ABSTRACT
Values are degrees of goodness or badness. Incomparability is value difference without inferiority. Two values are incomparable, then, if neither is better than or equal to the other. Where some values are incomparable, values are not linearly ordered but merely partially ordered. Their ordering can be represented visually by simple Hasse diagrams. The pervasiveness of incomparability is shown by the widely discussed small improvement argument, explained here and also by the need for evaluating a plurality of values on multiple scales. Many people feel compelled to linearize values, but this often produces blatant logical fallacies. There are various theories of value (axiologies), but all must deal with incomparable values. This book develops a theory of incomparable values using formal logic, the axiomatic method, and model theory. Because of their technicality, these methods have rarely been used in value theory, but they have great advantages in clarity, rigor, and precision. There are good reasons to avoid facile rejection of them but also dangers in their uncritical use.
