Justice as Fairness by J. Rawls (1971 and 2001) will be reconsidered in a formal way. We reformulate his theory in an axiomatic manner and revise his original position. We propose a new concept of fundamental rights as membership of the original position, and on this basis, we justify Rawls’s thesis of the priority of the first principle over the second. This would address the criticisms of Arrow (1973) and Hart (1973). This revision of the original position will enable us to deduce the two principles without reference to the primary goods or maximin principles. Therefore, the criticisms of Harsanyi (1975) and Sen (1980) do not apply to our theory. We do this by providing a rigorous definition of reflective equilibrium, which Rawls did not do, and we show that the two principles of justice are in reflective equilibrium but the libertarian principle of Nozick (1974) is not.