Explain the systems of Shadarshan

The system of Shadarshan refers to the six major philosophical schools of thought in ancient Indian philosophy. These schools, which provide different interpretations of life, universe, and existence, were integral to shaping intellectual discourse in India. The term "Shadarshan" literally translates to "six systems," and each system offers distinct perspectives, though they often share some common principles, such as the belief in the soul (Atman), the concept of karma, and the idea of liberation (moksha). The six systems are often divided into two categories: the orthodox (Astika) schools, which accept the authority of the Vedas, and the heterodox (Nastika) schools, which do not. However, these systems influence each other and contributed to a rich tradition of philosophical thought.

1. Nyaya:
   The Nyaya school focuses on logic, reasoning, and epistemology. Founded by the sage Gautama (or Akṣapada), it primarily deals with the theory of knowledge and the means by which knowledge can be acquired. Nyaya asserts that valid _______ _____ _________ ________ __________ ____ _______ ___ ____ _____ __________ _____.
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