Axiology, from the Greek axia (αξια, value, worth), is the study of value or quality. It is often thought to include ethics and aesthetics—philosophical fields that depend crucially on notions of value—and sometimes it is held to lay the groundwork for these fields, and thus to be similar to value theory and meta-ethics. The term was in the 19th and early 20th centuries, but in recent decades, value theory has tended to replace it in discussions of the nature of value or goodness in general.
One area in which research continues to be pursued is so-called formal axiology, or the attempt to lay out principles regarding value with mathematical rigor.
For instance, the state of affairs of a world with no war is a moral ideal and the individual Socrates is virtuous, whereas the practice of paying back debts is obligatory and acts of theft prohibited.
The axiological face of morality, unlike its deontic counterpart, is open-ended.
But this double role of normative discourse inevitably raises the idea of supererogation, the category of actions that are praiseworthy (either in creating good states of affairs or in reflecting a particularly virtuous trait of character) yet at the same time not obligatory.
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