Keywords
Existence , ontology , epistemology , number , absolute , fallible , infallible , humanist/maverick , nominalist , fictionalist , priori , Ganita / Ganana (mathematics / counting
Abstract
Number is the basic and fundamental concept of mathematics which has undergone expansion and generalization over many centuries. Number is so common in mathematics that for many peoples it is synonym of mathematics. According to History of Hindu Mathematics (Datta and Sing, 1935), mathematics is the science of number and counting. Most probably, the most common feature of number lies in its use in counting and its important contribution to mathematics lies in its use in measurements. Numbers, operations on numbers and their functions have occupied important role in mathematics. Most probably, the importance of mathematics lies on such things for most peoples. But, here in this article, attention is not focused along such line of thinking, but rather on the very nature and existence of number itself. Traditionally, ontology is the aspect of philosophy that specially deals with the existence of mathematical object like number. Recently, the ontological aspect of philosophy of mathematics has been extended to cover origin and relationship with the language of mathematics in addition to the traditional issue of Platonism. So, the main questions to be addressed along such line of thinking are being: " What are numbers and Where are numbers? ". As mentioned by Alfred Renyi in Socratic Dialogue in Mathematics, the article deals about numbers rather than number itself as mathematicians generally do. For that purpose, the questions have been examined in the light of Platonic thinking, absolutists' philosophy of mathematics, social constructivist philosophy of mathematics (Ernest, 1991, 1998) including humanist/mavericks position (Hersh 1999), and ultimately with respect to Nietzsche-Foucault position. An attempt is made to deal about the existence of number in the respect of different philosophical positions developed through long historical development.
