A number of philosophers, linguists and psychologists have made the dual claim that metaphor is cognitively significant and that metaphorical utterances have a meaning not reducible to literal paraphrase. Such a position requires support from an account of metaphorical meaning that can render metaphors cognitively meaningful without the reduction to literal statement. It therefore requires a theory of meaning that can integrate metaphor within its sematics, yet specify why it is not reducible to literal paraphrase. I introduce the idea of a “second-order meaning”, of which metaphor is but one instance, that is a function on literal-conventional, i.e., first-order meaning, and outline a linguistic framework designed to provide a representation of linguistic meaning for both. This framework is designed to represent linguistic units ranging from a single word to an entire text since I argue that the by-now familiar position that the sentence is the appropriate unit for metaphor has mislead us into asking the wrong questions about metaphorical meaning. With this apparatus, we can specify the conditions under which an utterance may transcend the constraints on first-order meaning (transgressions not always apparent on the sentential level), without thereby being “meaningless”. Conversely, we can specify the conditions that may render apparently odd utterances first-order meaningful rather than metaphorical. In this way we see how metaphorical language differs both from deviant language and from specialized language such as technical language, fanciful and fantastical language (in fairy tales, science fiction, etc.).