Why Do the Sun and Moon Get Bigger Near the Horizon?

Often when globe Earthers hear that the law of perspective is the reason that ships disappear beyond the horizon, as well as the reason that the Sun and Moon rise and set in the sky, their next question is why, then, do the Sun and Moon appear to get bigger near the horizon? Understandably, a long row of streetlamps appears to rise in height until reaching overhead and then sets on the horizon, similar to the Sun and Moon, but unlike the Sun and Moon, the lampposts, boats, and most other things claimed to disappear due to perspective also shrink in size as they recede from the observer. So why, if the Sun and Moon rise and set due to the law of perspective, do they also not appear to shrink as they approach the horizon?