Introduction

What is this thing?

This book is a study of unity, multiplicity, and references. It examines the world, our experience of it, and our thought about it, while focusing on the relation of the part to the whole. It is about our concepts: how they are formed, how they are shaped by the world, and how they in turn shape the world. It is mildly ironic to examine reality by first taking it apart and then putting it back together: perhaps that is my karma as an engineer.

This book is also a study of three general types of things: everything, something, and nothing. These things are examined from three points of view: the physical, the subjective, and the conceptual. One of the main goals of this book is to develop a somewhat formal language for cognition: to do so, it relies heavily on the sciences of set theory and mereology.

This book takes primarily a holistic, or nondualistic, perspective: in other words, it begins by examining everything . It then proceeds to examine something , which is formed by dividing everything . This division is often carried out hierarchically: parts themselves are subdivided, thereby forming a structure that resembles a tree. This nondualistic orientation holds that the whole comes before (or is ontologically prior to) its parts. Last but not least, nothing is discussed, in no small part because it nicely complements the discussion of everything. Nothing is also significant in virtue of being a reference: references are those things which allow us to build concepts out of smaller constituents, and whose manipulation is called thought.

Why did I write this thing? I wrote this book in order to share several simple ideas. These ideas pertain to the relations between parts, wholes, and references, which are familiar subjects to all of us. But despite their frequent use, these subjects receive relatively little attention. This book attempts to remedy that situation: it strives to lay a broad foundation for thinking about parts, wholes, and references from a number of different points of view.[1]

Why should you read this thing? Perhaps you have some interest in the organization and operational principles of our material and mental lives. Perhaps you have an affinity for a “holistic” or “nondualistic” approach, and you would like to understand more about the relationship of parts to wholes and how that influences, and is influenced by, cognition. You might also be interested in understanding the parallels between set theory and cognition.

Although the subject matter of this book is wide-ranging, most of it is related to parts, wholes, references as these things relate to the structures behind language and cognition. The title is indicative of this subject matter: cognition (psychology) and set theory (mathematics) are interwoven. Since the technical details of this endeavor are of interest only to a small portion of readers, the first several parts of this book are relatively informal; the formal details are presented in the last part of this book.

What is the structure of this thing? This book is written in four parts.

The first part of this book is an introduction to things . Things are split into three general types: everythings, somethings, and nothings. This three-part division of things is based on the space which things occupy; a thing is defined in terms of its spatial boundaries.

Space, in the sense that term is used in this book, is not limited to a single physical (three-dimensional) space: it may be multidimensional (i.e. one which may have an arbitrary number of dimensions, and which is sometimes called N-space) or even a conceptual space. The dimensionality of the space is assumed to be equivalent to the objects in it: for example, four-dimensional space is necessary to contain four-dimensional things. As an example, a four-dimensional thing could be a three-dimensional thing that occupies a temporal extent (i.e. a single, continuing three-dimensional thing may be considered to be a four-dimensional thing).[2]

The second and third parts of this book discuss universes and several primary relations between these universes, respectively. The universes are created by successively partitioning the physical universe. First, the physical universe is divided into two parts, the subjective and the objective. The subjective part is further divided into perceptual and conceptual parts. In this way, three things are created, which are called universes. The reason for partitioning everything in this way, as opposed to some other, is that the resulting parts are composed of references : the conceptual universe refers to the subjective universe, which in turn refers to the physical universe.

References form the basis of universes: the division between one universe and another similarly divides the referrers from the referents. For example, the subjective universe contains references to the objective universe. From the subjective point of view, these references are responsible for perception. From the objective point of view, references are physical things just like any other. This dual characteristic of references is what makes them so special, and what makes the boundaries between universes composed of references so odd.

The fourth and final part of this book is aimed at technically-oriented readers: it offers a more formal summary of most topics discussed in the book.[3] Finally, the various appendices should be treated as reference material for the rest of the book: it is advisable to at least skim that section first.



[1] I have a passion for mathematics, philosophy, and psychology, which I anticipate many readers will share. Despite my passion, I sometimes find the presentation of these subjects somewhat impenetrable. Therefore, a primary aim of this book is to make mathematics relevant, philosophy unconvoluted, and psychology beautiful.

[2] For some readers, it may clarify things to think in terms of “events” and “spacetime” instead of in terms of “things” and “space” , since the former terms connote having more than three dimensions. However, the former terms imply four-dimensional physical entities: in the general case, being limited to either four dimensions or the physical world is undesirable (since this might exclude such things as perceptual spaces).

[3] The summary of the book does not contain a summary of the entire book, but only a summary of the parts of the book that have been written before the summary.