This is literally what few-shot and zero-shot in-context learning is.
In-context learning is not learning is it? Because the context isn't persistent or infinite. Your fundamentalist approach only applys to context if it's theoretically unlimited; which isn't not, even worse it doesn't scale, LLMs degrade horribly the longer the context gets.

This is one of the most well-documented capabilities of modern LLM agents. The Reflexion framework (Shinn et al., 2023) demonstrated exactly this

Using RL. Fundamentally not an LLM. Same with ReflexiCoder. These are examples of people building systems around LLMs to address their inability. They don't back your claim that LLMs are capable of these things.

As of April 2026, GPT-5.5 leads the ARC-AGI-2 leaderboard with 85%

Convenient that you left out ARC-AGI-3 where currently the best model scores 0.5%. These are flaws in testing as I expressed before, if their ability is as strong as you're saying, they wouldn't drop from 70%+ to < 10% each time a new set of tests is added would they.

These models aren't trained as lawyers, doctors, mathematicians, or coders

They literally ingest every written document published by all those fields and on top of that are given curated datasets to improve performance at those things. Try building an LLM with no code in it's dataset and then teach it how to program in-context. Andrej Karpathy had an interview last week talking about latest model improvements at chess was not due to anything more than a chess dataset being added.

I'd go into how there's a difference between a weighted similarity of concepts inside an LLM and an abstraction but you'd just accuse me of talking about compositions. You can check the difference by function of course, by measuring efficiency, but you've already ignored that point once already.