It's largely dependent on what we think "reason" means, is it not? That's not a pro argument from me, in my world LLMs are stochastic parrots.

To say any specific LLM can reason is a somewhat significant claim.

To say LLMs as a class is architecturally able to be trained to reason is - in the complete absence of evidence to suggest humans can compute functions outside the Turing computable - is effectively only an argument that they can implement a minimal Turing machine given the context is used as IO. Given the size of the rules needed to implement the smallest known Turing machines, it'd take a really tiny model for them to be unable to.

Now, you can then argue that it doesn't "count" if it needs to be fed a huge program step by step via IO, but if it can do something that way, I'd need some really convincing evidence for why the static elements those steps could not progressively be embedded into a model.

No such evidence exists: we can construct such a model manually. I'd need some quite convincing evidence that any given training process is approximately equivalent to that, though.

That's fine. I've made no claim about any given training process. I've addressed the annoying repetitive dismissal via the "but they're next token predictors" argument. The point is that being next token predictors does not limit their theoretical limits, so it's a meaningless argument.

The architecture of the model does place limits on how much computation can be performed per token generated, though. Combined with the window size, that's a hard bound on computational complexity that's significantly lower than a Turing machine – unless you do something clever with the program that drives the model.

Hence the requirement for using the context for IO. A Turing machine requires two memory "slots" (the position of the read head, and the current state) + IO and a loop. That doesn't require much cleverness at all.

Then say "no one has demonstrated that LLMs can reason" instead of "LLMs can't reason, they're just token predictors". At least that would be intellectually honest.

By that logic isn't it "intellectually dishonest" to say "dowsing rods don't work" if the only evidence we have is examples of them not working?

Not really. We know enough about how the world to know that dowsing rods have no plausible mechanism of action. We do not know enough about intelligence/reasoning or how brains work to know that LLMs definitely aren't doing anything resembling that.

"LLM can reason" is trivially provable - all you need to do is give it a novel task (e.g. a logical puzzle) that requires reasoning, and observe it solving that puzzle.

How do you intend to show your task is novel?

"Novel" here simply means that the exact sequence of moves that is the solution cannot possibly be in the training set (mutatis mutandis). You can easily write a program that generates these kinds of puzzles at random, and feed them to the model.