contradiction

Comprehensive learning aspires to integrate more and more of Humanity’s traditions of learning to better comprehend the world and how it works. As we learn more and more from these diverse ways of knowing, it becomes increasingly likely that the perspectives, hypotheses, and frames of reference we encounter will seem incompatible or even inconsistent with others. This resource suggests how to better accommodate these ambiguities as tools for our comprehensive practice.

This way of accommodating ambiguity in our learning is a central theme in the profound 2007 book “How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics” by William Byers. The book examines ambiguity while it surveys the folklore of mathematics culture and the philosophy of mathematics. It is easy to read and serves as a good introduction to mathematics for readers with weak math skills. It might be especially valuable for those wanting to expand the compass of their comprehensive learning with mathematics.