Cognitive Set Theory

Alec Mead Rogers

Printed in the United States of America.

2012-04-27

Revision History
Revision 1.0 April 2012
First Edition.

This book is dedicated to all the people with whom I ever ate lunch, many of whom were forced to discuss the nature of existence of the salt and pepper shakers.

Also, I would like to thank the salt and pepper shakers: I never doubted you for an instant.

Table of Contents

Introduction
I. Things
1. Everything
1. The Whole
2. Universes
3. The Integrity of Wholes
2. Something
1. Parts
2. Atoms
3. Properties
4. Dichotomy
5. Dimensions
6. Hierarchy
3. Nothing
1. Nothing
2. References
3. Existence
4. Identity
II. Universes
4. The Physical Universe
1. Dimensions of the Physical Universe
2. Parts of the Physical Universe
3. The Subjective/Objective Dichotomy
3.1. The Objective Domain
3.2. The Subjective Domain
5. The Subjective Universe
1. Dimensions of the Subjective Universe
2. Parts of the Subjective Universe
3. The Conceptual/Perceptual Dichotomy
3.1. The Perceptual Domain
3.2. The Conceptual Domain
6. The Conceptual Universe
1. Dimensions of the Conceptual Universe
2. Parts of the Conceptual Universe
2.1. The Sentence
2.2. The Noun Phrase
2.3. The Verb Phrase
III. References
7. Subjective/Objective References
1. Perception
2. Communication
8. Perceptual/Conceptual References
1. Conception
2. Naming
9. Conceptual/Conceptual References
1. First-Order Concepts
2. Higher-Order Concepts
IV. Conclusion
10. Informal Summary
11. Formal Summary
12. Epilogue
A. The Root Text
B. Reference Material
1. Mathematical Symbols
2. Typographical Conventions
3. Ideographic Conventions
4. Universes and Relations
5. Glossary
C. Bibliography

List of Figures

2.1. Nominal Dimensions
2.2. Ordinal Dimensions
2.3. Interval Dimensions
2.4. Separate Hierarchies
2.5. Venn Diagram
2.6. Combined Hierarchies
2.7. A Meronomy
2.8. A Taxonomy
2.9. A Discontiguous Meronomy
2.10. An Atom: Zero Dimensions
2.11. A Line: One Dimension
2.12. A Plane: Two Dimensions
2.13. A Space: Three Dimensions
2.14. A Timeline: Four Dimensions
2.15. Multiple Timelines: Five Dimensions
3.1. Green Tomatoes
3.2. Tomatoes, Green
5.1. Senses
5.2. Western Sense Model
5.3. Eastern Sense Model
5.4. Combined Model of Sensation
6.1. The the
6.2. A Taxonomy of Several Types of Nouns
6.3. Apple Percepts
6.4. Apple Concepts
7.1. Blind Spots
8.1. A Decision Boundary
11.1. The Cognitive Structure of Nouns
B.1. Things
B.2. Relations
B.3. Parts
B.4. References
B.5. The References Between the Universes
B.6. The Meronomy Depicting the Universes
B.7. The Universes

List of Tables

2.1. Set Theory and Mereology Compared
5.1. The Dimensions of the Modalities
B.1. Symbolic Notation

List of Equations

11.1. Universe
11.2. Reference
11.3. Parts
11.4. Negation
11.5. Set
11.6. Element
11.7. Subset
11.8. Atoms
11.9. Universes
11.10. The Empty Set (Nothing)
11.11. The Full Set (Everything)
11.12. Physical Universe
11.13. Subjective Universe
11.14. Conceptual Universe
11.15. Perception
11.16. Dichotomy
11.17. Conception
11.18. Collection
11.19. Naming
11.20. Communication
11.21. Connection
11.22. Overlap
11.23. Conceptual Order
11.24. Dimensionality
11.25. Hierarchy
11.26. Identity
11.27. Intrinsic Identity
11.28. Extrinsic Identity
11.29. Referential Identity
11.30. Isomorphic Identity
11.31. Classical Logic
11.32. Existential Quantifiers
11.33. Properties
11.34. Nouns as Applied Adjectives
11.35. Statements Expressing Relations
11.36. Statements Expressing Things