The Linguistic Limitations of Sets

If I say there exists an inside (i);

I am also saying there exists and outside (o).

I could then come up with a third category - a boarder one:

The set that contains o and i.

The definition of inside is: "the inner side of a thing."
So, let us presume that the broader category including i and o is called t (things).

But, we have produced a useless statement - a trap!

Because, the definition of a thing is "an object that one need not, cannot, or does not wish to give a specific name to."

The problem is we just gave this overarching class a name: thing; which is nonspecific..
But, I wanted to be specific with my naming, I wanted the name to only include inside and outside.

I wanted the entire set to only be comprised of (i,o).

But, what I am neglecting, is the fact the () carries some significance to it.

I don't have to define it as a 'thing' because the moment I put () around i,o...it becomes a singular entity.
What I am highlighting is a predicated relationship:

An outside is defined as "the external side of something," while an inside is: "the inner side of a thing."
The common factor being a 'thing'.

My point being is this:

The definition of inside is predicated by an outside and and vice versa;

Furthermore, they also share the existence of a 'thing'.

But, this 'thing' must be nonspecific, but my use runs contrary to its definition;

I want the set to only include inside and outside.

So,

these become my questions:

what would be the above (overarching) class of a inside/outside?

Even if the overarching set could be categorized by a word, would it not be a tautology?

If anything ever takes upon the existence of all, can 'all' not only be defined by the parts that make up all?