What the numbers mean? A matter of context!

Abstract

In formal languages, it is generally assumed that the symbols having the form of numbers just denote the usual mathematical numbers. In this paper, we argue that a numeric symbol is a symbol as any other and therefore may have different meanings in different contexts. Enumerating various kind of contexts in which the numeric symbols can make sense and which one, we come up with a generalized framework in which relationships between contexts, unit conversion and geometric transformations are treated in a uniform way. It also reveals the epistemological richness of what the numbers conceptually capture. Finally, this framework raises the question of contexts as types.