John Baldessari’s Blasted Allegories (1977-1978) represent a concerted reconsideration of the most active and critical pursuits of the 1960s and ‘70s, including structuralism, post-structuralism, systems-based art, constraint-based approaches to composition, chance, and allegory. Thirty-five of the sixty-some Blasted Allegories are designated here as “later” works in the series because they share formal and structural characteristics; they present arrangements of colored photographs on neutral matte board. Although the later Blasted Allegories initially appear as colorful sentences, the close readings undertaken in this dissertation reveal that these pieces have been generated by the imposition of individual sets of constraints on a combinatorial system. In addition, many of these works appropriate structural models from cultural anthropologist Claude Lévi-Strauss, narratologist A. J. Greimas, and grammarian Noam Chomsky; even though they subsume the rules implied by these structural models, they undergo a post-structural critique wherein fixed relationships are destabilized by word play, homophones, rhyme, and the imposition of such additional operations as algorithms. This dissertation demonstrates how Baldessari solicits art as an experience of cognitive construction, pleasure, and protracted play with the possibilities of meaning. His crypto-narratives take readers along the cognitive spiral theorized by psychologist Jean Piaget that begin with sensory perceptions, expand into operational understandings of these works as products of a combinatory system, and can be built into logical and mathematical apprehensions of the resultant texts. Like many of the embedded models, Piaget’s spiral is counterbalanced in this series by the conflation of vying cultural models into a cacophony of signification. Baldessari’s texts play with readers’ proclivities to search for meaning. The artist solicits protracted interactions from viewer/readers, who are able to discern multiple, simultaneous readings and thus relinquish an ensconced approach toward art as a synthesis of embedded cultural models. Baldessari’s series engages conceptions of allegory as a procedure, a condition of the text, and a hedge against reductive, overarching interpretations. Working in a Duchampian vein, Baldessari posits the components of new syntaxes for art that return readers to these pieces, where variable interactions between readers and these heteroglossic texts ressemble open systems that can unsettle artist-imposed significations.