One claim about Libertarians that won't withstand any real scrutiny — yet is very common amongst journalists and educators — is that Libertarians don't believe in doing anything to address the immediate needs of the poor. If asked to defend the claim, those who make it will either note Libertarian opposition to various state programmes, and with a crude induction draw the inference that Libertarians don't believe in doing anything to achieve the ostensible goals of those programmes, or they'll note the Libertarian objection in principle to any state programme with such goals, and treat this as QED.

Well, let's lay the form of that out:

L does not believe that X should be done by S,
therefore
L does not believe that X should be done.

Oooops! That isn't really very logical, is it? I mean that we can find plenty of X and S where this won't work, when we make ourselves L.

Libertarians don't believe that the state should do a lot of things, including farming, financial intermediation, and managing roads. Genuine anarchists go further, to claim that the state shouldn't do anything. That hardly means that they don't think that these things should be done by someone. It doesn't even mean that they won't agree that they should be those who do these things. (Indeed, people who rely upon the state are most likely to say that it ought to do whatever it does at the expense of someone else, as when they call for higher taxes on those who make more money.)

This point of logic ought to be obvious. Well, many journalists and educators are such damn'd fools that they truly don't see it, and an awful lot are knaves, who see it but don't want it to be seen by others.

One way that I see the eristicism effected is by the specious society-state equation — by treating the state as if it is society, which is to say as if it is us. Formally, this would be

L does not believe that X should be done by the state,
which is to say that
L does not believe that X should be done by society,
which is to say that
L does not believe that X should be done by any of us.

except that it's not explicitly expanded in this way, else the jig would be up. One place you'll see this eristic equation employed is in many quizzes that purport to tell the taker what his or her political classification is. If he or she answers affirmatively to a claim such as that society should help the poor then the typical quiz will score that towards state socialism and away from classical liberalism (of which Libertarianism is the extreme).

(Actually, one needs to be very careful whenever encountering the word society. In practice, it is often used to mean everyone else. Sometimes it's used to refer to some hypothetical entity which is somehow more than a group of people and their system of interaction; this latter notion tends to operationalize, again, as everyone else. Equating society with the state, and coupling this with demands for the state to make greater demands on other people is a popular way of making society mean everyone else.)

The fact is that one simply cannot tell, one way or another, from the datum that a person is a Libertarian whether he or she thinks that some goal ought to be pursued, unless the goal involves what a Libertarian would label coercion; because Libertarianism itself is no more than a belief that one ought not to initiate the class of behaviors to which they apply this label. A person can be a Libertarian and be all for voluntary redistribution, or that person might indeed be someone who embraced some of the more callous proclamations of Ayn Rand, or the Libertarian might hold some intermediate postion. Libertarianism itself is neutral.

(Within the Randian camp, there has been a willful confusion of the fact that Libertarianism itself has limited scope with the proposition that any given person who is a Libertarian must somehow have no view about matters not within that scope, or with the claim that a Libertarian must think that anything not prohibitable is good.)

Parallels can be found here with the claim that atheists do not believe in morality of any sort. Not only is the underlying fallacy very similar, but the implication in each case is that, should the persons in question believe that something ought to be done, they are more likely to see themselves as the someone who ought to do it.