This dissertation investigates some philosophical theories of metaphor, those of Aristotle, Black, Lakoff and Johnson, Kittay, Mac Cormac, Searle, and Davidson, then proposes a theory that incorporates some of their insights while seeking to avoid their weaknesses. Part I constitutes exposition and critique of these theories; Part II presents the outline of a resulting philosophical theory of metaphor, a semantic intentionality theory that mediates primarily between the theories of Searle and Kittay. This semantic intentionality theory of metaphor is grounded in a compositional general semantic account and claims that for metaphor to be present, there must be (1) an appropriate conventional meaning of the linguistic item to be used, (2) a propitious discourse situation (context), and (3) a metaphorically competent speaker/writer who intends to speak/write metaphorically. Metaphor turns out to be a speaker/writer's semantic use of conventional meaning to express a meaning inexpressible in literal language. Most metaphor is therefore entirely novel; conventional metaphors are rare. There is a radical blurring of the traditional semantic and pragmatic categories. Metaphorical meaning is semantic in nature and must be sharply distinguished from metaphorical interpretation. It arises when speakers' metaphorical intentions (possibly not fully conscious) operate to select appropriate conventional meanings whose respective affinity and contrast relations with other items in their semantic fields are transferred to organize and structure a semantic field not previously structured by those specific relations. There is no special kind of metaphorical truth nor does the theory require a specific general theory of truth to the exclusion of others. Metaphor is more cognitively important and widespread in natural language than philosophers used to think. But it is less widespread than some current philosophical theories of metaphor claim: they tend to overlook the vast polysemy in literal language and often (wrongly) assimilate a synchronic account of metaphor to a diachronic account.