Michael A. Sells, in his book, Mystical Languages of Unsaying, claims that apophasis, defined formally, can be applied to Eastern texts. He distinguishes between apophatic theory and apophatic discourse, and focuses on the latter in his study of five Western mystics. This paper is an attempt to confirm his claim; I identify places in Vedic period literature, mostly in the early Upaniṣads, where there are either movements of implicit or explicit apophatic theory as well as movements of apophatic discourse. I also attempt to situate apophasis in the context of the Vedic cultural understanding of speech and preoccupation with open space. Speech was understood to consist of four parts, three parts hidden, and one part manifest. The manifest speech of human beings was considered the lowest part of speech, and the Kapiṣṭhala Saṃhitā goes so far as to say that it is the untruthful part of speech. There is also a continual search for open space in Vedic culture that can be traced from the Ṛg Veda through the early Upaniṣads. During the Ṛgvedic period, open space was needed for a nomadic lifestyle built on animal husbandry and forceful expansion. The early Upaniṣads were composed during a time of increased urbanization, and while the value of open space was retained, it was reimagined in accordance with the changed environment. I suggest that apophasis, studied in conjunction with the Vedic understanding of space and speech, shows that it may have been one way for Vedic people to search for open space and open themselves up to, what they believed, was a more extensive, unlimited, and spacious language beyond the confines of the sounded word.