If you believe that liberty is the paramount political good, then you probably will be some sort of libertarian; if you believe that socioeconomic equality is the highest political good, then you will not. But there is no way of proving that liberty or equality or some other abstraction should be paramount. These disputes are metaphysical, meaning that they are, by definition, beyond resolution through logic or through any process rooted in empirical evidence. Unless you are a professor paid to do so, engaging in metaphysical speculation is almost always fruitless. No valid process of reasoning can take us from the evidence of our senses to transcendent truth. Your conception of justice may be valid or it may be invalid, but there is no way to prove it in either case. We have spent ten thousand years devoted to such discussions, and we have made no progress.
That's an important hedge - engaging in metaphysical speculation is almost always fruitless. Because in the next sentence Williamson gives us an example not only of metaphysical speculation, but a full-fledged metaphysical dogma: "No valid process of reasoning can take us from the evidence of our senses to transcendent truth." I would be interested in the valid process of reasoning through which Williamson established this truth for himself. For it will of necessity involve many metaphysical ideas - for example, just what transcendent truth is, what the evidence of our senses is, and what the relationship between the two is, disputes about which, according to Williamson, are by definition beyond resolution through logic. So how did Williamson resolve it?
And as far as our conception of justice may go, Williamson may hold that there is no way to prove a conception of justice valid or invalid, but he certainly holds that there are ways to prove that reasoning about justice is valid or invalid. In fact, Williamson's implicit claim is that all reasoning about justice is invalid, if we mean by valid a chain of argument that should persuade the reasonable and open-minded person. But if we can make metaphysical claims about the nature of reasoning about justice, why can't we make metaphysical claims about justice directly?
Perhaps Williamson means to prove his case historically, as hinted at in his last sentence. But such a proof is circular, for those ten thousand years of discussion have made no progress only if all the reasoning in them has been invalid - and there are plenty of people who think there was some pretty sound reasoning about justice going on at least sometimes in those ten thousand years (see Aquinas, Thomas).
Speculative metaphysics is, unfortunately, unavoidable. The question is whether it will be done well or poorly, or openly or in hiding. Humean arguments like Williamson's are a big bluff (perhaps an unconscious bluff), claiming to eschew metaphysics while taking for granted profound metaphysical assumptions. These assumptions are often about the nature of human reason rather than nature directly, but they are no less metaphysical for that, for human reason is a part of nature. But we may be less likely to recognize them as metaphysical - which is why they often work as a bluff.