________________
Bhart hari's paradox
291
can be supported by some arguments of rather considerable strength and generality. We will present these arguments informally at first, making use of commonsense notions. Then they will be related to modern ideas from the theory of sets, with the aim of making the arguments more rigorous. No historical claims should be read into the discussion of this section. Its purpose is to examine Bhartshari's paradox as a living problem, and in the process to make an effort to crystallize from it the sharpest possible formulation.
The proposition that the significance relation is uonameable can most easily and directly be derived from a still more general proposition :
Ri. The significance relation is unsignifiable. What this means in the context of the present paper is that there is no expression, of any grammatical category, which bears the significance relation to the significance relation, Equivalently : the vācya-vācaka relation has no vācaka, and is not itself a vācya. Once unsignifiability of the relation has been established, its unnameability will follow as a special case.
We will now sketch a proof for B4 from the still more general proposition that no relation can be one of its own relata. If this holds for all relations, it holds for the significance relation as a special case (RI); and from that special case, Bl would follow as a still more special case.
To build up some intuition concerning the problem, consider the naming relation, wbich obtains between names and their bearers : between the name 'Krsna' and the ful blue god, between the name 'Gaurišarkara' and the highest mountain on earth, and so forth. It takes its place as one relation among others: the parent-child relation among humans, the dominance relation within a herd of elepbants, the natural ordering relation of the positive integers. In general there is no semantic problem about naming various relations : we fix the relation in our mind and then discover or invent some name for it. However a specific problem does
Jain Education International
For Private & Personal Use Only
www.jainelibrary.org
