This axiom is normally taken for granted, as if it had no significance.
However, it is profitable to speculate about what the world of sets might
look like if it were false. It turns out that the pairing axiom assumes
that the world of sets is one-sorted. Dropping it gives one a novel
approach to typed set theory, and we explore this approach in this talk.
This is a tentative speculative talk (work-in-progress) and it is aimed at
a general Pure audience, not specifically at set theorists.