Mythic algebra was developed in a trio of papers in the Journal of Literary Semantics. It models mythology and storytelling with algebraic sets. Expanded into a proto-mathematical system, it provides a hierarchical range of functions which can also apply to language and symbolic processes. Its relation to the three basic ‘laws of thought’ of classical logic is analyzed. Correspondences are also found with the Peircean division of a sign into icon, index, and symbol. Further applications are made to metaphor and irony.