The mathematician Israel Gelfand once said: “The most important thing a student can get from the study of mathematics is the attainment of a higher intellectual level.”1 We might twist this slightly to say that “the most important thing a human being can get from the study of mathematics is an understanding of oneself as […]
Author Archives: Thomas Cothran
The difference between atheism and theism is fundamentally a difference between mythic and scientific thinking. That is to say, it is a difference between those who insist that reality is what is revealed by rational procedures, and those who retreat from the demands of critical thinking to the cover provided by imaginative storytelling. Which camp […]
To be a teacher, you must have some level of mastery of the subject matter to be taught. Perhaps you have volunteered as a substitute teacher and scrambled to learn the material. Perhaps you have homeschooled a child and found the need to brush up on a subject you barely remember. Or perhaps you have […]
Suppose that you pick up a textbook in an unfamiliar branch of mathematics and thumb to a random page. You might find a statement such as: if there are injections f: A-> B and g: B -> A, then there is a bijection h: A -> B1 Such statements probably strike you as utterly mystifying. […]
In “What Is It Like to Be a Bat?”, Thomas Nagel argues that consciousness cannot be explained by contemporary physical science. The inner lives of bats must be so different from our own, not least in their reliance on echolocation over sight. Although scientific methods tell us a great deal about bats, the subjective, inner […]
Philosophers ask many questions about many things, including their own discipline. One of the important questions about the discipline of philosophy is this: Is philosophy a reliable means of knowledge? The question whether philosophy can amount to knowledge becomes particularly acute when it is considered in the contrast with the hard sciences. The history of […]