Does anybody really support mind-independent reality? I’m not sure that Apustimelogist doesn’t understand transcendental idealism. But rather he’s continually testing it from a positivist standpoint. But I don’t think that gap can necessarily be bridged. Because the positivist says I can measure, test, observe, recognise, describe etc the world we are in and if there is anything else to it, show it to me so I can measure it? If you can’t, then why should I accept that it is there at all?
Also that I have all the understanding etc that I need to do my thinking already in the world I am experiencing already. So all this philosophising about the logic of considering idealism is just a thought experiment, a tongue twister, nothing more.
So I don’t think this is an exercise in getting someone to understand the other’s point of view, necessarily. They may well understand it well enough already, but rather an exercise in explaining away the gap which needs bridging between the two opposing views. To build so many bridges that the gap is imperceptible any more, or that the gap is nothing more than a wrinkle in a whole and that there isn’t really a gap.
I like thought experiments and your mountain experiment works well for me. Another way of seeing it is from the standpoint of life as a whole, rather than the mountain, as one unit, all life as one being.
So all life is one entity, or being and in the world we find ourselves in, this being is budded, or cloned into millions of parts, or sub-beings. Which we see as all the living organisms on the planet. Each sub-being experiences the world differently depending on which part, or portion of the being they are. So an ant, experiences the world differently to a bat for example.
Now this being might be the origin of both those sub-beings and all that they experience, indeed the world might be a facet of that being which is experienced as a physical world of experiences through a process of becoming. A process of becoming a mind, which then experiences the world that it is budded into.
The world these sub-beings experience isn’t an externally existing world of physical objects, external to the greater being, but a product, or projection of that being, experienced differently by the different classes of sub-being. Mind and the world mind experiences, may be two sides of the one coin of being a being and all part of the one being. Time and extension(space and material), are produced from and by the being.
This thought experiment opens a bridge to understand how the physical world may be a “projection” of mind, and not external, while appearing to be.