The Nyaya or Hindu logic was founded by Gautama Rishi, who is also known by the names Akshapada and Dirghatapas. The Nyaya and the Vaiseshika are analytic types of philosophy. The word Nyaya signifies going into a subject, i.e., investigating it analytically. In this sense of analysis, the word Nyaya is exactly opposed to Sankhya, synthesis. The Nyaya is sometimes called Tarka-Vidya or the Science of Debate, Vada-Vidya or the Science of Discussion. Tarka is the special feature of the Nyaya.

Excerpt from All About Hinduism by Sri Swami Sivananda

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The Six Darsanas are the intellectual section of the Hindu writings, while the first four are intuitional, and the fifth inspirational and emotional. Darsanas are schools of philosophy based on the Vedas. The Agamas are theological. The Darsana literature is philosophical. The Darsanas are meant for the erudite scholars who are endowed with acute acumen, good understanding, power of reasoning and subtle intellect. The Itihasas, Puranas and Agamas are meant for the masses. The Darsanas appeal to the intellect, while the Itihasas, Puranas, etc., appeal to the heart.

Excerpt from All About Hinduism by Sri Swami Sivananda

Read more here: » Six Darsanas : The Six Darsanas in the Hindu Scriptures