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Bhartrhari's paradox is the title of a 1981 paper by Hans and Radhika Herzberger which drew attention to the discussion of self-referential paradoxes in the work Vākyapadīya attributed to Bhartṛhari, an Indian grammarian of the 5th century.
In the chapter dealing with logical and linguistic relations, the Sambandha-samuddeśa, Bhartrhari discusses several statements of a paradoxical nature, including sarvam mithyā bravīmi "everything I am saying is false" which belongs to the liar paradox family, as well as the paradox arising from the statement that something is unnameable or unsignifiable (in Sanskrit: avācya): this becomes nameable or signifiable precisely by calling it unnameable or unsignifiable.
Bhartrhari's interest lies not in strengthening this and other paradoxes by abstracting them from pragmatic context, but rather in exploring how a stubborn paradox may arise from unproblematic situations in daily communication.
An unproblematic situation of communication is turned into a paradox — we have either contradiction (virodha) or infinite regress (anavasthā) — when abstraction is made from the signification and its extension in time, by accepting a simultaneous, opposite function (apara vyāpāra) undoing the previous one.
For Bhartrhari it is important to analyse and solve the unsignifiability paradox because he holds that what cannot be signified may nevertheless be indicated (vyapadiśyate) and it may be understood (pratīyate) to exist.