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The human element is vital, it is how we formulate the ideas about why things happen the way they do, those feelings and emotions give us our hunches that lead to solutions. Science is what verifies those hunches and sifts out the emotional noise from what works, its how you test the hypothesis your emotions tell you should work.
Without emotions there would be no gut, with no gut there is no effective way to come up with theories, science would be left to test every possible combination in an infinite universe until it arrived at a solution, which of course would never work.
In the end lots of people use their emotions to create theories about what poicies work and what dont, its the science and the data that ultimately tells us when they are wrong or right.
So you have it backwards in a way, you dont use logic and then when you reach a point it cant extend you use the human element.. You start with the human element and then use science to keep it in check and keep it on course, to objectively measure if your solution is a success or a failure.
Take your example of human dignity and minimum wage, these are things that very much can (and have been) tested with science, and as I described it starts with the human element (to define what human dignity means) but it ends with science, to see if what we say human diginity means, whatever that is, is the measurable result of the solutions we employ.
One aspect of human dignity comes from minimum wage discussions, people would generally agree that a person living in decrepit and deplorable conditions is contrary to human dignity. We might all agree human dignity is honored if the most people live in conditions where they have warmth, a bed to sleep in, and a full stomach, at a minimum, thats the human element. Science however can measure these things, they can objectively test things like "If we have minimum wage, or increase the minimum wage, do we see more people living in better conditions, or do we see people who were barely surviving living in worse conditions".. science can test this, objectively tell us and ultimately indicate if minimum wage honors human dignity or destroys it.
In the end a truely worth politicial wont say "We need minimum wage", that is an agenda.. what they will say is "We need to reduce the number of people starving, and we will use science to test what policies do that, if i am wrong an minimum wage doesnt help the starving I wont support it, If i am and my idea of a higher minimum wage is verified by science to be effective, then I will support it, lets test it and see, and not be scared to admit we are wrong"
