Deep disagreements in the group separated 'true (third way) neoliberals' around Rüstow and Lippmann on the one hand and old school liberals around Mises and Hayek on the other. The first group wanted a strong state to supervise, while the second insisted that the only legitimate role for the state was to abolish barriers to market entry. Rüstow wrote that Hayek and Mises were relics of the liberalism that caused the Great Depression. Mises denounced the other faction, complaining that Ordoliberalism really meant "ordo-interventionism".  :19–20
The liberal philosophical tradition has searched for validation and justification through several intellectual projects. The moral and political suppositions of liberalism have been based on traditions such as natural rights and utilitarian theory , although sometimes liberals even requested support from scientific and religious circles.  Through all these strands and traditions, scholars have identified the following major common facets of liberal thought: believing in equality and individual liberty , supporting private property and individual rights, supporting the idea of limited constitutional government, and recognising the importance of related values such as pluralism , toleration , autonomy, bodily integrity and consent .