The purpose of this introduction is to lay out the background for the chapters in this volume. The major issue discussed in this chapter, within the whole context of this volume, concerns the role of paradigms in the construction of any scientific or even artistic theory. What does it take to make a theory artistically and scientifically acceptable? Consequently, the first part of this chapter will cover how we should view the whole scientific enterprise. The second part will cover how paradigms need to be included within a hierarchical framework that clarifies how paradigms are related to theories, models, and dimensions (L'Abate, 2009a, 2009b).