Rand Paul

[Tiberius]

FWIW I doubt that any of the Libertarians I am personally acquainted with would go for being labeled any kind of anarchist. They'd consider it an insult. Can't see why, myself. After all, it fits the definition of anarchy, doesn't it?

No, it really doesn't. The definition of anarchist (from Dictionary.com):

"a person who seeks to overturn by violence all constituted forms and institutions of society and government, with no purpose of establishing any other system of order in the place of that destroyed."

The definition of Libertarian (same source):

"a person who advocates liberty, especially with regard to thought or conduct."

No Libertarian wants to overturn all institutions in society / government and leave them without any kind of replacement. Libertarians require government to exist to enforce laws and protect liberty. Liberty being the "freedom from arbitrary or despotic government or control". Libertarians don't hate government; they hate excessive government.

But these guys consider anarchism to be radical left wing political philosophy, no better than my socialist leanings. Oh, well.

Strange, I know a load of anarchists who would make the same claim (that anarchism is a radical left-wing political philosophy). I see it differently; anarchism is the absence of a government, which logically must support multiple forms of economics (from communism to capitalism). An "anarchist society" would likely have factions that were communistic (i.e. everyone shares what they produce), and those that were capitalistic (i.e. everyone trades what they produce). Neither communism or capitalism requires government enforcement; both can be voluntary. Most forms of socialism on the other hand cannot possibly be anarchistic, since they require a state to own the means of production.

For me, the whole purpose of government is to take care of the citizenry, social welfare is it's primary purpose. If it can't manage that, what good is it?

Social welfare is but one way the government takes care of its citizens, notably, the ones that are worse off. However, there are more people than just the worse off in society which require protection. That is why governments must also manage the justice system (to punish citizens who harm others), the legislature (to enact laws that protect citizens), and the military (to protect citizens from foreign nations).