Sam Sanders, Junior Professor
Keita Yokoyama, Assistant Professor
During our project, we will obtain a partial answer to the Big Question: "What are the limits of Mathematics in advancing human knowledge?" by exploring the philosophical implications of new results in Reverse Mathematics and Nonstandard Analysis. Because of the concrete connections to Physics, this new field is called "Concrete Reverse Mathematics". We are motivated by the following fundamental questions: #1 "Is physical reality continuous or discrete?" #2 "What are good foundations for Mathematics?" #3 "Do infinitesimals exist?" The development of Concrete Reverse Mathematics will allow us to answer questions #1 to #3. In turn, these answers will identify several limitations of Mathematics in advancing human knowledge. In this way, we will produce convincing evidence for the importance of Logic and the Foundations of Mathematics for Mathematics, Physics, and the Philosophy of Science. Thus, we hope to attract the interest of scientists active in the latter fields. In our opinion, the importance of our project is best reflected in its fundamental scope, its preference for Big Questions and its contrarian nature with regard to (over)specialization. Besides publishing our results in academic journals of the highest quality, we intend to proliferate our results to a more general audience. We will produce several "popular" papers suitable for a wider audience with an interest in Philosophy or Mathematics. We expect at least 14 peer-reviewed articles to result from our project. We intend to publish 3 papers for a wider audience. In the long run, we hope that the results of our project will inspire young researchers and instill a passion for deep philosophical and transcendental questions in science that have motivated us and Sir John Templeton.