I see no way to secure liberalism by trying to put its core values beyond any but internal or consensual reasoning. The resulting slide into relativism leaves a disastrous parallel between 'liberalism for the liberals!' and 'cannibalism for the cannibals!'

"Is Universalism Ethnocentric?", in C. Joppke and S. Lukes (eds.) Multicultural Questions (Oxford: OUP, 1999) p. 36. Quoted in Steven Lukes, "Liberalism for the liberals, cannibalism for the cannibals", Critical Review of International Social and Political Philosophy, vol. 4, no. 4 (2001) p. 35

The games we play become open-textured and our motives or real reasons for | making our moves can be distinguished from the intentions expressed in the act | of making them. But this leaves an ambiguity, if we, the actors, hoped to | emerge as persons whose identity is not defined by any or all of the games of | social life. Talk of motives or real reasons may signal only a deeper level of | intentions, as when a chess master who seems to be merely defending against a | threat is really setting a trap. Or where motives are external to the game of the | moment, they may still belong to another game. | Self-direction becomes the moral independence which goes with individuality in | Mill, especially if Kant’s connection is made between a free will and a will made | under moral laws.