> I'm a mathematician, so I can only work in what I can define symbolically.

This is a limitation of you, not an argument. Of course everything will look the same to you if that's the only way you can represent them.

We have more disciplines than mathematics because mathematically is not the only valid way to explore things.

Yes, of course. I'm not trying to establish further argument or to criticise. But it isn't fruitful to have a conversation where both parties have different definitions in mind. Since my original comment referred to the mathematical definition, it is important for me to clarify that.

The rest of my comment is to try to find some middle ground, of which there is plenty in philosophy. If the raw theory of mind arguments for humans were already applicable for recognizing the limitations of LLM designs, we would be much further along than we currently are.