The Linguistic Limitations of Sets I understand what your saying about the universal set and the idea of inside and outside was simply an example to illustrate a deeper point. I see the flaws you have pointed out in this example, but what I am trying to ask still remains.
I think my question comes back to the incompleteness theorem in a way and the notion that within any system there can be something that is true but unprovable.
My main point was if you get something that is all inclusive -whether all refers to the universal set or all refers to a specific subset that is just (I,O) - that word we use to define this
all will only be definable by its parts.
And, if that is the case, this singular notion of all - universal or a subset - it really refers to something that is not singular. It in a sense becomes a failure of our language because if I was asked to define life?
The correct answer would be to include everything that I've ever had be a part of my life, I am asked to do so within the confines of language and all my words would fail me because I could never describe the entire human experience using simply words to express it.
So, it becomes somewhat of a meaningless question because no answer will suffice because any answer would require the use of words.