The word he's looking for is "formal system".

For some reason he doesn't like doing mathematical demonstrations so he shuns the practice of doing them, and invented a new word to describe that way of using formal systems.

https://en.wikipedia.org/wiki/Formal_system

To me it sounds like this stuff:

https://en.wikipedia.org/wiki/Chomsky_hierarchy

But maybe it is more like fractals and emerging complex systems?