Agent Smith         
         ↪baker The key difference is that a hinge proposition is not to be doubted.
An assumption might be subjected to subsequent rejection, as in a reductio argument. An axiom is taken as self-evident.
That the bishop stays on the same colour is neither subject to refutation nor self-evident, but it is a hinge for the purposes of playing chess.
A small distinction, but worth noting — Banno
Hermeticus         
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