ABSTRACT
This chapter first describes interaction as an algebraic magnitude in its general terms, and then focuses on the living metaphors: substitution and projection. In the presence of shared metaphorical concepts, the virtual space open to projection is limited by the requirement of consistency. In the presence of living metaphors located in texts, it is both controlled by textual coherence and enriched by contextual components. Once the whole space of conceptual interaction has been traversed, it is possible to face the question of analogy, which is traditionally associated with metaphor. The typical figure of analogy is simile rather than metaphor. When applied to metaphor, analogy is a strategy for keeping projection under control, and as such, it shares some significant features with mitigation and approximation. However, substitution and projection are not on the same level. Projection is open to any metaphor, but a substitute, and therefore the option between substitution and projection, is only available for some kinds of metaphor.
