Logical operation is quite well defined, with or without regards to human perception of that logic. The idea that logic may not be understood does not contradict the idea that an internal logic (may) underlie physical systems. (Note, maybe see my clarification below, here. )

Granted logic is somewhat mysterious and it is hard to imagine what a different kind of logic would look like. However, that is immaterial to my idea. The idea is just that you have signatures of illogic (e.g., both statements (a.) if A, then B, and (b.) if A, then not B, both true at the same time) which seem to be non-present in physical systems.