It's not clear to me what point you're trying to make. Why do we need an "articulated theory of abstract reasoning" to say that passing the bar exam or writing code for novel, nontrivial tasks requires reasoning? Seems rather obvious.
You are making a claim that there is some attribute of importance. For that claim to be persuasive, it should be supported with an explanation of what that attribute is and is not, and evidence for or against the meeting of those criteria. So far all you have done is say "Look at the text it puts out, isn't that something?"
It's just empty excitement, not a well-reasoned argument.
You keep avoiding this question: does passing the bar exam and writing code for novel, nontrivial tasks require reasoning or doesn't it?
You aren't answering because saying no will sound ridiculous. We all know it requires reasoning.
As for an "attribute of importance", I guess that's subjective, but I've used ChatGPT to write code in a few minutes that would have taken me hours of research and implementation. I've shipped that code to thousands of people. That's enough for it to be important to me, even ignoring other applications, but you certainly have the right to remain unimpressed if you so choose.
For a human, it takes human reasoning. But a xerox machine can also output the correct answers given the right inputs, which is exactly what you can say about an LLM.
The "attribute of importance" I'm referring to is "rationality". You keep talking about it like it means something but you can't define it beyond "I'm pretty sure this text was made using it".
Does a tape recording of a bird song "know" how to sing like a bird?
Those aren't good analogies. An LLM isn't like a xerox machine or a tape recorder. Again, the answers to the bar exam it passed weren't in its training data. Nor was the code it wrote for me.
I'm using the common, colloquial definition of reasoning. I don't think we need an academic treatise to say that passing the bar exam (without copying the answers) or writing code for a novel task requires reasoning.
You're right that we don't fully understand how the LLM is doing this, but that doesn't mean it isn't happening.
