Gautama, also known as Akshapada Gautama, is credited with developing the anvaya-vyatireka method, which is a logical technique for establishing causal relationships.

In Nyaya philosophy, the ultimate goal of human life is to achieve moksha, which is a state of liberation from the cycle of birth, death, and rebirth.

The Nyaya school of Indian philosophy is known for its emphasis on pramana, or valid means of knowledge. Nyaya philosophers argue that there are four valid means of knowledge: perception, inference, comparison, and testimony.

The Vaisheshika school of Indian philosophy posits six categories of reality: substance, quality, action, generality, particularity, and inherence.

Nagarjuna, a renowned Buddhist philosopher, is credited with developing the concept of sunyavada, which asserts that all phenomena are empty of inherent existence.

In Advaita Vedanta, Brahman is considered the ultimate reality, which is described as being infinite, unchanging, and non-dual.

Sankara, a prominent Advaita Vedanta philosopher, emphasized the importance of karma and samsara in the cycle of existence.

In Mimamsa philosophy, the primary goal of human life is to fulfill one's dharma, or righteous duties, as prescribed by the Vedas.

Mahavira, the founder of Jainism, is known for his theory of anekantavada, which asserts that reality is complex and multifaceted, and cannot be fully understood from a single perspective.

In Samkhya philosophy, the three gunas, sattva, rajas, and tamas, are considered to be the fundamental qualities that make up all matter and determine its characteristics.

Charvaka, a materialist philosopher, is known for his theory of svabhavavada, which emphasizes the natural and material aspects of reality and rejects the concept of a supernatural realm.

In Yoga philosophy, the ultimate goal is to achieve kaivalya, a state of isolation and liberation from the cycle of birth, death, and rebirth.

Dharmakirti, a Buddhist philosopher, is renowned for his theory of pramana-vada, which explores the nature and validity of knowledge.

In Purva Mimamsa philosophy, the primary goal of human life is to fulfill one's dharma, or righteous duties, as prescribed by the Vedas.

Kanada, the founder of the Vaisheshika school of Indian philosophy, is known for his theory of satkaryavada, which asserts that the effect pre-exists in the cause in a subtle form.