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It is a well accepted view that Vishnu is source of all avatars including Krishna. This is what we all heard from childhood. I also came across the opposite opinion that Krishna is source of Vishnu.
I have seen other possible duplicates, it seems there are few verses to support each sect's views. Why does one focus only on them and not on others? On what basis others are rejected? What is the reasoning behind this?
Which all schools accept this idea?
Why is Krishna considered as source of Vishnu?
The answer is based on analysis by Jiva Goswami in his Sandarbhas.
This belief is based on Srimad Bhagavatam & other Vedic literatures.
Few reasons Srimad Bhagavatam is considered as sarva-pramananam cakravarti - emperor of all evidences:
After composing all the Vedas, puranas and mahabharat, Vyasa was still dissatisfied and then finally wrote Bhagavatam and got satisfied.
Many other puranas glorify Bhagavatam as the best.
Garuda purana declared this to be natural commentary on Vedanta Sutra and most complete of all.(see here)
Some more reasons will be given later, for now we will leave it here.
Verse 1.3.28
ete cāṁśa-kalāḥ puṁsaḥ kṛṣṇas tu bhagavān svayam indrāri-vyākulaṁ lokaṁ mṛḍayanti yuge yuge
All these incarnations are either plenary portions or parts of the plenary portions of the puruṣa-avatāra. But Kṛṣṇa is the Bhagavan Himself. In every age He protects the world through His different features when the world is disturbed by the enemies of Indra.
This is the emperor of all verses in the Bhagavatam, for it is the most conclusive, unambiguous, declarative, absolute and categorical in establishing the Supremacy of Lord Krishna.
This is discussed in Krishna Sandarbha in great detail.
Jiva Goswami calls this paribhasa-sutra of Srimad Bhagavatam.
Paribhasa-sutra of any book, is stated only once, generally in the beginning, provides the key for proper understanding of the entire work and governs even a great literature that contains millions of statements.
Srimad Bhagavatam describes the ultimate phase of the Absolute truth and the supreme goal of life. It is not a random collection of stories. Hence, the seriousness of the subject matter of Bhagavatam demands it to be prefaced by a Paribhasa-sutra.
Lord Sri Krishna is repeatedly described in the verses of Srimad Bhagavatam. The verses of the Bhagavatam may be compared to an army and this verse may be considered commander of that army.
Bhagavatam describes activities of various incarnations of Lord Krishna which are mysterious(SB 1.3.29) as seen from the declaration 12.13.11. Since, the third chapter of 1st Canto summarises the incarnations and their activities, and verse 1.3.28 connects all the incarnations, it is indeed paribhasa-sutra of Bhagavatam.
Another example of this is the paribhasha-sutra “vipratishedhe param karyam,"(When two grammatical rules are contradictory, second should be done) which governs the entire text of Panini's Ashöadhyayi.
Meaning of the Emperor Verse:
ete - "All these" refers to incarnations(previous described in SB 1.3)
ca - and (all the incarnations that are not mentioned in this list)
amsa-kalah -> are plenary portions or parts of the plenary portions and kalās, or in other words, vibhūtis (displays of lesser power).
pumsah -> of the purusa incarnations who expanded from Bhagavan
krsnas-> Lord Krishna who is counted as 20th incarnation in this list
tu -> but
- It distinguishes Lord Krishna from "amsa-kalah"
- Also means certainly or indeed or used for emphasis; thus the word "tu" emphasized that only Krishna is the original form of Bhagavan and Narayana or any of the other secondary expansions of the Lord, are not the original forms.
bhagavan svayam -> is that very Bhagavan who is original source even of the Purusa.
He is the source of all the incarnations(in fact, ultimate source of the sources of incarnations) and not simply an expansion of Vishnu. This is emphasized by the use of the word "svayam"(in person).
Let's go into details :
In the above verse, by the principle “the predicate should not be stated without specifying the subject,” the characteristic of being Bhagavān (bhagavattva) [i.e., the predicate] is established as belonging specifically to Kṛṣṇa [the subject], and not the reverse, that the characteristic of being Kṛṣṇa (kṛṣṇatva) is established of Bhagavān. Consequently, because Śrī Kṛṣṇa alone has been determined as being the repository (dharmī) of the characteristics of being Bhagavān (bhagavattva), it is thereby proven that He is the original source (avatārī) of all avatāras and not [merely] a manifestation of the Puruṣa. Sūta expresses this very fact by the word svayam (“Himself ”), which is to say that He is Bhagavān in and of Himself, not because He has appeared from Bhagavān, nor because of the superimposition (adhyāsa) of “Godhood” (bhagavattā) upon Him(as Advaitins think).
When it is said, “Kṛṣṇa is Svayaṁ Bhagavān,” the known subject is Kṛṣṇa, because He was already mentioned as the twentieth avatāra. His being Svayaṁ Bhagavān, however, was not known. This additional information is now being provided in the present verse. If the sentence is interpreted in reverse order, i.e., “Svayaṁ Bhagavān is(has taken form of) Kṛṣṇa,” then we have a case where the subject is unknown, because no earlier reference was made to any Svayaṁ Bhagavān. If such is the case, Suta would have said something like 'narayanas tu bhagavan svayam krishna narayana eva'. Svayam means “by His very own Self ” and not because of any other medium or upādhi. The quality of being Bhagavān is intrinsic to His nature and not a superimposition.
Further Analysis:
1)Consistency: Opening and concluding statements of a composition match with each other.
In the opening verse of this chapter of the Bhāgavata (sb 1.3.1), Sūta Gosvāmī used the two words pauruṣam and bhagavān, while in the concluding verse of the section (sb 1.3.28), he uses the two words puṁsaḥ and bhagavān. Because the word puṁsaḥ is a synonym [for puruṣa] and because the word bhagavān is identical, Śrī Sūta here reminds us that these are the very same two words employed earlier. To dispel all obstacles to clear understanding, the learned use the same or equivalent words in their opening (uddeśa) and concluding statements (pratinirdeśa). For example, in the section that deals with the topic of Jyotiṣṭoma, in the injunction “In each spring worship by jyotiṣ,” the word jyotiṣ refers to the Jyotiṣṭoma sacrifice.
If a speaker were to introduce one subject in the beginning and a different one in the conclusion, it would be difficult to understand his or her intention. This repetition of the same words in the opening and closing statements also shows not only that Bhagavān is distinct from and is the source of the Puruṣa, but that Kṛṣṇa is Bhagavān Himself.
2A)Reconciliation: More significant facts are placed at the end of the composition.
One should not doubt this conclusion on the plea that Kṛṣṇa is also listed among the avatāras. [Such an allegation is dispelled] by the hermeneutical principle: “Among prior and succeeding [injunctions], the former is weaker, like prakṛti [the fundamental part of a yajña, or ritual, which is overridden by the atonement process (vikṛti)]” (Jaimini-sūtra 6.5.54)
Though 1.3.23 mentioned Krishna in the list of incarnations, 1.3.28 dispels the doubt that he is just one of the incarnations. 1.3.28 being stated at the end has more weightage than 1.3.23.
2B)A Direct Statement Overrides the Context
Alternatively, the statement “Kṛṣṇa, however, is Bhagavān Himself ” (sb 1.3.28), is validated by the hermeneutical principle that a direct statement (śruti) overrides the context (prakaraṇa) [which in this case is concerned with the avatāras]. An example of the application of this principle is found in the commentary of Śaṅkarācārya on Vedānta-sūtra, “Because a direct statement (śruti) carries greater authority [than the context (prakaraṇa)], there is no contravention [of the fact that these fires (manaścit and so on) are independent of ritual action (kriyā), being associated with knowledge (vidyā) instead]” (vs 3.3.50).
Although Kṛṣṇa is listed as the twentieth avatāra and is thus included within the context of the avatāras, His characteristic of being an avatāra is overridden by the direct statement (śruti), “Kṛṣṇa (alone) is Bhagavān Himself.”
Consequently, here also, in the context of the discussion of the avatāras, Sūta Gosvāmī did not use the word bhagavān for any other avatāra but did so only in reference to Kṛṣṇa: “Bhagavān removed the burden [of the earth]” [sb 1.3.23].
Hence, His inclusion in the list of avatāras is because of the fact that although He is Bhagavān Himself and is ever situated in His own intrinsic nature, He sometimes becomes visible to the world at large, nourishing a special sweetness through His divine play (līlā), such as taking birth, in order to bestow uniquely astonishing bliss upon His personal associates.
3A)Distinction: Importance of the word "tu"
According to Amara-kośa, a noun followed by tu has no relation to anything that precedes it.(tv-antāthādi na pūrva-bhāk).
"tu" here divides the sentence, since tu is used to indicate that the subject matter following is different from previous ones, it distinguished Lord Krishna from amsa kalah. Thus tu conclusively declares that Krishna is the original Supreme Personality of Godhead
Alternatively, the word tu implies restriction, in the sense of “only” or “exclusively.”(syur evaṁ tu punar vai vety avadhāraṇa-vācakāḥ)
Then, the śruti, or express statement, is understood as definitive (sāvadhāraṇā). Thus, by the principle, “The definitive śruti is stronger [than other statements]” (sāvadhāraṇā śrutir balavatī), even if Mahā- Nārāyaṇa, Rama or others are referred to as Svayaṁ Bhagavān in certain statements of the Śruti itself, this is to be understood in a secondary sense by virtue of the above direct statement. (This is to say that Nārāyaṇa can be indirectly considered as Svayaṁ Bhagavān only in relation to all the avatāras that expand from Him, but not in relation to His own source, Śrī Kṛṣṇa. This is to be concluded because there cannot be two forms of Svayaṁ Bhagavān)
3B) The Distinction between the Whole and Its Parts
In this regard, the following is to be said: The aṁśa’s identity of prowess, nature, and so on with that of the aṁśī is to be understood as due specifically to their oneness [of categorical being ( jātīyatva)]. This situation is comparable to that of rivulets flowing from an inexhaustible lake, where the inexhaustibility of the rivulets is due to the inexhaustibility of their source[SB 1.3.26]; otherwise, it would be impossible to distinguish between the part (aṁśa) and its all-encompassing whole (aṁśī).
Consequently, a hierarchy (tāratamya) certainly exists between the avatārī and His avatāras.
Thus, in the eighth chapter of the Third Canto, Vāsudeva is described as superior even to Saṅkarṣaṇa:
The four topmost celibate sages (the Kumāras), desiring to know the truth regarding He who is superior even to Bhagavān Saṅ- karṣaṇa, approached and inquired from Him [Saṅkarṣaṇa], the original Deva, whose consciousness [sattva, i.e., jñāna] is unobstructed and who was situated in the Pātāla region. At that time, He was worshiping [through complete meditative absorption] His own source, [whom the Vedas] proclaim as Vāsudeva.
(sb 3.8.3–4)
Otherwise, the phrase kṛṣṇas tu would become redundant, because its purpose would be served merely by the phrase, bhagavān svayam.
Therefore, since a distinction exists between the part (aṁśa) and the whole (aṁśī), the meaning of the statement, “Kṛṣṇa, however, is Bhagavān Himself” (kṛṣṇas tu bhagavān svayam) is appropriately explained.
The second half of the verse is not connected syntactically with the first half, because the word tu indicates a break in sentence structure. Consequently, the statement, “Kṛṣṇa, however, is Bhagavān Himself,” is complete in itself.
The second half of verse indicates the purpose of Lord's or his incarnations' advent in each yuga.
4)Philosophy: Philosophical statement is more authoritative than that which is historical.
The Paribhasa sutra of a book is like a ruling king, whom all others(statements) have to obey. So, if a statement doesn't obey Paribhasa sutra, the reader may reject it, or interpret that statement to make it agree with the Paribhasa-sutra.
5)Contradictions: Apparent contradictions to Paribhasa-sutra are refuted and correct meanings are given (to align with Paribhasa-sutra)
For ex, the pastime of Krishna and Arjuna meeting Maha-Vishnu mentioned in SB 10.89 is explained in detail in this perspective.(see here) The word amsena in 10.43.23 doesn't mean an expansion of Lord Narayana, but rather means accompanied by all His plenary portions.
The statement "kalabhyam nitaram hareh" (SB 10.20.48) may also be presented as a statement contradicting our paribhasha-sutra, and someone may claim that these words mean "Hari appeared in the forms of His two expansions, Krishna and Balarama." Actually, however, this is not the proper interpretation of these words. "Kalabhyam" (by the two plenary portions) is not actually one word, but the two words "kala" and "abhyam", joined by sandhi. The phrase "hareh kala" means the earth planet, which is one of Lord Hari's many potencies, and “abhyam" means "by Krishna and Balarama". The actual meaning of this statement is: "The earth planet, which is Lord 's potency appeared very beautiful because of the presence of Krishna and Balarama."
Similarly other examples are found in 10.2.41,10.2.18,4.1.59 etc are also clarified.
The false claim that Balarama and Krishna appeared from the hair of Vishnu based on some verses of Vishnu purana and Mahabharata is thoroughly refuted.
Sridhara Swami, the oldest commentator also resolves some contradictions this way.
For eg: In 2.7.26: Motilal edition translates it as: "In order to remove the distress of earth which was pounded of Daityas, he, of white and black hair(Balarama & Krishna), will be born by his own amsa."
Sridhar swami doesn't agree with such translation since white hair can't be seen on Lord's head since he doesn't become old.(I discussed here how even normal devatas don't get old). Also it contradicts clear statement krsnastu bhagavan svayam. He comments:
mat-kesav evaitat kartum saktav iti dyotanartham | rama-krishnayor varna-sucanartham ca kesoddharanam iti gamyate | anyatha tatraiva purva-para-virodhapatteh, krishnas tu bhagavan svayam iti etad-virodhac ca
Also, in the story of Candra-kalankapatti-karana in the Prabhasa-khanda of the Skanda Purana, in the description of Lord Krishna's appearance, Krishna is described as Lord Vishnu Himself. By using the words "svayam vishnuh (Vishnu Himself)", the concocted idea that Krishna is an incarnation of Lord Vishnu's hair is refuted by Vyasadeva.
At various instances, Jiva Goswami uses Sridhara Swami's explanations.
After quoting several verses that apparently contradict paribhasa sutra and resolving them with correct meanings, Jiva Goswami declares
"Our paribhasa-sutra (krsna tu bhagavan svayam) now appears as a great heroic king who has just defeated hundreds of enemies in the form of opposing arguments and completely brought them under his submission to the great delight of all onlookers. I shall now bring into view the multitude of arguments that forms the footsoldiers, cavalry, chariot warriors and elephant-riding warriors of his army."
6)Complements: Verses supporting Paribhasa-sutra
Many other verses from Bhagavatam prove that Krishna is the source of all incarnations like lila-avataras and guna avataras. Some examples are 10.2.40,10.14.20,10.8.15,10.10.34,10.58.37,10.87.46 etc..
SB 9.24.55:
shöamas tu tayor asit svayam eva harih kila it "The eighth son of Vasudeva and Devaki was the Supreme Personality of Godhead Himself-Krishna." The use of the word "kila (certainly)" to emphasize the statement of this verse perfectly corroborates the statement of our paribhasha-sutra.
vasudeva-grihe sakshad bhagavan purusha eva (SB 10.1.23)
SB 10.14.32:
nanda-gopa-vrajaukasam yan-mitram paramanandam purnam brahma sanatanam
"How greatly fortunate are Nanda Maharaja, the cowherd men and all the inhabitants of Vrajabhumi! There is no limit to their fortune because the Absolute Truth, the source of transcendental bliss, the eternal Supreme Brahman, has become their friend."
That Shri Krishna is the Original Personality of Godhead is especially confirmed by the phrase "purnam brahma sanatanam"
7)Principal subject: Krishna's glories are described throughout SB.
The Tenth and the Eleventh cantos that constitute almost half of Srimad Bhagavatam, describe Lord Krishna's pastimes exclusively. Further First Canto describes about Krishna in detail. The first Nine Cantos summarily describe Lord's other forms. Further, each of the twelve cantos describe Krishna as the Supreme Personality of Godhead in various instances.
In the Second Canto, Lord Krishna is described as the Supreme Personality of Godhead in the account of the conversation between Brahma and Narada(10 verses dedicated toward Krishna in SB 2.7).
In the Third Canto, Lord Krishna is also described in the account of the conversation between Vidura and Uddhava.
In the Fourth Canto, Lord Krishna is described, and the following verses: "That Nara-Narayana Rishi, who is a partial expansion of Krishna, has now appeared in the dynasties of Yadu and Kuru in the forms of Krishna and Arjuna respectively, in order to mitigate the burden of the world." (SB 4.1.59), and "Prithu Maharaja was a powerful incarnation of Lord Krishna's potencies; consequently any narration concerning His activities is surely very pleasing to hear, and it produces all good fortune".* (SB 4.17.6) may be presented as evidence to show that Shri Krishna is the actual subject described in the verses of the Bhagavatam etc....
Hence, the description of Lord Krishna is the principal subject matter of the Bhagavatam.
8)Common Interest: All the various speakers and all the audiences of Srimad-Bhagavatam want to hear and glorify Krishna.
Example of Speakers: Suta Goswami(1.2.5), Sukadeva Goswami(2.4.20), Maitreya Rsi(4.17.8) Example of Hearers: Saunka Rsi(1.1.12-14), Maharaja Pariksit(1.19.5 , 10.1.1-13), Vidura(4.17.6-7)
In accordance in Narada Muni's instruction "And thus you can think of the pastimes of the Lord in trance for the liberation of the people in general from all material bondage."(SB 1.5.13).
Vyasadeva's meditation or trance in (1.7.6-7), reveals that Krishna is the primary subject of Bhagavatam.
yasyāṁ vai śrūyamāṇāyāṁ kṛṣṇe parama-pūruṣe
SB 1.7.7 — Simply by giving aural reception to this Vedic literature, the feeling for loving devotional service to Lord Kṛṣṇa, the Supreme Personality of Godhead, sprouts up at once to extinguish the fire of lamentation, illusion and fearfulness.
9)Substitute: Bhagavatam is itself considered one of the forms of Sri Krishna.
Though the sun of Krishna has set, the sun of Bhagavata Purana has risen 1.3.43
This Bhāgavata Purāṇa is as brilliant as the sun, and it has arisen just after the departure of Lord Kṛṣṇa to His own abode, accompanied by religion, knowledge, etc. Persons who have lost their vision due to the dense darkness of ignorance in the Age of Kali shall get light from this Purāṇa
10)Name: No other holy name of Lord is equal to Krishna.
sahasra-namnam punyanam, trir-avrttya tu yat phalam; ekavrttya tu krsnasya, namaikam tat prayacchati
Once chanting the holy name of Krishna is equivalent to the purifying effect of chanting the other names of Lord three thousand times(Vishnu sahasra nama thrice)
(Brahmanada Purana 2.36.19). See here
11)Reconfirmation: Other literature also refer to Krishna as the Original Personality of Godhead.
Jiva Goswami quotes from Mahabharata, Brahma Samhita and Brahma Vaivarta purana, Padma purana, Bhagavad Gita.
12)Supreme Form: The eternality and supremacy of the form of Sri Krishna is confirmed within the Bhagavatam and other literatures as well.
eg: 3.2.12 yam martya lilaupayikam., 11.6.5 tasyam vibhrajamanayam.., 10.14.1 naumidya te bhra vapuse.., 10.14.14 narayanas tvam na hi. Bhagavad Gita(11.51-54)
What about evidences contradicting this view?
Someone may object: by speaking few arguments, you have attempted to refute the great mass of evidence against your theory. I can't believe you.
Reply: In the Vedanta-sutra and other Vedic literatures many lengthy arguments are refuted in a few words. The length of an argument is not the criterion of whether it is true or not. Even in the material world we may see an example of this, for sometimes a single strong fighter may defeat a thousand soldiers in the battle. In the same way a single strong argument may defeat thousands of illogical words.
In truth, apparent contradictions in other puranas also can be resolved.
Hari-vamsha describes Lord Krishna as an incarnation of Lord Upendra (Vamana). This false conception is refuted by the following words spoken by Lord Krishna in the Bhagavatam, which describe Lord Krishna's return to His own eternal abode in the spiritual world (11.6.31). That Lord Krishna, after leaving the earth planet, returned to His own abode in the spiritual world is also confirmed in the following statement of Brahma (Bhagavatam 11.6.27)
In some places in the scriptures it may say that Lord Vaikunöha, the son of Vikunöha-devi, appeared as Lord Krishna; in other places it may say that Kshirodakashayi Vishnu appeared as Lord Krishna; in other places in the scriptures it may say that the purusha-incarnations appeared as Lord Krishna; in other places in the scriptures it may say that Narayana Rishi appeared as Lord Krishna; in the Brihat-sahasra-nama Prayers in the description of the identity of Lord Balarama and Lord Lakshmana, it may say that Lord Ramacandra appeared as Lord Krishna; in other places in the scriptures it may say that a hair of Lord Narayana appeared as Lord Krishna; and in other places in the scriptures there may also be other descriptions of how other forms of Godhead have incarnated as Lord Krishna. How are these contradictory statements to be resolved? Actually all these statements are true, for all forms of the Personality of Godhead are simultaneously present in the form of the Personality of Godhead, Shri Krishna, and when Shri Krishna descends to this material world, all other forms of Godhead also descend with Him(for He is source of all and for detailed explanation, refer Krishna Sandarbha)
That all forms Godhead are manifested from the body of Lord Krishna is confirmed by the following statement of Uddhava (Shrimad-Bhagavatam 11.11.28):
My dear Lord, as the Absolute Truth You are transcendental to material nature, and like the sky You are never entangled in any way. Still, being controlled by Your devotees’ love, You accept many different forms, incarnating according to Your devotees’ desires
That Bhagavatam is the best of all Vedic literatures is confirmed in the following verse (SB 9.22.22-23):
"From Vyasadeva, I [Sukadeva Gosvami] was born, and from him I studied this great work of literature, Srimad-Bhagavatam. The incarnation of Godhead Vedavyasa, rejecting his disciples, headed by Paila, instructed Srimad-Bhagavatam to me because I was free from all material desires."
Vyasadeva had instructed the Four Vedas and the Puranas to His disciples, but He did not teach them the Bhagavatam. Only Sukadeva was qualified to study the Bhagavatam, because he was free from all material desires. This shows the superiority of the Bhagavatam to all Vedic literatures.
Because Bhagavatam is the best of all Vedic literatures, the statement of the Bhagavatam, that Sri Krsna is the Supreme Personality of Godhead, should be accepted as the actual truth.
In this context the example of the village-chief and the king may be given. In the village chief's assembly hall a certain thing may be praised as the best of all, and in the king s assembly hall a different thing may be praised as the best of all. The standards of the village chief and the king are not on the same level. What is considered best by the king may be accepted as superior to what is praised by the village chief. In the same way, the Bhagavatam is the best of all scriptures, and because in the verses of the Bhagavatam Sri Krsna is glorified as the Original Personality of Godhead, this must be accepted as truth, even if someone may be able to find some evidence to contradict it in some other Vedic literatures. Any scriptural statement contradicting the Bhagavatam's affirmation "Krsnas tu bhagavan svayam" (Sri Krsna is the Original Personality of Godhead) should therefore be rejected, and there is no impropriety in this
We see in Bhagavatam 10.77.30:
"Such is the account given by some sages, O wise King, but those who speak in this illogical way are contradicting themselves, having forgotten their own previous statements."
This verse clearly describes how untrue statements may sometimes be found in the Vedic literatures. The careful reader must be prepared, therefore, to sometimes reject scriptural quotations. The guideline for accepting and rejecting such statements should be the authority of Bhagavatam.
When Bhagavatam was spoken by Sukadeva Goswmai, even great sages like Narada and Vyasa were present to hear. Although these two sages were Sri Suka's guru and grand-guru, respectively, when they heard Srimad Bhagavatam issuing from his lips, they felt as if they had never heard it before. For this reason it is said here that he taught this most significant wisdom even to them. As mentioned in suka mukhad amrta drava samyutam: "The Bhagavatam is enriched with nectarean juice from the mouth of Suka" [Bhag 1.1.3]. Thus in this sense also Bhagavatam is more glorious than any other scripture. Statements about the superiority of other Puranas, such as the Matsya Purana, are only relatively true.
So even if, as some people think, other Puranas are subordinate to the authority of the Vedas, Bhagavatam directly denies this idea in regards to itself. In other words, the Bhagavatam claims its own authority independently. Thus its position is that of the highest sruti authority, as is stated, "How did it so happen that King Pariksit met this great sage, making it possible for this sruti text for the pure Vaishnavas to be manifest?" [Bhag 1.4.7]"
It's not that Sruti(Vedas, especially Upanishads) teach something different, but they speak in indirect way.
Krishna says in 11.21.35
parokṣa-vādā ṛṣayaḥ parokṣaṁ mama ca priyam
"The Vedic seers and mantras, deal in esoteric/indirect terms, and I am pleased by such indirect descriptions"
Bhagavatam's declaration being greatest purana is absolute and thus Bhagavatam's conclusions are highest.
Which other sampradayas accept this idea?
There are other sampradayas like Rudra Sampradaya(Pustimarg) & Nimbarka Sampradaya who accept that Krishna is the source of all.
On what basis is Krishna claimed to be source of Vishnu?
It is believed so based on the following verse from Srimad Bhagavatham.
It says, at the beginning, the Supreme one (Lord Krishna) manifests in the form of purusha (Vishnu). This purusha has three forms: Karanokadasayi Vishnu, Garbodhakasayi Vishnu and Kshirodakasayi Vishnu. Hence, they believe that Krishna is the source of Vishnu.
From Srimad Bhagavatham canto-1 chapter-3 verse-1:
jagṛhe pauruṣaṁ rūpaṁ bhagavān mahad-ādibhiḥ
sambhūtaṁ ṣoḍaśa-kalam ādau loka-sisṛkṣayā
Meaning: In the beginning of the creation, the Lord first expanded Himself in the universal form of the puruṣa incarnation and manifested all the ingredients for the material creation. And thus at first there was the creation of the sixteen principles of material action. This was for the purpose of creating the material universes.
Purport: The Bhagavad-gītā states that the Personality of Godhead, Śrī Kṛṣṇa, maintains these material universes by extending His plenary expansions. So this puruṣa form is the confirmation of the same principle. The original Personality of Godhead Vāsudeva, or Lord Kṛṣṇa, who is famous as the son of King Vasudeva or King Nanda, is full with all opulences, all potencies, all fame, all beauty, all knowledge and all renunciation. A part of His opulence is manifested as impersonal Brahman, and a part of His opulence is manifested as Paramātmā. This puruṣa feature of the same Personality of Godhead, Śrī Kṛṣṇa, is the original Paramātmā manifestation of the Lord. There are three puruṣa features in the material creation, and this form, who is known as the Kāraṇodakaśāyī Viṣṇu, is the first of the three. The others are known as the Garbhodakaśāyī Viṣṇu and the Kṣīrodakaśāyī Viṣṇu, which we shall know one after another. The innumerable universes are generated from the skin holes of this Kāraṇodakaśāyī Viṣṇu, and in each one of the universes the Lord enters as Garbhodakaśāyī Viṣṇu.
See Which all sects accept three forms of Vishnu as described in Satvata Tantra? which gives references for these three forms of Vishnu.
Which all schools accept this idea?
It is accepted by Gaudiya Vaishnavas, Nimbarka's sect, Vallabhacharya's sect, Pranami sect and Radha Vallabha sect which I wrote in this answer too.
And why they accept one and reject other is based on the beliefs. One believe Krishna as supreme and other believe Vishnu.
This is major verse,
Verse 1.3.28 of bhagavata
ete cāṁśa-kalāḥ puṁsaḥ kṛṣṇas tu bhagavān svayam indrāri-vyākulaṁ lokaṁ mṛḍayanti yuge yuge
All these incarnations are either plenary portions or parts of the plenary portions of the puruṣa-avatāra. But Kṛṣṇa is the Bhagavan Himself. In every age He protects the world through His different features when the world is disturbed by the enemies of Indra.
Since, this has been adequately explained in the accepted answer, let me just summarize and then add few more verses and explanations.
In the beginning of Bhagavatam, this chapter concerning the mysterious appearance of the Lord (janma guhyam bhagavato, SB 1.3.29) is called a sutra, since it threads together (suc) statements concerning all the avataras. And in this chapter, ete camsa-kalah pumsah krsnas tu bhagavan svayam is a paribhasasutra, which supplies a general definition for the whole work. Thus, wherever avataras are described in the Bhagavatam, others should be known as expansions of the purusavatara, but Krsna should be known as svayam bhagavan. This conclusion is prevalent everywhere in the Bhagavatam. It has been said:
paribhasa hy eka-desastha sakalam sastram abhiprakasayati yatha vesmapradipa The paribhasa statement, situated in one place, lights up the whole scripture, just as a lamp lights up the whole house.
This sutra appears once in the work and is not continually repeated. Though there are millions of statements in the scripture, this sutra controls them all like a king. Thus statements which contradict the sutra must be explained so that they agree with the sutra. That is because these contrary statements are weak, since they belong to secondary subjects in the work, and because the sutra’s statement is strong, being supported by direct statement.
SB 1.9.18 eṣa vai bhagavān sākṣād ādyo nārāyaṇaḥ pumān mohayan māyayā lokaṁ gūḍhaś carati vṛṣṇiṣu
Krishna is here referred as adyo narayana which means first narayana.
SB 10.72.15
śrutvājitaṁ jarāsandhaṁ nṛpater dhyāyato hariḥ āhopāyaṁ tam evādya uddhavo yam uvāca ha
Here Krishna is referred as adya harih which means first Hari or primeval Hari.
Thus, Krishna is root Hari,root Narayana. He is source of all incarnations.
Like the 1.3.28 has guided whole Bhagavata, now it's application will be extended to other puranas as well.
Let's turn to Vishnu Purana now:
The critic may present these below verses to discredit 'krsnastu bhagavan svayam'
aṁśāvatāro brahmarṣe yo ’yaṁ yadu-kulodbhavaḥ | viṣṇos taṁ vistareṇāhaṁ śrotum icchāmy aśeṣataḥ || cakāra yāni karmāṇi bhagavān puruṣottamaḥ | aṁśāṁśenāvatīryorvyāṁ tatra tāni mune vada || maitreya śrūyatām etad yat pṛṣṭo ’ham idaṁ tvayā | viṣṇor aṁśāṁśa-sambhūti-caritaṁ jagato hitam ||(VP 5.1.2-4)
"I wish now to hear a more particular description, holy Rishi, of the portion of Vishńu that came down upon earth, and was born in the family of Yadu. Tell me also what actions he performed in his descent, as a part of a part of the supreme, upon the earth. I will relate to you, Maitreya, the account which you have requested; the birth of a part of a part of Vishńu, and the benefits which his actions conferred upon the world."(Translation by HH Wilson).
However, the interpretation in line with 'krsnastu bhagavan svayam' is as follows:(taken from Chaitanya Mata Manjusha commentary of Srinatha pandita)
The explanation of the above controversial words is this, sequentially:
(1) aṁśāvatāraḥ (the Avatāra of an aṁśa) signifies: aṁśānāṁ nārāyaṇādīnām avatāraḥ yasmāt saḥ, “He from whom there is an Avatāra of aṁśas such as Nārāyaṇa,”
(2) aṁśāṁśena avatīrya (after descending with an aṁśa of an aṁśa) means: aṁśaḥ brahmādayaḥ teṣām aṁśena yādava-rūpeṇa saha avatīrya, “after He descended with the Yādavas, who are aṁśas of aṁśas such as Brahmā,” since it will be said: bhavadbhir aṁśair yaduṣūpajanyatām, “[Brahmā told the gods:] You should take birth as aṁśas among the Yadus” (Bhāgavatam 10.1.22), and
(3) viṣṇor aṁśāṁśa-sambhūti-caritam (the deeds of He who appeared with an aṁśa of an aṁśa of Viṣṇu) is understood as follows. At first, viṣṇoḥ caritam means śrī-kṛṣṇasya caritam (Śrī Kṛṣṇa’s deeds). What were they like? They were aṁśāṁśa-sambhūti, which means: aṁśānāṁ brahmādīnām aṁśāḥ yādavāḥ teṣāṁ samyak samīcīnā bhūtiḥ sampattiḥ yasmāt yatra vā, “either (A) because of which there is the complete prosperity of the Yādavas, who are aṁśas of aṁśas such as Brahmā; or (B) in which the prosperity of the Yādavas, who are aṁśas of aṁśas such as Brahmā, becomes complete.”
Now, one may say that Krishna is incarnation of Vishnu's hair based on 5.1.59 and the succeeding verses.
evaṁ saṁstūyamānas tu bhagavān parameśvaraḥ | ujjahārātmanaḥ keśau sita-kṛṣṇau mahā-mune || uvāca ca surān etau mat-keśau vasudhā-tale | avatīrya bhuvo bhāra-kleśa-hāniṁ kariṣyataḥ || vasudevasya yā patnī devakī devatopamā | tasyām aṣṭamo garbho mat-keśo bhavitā surāḥ ||(Vi Pu. 5.1.59-60,63)
When Brahmá had ended, the supreme lord plucked off two hairs, one white and one black, and said to the gods, "These my hairs shall descend upon earth, and shall relieve her of the burden of her distress."
"This my (black) hair shall be impersonated in the eighth conception of the wife of Vasudeva,.." (Only relevant portion of translation taken from HH Wilson)
However, the succeeding verses themselves refutes the above translation/interpretation where in Vishnu says "I will myself incarnate in the eighth conception of Devakí; and you shall immediately take a similar character as the embryo offspring of Yaśodá."
Therefore, the understanding of the verses that seem to say Krishna is incarnation of Vishnu's hair is:
The Lord took(manifested) one white hair and one black hair from Himself, not that He plucked them, since His hair is transcendental; pulling them off does not make sense. The gist is He raised both hairs; then He showed them. He did this to indicate the color.
Alternatively, [mat-keśau is interpreted as a karma-dhāraya compound]: mama kaṁ sukhaṁ tat-svarūpau īśvarau ca, “They are My happiness (mat-ka = mama sukha) and They are two Lords,” whose nature is happiness.
In regard to tasyām aṣṭamo garbho mat-keśo bhavitā, “My (black) hair will become the eighth embryo in her womb” (Viṣṇu Purāṇa 5.1.63, cited above), mat-keśaḥ (My hair) means śrī-kṛṣṇaḥ. The explanation is the same as before (“He is My happiness (mat-ka) and He is the Lord (īśa)”). Or else matkeśa means: mama kaṁ sukhaṁ yasmāt saḥ ca asau īśvaraḥ ca, “He is the Lord, because of whom I have happiness.”
It can interpreted in few other ways, so as to agree with 'krsnastu bhagavan svayam' and also the succeeding statement in Vishnu purana. I will add them when I get time.
There is also a verse in Mahabharata which seems to say Krishna and Balarama are incarnations of Vishnu's hair, again that is not appropriate because at many places in Mahabharata that is refuted and that verse also can be explained like the Vishnu Purana verse.
Thus in the Chandogya Upanisad it is said jyayams ca purusah: the purusa is greater than that; sarvam khalv idam brahma: everything is brahman; yat prana aditya: the pranas are the Adityas. Having said this, everything is summarized by saying krsnaya devaki-putraya: this purusa sacrifice is subservient to Krsna, the son of Devaki. (Chandogya Upanisad 3.17.6) By this it is understood that Krsna is superior to the purusa.
In Gopāla-tāpanī Upaniṣad the Kumāras ask Brahmā “Who is the supereme deva?” Brahmā answers “Kṛṣṇa is the supreme lord.” In the conclusion it is said:
tasmāt kṛṣṇa eva paro devas taṁ dhyāyet taṁ rasayet taṁ yajet taṁ bhajed iti oṁ tat sad iti ||
Therefore Kṛṣṇa is the supreme being. One should meditate on him, experience his sweetness, worship him and serve him. Gopāla-tāpanī Upaniṣad 1.48
Sometimes Kṛṣṇa is called an aṁśa. He is complete but since he reveals a limited portion to ordinary men as expressed in nāhaṁ prakāśaḥ sarvasya yogamāyā- samāvṛtaḥ: covered by my māyā, I am not revealed completely (BG 7.15), he appears like an aṁśa to ordinary people. Thus he is called an aṁśa. However the real meaning is “He is like an aṁśa.”
Here are the reasons:
All these are either portions or minute portions of the Puruṣa, but Kṛṣṇa is Svayam Bhagavān. (Bhagavata Purāṇa 1.3.28)
O Devī! All avatāras emanate from the Supreme Brahman in the form of Kṛṣṇa. But Kṛṣṇa, who is both inclusive of attributes (saguṇa) and beyond all attribution (nirguṇa), is the avatārī Himself. (Nārada Purāṇa 2.58.45)
All these avatāras are either portions or minute portions of the Puruṣa, but Kṛṣṇa is Svayam Bhagavān. (Brahmā-vaivarta Purāṇa 4.117.12)
We find some contradictions in other scriptures, what about that?
Jiva Goswami provides two examples to show how Bhagavata Purana overrides other scriptures.
First example:
https://vedabase.io/en/library/sb/10/57/30/
In Akrūra’s absence ill omens arose in Dvārakā, and the citizens began to suffer continually from physical and mental distresses, as well as from disturbances caused by higher powers and by creatures of the earth.
Brahmanda Purana gives a similar description:
At that time, the kingdom suffered a great drought. As a result, the Kukkuras and Andhakas propitiated Akrūra. When Akrūra, the chief among those charitably disposed, returned to Dvārakā, Indra sent heavy rains in the midst of the sea. (Brahmāṇḍa purāṇa 2.71.90)
After this (SB 10.57.30), Śrī Śukadeva speaks the verse (SB 10.57.31), in which he refutes the validity of such statements. He reasons that people who speak in this manner forget that nothing inauspicious could ever occur in the presence of Kṛṣṇa.
https://vedabase.io/en/library/sb/10/57/31/
Some men proposed [that the troubles were due to Akrūra’s absence], but they had forgotten the glories of the Supreme Lord, which they themselves had so often described. Indeed, how can calamities occur in a place where the Personality of Godhead, the residence of all the sages, resides?
Second example:
Śuka echoes the same conclusion in verse 10.77.30.
Such is the account given by some sages, O wise King, but those who speak in this illogical way are contradicting themselves, having forgotten their own previous statements.
Prior to this, Śuka had described how Kṛṣṇa became morose when He saw Śālva cutting off the head of His father, Vasudeva. This was a mere illusion created by Śālva through his magical powers. In other words, Śukadeva, who is the original speaker of the Bhāgavata purāṇa, does not accept the versions of events that might be found in other Purāṇas when they are seen to contradict the import of the Bhāgavata teachings. His reasoning is that the sages who condone such statements forget their own words in which they describe Kṛṣṇa as the Supreme Person. How could Kṛṣṇa fall into illusion? And how could any inauspicious event occur independent of His will?
These statements demonstrate the Bhāgavata purāṇa’s supreme authority over other scriptures. Therefore, if one finds any statement in other scriptures describing Nārāyaṇa or Vāsudeva as supreme, it is to be understood that these forms are expansions of Kṛṣṇa. This was concluded by Brahmā in his prayers to Kṛṣṇa.
nārāyaṇo ’ṅgaṁ nara-bhū-jalāyanāt tac cāpi satyaṁ na tavaiva māyā (SB 10.14.14)
Lord Nārāyaṇa is Your expansion, and He is called Nārāyaṇa because He is the generating source of the primeval water of the universe. He is real, not a product of Your illusory Māyā.
Kṛṣṇa also counts Vāsudeva as one of his vibhūtis (SB 11.16.29).
Śrī Jīva Goswami points out an additional reason for the supreme authority of Bhāgavata purāṇa. He maintains that the superiority of a text may also be understood from the preeminence of its speaker. Bhāgavata purāṇa was spoken by the topmost illustrious sage, Śukadeva Goswami, who was favored by Vyāsa over all his other disciples(https://vedabase.io/en/library/sb/9/22/21-24/). The extraordinary character of Śukadeva is described in various places in Bhāgavata purāṇa, such as in 1.2.2-3, 1.4.5 and 12.12.68.
Moreover, Bhāgavata purāṇa was recited in the council of great sages, such as Vyāsa, Nārada, Vasiṣṭha, Parāśara, and Paraśurāma. This assembly included three of the avatāras from the list of twenty two given in the third chapter of the First Canto. There is no other scripture within the Vedic canon recited in a gathering of sages and scholars of such magnitude. This suggests that whatever was spoken by Śukadeva had the approval of these sages and scholars. The sages present included the authors of various theological and philosophical systems. Consequently, what is concluded in Bhāgavata purāṇa supersedes all other doctrines propounded in other scriptures.
References:
https://bhaktitattva.com/2019/01/25/krsnas-tu-bhagavan-svayam/
