Incomparable Values Analysis, Axiomatics and Applications
People tend to rank values of all kinds linearly from good to bad, but there is little reason to think that this is reasonable or correct. This book argues, to the contrary, that values are often partially ordered and hence frequently incomparable.
Proceeding logically from a small set of axioms, John Nolt examines the great variety of partially ordered value structures, exposing fallacies that arise from overlooking them. He reveals various ways in which incomparability is obscured: using linear indices to summarize partially ordered data, relying on an inadequately defined concept of parity, or conflating incomparability with vagueness. Incomparability can enrich and clarify a range of topics including the paradoxes of Derek Parfit, rational decision theory, and the infinite values of theology. Finally, Nolt shows how to generalize many of the concepts introduced earlier, explores the intricate depths of certain noteworthy partially ordered value structures, and argues for the finitude of value.
Incomparable Values will be of interest to scholars and advanced students working in ethics, value theory, rational decision theory, and logic.
Part I. Preliminaries
1. Incomparability, Axiologies, Axiomatics, and Model Theory
2. Logic, Comparison, Hasse Diagrams, and Set Theory
Part II. Basic Formal Axiology
3. Arithmetical Value Structures
4. Cartesian Models
5. Integer Multiplication, Delimitation, and Commensurability
6. Incomparability Obscured
7. Aggregating Welfare over Populations
8. Evaluating and Comparing Situations
Part III. Ethical Decision Theory
9. The Deontic Logic of Decision
10. Rational Ethical Decisions
Part IV. Bounds
11. Absolute Value and Concept Generalization
12. Bounds of Finite Value Sets
13. Value Analysis
14. Incomparability and Infinity
"This book is an outstanding contribution to the literature. Its combination of formal rigour and thoroughness with philosophical acumen is rare. This type of work is very much needed in axiology and ethics. The discussion of incomparable values in the book is by far the most detailed and precise to date. In addition, the book contains much material that should be of interest to axiologists, ethicists and decision theorists quite independently of its connections to value incomparability."
Erik Carlson, Uppsala University, Sweden