arthāpatti is recognised as a separate instrument of knowledge (pramāṇa) almost only by Mīmāṃsakas. Śabara’s discussion of it is interesting, but short, so that Kumārila’s one is really the reference point for all future authors accepting or criticising arthāpatti as a pramāṇa.

The section on arthāpatti in Kumārila’s Ślokavārttika (henceforth ŚV) is shorter than the ones dedicated to language, but longer than the one dedicated to upamāna ‘analogy as an instrument of knowledge’ (which is not surprising, giving its residual role in both Nyāya and Mīmāṃsā) and to abhāva ‘absence as an instrument of knowledge’. The latter fact is perhaps more surprising and may attest to the importance of arthāpatti in the Bhāṭṭa Mīmāṃsā epistemology.

The basic definition, of great influence in the successive literature, is found already in the first verse (unlike in the case of śabda in the śabdapariccheda of the ŚV):

When a thing, which has been known through the six instruments of knowledge cannot be otherwise |

[and] it postulates something else, which cannot be experienced, that case is exemplified as [an instance of] arthāpatti || 1 ||

Śabara’s definition of arthāpatti, by contrast, read as follows:

There is also arthāpatti, which is the postulation of a[nother] thing, when a seen or heard thing is not logically possible

Thus, Kumārila agrees on the presence of a postulation-moment in arthāpatti and, like Śabara, does not (yet) clarify whether this postulation is performed by the cognising subject or occurs automatically. He uses na anyathā bhavet `cannot be otherwise’ as a gloss of na upapadyate `is not logically possible’. He neglects, in this first definition, the difference between śruta– and dṛṣṭārthāpatti, something which might have to do with the fact that some Mīmāṃsakas disagreed with it (the ones who were later known as Prābhākaras). Anyway, Kumārila comes to this distinction in the immediately following verse:

“Seen” [in the ŚBh, means experienced] by all five instruments of knowledge (apart from Linguistic Communication), [because] the [arthāpatti] arisen (udbhava) from the “heard” [in the ŚBh] has been said to be different from that |

Because this [śrutārthāpatti] is different from the previous one insofar as it [alone] includes the instrument of knowledge || 2 ||

Here the distinction goes one step beyond Śabara, insofar as Kumārila explains that in the case of śrutārthāpatti what is postulated is the sentence which leads to the valid piece of information, and not the latter alone.

Next, Kumārila further distinguishes subtypes of dṛṣṭa– and śrutārthapātti according to the pramāṇa upon which they are based. The verses follow the traditional sequence in the enumeration of pramāṇas (pratyakṣa, anumāna, śabda, upamāna, arthāpatti and abhāva).

Among the two, the [postulation] of the ability to burn of fire, based on [its] burning is due to a sense cognition, [whereas] in the case of the sun the [postulation] of its being connected with that ability (that of moving) is due to the motion, which is inferred (out of the fact that one always sees the sun in a different place, but never sees it moving) || 3 ||

The śrutārthapatti will be spoken of later |
When a cow is known as analogous to a gayal, the fact that this (cow) is cognisable is considered [an instance of arthāpatti based on an analogy] || 4 ||

The postulation of the fixity of [linguistic expressions] is due to the ability to communicate knowledge, which has been understood in the case of language because of arthāpatti, in order to establish the denotative power [of linguistic expressions] || 5 ||

In other words, through arthāpatti one understands that linguistic expressions, which communicate meanings, must have the corresponding power. And through a further arthāpatti one derives that in order to make sense of this power they must be fixed:

The denotation would not succesfully occur otherwise (i.e., if linguistic expressions did not have the power to convey meanings). Having understood that, again, with a new arthāpatti one ascertains that the linguistic expressions, which have the power to express are fixed || 6–7 ||

This will be said in the [commentary on] PMS 1.1.18 `because [linguistic expressions] are employed for the sake of others’ (i.e., to communicate with other people) |

The list is concluded by the mention of arthāpatti based on absence as an instrument of knowledge and by the promise of further details in the ŚV chapter on inference:

Here (in this chapter) we show the establishment of the fact that Caitra is out of the home specified by his absence, which is ascertained thorugh absence as an instrument of knowledge || 8 ||
This can exemplify another arthāpatti, arisen out of absence as an instrument of knowledge |
An elaboration of examples of other (arthāpattis) [can be found] in the [treatment of] flaws of the inferential locus || 9 ||

pramāṇaṣaṭkavijñāto yatrārtho nānyathā bhavet | adṛṣṭaṃ kalpayed anyaṃ sārthāpattir udāhṛtā || 1 || dṛṣṭaḥ pañcabhir api asmād bhedenoktā śrutodbhavā | pramāṇagrāhiṇītvena yasmāt pūrvavilakṣaṇā || 2 || tatra pratyakṣato jñānād dāhād dahanaśaktatā | vahner anumitāt sūrye yānāt tacchaktiyogyatā || śrutārthāpattir atraiva parastād abhidhāsyate | gavayopamitā yā gaus tajjnānagrāhyatā matā || 4 || abhidhānaprasiddhyartham arthāpattyāvabodhitāt | śabde bodhakasāmarthyāt tannityatvaprakalpanam || 5 || abhidhā nānyathā sidhyed iti vācakaśaktatām | arthāpattyāvagamyaivaṃ tadananyagateḥ punaḥ || 6 || arthāpattyantareṇaiva śabdanityatvaniścayaḥ | darśanasya parārthatvād ity asminn abhidhāsyate || 7 || pramāṇābhāvanirṇītacaitrābhāvaviśeṣitāt | gehāc caitrabahirbhāvasiddhir yā tv iha darśitā || 8 || tām abhāvotthitām anyām arthāpattim udāharet | pakṣadoṣeṣu cānyāsām udāharaṇavistaraḥ || 9 ||
This is only a preliminary translation and commentaries and suggestions are more than welcome!