As is well known, a number of traditional philosophers and religious thinkers in both the East and the West claimed that the ultimate reality or the mystical experience intuiting the reality is ineffable well beyond the reach of human concepts and words. But, can we speak meaningfully of something that it is unspeakable ? Does not such a speech make the thing actually speakable ? On the other hand, it seems that most hearers or readers could follow this use of ineffability without taking it to be self-contradictory. The phrase 'the paradox of "unsayable"' is meant to refer to such a paradoxical situation. In this paper, I refer to a passage in Bhartrhari's magnum opus, the Vakyapadiya, to see how this fifth-century grammarian-philosopher of India resolved the paradox in question. Bhartrhari's strategy will afterward be enlarged and supplemented to deal with certain related issues.