(Not very familiar with math.)

The Heyting-algebraic definition of implication makes intuitive sense to me, or at least after you state your confusion. ‘One circle lies inside the other’ is like saying A is a subset of B, which is a statement that describes a relation between two sets, and not a statement that describes a set, so we shouldn’t expect that that mental image would correspond to a set. Furthermore, the definition of implication you’ve given is very similar to the material implication rule; that we may substitute ‘P implies Q’ with ‘not-P or Q’.

Also, I have personally been enjoying your recent posts with few prerequisites. (Seems to be a thing.)

Will there be LaTeX support?