So far we've talked about two kinds of meaningfulness and two ways that sentences can refer; a way of comparing to physical things found by following pinned-down causal links, and logical reference by comparison to models pinned-down by axioms. Is there anything else that can be meaningfully talked about? Where would you find justice, or mercy?

You find them inside counterfactual statements about the reactions of an implied hypothetical representative human, judging under under implied hypothetical circumstances in which they have access to all relevant knowledge. There is clearly justice if a wide variety of these hypothetical humans agree that there is, under a wide variety of these hypothetical circumstances; there is clearly not justice if they agree that there is not. If the hypothetical people disagree with each other, then the definition fails.

Talking about things like justice, mercy and duty is meaningful, but the meanings are intermediated by big, complex webs of abstractions which humans keep in their brains, and the algorithms people use to manipulate those webs. They're unambiguous only to the extent to which people successfully keep those webs in sync with each other. In practice, our abstractions mainly work by combining bags of weak classifiers and feature-weighted similarity to positive and negative examples. This works better for cases that are similar to the training set, worse for cases that are novel and weird, and better for simpler abstractions and abstractions built on simpler constituents.