Does it follow that B is not-A and that C is not-A?

I don't think so. — Millard J Melnyk

Interesting theory. Plausible if the "is" and "is not" are those of similarity not full identity:

We say "the son resembles the father" rather than
"the father resembles the son." We say "an ellipse is like a circle," not "a circle is like an ellipse," — Tversky, Features of Similarity

I can not find any case where "A is not B" is not equally well conveyed by "A is other than B". — Millard J Melnyk

What are you getting at?

Let's say it's true that A is not B.

Let's also say that A is not C.

Does it follow that B is not-A and that C is not-A? — Millard J Melnyk

Not necessarily. Cats are not tigers. Cats are not lions. But tigers are cats. And lions are cats.

So what I'm looking for a case where, for a true statement "_____ is not _____", the statement "_____ is other than _____" would not be just as true and convey the same meaning, even though they feel like they're different. — Millard J Melnyk

My house key is not in my pocket. True.
My house key is other than in my pocket. No clear sense.

This shows that in English we need the concept 'not' and also the concept 'other than'. Handily, we have both expressions, each useful in its own way.

Yes, that jives with what I've come up with so far.

As to

My house key is other than in my pocket. — Cuthbert

, I wouldn't say that the sense is unclear. It's awkward English, but if a non-native speaker said that to you, I think you'd easily figure out what they meant.

And as far as I can tell, the vagaries of both statements ("not in my pocket" vs "other than in my pocket") are the same, too. It's just that we're so accustomed to negation as a device that it feels more clear cut even though I really can't explicate a way in which it actually is.

From the same question posted on reddit:

//
|| Yes, A, B, and C are different individual things/entities/objects/whatevers. ||

Okay, so then as I said there's no standard interpretation for what "not-A" means, because neither natural language nor logic supports negating an individual.

|| As far as I can see, in every case where a person might want to say "it is not ____" they can equally well say "it is other than ____" without losing anything semantically -- i.e., meaning or veracity. ||

This does seem correct. I'm not sure I understand the "difference in the impression" between the two expressions, or the implications for their meaning the same thing, though.
//

Then someone else there pointed out: "Frege did discuss about the fact that words semantically coextensive may have different psychological connotations, you may try to look in there."

My interest is in how these things play out discursively in social interactions of all kinds. Discussions tend to go circular when people are vested in their positions. The more circular they get, the more thought-terminating clichés get bandied about. "Not" is far more thought-terminating then "other than", and it plays on us cognitively in less closed, terminating ways. Maybe most importantly, "other than" directs our attention to what actually is, while "not" directs our attention to what actually is not (unless "not" was false). There is something inherently incoherent and unconstructive about directing attention onto the very "thing" that in the first place is not there to receive any attention whatsoever.

So, if it's solid that "other than" is a peachy substitute for "not", I can point that out when people go loopy and encourage them to actually try the substitution and realize the difference it makes. Getting people to experience an alternative to their preprogrammed ruts of thought and speech is far more effective than arguing that they should change their habits and get out of their ruts.

There is another thread going around now here. It's about the difference between opposing and negating. Opposing seems similar to "other than", while negating seems "not", which is maybe why "not" is a silencer, while "other than" is stimulating.

Concise Crossword:

Across
1. Cat (5)

I see the sense in that. Only thing, there is a big difference in that opposing necessarily requires two distinct and identifiable entities/ideas that are mutually contrary in some way. "Other than" requires only one.

that are mutually contrary in some way — Millard J Melnyk

Doesn't the same hold for not and other than? Money is not fish. It is other than fish. For money to be not fish money and fish gotta be mutually contrary in some way. You can eat fish but yòu can't eat money. Money is dead while fish is alive. You can pay with money but not with fish. In a lot, if not all, aspects they negate each other. They negate each other in a lot of aspects. All these aspects together make fish other than money. Maybe these aspects even oppose each other. Being made of paper or metal opposes not being made of paper (or metal). Hot is not cold. It is other than cold. They are opposite to each other. Do they negate each other? Maybe saying cold is not heat disconnects them while saying it's other than invites for discussion.

"Heat is not cold."
"Okay."
"Heat is other than cold."
"In what sense?"

Not divides. Other than connects. You are not me. You other than me. Can you feel the difference?

The way I see it, is not means not the same as. The OP's argument, to make sense, would require that the is in is not to mean the same as. Semantic confusion, that's all.

To clarify:

A is not B means A $\neq$ B and not that A $=$ ~B.

feline

lol, got me. I managed to cross wires between mathematical negation and what we're talking about here. My bad.

LMAO I knew I shouldn't have tried. Always sucked at word puzzles. And math. XD

It's awkward English, but if a non-native speaker said that to you, I think you'd easily figure out what they meant. — Millard J Melnyk

Sure. They would mean it's not in their pocket. When someone types 'Untied States' by mistake you know what they mean. But 'untied' does not mean 'united'.

And 'other than' does not mean 'not'.

Some thing can be said to be 'other than' a different thing. 'In my pocket' is not a thing. My pocket is a thing. 'My house keys are other than my pocket' is true. 'My house keys are other than in my pocket' does not make sense.

We have the two expressions because they have different senses and meanings.

So, if it's solid that "other than" is a peachy substitute for "not", I can point that out when people go loopy and encourage them to actually try the substitution and realize the difference it makes. — Millard J Melnyk

I did what you suggested and got nonsense. Turns out I need both expressions in different contexts.