Bring nctm standards to life: best practices, middle School: Exemplary Practices for Middle Schools Book

A.W. Moore's masterly study demonstrates how a proper appreciation of the infinite is crucially important in deciding the limits of our knowledge and providing meaning for our lives. After an illuminating historical exposition of the key debates from the Ancient Greeks to the present day, Moore advances his view that our radically finite lives are aspects of an infinite whole. This is something that we are shown, not something that we can know. We cannot fully grasp the infinite (despite Cantor's best efforts), but self-conscious introspection invites us to apply a-priori Ideas of the infinite to reality. For example, continuous lines and shapes are really self-contained wholes but can be treated by mathematicians as if they were sets of infinitesimal points. What I find remarkable is that Aristotle had already solved many of these problems through advancement of the 'potential' infinite.