I don't know how you arrived at that conclusion. This is no mystery. LLMs work by making statistical predictions, and even the word "prediction" is loaded here. This is not inference. We cannot clearly see it is doing inference, as inference is not observable. What we observe is the product of a process that has a resemblance to the products of human reasoning. Your claim is effectively behaviorist.
> An LLM is for sure using evidence to get to conclusions, however.
Again, the certainty. No, it isn't "for sure". It is neither using evidence nor reasoning, for the reasons I gave. These presuppose intentionality, which is excluded by Turing machines and equivalent models.
> [w.r.t. "analyze"] I have seen LLM do this, precisely according to the definition above.
Again, you have not seen an LLM do this. You have seen an LLM produce output that might resemble this. Analysis likewise presupposes intentionality, because it involves breaking down concepts, and concepts are the very locus of intentionality. Without concepts, you don't get analysis. I cannot understate the centrality of concepts to intelligence. They're more important than inference and indeed presupposed by inference.
> Philosophically I would argue that it's impossible to know what these processes look like in the human mind, and so creating an equivalency (positive or negative) is an exercise in futility.
That's not a philosophical claim. It's a neuroscientific one that insists that the answer must be phrased in neuroscientific terms. Philosophically, we don't even need to know the mechanisms or processes or causes of human intelligence to know that the heart of human intelligence is intentionality. It's implicit in the definition of what intelligence is! If you deny intentionality, you subject yourself to a dizzying array of incoherence, beginning with the self-refuting consequence that you could not be making this argument against intentionality in the first place without intentionality.
> At what point do we say that the distinction between the image of man and man itself is moot?
Whether something is moot depends on the aim. What is your aim? If you aim is theoretical, which is to say the truth for its own sake, and to know whether something is A or something is B and whether A is B, then it is never moot. If your aim is practical and scoped, if you want some instrument that has utility indistinguishable from or superior to that of a human being in the desired effects that it produces, then sure, maybe the question is moot in that case. I don't care if my computer was fabricated by a machine or a human being. I care about the quality of the computer. But then, in the latter case, you're not really asking whether there is a distinction between man and the image of man (which, btw, already makes the distinction that for some reason you want to forget or deny, as the image of a thing is never the same as the thing). So I don't really understand the question. The use of the word "moot" seems like a category mistake here. Besides, the ability to distinguish two things is an epistemic question, not an ontological one.