ABSTRACT
Some values may be infinite relative to others. Infinite and incomparable values interact intriguingly, and examples from philosophy and theology are considered, as are concepts of infinity in mathematics. Values of both kinds can be represented in Cartesian models that are “souped up” by allowing as components of the n-tuples that represent values not only real numbers, but also the infinitesimal and infinite numbers of nonstandard arithmetic. Concepts of relative infinity and relative finitude are generalized from positive values to all values (positive, negative, zero, or incomparable with zero) using the absolute value operator. The result is a coherent and very general account of finite and infinite commensurability. Infinite relationships may also occur in other sorts of models, too, and these are briefly considered. Yet while we can consistently imagine infinitely commensurable values, we never encounter them in practice. This chapter and the book conclude with an argument that since life began, there have been no infinite objective welfare disparities among living things.
