Kauṭilya (or Kauṭalya) speaks of four kinds of vidyā: Ānvīkṣikī, Trayī, Vārtā and Daṇḍanīti. Trayī refers to the three Vedas (Rk, Sāman, and Yajuḥ), i.e., theology; Vārtā means agriculture, animal husbandry, and commerce, i.e., economics; and Daṇḍanīti stands for the management of the state, i.e., politics. What is Ānvīkṣikī?

Kauṭilya himself explains that Ānvīkṣikī comprises three studies: Sāṃkhya, Yoga and Lokāyata. Since he mentions the first two separately, it has been assumed that he refers to the earlier Sāṃkhya (not the syncretic Sāṃkhya-Yoga); the Yoga is obviously Patañjali's Yogasūtra, and the Lokāyata must be the materialist philosophy of the Cārvāka-s.

Shamasastry in his English translation of the KA was not so sure about the identification of Lokāyata. He wrote within parentheses: ‘Atheism?’ The two earliercommentaries, Jayamaṅgalā and Nītinirnīti, however, clearly identify Lokāyata with Nāstika philosophy expounded by Bṛhaspati.

The only discordant note is heard in the Malayalam commentary (c. twelfth century). It explains Lokāyata as the Nyāyaśāstra taught by Brahman, Gārgya et al. MM. T. Ganapati Sastri preferred to follow this gloss in his new Sanskrit commentary. MM. Phaṇibhūṣaṇa Tarkavāgīśa was also of the opinion that in ancient times the Nyāyaśāstra was called Lokāyata.

So we have one problem here: What did Kauṭilya mean by Lokāyata—materialist philosophy or logic?

The word, Ānvīkṣikī, too is open to various interpretations. Some have taken it to mean an esoteric doctrine (ātmavidyā), some others, logic (tarkavidyā).