In the final section of A Theory of Justice, John Rawls contrasts justification and proof. He says:

We can draw several conclusions from this passage. For Rawls, justification is not simply about understanding logical implications or inferences. A proposition may be a logical implication of some set of premises, but realizing this is not itself a form of justification. Justification is about giving oneself or others sufficient reasons to believe some proposition. Of course, often the best way to provide someone with sufficient reasons to believe some proposition is to show that it is a logical implication of some other beliefs we already accept, and this may be why Rawls says that, ideally, to justify a conception of justice to someone is to give him a proof. But there are other ways to provide someone with sufficient reasons for belief, for example, showing that a theory’s conclusions are “comprehensive and compelling.” Proofs are thus one way, but not the only way, to pursue justification.