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Nyaya (Sanskrit) The first of the six Darsanas or Hindu schools of philosophy. This school has been called the Analytic or Logical School; nevertheless the title of the school would rather mean synthesizing by way of analogy or apposite likenesses, and hence it could equally well be called the synthetic or constructive method of reasoning. Nyaya is applicable to its method of treating all subjects, physical and metaphysical, rather than to its aims. This school has entered thoroughly into the laws and processes of ratiocinative thought, and in consequence has worked out a formal system of reasoning which forms the Hindu standard of logic.
The Nyaya school draws a clear distinction between matter and spirit, and has developed a careful and ingenious system of psychology. It distinguishes between the jivatmans, which are virtually infinitely numerous and eternal, and paramatman, which is one only, the kosmic hierarch, and therefore the seat of eternal wisdom and, so far as its own hierarchy goes, the Isvara (lord) of all things therein. The Nyaya is said to have been founded by the sage Gautama or Gotama.
The Vaiseshika school, founded by the sage Kanada, considered a contemporary of this Gautama, is sometimes considered to be a branch of the Nyaya school because the two schools in their teachings supplement each other. The Vaiseshika is also called the Atomistic School, because it teaches the existence of a transient or illusory universe composed of aggregations of everlasting atoms or life-atoms, which are really but the vehicular expressions of the jivatmans of the Nyaya.

See more at Wikipedia.org...

Nyaya (Sanskrit) The first of the six Darsanas or Hindu schools of philosophy. This school has been called the Analytic or Logical School; nevertheless the title of the school would rather mean synthesizing by way of analogy or apposite likenesses, and hence it could equally well be called the synthetic or constructive method of reasoning. Nyaya is applicable to its method of treating all subjects, physical and metaphysical, rather than to its aims. This school has entered thoroughly into the laws and processes of ratiocinative thought, and in consequence has worked out a formal system of reasoning which forms the Hindu standard of logic.
The Nyaya school draws a clear distinction between matter and spirit, and has developed a careful and ingenious system of psychology. It distinguishes between the jivatmans, which are virtually infinitely numerous and eternal, and paramatman, which is one only, the kosmic hierarch, and therefore the seat of eternal wisdom and, so far as its own hierarchy goes, the Isvara (lord) of all things therein. The Nyaya is said to have been founded by the sage Gautama or Gotama.
The Vaiseshika school, founded by the sage Kanada, considered a contemporary of this Gautama, is sometimes considered to be a branch of the Nyaya school because the two schools in their teachings supplement each other. The Vaiseshika is also called the Atomistic School, because it teaches the existence of a transient or illusory universe composed of aggregations of everlasting atoms or life-atoms, which are really but the vehicular expressions of the jivatmans of the Nyaya.