  The Navya-Nyāya account of number has been likened in content and sophistication to that of Frege, and is indeed fascinating. The Manual of Reason says only that numbers are qualities (guṇa-s), that they are the ground for numerical judgements, and that they range from 1 to a very high number called parārdha (1014. Note here again discomfort with the idea of infinity). The view that numbers are qualities is in fact associated with old Vaiśeṣika, and turned out to be irreconcilable with the structure of the Vaiśeṣika ontological system. We may speak of there being three horses in the field, but also of there being 24 qualities in the Vaiśeṣika system. Yet a quality cannot by definition reside in another quality—hence numbers cannot be qualities. This problem led the Navya-Naiyāyikas to develop a new account of numbers, based on a new type of relation called the paryāpti or ‘completing’ relation.