Michael Jordan

Spirit of the East provides an illustrated, in-depth but accessible introduction to the major faiths and philosophies of India, China and Japan. The book focuses not only on the inner spirit of the East, that is the religious teachings, scriptures, lives of teachers, ethics and morals but also on its outer manifestation in the world of affairs through rituals, myths, architecture, holy places and symbols. Further the interplay between the historical, cultural and religious beliefs of each of the Eastern traditions is explored and illustrated.

In what follows I argue for an epistemic bridge principle that allows us to move from real mathematics to ideal mathematics without losing anything that is characteristic of either methodological class. Mathematics is a collection of actions performed in the pursuit of mathematical understanding. The actions are the processes of proving claims that come in such forms as lemmas, theorems, or conjectures. These proofs can be accomplished through a variety of means including logical deduction, geometric intuition, diagramming, or computer assistance. What is common to each of these is the characteristic of being convincing to a sound mathematical mind. Even though what in particular makes each of these methods of proof convincing differs, that they are convincing is enough to usher forth mathematical understanding. The chapters of this dissertation explore a new naturalistic metaphysics for under- standing “where mathematics comes from”, recent psychological findings in the the nature of mathematical reasoning, the concatenation of two historical forms of reasoning, the possibility of an epistemic bridge between real and ideal methods, and the implication of this new bridge principle for the long-standing concern that Go ̈del’s Incompleteness Theorems shake the foundation of modern mathematics.