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Studies in Indian Philosophy
Regularity Theorem : No relation can be one of its own relata. The label attached to this theorem underscores its reference to some "regular" theory of sets, that is some theory incorporating the axiom of regularity or an equivalent principle.19
Without committing ourselves to any special assumptions regarding the nature of language or the naming process, but only to some more fundamental assumptions concerning the nature of sets, a substantial case can now be built up to support the upnameability thesis. In the first place, RI is an immediate corollary to the regularity theorem, quite indepen. dently of any questions about the exact interpretation or English translation of 'vācya-vācaka', so long as it is treated as a relation baving some regular set for its extension. In the second place, Bl is a consequence of Rl assuming only that whatever can be named can be signified.
Having approached the unnameability thesis now from more general considerations, it is possible to reinforce our paradox by establishing a whole family of variations on Bi. As an introduction to these variations, let us reflect briefly on one natural response to the paradox. Up to this point we have used the term "name" in an unusually extended sense, to include proper names, definite descriptions, and even demonstratives. In accordance with this broad usage, one could hardly deny that Bl contains a name (the phrase "the significance relation') for that very thing which Bl declares to be unpameable. Now someone might suggest that what drives one into the paradox is just this policy of using the term "pame” in an extended sense.
Consider the alternative policy of restricting the term " name” to proper nouns like 'Kệsna' or 'Gaurišarkara ', One way of implementing this policy might be to use the term “ denote" for the more extended concept, so that definite descriptions and demonstratives would be said to denote but not to name that which they signify. Now, taking a
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