This feels like we're playing word games which don't actually let us make useful claims about reality or predictions about the future. If we're talking purely about the model internals, without reference to their outputs, then your claim is wrong because we don't have a good enough understanding of the model internals to confidently rule out most possibilities. (I'm familiar with the transformer architecture; indeed this is why I asked what definition of the word reasoning the OP cared about. Nothing about transformers as an architecture for _training model weights_ prohibits the resulting model weights from containing algorithms that we would call "reasoning" if we understood them properly.) If we're talking about outputs, then it's definitely wrong, unless you are determined to rule out most things that people would call reasoning when done by humans.
I might be able to learn more by chatting with you.
I think that the trained transformer has fixed weights and therefore cannot learn.
I think learning is one aspect of reasoning, and is demonstrated by challenges like navigation or puzzle solving where learning that one route to a solution is impossible is important.
I also think that the single forward pass of the model means that cyclic reasoning isn't feasible and that conditioning output by asking the model to "think" even when that thinking is done on the single forward pass means that logical processes are ruled out. The model isn't thinking in that case, the probabilities of the final part of the output are conditioned by requiring a longer initial output.
