Per the actual definition "Socialism is a political, social, and economic philosophy encompassing a range of economic and social systems characterised by social ownership of the means of production. It includes the political theories and movements associated with such systems. Social ownership can be public, collective, cooperative, or of equity.[10] While no single definition encapsulates the many types of socialism, social ownership is the one common element. Socialisms vary based on the role of markets and planning in resource allocation, on the structure of management in organizations, and from below or from above approaches, with some socialists favouring a party, state, or technocratic-driven approach. Socialists disagree on whether government, particularly existing government, is the correct vehicle for change."

Which really puts all those programs, if one considers the Government "the people" into the realm of socialism. Social Security, The Military, The Education System, the Interstate System, Highway Systems at the state level are all socialist programs in the United States based on this definition. Capitalism and socialism, based on their definitions can co-exist and do in most countries that are considered one or the other.