The crux of the Flat Earth Wiki's argument for the Sinking Ship Effect is vanishing points, is it not. The beginning of the argument is that humans cannot see to infinity, so there has to be a finite vanishing point. Mathematically, this cannot and does not make sense.
If the actual height of an object is d and the distance to it is x, the perceived height h(d,x)=d/x. It's that simple. (All values assumed to be non-zero)
At the vanishing point, wherever it is, h(d,x)=0. That's what it means by vanishing. Let's solve for a distance x where this happens. 0=d/x -> 0*x=d -> 0=some non-zero number. Hmm... That doesn't quite work with math. But what this shows, is that mathematically there cannot be a finite vanishing point.
So where is the vanishing point, then? At infinity. h(d,∞)=d/∞. But wait. We can't actually divide by infinity. Thankfully, calculus has a way for us to do this, called limits. lim(x+->∞)d/x=0. The mathematical law at work here is that if the degree of the denominator (1) is greater than that of the numerator (0), it approaches 0 at infinity. So this means that if an object could be seen from infinity, then and only then would its perceived height be 0.