Here the word “beyond” clearly means “further away than”.
This is not.
Well, it is. It's the way I'm using the word.
If you choose to misrepresent the guy's argument, his argument sure is going to souind silly; but do you think you'll have much luck convincing him of your views if you open your argument with such an obvious strawman?
I'm not deliberately misrepresenting his argument, I'm starting to think I don't understand it.
I've had a go at showing what I'm trying to say but I am pretty awful at drawing diagrams.
So you have a tall building on the right and two viewing points on the left. In the RE model the horizon is simply the edge of the earth. It's nothing to do with how far you can see although if the horizon is far enough away then that may become a factor and the horizon would not be a sharp line as it usually is at low altitudes.
So if you're at the viewing position on the right at a certain viewer height then the red line is drawn so it touches the earth - that's the horizon. Everything below that line beyond the horizon is occluded by the earth, hence the bottom of the building not being visible. Everything above that line is visible because you have clear line of sight to it.
If you're further away the the left viewing position and the same viewer height then the horizon will be the same distance from you - blue line - but because you're further away, and thus further round the globe, you can see less of the distant building.
The Turning Torso video demonstrates all this quite nicely. Obviously this is all massively out of scale, in real life you're only talking about 1 or 2 degrees in most cases round the earth so the leaning away of the building would not be noticeable.
If you're at the left viewing position but at a higher viewer height - green line - then the horizon is further away and you can see more of the building.
If the horizon was simply the "edge of nothing but our vision", then why would you see any of the building which is further away than the horizon? And this is where I fear I've not understood his argument. Maybe you or he could draw something to demonstrate.