Statement 1:
The fact that perspective lines converge is evidenced right there in reality.
Statement 2:
The horizon line isn't an "infinite distance away"...
There's the crux of the matter: where certain lines of perspective appear to converge is the cause of a horizon line on a flat earth. Has to be.
The reason why this is even an issue for you is that you need an explanation for a horizon line at a definite distance (H) on a flat surface; and given that the explanation for that horizon line is Perspective, it must be able to give a non-zero solution for H. It can't be ∞.
But if not ∞, then what is it? It should be calculable. Rowbotham never said, but from his explanation of Perspective and where H lies, I deduced that finite value to be height of eye level times the tangent of 1 arcminute. I can't remember if you agreed or ever even commented. I've never seen you give a finite solution for H. You only declare it's not infinite. That's funny, because we alleged ancient Greek dependents don't believe H is infinite either, but we do give finite values for distance to H without reliance on those ancient Greeks notions of infinite vanishing points.
So let's be clear and not conflate terms to confuse the issue.
The issue isn't whether or not "Greek Infinite Theory" is true or not. I don't need it to be true for a horizon to have a definite, non-infinite distance on a convex surface. Perspective is not the reason for the horizon on a convex surface.
The issue is what causes the appearance of a horizon, and how far away is it on a flat plane? If Perspective is the reason (or part of the reason) for a horizon line on a flat surface, then its YOU who needs for Perspective to solve the distance to the horizon question. Therefore, it's YOU who cannot tolerate the "Greek Infinite Theory." I can tolerate either it's truth or fallacy because my calculation of distance to the horizon doesn't depend on it. Yours does, and it can't be ∞.
It's not up to me or anyone else to have to prove that lines of perspective converge at an infinite distance (although the video by ICanScienceThat does a good job of that) because our explanation for the horizon line doesn't depend on it. What needs to be proved is that horizon line is caused by Perspective.
So prove this.
Show us that the values for H match what we can observe. They're not matching with observation for me. The RE calculation (that don't rely on vanishing points being at an infinite distance) match reality.
You can start with "horizon always is at eye level", since it's a fundamental principle for H being at a finite distance in Perspective Theory.
... and train tracks don't appear to merge at an infinite distance away. The reality of finite perspective is on our side.
This is sleight of hand logic you use to shift the focus and the burden of proof. If H (a finite point) is due to Finite Perspective, prove it. Calculate the finite distance at which train tracks converge and then measure it to see if it's correct. Calculate the finite distance to the horizon and then measure it to see if it's correct.
You don't get to declare it's correct by default until someone can prove that the ancient Greeks were correct. We don't need Greek Perspective truth to refute you. That's a bogus issue you've raised to insulate yourself from bearing the burden of proof yourself.
If H is finite, show me. I agree it's finite, but that's because I don't agree an infinite VP has anything to do with H. You need lines of convergence to coincide with H. I don't. You need ancient Greeks to be wrong. I don't. You say Perspective gives H a finite value. Fine. Prove it. Calculate a finite value for H using Perspective. Don't deflect by demanding that skeptics disprove the ancient Greeks. That doesn't protect you from having to defend yours (and Rowbotham's) Perspective explanation for finite H.
There is no evidence whatsoever for this infinity nonsense. None. You need to speculate that it exists, whereas we can see that the lines converge.
There is no evidence whatsoever for Perspective being the reason for a horizon line and why ships disappear behind it hull first or why the sun sets behind it bottom first.
There's no evidence whatsoever that the horizon line is always at eye level.
There's no evidence whatsoever for Perspective being the magic, ad hoc solution for any discrepancy between what is observed and what would be predicted to be observed on a flat surface.
If you want to claim Perspective gives finite distances for vanishing points, and that a point on the horizon line is one such finite distance, the calculate it. Predict it and then show that the calculated prediction is true. Don't hide behind ancient Greeks and offer vague, indefinite claims and demand it be disproved vice having to bear the burden of proving it. Show that Perspective works to produce a value for H that can be checked for accuracy. We do it all the time in RE, and never have to rely on lines of perspective converging at infinity.