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Can anyone share or tell: where can I find a summary explaining those ancient Indian philosophies of those non-Buddhist schools that had debated with Buddhist, especially Nalanda, masters? For example, those philosophies of those opponents in Indian Buddhism Śāstras (i.e. treaties).

I ask because I am studying some texts on and also pondering on the tenets system/theory of Indian Buddhism, and I would like to be rigorous in understanding what non-Buddhist philosophies are refuted grounding in reasoning by Indian Buddhism (Nalanda) masters.

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You might be looking for a scholarly paper which lists the non-Buddhist schools and their philosophies (for which I don't have an answer).

The sutta which comes to mind as likely relevant to your question is Brahmajāla Sutta (DN 1) -- which I think lists sixty or so wrong or non-Buddhist views.

Piya Tan as a more detailed (highly referenced) translation and commentary of this sutta (and of many other suttas too). The URLs on his site aren't quite stable but they're currently:

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I am not aware of any sources claiming actual debates taking place at Nalanda with non-Buddhists, but I do believe the curriculum was such that debates took place with students trying to accurately and faithfully take the place of non-Buddhist Indian schools of thought, in order to show that Buddhist systems were superior and would overcome them.

"Besides Theology and Philosophy, frequent debates and discussions necessitated competence in Logic. A student at the Mahavihara had to be well-versed in the systems of Logic associated with all the different schools of thought of the time as he was expected to defend Buddhist systems against the others."

I think this was achieved through internal debates where students of Nalanda would try to faithfully represent the other schools of thought.

Perhaps the Sarvadarśanasaṅgraha would also be of help for a non-Buddhist compendium of various extent philosophical schools of India in the author's extent period.

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DN 2 has descriptions of various shramanic teachings at the time of the Buddha including by the following teachers: Pūraṇa Kassapa, Makkhali Gosāla, Ajita Kesakambalī, Pakudha Kaccāyana, Sanjaya Belatthiputta and Mahavira (Jainism). Also MN 101 further compares Jainism and Buddhism.

These suttas contrast the Buddha's teachings with these other teachings.

A good comparison between Hindu Vedanta and Buddhism can be found in Vedanta and Buddhism: A Comparative Study by Helmuth von Glasenapp.

Please also see "Have any Buddhist thinkers responded to the critique of the Brahma Sutras?".

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