> Not arithmetic or boolean algebra.

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.