That you might not define floating point numbers to be "symbols" aside, the inputs and the outputs are symbols and the intent and purpose of the creation is strictly symbolic.
It's right there in the name "Large Language Models". Language. Not direct experience, not emotion, not anything else. Language. i.e. symbolic representation.
This does not cover the full spectrum of intelligence humans have, and it shows. And yes, the model can spin up Python parse the output and get mathematical intelligence but there is still a big gap.
As I say, I see the holes. I'm just trying to figure out what it is I see and how to describe it. It's particularly difficult because we don't fully understand how human thinking works but I will say I believe human thinking is a lot more than informal statistical correlation.