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The opinions of Kumarila Bhatta on Puranas are precisely mentioned by Ganganath Jha in his book Purva Mimamsa in it's sources -
The opinions of Kumarila Bhatta on Puranas are very straight forward and bold. Kumarila says that all these puranas are the literature purely of a descriptive nature. According to him the puranas are not but merely "Arthavada"...
4
Krishna promised such thing when he left for Mathura with Akrūra:
गोप्यश्च दयितं कृष्णमनुव्रज्यानुरञ्जिता: ।
प्रत्यादेशं भगवत: काङ्क्षन्त्यश्चावतस्थिरे ॥ ३४ ॥
तास्तथा तप्यतीर्वीक्ष्य स्वप्रस्थाने यदूत्तम: ।
सान्त्वयामास सप्रेमैरायास्य इति दौत्यकै: ॥ ३५ ॥
[With His glances] Lord Kṛṣṇa somewhat pacified the gopīs, and they also followed ...
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Short answer:
As per this shloka (which you quoted in question), 18 Mahaapuraanas are:
Madwayam: 1. Maarkendya, 2. Matsya
Bhadwayam: 3. Bhavishya, 4. Bhaagavat
Bratrayam: 5. Brahma, 6. Brahmaanda, 7. Brahmavaivarta
Vachatusthayam: 8. Vaamana, 9. Vishnu, 10. Varaaha, 11. Vaayu*
ANaPaLinGa KuSkani: 12. Agni, 13. Naarada, 14. Padma, 15. ...
2
Many Hindu scriptures state what that Guruji has stated. That there is nothing in this universe miniature of which is not found in the human body.
The 2nd Chapter of the Yogic treatise Shiva Samhita states:
In this body, the mount Meru – i.e., the vertebral column – is surrounded by seven islands; there are rivers, seas, mountains,
fields; and lords ...
2
The following text was from a Vedic scholar's ( Sri Kiron Krishnan) notes on this subject.
A simple search on the origin of this cruel myth shall put light on one of the many Hindu attempts to blaspheme God and Vedas, for the superiority of their gods and incarnate bands.
The mention is made first in Yajur Veda Maitrayani, Kathaka Samhitas, in a litany, ...
1
There are few instances when such promise was made.
First one when Krishna was leaving for Mathura:
tās tathā tapyatīr vīkṣya sva-prasthāne yadūttamaḥ | sāntvayām āsa
sa-premair āyāsya iti dautyakaiḥ ||
As he departed, that best of the Yadus saw how the gopīs, were
lamenting, and thus he consoled them by sending a messenger with this
loving ...
1
Maha Puranas
As discussed in this answer, list of Maha Puranas is:
Brahma
Padma
Vishnu
Vayu (includes Shiva Purana)
Bhagavata
Narada
Markandeya
Agni
Bhavisya
Brahmavaivarta
Linga
Varaha
Skanda
Vamana
Kurma
Matsya
Garuda
Brahmanda
Upa Puranas
As per Kurma Puraana: Purvardha: Chapter 1, list of Upa Puranas is
Sanatkumura
Nirasimha
Skanda
Siva-Dharma
...
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