With reference to what Magnus defined as volume, I agree that it is clearly absurd for A to have volume x and volume 2x at the same time. 2 is not equal to 2 times 2.
Having said that, there are two ways in which set (A = {1, 2, 3, A }) exists:
p) The set A encompasses items 1, 2, 3, and A. Much like how list A, lists the lists 1, 2, 3, and itself (A). I don’t think you disagree with this. But I think you disagree with the following:
q) The A in set (A = {A…1, 2, 3…A }) is such that A contains A, and A is contained by A. A… implies that no number begins before A, and …A implies that no number comes after A.
Take x as your starting point on a computer. If your starting point on a computer consists of folders …1, 2, 3…, and A, and you click A, you get …1, 2, 3…, and A. You click A again, the same thing happens again. This happens ad infinitum. Going back to x, if you try to come out of the folder that you are in (which is A), by going up a folder to the folder that encompasses the folder that you are in, you find yourself with …1, 2, 3…, and A. Go up another layer in an attempt to get the to the root folder, and you get the same thing again. This happens ad infinitum. A is that which is between any and every identified folder, number, or thing. A = infinity.
Given our previous discussions, you are strongly in opposition to q. Note that I am not saying A has volume x plus volume x + x + x…ad inifnitum. I am saying A’s volume is infinite. So it’s not a case of one thing having two different volumes at the same time. A is that which is between any and every identified item. You can either interpret set (A = {1, 2, 3, A }) as absurd by viewing A as being non-infinite, or you can interpret as non-absurd by viewing A as infinite.
set (A = {1, 2, 3, A }) is representative of how A is fully between items 1, 2, and 3.