An Integrated Course in Logic, Philosophy, History, and Theology: Extensions of Logic and the Limits to Knowledge

摘要

The new course 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 Godel, Turing. Arrow, quantum physics, and others. Epistemological issues will he 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 "Wliat 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.