Among the Six-schools of Indian philosophy, Uttara-Mimamsa or Vedanta (with all it's variations such as Advaita, vishishtadvaita, dvaita etc.) is known to accept Puranas as A Valid Authority for Knowledge.
But What About the other, non Vedantic Darshanas such as Samkhya, Yoga, Nyaya, Vaishisheka and Mimamsa? Do they accept Puranas as authority or reject them? What about various Tantric Schools?
CHATURDHASHA VIDYASTHANAS ( knowledge system in its entirety) , does include Puranas and darsanas such as nyaya vaisheshika etc. (tantric school s do not seem to be included though)..
It is possible that one branch of a knowledge system is quite independent of another branch, owing to the difference in their subject matter. But that doesn't mean they mutually reject one other as a valid authority. for eg. Purana lakshanas may not be relatable with nyaya.
Prasthabheda and Vishnu Purna infact extends the to 18.
PurAna nyAya mimAngsA dharmshAstrAnga mishritAh | VedAh sthAnAni vidyAnAm dharmasya cha chaturdasha ||”)Yajnavalkyasmrithi 1.3)
All the scriptures have the supreme Lord as their purport. Here the different prasthAnas are dealt with in brief. The Vedas are four in number—Rgveda, yajurveda, sAmaveda and atharvaveda. The vedAngas are six—shikShA (science of pronunciation), yyAkaraNam (grammar), niruktam (etymology), Chandas (metre), jyoutiSham (astronomy and astrology), and kalpa. The upAngas are four— purANa, nyAya, mImAmsA and dharmashAstras. The upapurANas are included in the purANas, vaisheShika is included in nyAya, vedAnta in mImAmsA, and mahAbhArata, rAmAyaNa, sAnkhya, yoga, pAshupata, vaiShNava, ertc., are included in dharmashAstra. Thus altogether there are fourteen vidyAs. So has it been said by sage YAjnavalkya—“The purANas, nyAya, mImAmsA, dharmashastra and the Vedas (including vedAngas) together constitute the fourteen vidyAs”. These, along with the four upavedas are the eighteen vidyAs. The four upavedas are—Ayurveda, dhanurveda (archery), gAndharvaveda (music) and arthashAstra (political science). These only are the prasthAnas for all Astikas. (Prasthabheda Translation Sri SN Saastri)
The well-known poetic work Naisadham mentions that Nala was conversant with these fourteen branches of learning. The poet (Sriharsha) plays on the word "caturdasa": he says that "Nala accorded caturdasa to the caturdas-vidya"(Hindu dharma the universal way of life part 5 chap 3)
PS - it also true that some streams, partially accept/reject the other.
All schools of thought have their own sutras. For example, Vedanta has Brahma Sutras and Yoga has Patanjali Sutras. You should look within those Sutras to see if they accept or reject. Overall most Puranas only are accepted within theistic sects such as Vaishnavism, Shaivism, Shaktism, or Ganapatya. The issue is the fact Ishvara exists or that Ishvara is personal/with a form or traits which is supported as supreme in the Puranas.
None of the 6 schools of philosophy use Puranas as authority. They accept one authority - that is Vedas. You may find references to these philosophies in some Puranas. But if there is a conflict between philosophy and Puranas, you need to stick to the original writings of the 6 philosophies.
