perception, inference, testimony, and analogy. Hypothesis is not considered a valid source of knowledge because it is not based on direct observation or logical reasoning.

Non sequitur is the logical fallacy in which a conclusion is drawn from a premise that is not supported by evidence. The term literally means "it does not follow" in Latin.

Eternity is not a category in the Nyaya-Vaiseshika school's theory of categories. The six categories are substance, quality, action, generality, particularity, and inherence.

Deductive inference is the type of inference in which the conclusion is necessarily true if the premises are true. In other words, the conclusion is guaranteed to be true if the premises are true.

Analogical inference is not a type of inference recognized by the Nyaya-Vaiseshika school. The four types of inference recognized by the school are categorical inference, hypothetical inference, disjunctive inference, and conjunctive inference.