Gautama is known as the founder of the Nyaya school, while Kanada is credited with establishing the Vaiseshika school. These two schools eventually merged to form the Nyaya-Vaiseshika school.

The Nyaya school primarily focuses on epistemology, which is the study of knowledge and its sources. It seeks to establish reliable methods for acquiring knowledge and distinguishing between valid and invalid knowledge claims.

The Vaiseshika school posits six categories of existence (padarthas): substance, quality, action, generality, particularity, and inherence. These categories are used to analyze and explain the nature of reality.

The Nyaya-Vaiseshika school adopts a pluralistic view of reality, recognizing the existence of multiple independent entities and substances. It rejects the idea of a single, unified reality.

The Nyaya-Vaiseshika school holds a direct realist theory of perception, asserting that objects are directly perceived as they exist in the external world. It rejects the notion that perception is mediated by mental representations or ideas.

The Nyaya-Vaiseshika school primarily relies on deductive logic to establish its arguments and conclusions. It employs syllogistic reasoning, where a general principle is applied to a specific case to derive a valid conclusion.

Pramāṇas are the means or sources of knowledge recognized by the Nyaya-Vaiseshika school. These include perception, inference, comparison, testimony, and postulation.

The Vaiseshika school posits that all matter is composed of indivisible atoms called paramāṇus. These atoms are the fundamental building blocks of the universe and cannot be further divided.

Abhāva refers to the negation or absence of something. The Nyaya-Vaiseshika school distinguishes between two types of abhāva: absolute absence (atyantābhāva) and relative absence (anupalabdhi).

Dharma and adharma refer to moral virtues and vices, respectively. The Nyaya-Vaiseshika school recognizes certain actions as morally good (dharma) and others as morally bad (adharma).

Moksha, or liberation, is the ultimate goal of the Nyaya-Vaiseshika school. It is conceived as a state of freedom from suffering and the cycle of rebirth (samsāra).

The Nyaya-Vaiseshika school adopts a dualistic view of the mind and body, considering them as distinct and separate entities. It posits that the mind is a conscious, immaterial substance, while the body is a material substance.

Karma refers to moral actions and their consequences. The Nyaya-Vaiseshika school posits that good actions lead to positive consequences, while bad actions lead to negative consequences.

The Nyaya-Vaiseshika school attempts to address the problem of evil through theodicy, which seeks to explain the existence of evil in a world created by a benevolent and omnipotent God.

The Nyaya-Vaiseshika School of Philosophy had a profound impact on the development of Indian philosophy, logic, epistemology, and scientific inquiry. Its ideas and methods continue to be studied and debated by scholars today.