Within Mīmāṃsā, it is found already in Śabara (see, e.g., his commentary ad MS 2.1.1) as indicating the activity of a person, designated by the verbal forms and directed to an object. In fact, such an activity is further specified by its requiring an object, an instrument and a procedure (respectively answering the question “what [does one do]?”, “through what?” and “how?”). In accordance to such an interpretation, Śabara paraphrases svargakāmo yajeta as yāgena svargaṃ bhavati. That is, an object/aim (according to the polysemy of the Sanskrit term artha, noticeably within Mīmāṃsā, see MS 1.1.5 et passim) is connected to the bhāvanā, the root of the verb is read as an instrument (yāgena), and the verbal action is designated by the conjugated verbal form alone (bhavati). Later on, Kumārila noticed that such an account does not make sense of the prescriptive character of, say, yajeta as opposed to yajati. Therefore, he introduced a further bhāvanā, called śabdabhāvanā. This one is peculiar to prescriptive forms (that is, liṅ, loṭ, leṭ, tavya, but also present indicative forms may do, if the semantic of the passage requires a prescriptive meaning) and it accounts for their faculty to make whoever listens to them feel compelled to perform the action indicated by the verbal root. It has still nothing to do with the actual performance of such action, it operates purely on a linguistic niveau and therefore Kumārila has named it “linguistic bhāvanā”. At that point, he had to qualify also the other bhāvanā, the one meant by Śabara. In opposition to śabdabhāvanā (or śābdībhāvanā), he called it arthabhāvanā (or ārthībhāvanā), that is “actual bhāvanā”, “objective bhāvanā”, or “purpose[-oriented] bhāvanā”. So, this latter designation is less precise than the first one and is mainly devised in opposition to the former. In fact, “bhāvanā” alone is commonly used to indicate the ārthībhāvanā.More in detail, the PP in §3.16 seem to reinterpret ārthībhāvanā as puruṣārthabhāvanā, so “bhāvanā having a human end [as its bhāvya]”, “purpose-[oriented] bhāvanā”. But is this a reinterpretation or the initial meaning of arthabhāvanā? It would rather seem an innovation of R., who drives from a parallel VN passage, but emphasises the etymological understanding of arthabhāvanā (whereas the VN passage speaks of arthabhāvanā as puruṣārthasādhana). In fact, the innovation of Kumārila, who distinguished between śabda- and arthabhāvanā seems to presupose the opposition between śabda (as language) and artha (as its object). Nonetheless, I could not find a precise explanation of arthabhāvanā as meaning “the efficient force directed on an external object” or the like. Mīmāṃsābālaprakāśa, a late Bhāṭṭa primer, explains: arthayata ity arthaḥ phalakāmaḥ puruṣaḥ (MBP, II adhyāya; 74.15-16, quoted in Kataoka 2004:167, fn. 190), and Kei Kataoka also suggests (personal communication, 1 October 2008) that “Kumārila probably has in mind puruṣa as artha”. This means that when Rāmānujācārya explains arthabhāvanā as puruṣaprayatnas, tatpravṛttir (§3), bhāvanā is tantamount to prayatna or pravṛtti and arthabhāvanā means arthasya, puruṣasya, prayatna. The equation artha-puruṣa can be justified as follows:
1. MBP's statement, and Bhatta Śaṅkara's explanation that, when interpreting artha as person, the meaning “person” should be derived from the understanding of artha from the root arth-, X class, “to desire” (hence, “a person who desires” is an artha, since “a” is, among other meanings, a kṛt suffix indicating the agent, according to the list in Ā III and to Kāśikā on Ā III 4.67) and not from the root arth-, IV class, “to be an object” (arthyate). By the way, the latter seems to be an artificially conceived root, not attested in the Amarakośa, nor in the Śabdakalpadruma, nor in the Dhātupāṭha, nor in modern dictionaries such as PW and Monier William's.
2. The symmetry between śabdabhāvanā and arthabhāvanā. It is in fact hardly the case that Kumārila devised the two names without linking them to each other. Pārthasārathi Miśra proposes two interpretations of the compound śabdabhāvanā, as a karmadhāraya and as a tatpuruṣa respectively. If it is a karmadhāraya, however, it is hard to conceive a symmetric understanding of arthabhāvanā, which should mean “that efficient force which consists in an object/a purpose”. On the other hans, if śabdabhāvanā is tantamount to “an efficient force (bhāvanā) which has a statement as its locus of action” (as with Pārthasārathi Miśra's explanation of śabdabhāvanā as a tatpuruṣa, see below), arthabhāvanā would mean “an efficient force which has an artha as its locus of action”. Artha in this connection cannot be the final object brought about by the activity, but only the locus where this activity finds place, that is, a person.
3. The fact that arthabhāvanā and śabdabhāvanā are also called by Kumārila arthātmikā bhāvanā and śabdātmikā bhāvanā and those explanations need to be made sense of in a symmetric way.
On the other hand, the understanding of śabdabhāvanā is made easier by Pārthasārathimiśra's etymological explanation, see Kataoka 2004: 167-8, fn. 190: “ahidhāyāḩ śabdasya bhāvanā abhidhābhāvanā (NRM VN, 77.1) and “abhidhīyata iti abhidhā pravartanā”. Hence, śabdabhāvanā could be explained as a karmadhāraya or as a tatpuruṣa.