Value comparisons require a scalar: In the brain, we roll out multiple possible thoughts / actions / plans, and then we need to do a comparison to decide which is better. You need a scalar to enable that comparison.

You probably need a total order (or at least a join in your partial order), and things like , $Z$ and $R$ have a natural one, but you could definitely find a total order from a partial order in basically any space you want your values to live in. Not sure it's really important, but I wanted to point that out.