Prospective, Retrospective, and Formal Division:

a contribution to philosophical arithmetic

Abstract

Division by zero is a controversial theme. Why is division by zero a relevant issue and how can this issue be  addressed from different perspectives? Fracterm is used as an abbreviation for fractional expression. Three types of occurrence of the division symbol in a fracterm are distinguished: prospective occurrence, retrospective occurrence, and formal occurrence. Mathematics mostly features retrospective occurrences of division, computer programming gives rise to prospective occurrences, and so does automated proof checking. The use of division in an axiom system may indicate the presence of formal occurrences of division symbols.