Semantic and formal analysis of language in Pāṇini

One of Pāṇini's distinctive traits in his approach to linguistics seems to have been the distinction between the semantic and the formal descriptions. For instance, Pāṇini describes the kārakas 'semantic functions' and only later has them being expressed by a certain vibhakti 'ending'. The first ones are named after the semantic roles they express (e.g., apādāna 'taking away'), whereas the latter are identified only through a number, so that no one is inclined to think that they have in themselves any semantic meaning. By contrast, Greek and Latin grammarians conflated the two, so that the endings themselves are identified with semantic labels, often misleading ones, such as "accusative".

I recently read that Bhaṭṭoji Dīkṣita maintained that the numeric labels for vibhaktis have not been invented by Pāṇini, but by his predecessors:

The names of the seven vibhaktis, viz., prathamā, dvitiyā, tṛtiyā, caturthī, pañcamī, ṣaṣṭhī and saptamī, however, are not defined by Pāṇini; they are borrowed, as Bhaṭṭoji Dīkṣita says, from the predecessors in the field.
(M.D. Pandit, svatantraḥ kartā, in V.N. Jhā (ed.), Vidyāvratin, Delhi 1992, p. 133)

The relevant passage by Bhaṭṭoji reads:

tatra su as jas ityādīnām saptānām trikāṇām prathamādayaḥ saptamyantāḥ prācām saṃjñās tābhir ihāpi vyavahāraḥ.

In this regard, the seven triplets of case-endings had the names 'first' through 'seventh' by the ancient [grammarians]. They are called like that here [i.e., in Pāṇini's grammar] as well. (BD on A 1.4.104, text from Pandit, my translation)

If Bhaṭṭoji is right, then probably someone else before Pāṇini was already paving the way towards a non-semantic concept of the case-endings.

On the relics of different partitions of the semantic-formal reality of language in the Aṣṭādhyāyī, see Artemij Keidan's "The kāraka-vibhakti device as a heuristic tool for the compositional history of Pāṇini's Aṣṭādhyāyī" (Rivista di Studi Orientali 2011).