Conceptual integration, or "blending," is a basic mental operation with constitutive and governing principles. It underlies human mental singularities and is at the heart of human invention and creativity. "Double-scope" blending is the highest form of conceptual integration and the hallmark of human higher-order cognition. A double-scope conceptual integration network has inputs with different (and often clashing ) organizing frames and an organizing frame for the blend that includes parts of each of those organizing frames and has emergent structure of its own. In such networks, both organizing frames make central contributions to the blend, and their sharp differences offer the possibility of rich clashes. Far from blocking the construction of the network, such clashes offer challenges to the imagination and the resulting blended frames can turn out to be highly creative. This paper illustrates the mechanisms of frame blending with central examples from linguistics, economics, and philosophy.