Chapter 3 first elaborates on the view of context-sensitivity as a nontrivial context-shift-dependence. Drawing on Chapter 2, it makes explicit the fibration of semantic contents over contexts of utterance. The latter makes it natural to introduce a generic context and to identify linguistic meanings with the semantic contents attached to that context. The correspondence established between linguistic items and mathematical ones leads to the hypothesis that the fibration of contents over contexts constitutes a “stack” (with respect to a natural Grothendieck topology). This correspondence is the final reconsideration, proposed in the book, of Russell’s logical analysis. The rest of Chapter 3 distinguishes two different concepts of meaning (as obtained by collation or as transposable to more specific contexts) and thereby supports a constructive conciliation of minimalism, indexicalism, and contextualism. It also puts forward a new picture of the demarcation between semantic and pragmatic components, as well as a more flexible notion of compositionality. It finally develops various applications to philosophy of language and to cognitive linguistics.