This chapter introduces the Propositional Calculus, a formal system designed to model logical reasoning based on the words "and," "or," "not," and "if...then." It explains the system's symbols, rules of inference (including the unique "fantasy rule"), and the concept of well-formed strings. The text explores the intended interpretations of these symbols and discusses the system's ability to derive universally true statements through purely typographical manipulation. Furthermore, it touches upon the system's consistency, limitations in handling contradictions compared to human thought, and its role as a foundation for more complex logical systems, all while interweaving these concepts with a dialogue inspired by Lewis Carroll and an analogy to a Bach composition