Normal can be used to express natural.

Usual, normal and typical are truer synonyms.

I am curious why you say 'supernatural' rather than 'unnatural'?

In terms of flexibility, I would say 'natural' has a different set of polysemic uses to the other three cases. That there is overlap is likely due to how metaphorical usage slowly alters into literal usage overtime.

In terms of basic sturtural use 'usual' is perhaps closer to 'natural' as they both use the same prefix in 'un-' whereas the other two have more unusual (or less 'natural') structures. it does sound out of place to say 'natural' here because creativity in linguistics allows for a greater sense of flexibility in how words can be repurposed.

I would say it is abnormal for humans to have more or less than two legs, and I would say that it is unnatural for humans to have more or less than two legs.

In short:

I don't think normal is equivalent to natural (which resorts to central tendancy). — Copernicus

It can be. Just like an apple is equivalent to a banana if we are using them as examples of fruit, natural and normal are equivalent if using them as examples of commonalities only, not specifically. Reminds me of how 'little' is used more by children and 'small' more by adults--certain cultural 'norms' of use, or 'natural' uses, dictate how we receive what is being said.

I see your usage of organically/naturally, ie without external intervention. Meaning "if left to their own devices". Though the more common lay usage would mean without human intervention, ie you would have to also be removed from the equation.

Though the more common lay usage would mean without human intervention — LuckyR

And who is it, and by what means of measure, is a usage defined as "common" or "lay usage"?

Do you not see the problem? — Banno

I fail to see the solution even more.

The norm is a point of semantic balance between extremes

Why do you wish to create your own language? What purpose is this meant to serve?

Can you fully define any word, outside of mathematics? One can stipulate a definition, but it remains a definition. What a word covers is remarkably complex and is subject to expansion and change through time. I suppose the best we can do in ordinary conversation is to articulate our intuitions.

Normal, as I see it, is something like within the range of expected results or behavior. Normal often implies consistency, routine, expectedness.

But then we soon hit walls. For someone with remarkable athletic skills, say Michael Joran, a normal day playing basketball is scoring 20 (I don't know) points. That is not the average for a non-professional.

And we can expand this in all kinds of ways.

But I don't think we can provide a comprehensive definition of "normal". It's somewhat as Wittgenstein said, the meaning of a word is how we use it in language.

I fail to see the solution even more. — Copernicus

That;s what happens when you ask questions without answers.

It's normal to be abnormal.

That doesn't make sense.

That;s what happens when you ask questions without answers. — Banno

I didn't know questions were asked after the answers were found.

Not my own language, but proper understanding. Needless to say, semantics need revisiting because the language experts seemed to lack philosophical depth.

I do not understand what the problem is. Words have different uses. It is not mathematics.

Nature is synonymous with Normal, but not always. Why is this such a problem for you? Do you have the same issue with Usual and Typical?

Words are words. They are not reality.

But here I'll repeat the quote:

4. Misuses and temptations

Austin would highlight several philosophical temptations:

[1] Reification — Treating “the normal” as a property things have, rather than a judgement relative to a practice.
[2]Illicit normativity — Smuggling ought into is under cover of medical or statistical language.
[3]False objectivity — Speaking as though “normal” names a natural kind rather than a shifting standard.
[4]Category drift — Moving from “statistically normal” to “functionally proper” to “morally acceptable” without noticing the slide.
— Banno

And note that these are ubiquitous in the responses so far. The discussion of "normal" hasn't yet begun. — Banno

Are any of these concerns peculiar to the word "normal," or are we using "normal" here just as an exemplar term to show the limitations of language generally and how error might creep in?

Would the word "book" or "run" work equally well here. What I would say about the term "normal" that makes it useful for the analysis is perhaps all of its obscured connotations that reveal when usage is analyzed. That is, when we say something is normal (following my numbers above), ) (1) we might be pointing at something concrete with in its nature (that is a normal apple in that it is red, round, etc.), or (2) it might be referencing statistical consistency (that is a normal apple in that varies minimally from the average), or (3) that it references something definitionally and analytically (all apples are red, that object is not red, therefore that is not an apple), or (4) that it references something moral (an apple is good because it provided Adam knowledge of good and evil).

I point this out to make the larger point that we can decide if our objective here is simply to offer a comprehensive dictionary where we consider as many contextual variations of the term "normal" and provide that for consideration or whether to take the more abstract question and ask how we define anything and whether there is a challenge the word "normal" provides that other terms do not.

Maybe the term "normal" with all its connotations provides us with a better diagnostic tool to show how usage and meaning are tied together, which might be lost with the words run and book, just because those don't have as many subtelties. But maybe they do and we've just not thought those through.

It's abnormal to be normal

It's abnormal to be normal — magritte

Normal is a bullseye no dart ever hits.

Why is this such a problem for you? — I like sushi

It's not the semantics but the true philosophical depth of the definition.

What is a 'true philosophical depth' of any definition?

Ontology and Epistemology are effectively the same, but also different. If that is what you are getting at?