What is the Greek root word for system of values?

There isn't a single Greek root word for "system of values." However, there are a few Greek terms that can be used to represent aspects of this concept:

* "Axia" (αξία) means "value" or "worth." It can be combined with other words to create terms related to values, like "axiological" (relating to values).

* "Ethos" (ἦθος) refers to "moral character" or "custom." It can be used to describe the values that shape a person's or a society's behavior.

* "Nomos" (νόμος) means "law" or "custom." It can be used to describe the rules and principles that govern a system of values.

* "Logos" (λόγος) means "reason" or "word." It can be used to describe the rational basis for a system of values.

Therefore, depending on the specific aspect of "system of values" you want to emphasize, you could combine these Greek roots with other words to create appropriate terms. For example, "axiological system" could be used to refer to a system based on values, while "ethico-nomical system" could refer to a system governed by moral and legal principles.