This dissertation is concerned with the formal analysis of metaphor. It focuses particular attention upon metaphor in literary works. The proposals in the dissertation concern: (1) what entities are included in a "metaphorical extension"--that is, the class of conceivable entities to which a word or phrase can be taken to apply truly under a particular metaphorical interpretation; (2) what we conventionally understood a metaphorically interpreted word or phrase to mean or imply (as opposed to suggest or connote); (3) how we can understand propositions which are literally inconsistent to be consistent because of metaphorical interpretation; (4) what we conventionally understand a metaphorically interpreted word or phrase to suggest or connote.