How do you call a word that is so rudimentary that it can't be defined without being redundant?
I think axiom should fit, but according to its official definition, an axiom is a statement that is taken to be true, and as far as I know, a word can't make an statement by its own.
Usage comes first, not definition. Dictionaries, glossaries, etc. are a commentary on usage, attempting to explain to new users of a word what the other people already using that word mean by it.
If someone starts calling some teddy-bears "squee-bears", they don't have to have a written-out definition in mind before they do this. Maybe later, if the term "squee-bear" catches on, someone will write down a definition for it, as a summary of how they've observed the term being used.
You'd have to be pretty strict about what you mean by 'definition' in order to claim this. When words are coined, it seems likely that the speaker knows what he means by the word, even if he hasn't written the definition down somewhere
When Bob comes up with the word "squee-bear", he knows a squee-bear when he sees one, but he might not yet have worked out exactly what makes it a squee-bear to him. He might not yet be able to offer a definition. And if Bob talks about squee-bears to Alice and Charlie, they might start using the word in slightly different ways from Bob.
This sort of thing happens in the history of science, for instance. People start talking about "planets" (originally meaning "wandering stars") or "atoms" ("indivisible units") and then only later does a community of speakers nail down exactly what they mean by "planet" or "atom" and it turns out that planets aren't stars and atoms aren't indivisible.
For people, language use is axiomatic — and messy. We talk about things even when we don't know what they are; we talk about things even when we're not 100% sure what we mean.
Definitions come later.
People run into problems when they put definitions ahead of reality. That's what we see, for example, when creationists try to talk about "species", or transphobes about "woman". They act as if they want a simplistic definition they learned as a child to apply forever, in all context, and for anyone who disagrees to be just wrong. But that's not how language works and it's not how reality works.
The vast majority of words in natural languages aren’t created by somebody like an invention. They slowly form over time and over populations. In fact, I don’t think any of the words in your comment were “coined” in the sense that, say, Shakespeare coined “dwindle”.
Just like species change, I suppose for any precise definition and pronunciation of a word, you could find a person who was the first to use it, but it would almost always be a tiny variation of an existing word, and wouldn’t be considered “new” to a native speaker at that time and place, just a mild accent.
Do any words like this actually exist, though? I'd wager that failure to define the word sufficiently is more of a limitation on the definer's vocabulary than the word itself.
I certainly can't imagine a word I couldn't define. Some words are defined by their interrelationship, and that can seem circular... but since that interrelationship is how we make sense of the world, I don't particularly see the problem. There's nothing fundamental about that.
Axiomatic is pretty good. Irreducible is another. However, I would argue there are no undescribable words. If that were true, no one could learn certain words in other languages
The definition of crack in that instance would be something along the lines of: “The snapping sound the air makes when creating a small sonic boom. Like that of a whip cutting through the air.”
Even onomatopoeia has synonyms. Like some people say Atchoo. Some say kerchew. And then other languages say other words for the same sound.
I think you can always define a word using other words, without repeating the word in question. Just sometimes you have to take a pretty wide circle and the explanation can end up complicated
That shouldn't be the case. Where that breaks down in more formal contexts is circular definitions. You don't want to define one word using others that simply reference the defined word in their own definition. All words can be defined using the other available words. At some point it would become circular, but that's of no consequence in the scope of all words.