ANOTEONTHENAVYA-NYAYAACCOUNTOFNUMBER
Old Nyaya viewed number as a kind of quality Cguna) which substances (and only substances) have. Like other qualities it inhered in its locus. Thus with regard to the relation between two-ness (dvitva) and two pots, the older Naiyayikas held that two-ness inhered in both the first and second pots, inherence being defined as a relation between one entity and several entities. This account leads to certain difficulties. Firstly, according to the Vaik+aszitra (I.1 .I 6) qualities can inhere only in substances. But if number is held to be a quality, then one cannot speak of the number of qualities a thing has. Qualities cannot themselves possess qualities. Secondly, it seems that on this view a particular substance can simultaneously be the locus of more than one number. Thus although two-ness inheres in each of the pots in the collection of two pots now before me, these two pots are also members of the collection of three pots bought this morning. Hence three-ness also inheres in the same two pots simultaneously with two-ness. In other words, a substance can apparently simultaneously admit of contradictory qualities (e.g. two-ness and three-ness).
The Navya-nyaya account of number seeks to avoid these difficulties. It distinguishes two sorts of two-ness. One of these is a generic character that inheres in each member of a pair. The other sort of two-ness is an imposed property (uprfdhi). It is related by a special relation called "~a~@pti" not to the members of pairs but to the pairs themselves. It is the property that guarantees that the loci of two-ness and three-ness are mutually exclusive. Parydppti, then, is the relation by which numbers reside in wholes rather than parts of wholes.
This theory has certain resemblances to the accounts of number offered by Frege and Russell, resemblances that have been remarked upon by several writers.' Thus Daniel Ingalls in his pioneering work Materials for the Study ofAGzu~~Ny&z Logic makes two claims in this regard. The first is that: This theory that numbers subsist by pury@G in effect points out what Frege first pointed out in the nineteenth century. The 'two-ness that inheres in each member of pairs' corresponds to the Western 'class of two members'. The 'two-ness that is related JournalofZndian Philosophy 13 (1985) 227-234. 0022-1791/85.10.