Positional value and linguistic recursion (Q935694)

The author attempts to shed new light on the nature of Pāṇini's grammar by paying close attention to positional numerals and to the formation of positional number words (positional grammaticalization). In this light, Pāṇini's grammar is seen to be ``a formal system in oral form, intended to produce grammatically correct Sanskrit words and sentences along with their correct pronunciation,'' ``the first formal system, well before Gottlob Frege's late nineteenth century \textit{Begriffsschrift} for first-order predicate logic.'' In support of his thesis, the author presents two natural language fragments which are also formal arithmetic theories, the first one with addition as single primitive notion, inside which one can simulate the formation of non-positional number word patterns which resemble positional numbers, the second one with addition and multiplication as primitive notions, allowing the definition of number units, positions, powers, and other positional features not definable in the first theory.