No system can be both consistent and complete. Worse, all logical statements are based on either paradox, circular reasoning, or axioms not provable from those statements. And I’m not exactly sure whether you meant that kind of intuitionism (the constructive maths kind) or the “don’t discount your intuition” kind but, yes, I very much do both. Both tell us that our models are limited, shadows on the cave wall and all (and it is no coincidence that cybernetics itself models that limitation very nicely). Maths tells us by formal proof, intuition and instincts by incessantly insisting that there’s a world outside of our heads, something that refuses to vanish even when we cease to believe in it. It’s actually quite a feat to shut that whole thing off, and I constantly wonder how people manage to not run into lamp posts all the time.
Lastly, let me share a nasty shower thought (literally, thought of it this morning in the shower): It would be very anti-Hegelian of you to be fundamentally opposed to the sublation of Hegelian dialectics. I even got quite formal with it (though please don’t ask me to write it in Greek), identifying sublation with MSTs. Mull about it.