We describe the creation and development of a course on mathematical logic and its extensions and limitations, in which coverage of technical material is interleaved with and related to discussion of relevant historical, linguistic, philosophical, and theological issues and of individuals of note. The new course, Logic, Limitations to Knowledge, and Christianity, presents an overview of topics in and related to logic, including development of formal logic and an axiomatic first-order logic. It explores the history of mathematics and logic in the Catholic Intellectual and wider Western Traditions, as well as the mutual interactions of mathematics, philosophy, language, and religion. It then considers extensions of first-order logic, and provable limits to knowledge: the three unsolvable problems of Euclidean geometry, and examples from Gödel, Turing, Arrow, quantum physics, and others. Epistemological issues will be emphasized throughout the course. The translation between natural language and expression in logical and reasoning formalisms is emphasized throughout. As a Core Curriculum course at Seton Hall University, fundamental questions such as "What is logic?" and "What are its limits?" will be considered within the framework of Christianity's broader view of the human person and human intelligence.