Uncovering the Mathematical Underpinnings of Indian Philosophical Systems

Advaita Vedanta, propounded by Adi Shankara, uses 'neti neti' to negate all positive assertions about Brahman, the ultimate reality, leading to the realization of non-duality.

Paramāṇus, or atoms, are considered the indivisible and indestructible fundamental units of matter in the Nyaya-Vaisheshika philosophy.

Nyaya, one of the six orthodox schools of Indian philosophy, is renowned for its focus on logical reasoning and the use of syllogisms to establish valid conclusions.

Sattva, Rajas, and Tamas are the three fundamental qualities (guṇas) that constitute Prakṛti, the material world, in Sāṃkhya philosophy.

Yoga, particularly the Yoga Sūtras of Patañjali, emphasizes the concept of karma and the cycle of rebirth, highlighting the importance of self-discipline and spiritual practices for liberation.

Mimamsa, one of the six orthodox schools of Indian philosophy, primarily focuses on the study and interpretation of the Vedas, the sacred texts of Hinduism.

Yoga, particularly the Yoga Sūtras of Patañjali, emphasizes the concept of moksha or liberation from the cycle of rebirth through spiritual practices and self-realization.

Brahman is the ultimate reality in Advaita Vedanta, representing the non-dual, infinite, and unchanging consciousness that underlies all existence.

Yoga, particularly the Yoga Sūtras of Patañjali, emphasizes the concept of ahimsa or non-violence as a fundamental ethical principle.

Hetvābhāsa is a logical fallacy in Nyaya-Vaisheshika that occurs when the consequent of a conditional statement is affirmed, but the antecedent is not necessarily true.

Yoga, particularly the Yoga Sūtras of Patañjali, emphasizes the concept of dharma or righteous conduct as a fundamental ethical principle.

Maya is the illusion or veil in Advaita Vedanta that obscures the true nature of reality, leading to the perception of duality and multiplicity.

Yoga, particularly the Yoga Sūtras of Patañjali, emphasizes the concept of ātman or the individual self, exploring its relationship with the ultimate reality, Brahman.

Hetvābhāsa is a logical fallacy in Nyaya-Vaisheshika that occurs when the antecedent of a conditional statement is denied, but the consequent is not necessarily false.

Yoga, particularly the Yoga Sūtras of Patañjali, acknowledges the concept of ishvara or the personal god, but emphasizes the importance of self-realization and spiritual practices for liberation.