Chapter 33: Knowledge as Sections over Experience

Epistemology reformulated. Knowledge is not justified true belief but a global section of a presheaf over an open cover of experience. Justification becomes satisfaction of gluing constraints; truth becomes section-existence. The Gettier Dissolution Theorem shows that Gettier cases are cover failures, not knowledge failures: the cover was too coarse to support a genuine global section. This chapter launches Part III by extending categorical ontology from the third-person question (“What exists?”) to the first-person question (“What can I know?”).