It seems possible that when your friend said, in effect, that there can never be any axioms for social justice, what they really meant was simply, "I don't know the axioms either." That would indeed be a map/territory confusion on their part, but it's a pretty common and understandable one. The statement, "Flying machines are impossible" is not equivalent to "I don't know how to build a flying machine," but in the short term they are making the same prediction: no one is flying anywhere today.
Actually, and I don't know if you've thought of it this way, but in asking for the axioms of social justice theory, weren't you in effect asking for something close to the solution to the Friendly AI problem? No wonder your friend couldn't come up with a good answer on the spot!
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My point was that they probably did think they meant both things, because the distinction between "it's impossible" and "I don't know how" is not really clear in their mind. But that is not as alarming as it would be coming from someone who did know the difference, and insisted that they really did mean "impossible."
Okay, I'll bite. What are they?
Hmm, I agree, but I don't think that it adequately explains the entire picture. I think it might have been two different ideas coming from two different sources. I can imagine that my friend had absorbed "applying formalized reason to society is bad" from popular culture, whereas "I don't know what founding propositions of social justice are", and subsequently "there might not be able to be such things" (like you talked about), came from their own internal evaluations.
I kinda wanted to avoid this because social approval etc., also brevity, but okay:
I know it loses a lot of nuance this way (to what extent must you help others? well, so that it works out optimally for everyone; but what exactly is optimal? the sum of everyone's life/positive feelings/lack of negative feelings? that's left undefined), but it works for me, at least.