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What was the opinion of Kumarila and Prabhakara, who were proponents of the Jaimini mimamsa, about the Puranas? In context of both mythology and history.

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" i.e. praise or dispraise of acts . Kumarila appreciates the authority of authors like Valmiki and vyasa saying that they were learned men of the Veda and agrees that they have written these works based on same line of veda. He thinks that the puranic works were composed keeping in view the diverse taste and i intelligence of audience and are written to please all of them .

On the topic found in puranas such as Genealogy of kings , history of families , future state of the world , acts of war , pilgrimage places etc. he says that part serves specific purposes. Like Stories of wars inspires men of the kings. Details of time and space is written to regulate the ordinary practice of men. Description of various places serves the purpose to identify
place to perform religious acts.

On the negative side he remarks that these stories in the puranas need not to taken as absolutely correct in regard to facts.

So overall Kumarila is looking at the puranas in very logical way , with very little or no room for fantasy. He thinks the stories of Puranas is an Arthavada only. And at some places where it is not possible to provide some logical explanation the concept of divine is brought forward to assist them .

He also accepts the authority of the puranas on the basis of they support enjoined acts and depecate forbidden ones . I.e. they support the Dharma and condem adarma.

Below are his views expressed in his works Tantra- vartika quoted by Ganganath jha.

With regard to Itihasa and purana , Kumarila takes a liberal view. In
all these works , direct injunctions are found embodied in a mass of
matter purely of a descriptive character ; These latter are relegated
to the category of 'ArthaVada' , being descriptive of acts done by
good and bad men of ancient and modern times. These are regarded as
"Arthavada" ,purely declamatory , because if the stories found therein
were really true , then ,with reference to these at least , the
injunctions to recite would be useless as no useful purpose could be
served by the reciting of mere descriptions or stories ; hence these
have to be taken as implying the praise or dispraise of acts and they
need not therefore be taken as absolutely correct in regard to facts.

In the justification of this method of instructions adopted inn
Itihasa and Purana , Kumaraila makes the following remarks (Tantra .
Va) i.e. Tantra Vartika - " Guided as they were by the study of veda
Valmiki , Vyasa and others composed their works on the same line of
veda , that is the reason why we find in the works of these writers
many apparently useless stories and descriptions - as in the veda and
as those for whose benefit these works were intended were persons of
varying degree of intelligence , and of diverse tastes , it was only
proper for them to introduce every kind of matter in their works so
that they might be of use to all men"

As regards the authority attaching to these works , it has been
held that some of the injunctions contained in them are such as are
based directly on veda , while some are based on considerations of
pleasure and pain experienced in the world. -: Among the Arthavada or
Declamatory passages also , some are those same that are found in veda
, some are based on ordinary experiences and some are purely imaginary
, like ordinary poetry. But all these have an authority due to the
fact that they eulogise enjoined acts nad defecate forbidden ones .As
regards those passages those are not capable of those being taken
along with vedic injunctions or Prohibitions - some are such as given
pleasure in the mere reading ; to this class belong such descriptions
as those of Gandhamadana and other sites. - : while other descriptions
of wars and battles serve the purpose of encouraging the brave as well
as coward , and thereby serve distinctly purpose for the men of the
kings.

In those cases where non of these explanations are possible - e.g.
Hymns addressed to deities - we assume an unseen transcendental
result . Then again puranic description of parts of the earth serves
the purpose of distinguishing places fit for the due performance of
religious and other acts. The history of the families of the men
serves to differentiate the people of different castes and is based
upon the memory of the men and also on direct perceptions . The
details of measurement of time and space are intended to regulate the
ordinary practice of men. So also the science of Astronomy and
Astrology- all these are based upon direct perceptions and
mathematical calculations.

The description of the future state of the things serves to point out
the characters of the various periods of evolving time and also the
result of righteous and unrighteous conduct. These are directly based
on Veda