Final answer:
The statement implying that radically egalitarian societies do not preserve individual liberties is false. Egalitarian societies, as envisioned by Rawls, provide a balance of equal basic liberties for all while also allowing for certain regulated inequalities that benefit the least advantaged, suggesting a coexistence of equality and individual liberties rather than a contradiction.
Step-by-step explanation:
The statement 'All radically egalitarian societies are societies that do not preserve individual liberties' is not logically equivalent to the principles advanced by John Rawls. Rawls's theory supports a form of egalitarianism where basic liberties are evenly distributed but does not necessarily reject individual freedoms. According to Rawls’s liberty principle, everyone has an equal right to a comprehensive system of equal basic liberties, which is compatible with everyone else’s freedoms. Additionally, the “difference principle” allows for social and economic inequalities under the conditions that they are to the greatest benefit of the least advantaged and attached to positions available to all under fair equality of opportunity. These conditions reflect a balance between equality and preserving individual liberties rather than a dichotomy that excludes one for the sake of the other. Therefore, the original statement is false as egalitarian societies can and often do value and preserve individual liberties.