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The Purva Mimamsa school doesn't accept that the names of individuals or gods in the Vedas actually refer to corporeal beings, but are limited to their etymological meaning, as explained in this post. For example, "Pravahani" means "one who carries things in an excellent manner", and does not actually refer to a person named Pravahani as the "son of Pravahana".

So if they don't accept Rishis, kings, and Devas as actual beings, then how does it explain their actions and behavior in the Smritis, Puranas, Mahabharata, Ramayana, etc?

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Good question! Let's distinguish between a bunch of different issues:

  1. How the Purva Mimamsa school viewed human names in the Vedas: The Purva Mimamsa school believed that the Vedas never refer to the name of a specific human being, because that would contradict the eternality of the Vedas. They thought that that seeming references to human names should be reinterpreted in their etymological sense; here's what Shabara Swami says in this excerpt from his commentary on the Purva Mimamsa Sutras:

    The Purvapakshin has cited the term "pravahani" (as a proper name occurring in the Veda, and hence proving that the Veda came after that person). - But this is not right. We do not know of any person of the name "Pravahana", hence the term pravahani cannot mean "the son of Pravahana"; in fact the prefix "pra" is well-known as signifying excellence, and the root "vaha" as signifying the act of carrying; and we do not know of any combination of these two (pra-vahana) as signifying any common well-known word; as regards the "i" (in the term "pravahani"), it is known as signifying "progeny" as well as "agent of an action"; so that the term pravahani signifies "one who carries things in an excellent manner" [and it cannot mean "the son of Pravahana", as we do not know of any person of the name of "Pravahana"]. - As far as the term "babara", it is only a word imitative of sound (produced by the blowing wind). This the two words ("pravahani" and "babara") only express the everlasting thing ("the blowing wind").

    So Shabara interprets Babara son of Pravahani, which on the surface seems to be a reference to a human named Babara who was the son of a human named Pravahana, as really a reference to the wind. The Vedanta school, on the other hand, accepts that the Vedas refer to human names, and explains this by saying that certain names and events recur in every creation; see my answer here. The Purva Mimamsa school, in contrast, didn't believe in the notion of multiple creations or even one creation; they thought the Earth was eternal and that the human race was eternal on the Earth!

  2. How the Purva Mimamsa school viewed the Devas: The Purva Mimamsa school was borderline agnostic/atheist on the existence of the Devas. See my answer here, and this journal paper, for details. Suffice it to say that they were vague on exact what the Devas were, but they at least believed the following: that the Devas do not have bodies, that the Devas do not consume offerings made in Yagnas, that the Devas are not allowed to do Yagnas themselves, and that the only role that Devas play in Yagnas is that offerings are made with reference to them as recipients. This excerpt from Shabara Swami's commentary on the Purva Mimamsa Sutras is illustrative of the Purva Mimamsa attitude towards the Devas:

    There is one opinion that by the term 'deity' we understand those beings, Ani and the rest, who are described in Itihasas and Puranas as living in heaven.... The other opinion is that "by the term 'devata' ('Deity') are meant just those to whom the name 'Deity' has been applied in the Mantra and Brahmana texts such as, - 'Agni is the Deity' - 'Vata is the Deity' - 'Surya is the Deity' - 'Chandrama is the Deity'"... [Both these opinions are rejected for various reasons.] For these reasons we conclude that Deities are those who are Sukta-bhak (to whom Hymns are addressed) and Havir-bhak (Recipients of offerings).... [T]hat 'recipient of offerings' should be the 'Deity' for whose sake the offering is made. Similarly with 'Sukta-bhak'.... [T]he character of 'Deity' becomes applicable to all those beings that are spoken of as those to whom anything is offered - be they corporeal or incorporeal, sentient or insentient[.]... [T]hat being becomes the 'Deity' of an offering, by whose name the Sacrificer makes the determination 'I shall present the offering to so and so'. [I]t is not in its material form that the Deity helps the accomplishment of the sacrifice - it does so in its verbal form; just as the Adhvaryu helps it with his hands, the Deity helps it with the name. Just as when ... though the action bears directly upon his hands, yet it is the Hotar priest himself that is regarded as helping the sacrifice - in the same manner, even though help is rendered by the Deity through the name connected with itself, yet it is the Deity itself that is regarded as helping the sacrifice.... [T]he word is not pronounced for the purpose of bringing about the notion of the thing denoted[.]... This is what has been explained by the Vrittikara - 'The notion of the thing denoted is not preceded by the word; hence the existence of the thing has been established (as apart from the word).' ... Says the Opponent - "In that case it is the word that becomes the Deity." Answer - This is an idea that it is not for us to refute; because such an idea, if expressed, does not militate against our view; on the contrary it lends all the more strength to the view [that different names of the same god should not be substituted for one another].

    So Shabara Swami doesn't actually endorse that the gods are nothing but words uttered in Yagnas, but he does not feel the need to refute that view, since he doesn't think that view would undermine any of the Purva Mimamsa school's doctrines. In contrast, the Vedanta school unequivocally supports the existence and corporeality of the gods.

  3. How the Purva Mimamsa school viewed events described in Hindu scripture: The Purva Mimamsa school believed that the Vedas consist primarily of two kinds of statements, Vidhi or injunctions concerning Dharma, and Arthavada or meaningless statements that just serve to glorify the actions prescribed in the Vidhis. For example, if the Vedas said "Indra performed the Agnishtoma and then defeated Vritrasura in battle. So if you want victory in battle you should perform the Agnishtoma." then the Purva Mimamsa school would say that you cannot conclude from that that a Deva named Indra actually killed an Asura named named Vritra. (And as I said above, they didn't even think Devas were allowed to do Yagnas!) Rather, it's just a way of encouraging people to do the Agnishtoma Yagna, because it really does lead to victory in battle. See this excerpt from Shabara Swami's commentary on the Purva Mimamsa Sutras for details. So bottom line, the Purva Mimamsa school believed that the Vedas provide no information whatsoever about events.

    And they felt the same way about events described in Smriti. For instance, in this excerpt from his Tantra Vartika, Kumarila Bhatta argues that the Mahabharata's description of battles is just Arthavada intended to encourage Kshatriyas to be brave.

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    Great Answer! Do we know why Devas are not allowed to conduct Yagnas? – DirghaChintayanti Sep 27 '17 at 11:29
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    @LakshmiNarayanan The Purva Mimamsa school argued Devas are not allowed to do Yagnas because Yagnas involve offerings to Devas, and you can't make an offering to yourself. They also argued that Rishis who are not allowed to do Yagnas, because you can only do a Yagna if you can name 3 Gotra Pravaras, and so if you're a Rishi who's the founder of a Gotra then you can't name any Rishis who came before you in the Gotra. I think this reasoning is fallacious, because countless scriptures describe Devas and Rishis doing Yagnas. But Mimamsakas would dismiss all such scriptural statements as Arthavada. – Keshav Srinivasan Sep 27 '17 at 13:29
  • So I'm guessing the Purva Mimamsa school has only existed in Kali Yuga, after the Mahabharata war and compilation of Sruti and Smriti by Vedavyasa, and not before? Because the impression we get from reading Smrti is that Devas and Rishis frequently made contact with humanity in previous yugas. What if they made contact now? What would Mimamsakas say? – Ikshvaku Sep 27 '17 at 13:50
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    @Ikshvaku To be clear, the Purva Mimamsa school didn't disbelieve in the existence of Rishis. (And they arguably didn't disbelieve in the existence of Devas, although they were vague on that.) But what they believed is that you cannot find out any information about events involving Devas, Rishis, or anyone else through either Shruti or Smriti. By the way, the Purva Mimamsa school was founded by the Rishi Jaimini, who was a shishya of Vyasa. Jaimini was present in the battlefield at the end of the Mahabharata war, which makes it ironic that Kumarila Bhatta didn't believe in the Mahabharata war. – Keshav Srinivasan Sep 27 '17 at 14:12
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    @SuryaKantaBoseChowdhury They did accept the Mahabharata and Puranas, they just thought that none of the events described in Hindu scripture, whether Vedas, Puranas, Mahabharata, etc. ever happened. They thought they were all just Arthavadas intended to glorify actions. For instance they thought the Mahabharata war never happened, it's just a way of encouraging bravery in kings. – Keshav Srinivasan Mar 20 '18 at 14:13

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