A logical frame is a box (a plane of consistency) - LLMs extend that plane and accelerate the fundamental construction just like Godel's proof did.
By that, I expect that our logic, no matter how robust, will be used against us.
Grazing the surface of the pre-socratics, you find that they engage with the "non logic".
Parmenides, THE Father of metaphysics and ontology, describes how he was bestowed knowledge - and it is anything but pure logic.