I agree generally with what you're saying. I was arguing against people who seem to have concluded LLMs can't do any reasoning because they're "just generating text based on probabilities". I've seen people express that point of view quite a few times and it seems to be based on a superficial and incorrect understanding of how LLMs work.
And although I think one could demonstrate fairly easily that ChatGPT is capable of some level of deductive reasoning, my last post wasn't even arguing about any actual capabilities of current LLMs. I was just saying you can't conclude that LLMs can't reason (even in theory) because they're "just generating text based on probabilities".
That said, it's not clear to me what the limits are on LLMs as they scale up. GPT-4 can usually add very large numbers together (I've tested it with 20 digit numbers) without any chain-of-thought, something older models struggled with. I think addition works well because you almost don't need internal working memory to do it. You can _usually_ compute a digit of the answer just by looking at 2-3 digits of each of the summands. Occasionally this isn't true: if you have a long sequence of columns that each sum to 9, then a carry from many digits away can affect the current digit. But that's rare.
Multiplication of large number, by contrast, does require working memory and an iterative algorithm. It makes a lot of sense that chain-of-thought helps with this. The text the LLM writes functions as working memory, and it iteratively generates the response, token by token.
Still, just scaling up the models has also helped a lot with multiplication (even without using chain-of-thought). Presumably larger models can have a larger part of the network devoted to arithmetic. It still doesn't compare to a calculator, and integrating LLMs with other tools or AI models sounds promising. But so far, the results of just scaling LLMs and training data has been surprisingly impressive.