A THEORY
OF COMPLEXES

Abstract:

In 'A Theory of Complexes', the simple form of the pure theory of identity found in logic books is subordinated to a complex form of the theory whose background ontology is one of structured individuals, or complexes.  In the complex form:

• The axioms of the simple form proceed from principles more basic.¹
• The semantic difference between (true) 'a = b' and 'a = a' supervenes on features of a and b.²
• Identicals such as nine and the number of planets differ in their modal properties and relations.³

'A Theory of Complexes' puts into question: the privileging of FOL individuals, the expressive completeness of FOL, and ontology-free logic.

1. Introduction
2. Haecceities and Individuals
• 2.1 Language and Logic
• 2.2 Identity In HI^*
• Minimal Identity
• Classical Identity
• Non-Classical Identity
• 2.3 Identity and Ontology
• 2.4 Tableau of Theorems
3. Complexes
• 3.1 Language and Logic
• 3.2 Extending HI
• 3.3 Identity in C
• 3.31 Minimal Identity
• 3.311 Reflexivity and Complexes
• 3.312 Reflexivity and C-Complexes
• 3.32 Classical Identity
• 3.33 Non-Classical Identity
• 3.4 C-Complexes and Particulars
• 3.5 Tableau of Theorems
4. Particulars
• 4.1 Language and Logic
• 4.2 Identity in P
• Haecceities and Individuals
• Embodiment and Containment
• Minimal Identity
• Identity and Unity
• 4.3 Classical and Non-Classical Objects
• 4.4 Extending P Classically
• Minimal Classical Identity
• Strongly Classical Identity
• Weakly Classical Identity
• 4.5 Extending P Non-Classically
• Minimal Non-Classical Identity
• Strongly Non-Classical Identity
• Weakly Non-Classical Identity
• 4.6 Tableau of Theorems
5. Particularity
6. Appendix: Be Glad It's Not Deviant!
7. References
8. Acknowledgement
9. Dedication

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Copyright© 1999, William J. Greenberg, all rights reserved.