Śākaṭāyana is a Sanskrit grammarian of the late Vedic period (Iron Age India, fl. roughly 8th or 7th c. BCE). His work is referred by scholars such as Yaska (around 5th or 6th c. BCE) and Pāṇini (fl. 4th c. BCE), as well as other Sanskrit grammarians, but is lost to us today.
In his The word and the world, the philosopher Bimal Krishna Matilal refers to this debate (which lasted several centuries) as an
interesting philosophical discussion between the nairuktas or etymologists and the pāṇinīyas or grammarians. According to the etymologists, all nouns (substantives) are derived from some verbal root or the other. Yāska in his Nirukta refers to this view (in fact defends it) and ascribes it to an earlier scholar Śākaṭāyana. This would require that all words are to be analysable into atomic elements, 'roots' or 'bases' and 'affixes' or 'inflections' — better known in Sanskrit as dhātu and pratyaya [...] Yāska reported the view of Gārgya who opposed Śākaṭāyana (both preceded Pāṇini who mentions them by name) and held that not all substantival words or nouns (nāma) were to be derived from roots, for certain nominal stems were 'atomic'. (p. 8-9)
His text may have been called the Lakṣaṇa Śāstra, in which he also describes the process of determining grammatical gender in animate and inanimate creation.