The Vedas are the oldest available records of the Indian literature. They are the literary monument of the Indo-European race- the Aryan mind. Vedas have influenced the Indian Philosophy to a great extent. Here, we must talk about the classification of Indian philosophy to understand this.
Some schools of Indian philosophy accepted Vedic authority, and others opposed it. Therefore, Indian philosophy is shaped by the Vedas in either positive or negative ways. Based on this, the schools or systems of Indian philosophy were classified into two classes: orthodox and heterodox.
The orthodox school is also known as Astika. Mimamsa, Vedanta, Sankhya, Yoga, Nyaya, and Vaisesika belong to this school. These six chief philosophical systems are popularly known as sad-darsana. The heterodox system, on the other hand, is known as Nastika. This school includes Carvaka, the Bauddha Philosophy, and the Jaina Philosophy.
This distinction between the orthodox and heterodox schools is not because one believes in God and the other does not. In the modern Indian language, Astika and Nastika are conventionally translated as theist and atheist respectively. However, during the classification of Indian philosophy, these two Sanskrit words would mean Astika- one who accepts the authority of the Vedas, and Nastika- one who does not believe in the authority of the Vedas.
Further, the Mimamsa and the Vedanta are the teaching continuation of the Vedic culture. These schools are directly based on Vedic texts. The initial school emphasizes the ritualistic aspect of the Vedas and the latter school talks about the speculative aspect of Vedas.
The other schools of sad-darsana like the Sankya, Yoga, Nyaya, and Vaisesika Are based on independent grounds, however, they did not challenge the authority of Veda. These schools try to show the testimony of Vedas was in harmony with their rationally established theories.
The Carvaka, Bauddha, and Jaina Systems arose mainly by opposing and rejecting the Vedic culture.
The Vedas serve as not just historical documents but foundational pillars upon which Indian philosophical thought has evolved. Their influence has shaped diverse schools of thought, leading to a rich tapestry of philosophical inquiry and reflection in Indian culture.
Reference
Dutta & Chatterjee: An Introduction to Indian Philosophy, University of Calcutta, 1968