Sure, but if you assume that physical reality can be simulated by a Turing machine, then (computational practicality aside) one could do the same thing with a human brain.
Unless you buy into some notion of magical thinking as pertains to human consciousness.
That isn’t a definition or even a coherent attempt.
For starters, what kind of cognition or computation can’t be implemented with either logic or arithmetic?
What is or is not “cognition” is going to be a higher level property than what basic universally capable substrate is used. Given such substrates can easily simulate each other, be substituted for each other.
Even digital and analog systems can be used to implement each other to arbitrary accuracy.
Cognition is a higher level concern.
My paper and pen version of the latest LLM (quite a large bit of paper and certainly a lot of ink I might add) also does not think.
I am surprised so many in the HN community have so quickly taken to assuming as fact that LLM's think or reason. Even anthropomorphising LLM's to this end.
For a group inclined to quickly calling out 'God of the gaps' they have quite quickly invented their very own 'emergence'.
It's just shorthand for "that's an extraordinary claim and nobody has provided any remotely extraordinary evidence to support it."