My point was that they probably did mean 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."

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.

Okay, I'll bite. What are they?

I kinda wanted to avoid this because social approval etc., also brevity, but okay:

1. Everybody is completely, equally, and infinitely entitled to life, positive feelings, and a lack of negative feelings.
2. One must forfeit gratification of axiom 1 to help others to achieve it. (This might be badly worded. What I mean is that you also have to consider the entitlement of others as well to etc etc etc in their actions, and while others are do not have the things in axiom 1, one should be helping them get them, not oneself.)

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.