Full Idea
It is set theory, and more specifically the theory of relations, that articulates order.
Gist of Idea
Set theory articulates the concept of order (through relations)
Source
William D. Hart (The Evolution of Logic [2010])
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.22
A Reaction
It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers.