Full Idea
We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering.
Gist of Idea
A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets
Source
William D. Hart (The Evolution of Logic [2010], 1)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.23