The question I ask is very simple. You say, "we know that due to 3-dimensionality of space ...". And I ask, "just *exactly* how do you know that space is 3-dimensional"? The only answer I have heard from you is that you just know it! For me, that is not sufficient.
There is an abstract problem here Alex. Somehow, you have processed some information and concluded that space is 3-dimensional (or 4-dimensional if you want to include Einstein's *theory* of relativity).
1. Exactly what information did you process to come to this conclusion?
2. Did you do this as an explicit conscious procedure? If so, can you tell me exactly how you did it?
The only answers which seem reasonable to me are as follows:
To question number 1: Exactly what information? I do not know. (Ah, it is an unknown!) Somehow I learned through my senses! But, what are my senses? I do not know that for sure either. (Ah, another unknown!)
But that means that, somehow, I have processed some unknown information (totally undefined) by some unknown procedure (totally undefined) and arrived at a valid model (a 3-dimensional space) of the original source of the information (reality).
Now any rational scientist will admit that the problem, as sketched out there, cannot be done! So I could not have done it! So the answer to question number two is clearly "I have no idea how I came to posses that solution".
The problem is that it has been done! The idea "a 3-dimensional space" appears to be an excellent solution (to a problem which is not at all well defined)! All this implies that, contrary to the standard position of a rational scientist, the problem is solvable.
So I looked at it and I found a solution! Maybe not the correct solution. Maybe not the same one I had before I solved the problem. Maybe not the same solution you have in your head, but a workable solution none the less. And I know exactly every detail of how I arrived at that solution! That means that my analytical procedure can be examined by others. I wish someone who has sufficient education to follow the math would examine it.
Actually, I don't believe this is a philosophical problem at all. It is a very specific mathematical problem. I think that to ignore this issue is a problem in the philosophy of science.
Thank you -- Dick