In Part 1 of this article, a cognitive developmental theory of metaphor is presented, suggesting that what is commonly conceptualized as a linguistic phenomenon originates in a preverbal cognitive-sensory matrix in which synesthesia and physiognomic expression are but two of many transformational manifestations. Tropological or equivalence transformations are seen to evolve into higher order abstractions of literal language and mathematical functions. In Part 2 of this article, the equivalence function is explained in terms of cognitive-sensory schemata. It is suggested that cognitive-sensory schemata are nonconscious ordering processes of sensory, motor, affective, and structural modalities that, when subjected to transfer operations, result in so-called metaphorical productions by way of a specific operation termed analogical transforms that generate such phenomena as stimulus generalization, transfer of learning, perceptual constancy, and analogical reasoning. Empirical data illustrate the theory. It is suggested that through developmental differentiation, figurative language evolves into literal language and other abstract equivalence operations. (Robert E. Haskell)