If the Purva Mimamsa school believes that the Earth and humans are eternal, then how does it explain ancestral Gotras, such descendants of Bharadwaj, Angirasa, etc?
That is a good question, one that I've pondered before. There's a section of the Purva Mimamsa Sutras devoted to showing that Rishis are not eligible to do Yagnas. The argument given is that you're only eligible to do Yagnas if you can name 3 Gotra Pravaras, i.e. three Rishis who came earlier than you in your Gotra. But if you're a Rishi who's the founder of a Gotra, then you cannot name any Rishis who came earlier than you in your Gotra. Now I think that reasoning is fallacious (many scriptures describe Rishis doing Yagnas), but regardless it shows that they did believe Gotras have a founder.– Keshav Srinivasan ♦Nov 23, 2017 at 17:45
1Now I'm not sure how they reconciled that with their belief that humans have lived forever on the Earth without interruption. Perhaps they believed all the Rishis who founded Gotras were themselves descended from Gotras founded by even older Rishis, who were descended from even older Gotras, going infinitely far back in time.– Keshav Srinivasan ♦Nov 23, 2017 at 17:55
@KeshavSrinivasan If Rishis also had Gotras, then that would contradict their claim in the Purva Mimamsa sutras that Rishis cannot do Yajnas.– IkshvakuNov 23, 2017 at 18:25
1Each Gotra should has its own set of Pravaras; see here: familypedia.wikia.com/wiki/Pravaras (Some Gotras have multiple sets of Pravaras for different branches of the family.) I'm not sure what the reason is for the number 3. You may want to post a separate question on that. But here's a section of the Purva Mimamsa Sutras (separate from the section about eligibility of Rishis) that discusses people without 3 Pravaras being ineligible to do Yagnas: tinyurl.com/ycqtz2xg– Keshav Srinivasan ♦Nov 23, 2017 at 20:09
1Yeah, the rules are oddly specific: "He should name one Rishi, he should name two Rishis, he should name three Rishis, he should not name four Rishis, he should not name more than five Rishis." I'm not sure what the reason for this is. Every Gotra has either 3 or 5 Pravaras anyway, although that may be an effect of this Vedic injunction. In any case, I'm not sure who the Purva Mimamsa Sutras is trying to exclude when it talks about "the man who is unable to name three Gotra-rishis". Maybe people who don't know their Gotra.– Keshav Srinivasan ♦Nov 23, 2017 at 23:17
The Purva Mimamsa school seems to have had varied views regarding the nature of Gotras. In this excerpt from his commentary on the Purva Mimamsa Sutras, the Purva Mimamsa philosopher Shabara Swami apparently recognizes the notion that Gotra indicates the Rishi from whom you’re descended:
Nor are sages entitled to perform of sacrifices, because they have no Gotra; Bhrigu and other sages cannot belong to the Gotra of the same Bhrigu and others.
The idea is that your Gotra Rishi has to be your ancestor, and a Rishi isn’t the ancestor of himself, so Rishis who are founders of Gotras do not themselves have Gotras and thus are not eligible to perform Yagnas.
But the Purva Mimamsa philosopher Medhatithi gives a different view of Gotras, in this section of his Manubhashya. He says that Gotras are beginningless divisions of Brahmanas:
It is by [names like Bhṛgu’, ‘Garga’ and ‘Gālaya.] that the gotras of Brāhmaṇas should be known; as these are the principal gotras; the name ‘gotra’ applying to them by convention, and not by virtue of their fulfilling the condition mentioned in the above-mentioned definition that ‘the first progenitor, imparting his name to the family, is its gotra;’ in fact, ‘Bhṛgu,’ &c., have been known as ‘gotra’ from beginningless time, and their use in this sense is as much without beginning as the use of the caste-names, ‘Brāhmaṇa,’ and the rest. Prior to Parāśara’s birth, no Brāhmaṇas could have been named after him; hence, if the ‘gotra’ consisted in the first progenitor, &c., then the Veda (which makes mention of Parāśara as gotra) would have a beginning in time. Thus, then, since the use of the name ‘gotra’ is beginningless, it is this ‘gotra’ that is to be used in the pouring of water-libations. The persons imparting their names to families are not beginningless; they are modern; and at a Vedic rite, so long as one can make use of eternal names, there can be no justification for pronouncing names that have had a beginning in time. For these reasons, what the Brāhmaṇa should do when offering the libation of water, &c„ is to pronounce the appropriate ‘gotra- name’—such as ‘may this offering go to the Gargya,’ or ‘to one belonging to the Garga-gotra’—and then pronounce the name of the person. Among the Kṣatriya and the other castes, however, there is no such usage regarding gotra. These latter do not retain the memory of their ‘gotra’ in the same manner as the Brāhmaṇas do. Hence, for them, the ‘gotra’ must be something pertaining to this world; and it is for these that the ‘gotra’ consists of the ‘first progenitor, the most renowned, who imparts his name to the family:’ hence it is that they are referred to in Śrāddha, etc., by this gotra-name, even though it is one that has had a beginning in time. These, Kṣatriya, etc., are not worthy of being called by such titles as ‘Havirbhuk,’ and the like.
This is a species of the more general Purva Mimamsa argument that Vedas cannot contain the names of people or events in the past, because that would contradict their eternality. The Vedanta school’s refutation of this argument is that names and events recur in every age, because the Vedas are like the blueprint for the creation of the Universe. In any case, Medhatithi’s position is that given the Purva Mimamsa view that the Earth is eternal and humans are eternal on the Earth, your ancestors have eternally been the same Gotra as you going infinitely back in time.