In forcing, we take a collection of forcing conditions and impose a partial order on them. The convention is that if $p$ is stronger than $q$, then we say $p < q$. This is perfectly fine, but it seems intuitively backwards to me. If I were designing the notation for forcing, I would want the stronger condition to be larger. (Something I read says, I think, that Shelah uses the opposite convention that I find more intuitive. Is this so?)

Further, if we are forcing with a collection of partial functions (as we often do), we want the stronger condition to be the partial function with the larger domain. This leads us to a definition of the poset order whereby $f < g$ iff $f \supset g$. This seems notationally awkward.

Nonetheless, Cohen must have had some good reasons choosing the order that he did. What is/was the rational for Cohen's notational convention? Does it have benefits today, or is it just an artifact of a older approach to forcing?