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 N, 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.
Yeah, sure. I should have said: there’s no plausibly useful & practical scheme that is fundamentally different from scalars, for this, at least that I can think of. :-)
You probably need a total order (or at least a join in your partial order), and things like N, 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.
Yeah, sure. I should have said: there’s no plausibly useful & practical scheme that is fundamentally different from scalars, for this, at least that I can think of. :-)