What is formal vs intuitive thinking?

Formal vs intuitive thinking is a concept in personal epistemology: You have both rigorous explicit schemas and fuzzy gut-feeling schemas — both matter.

Example: A senior engineer reviews a pull request. She can articulate the formal schema: 'functions should do one thing, names should reveal intent, error handling must be explicit.' But she also has an intuitive schema — a feeling that something is off about the code's structure — that she can't fully verbalize. The formal schema catches the naming violation. The intuitive schema catches the subtle coupling between modules that will cause pain six months from now. Ignoring either one produces worse decisions than using both.

This concept is part of Phase 11 (Schema Foundations) in the How to Think curriculum, which builds the epistemic infrastructure for schema foundations.