You are an Anarchist. You think that capitalism is evil, that the "market" is a subtle dictatorship, that wage labor is but hidden (or softened) slavery, that consumership is an illusion to manipulate minds, that the State is the institution of this system of exploitation. You want to promote human life, natural beauty, liberty, and things well and good. That's why you oppose all the above evil things. OK.
Now you face weird people who say they are anarchists, yet who promote those evil things you associate to the State you hate. How can that be? Are they hypocrites? Spies paid by big corporations to instill confusion? Are they crazy people incapable of coherent thinking? No, we're people just as sincere as you are; we also despise the current state of affairs and hate dictatorship, slavery and mind manipulation; and we're also motivated by our love of human life, natural beauty, liberty, and all things well and good. But we just have a different interpretation of what is evil.
How slight or how big is this difference? How much of it is a matter of a cultural gap in terminology and how much of it is actual irreconcilable ideas? Can we find a common pattern by which both of our groups may legitimately claim to be anarchist? Can we identify and circumscribe the root of our disagreements? Is it possible to find a peaceful way to resolve our disagreements, or will we have to kill each other before either or us may have his way? Well, if you'll allow me to argue my case, we can enter a sincere debate. And maybe we can find a resolution to settle our conflict in the anarchist way: through peaceful discussion.
Natural vs Imposed Authorities
Bakunin, in Dieu et l'Etat, makes a wonderful statement about what it means to be an anarchist.
He also introduces the notion of "Natural Authorities" (by lack of better word), as opposed to "Imposed Authorities".
Natural Authorities are people to whom we readily and voluntarily delegate decisions and actions because we think they are fit, after some rational examination. And of course we choose to delegate many things, for we can't be specialists in everything. The delegated activity may in Bakunin's words be shoemaking as well as architecture or science. It may be anything indeed.
Imposed authorities are people who claim to take the decision for you, whether you agree or not, and who use force to impose their decision should you not comply. Your examination, rational or not, is optional to them; though of course they may crook you more easily if they can somehow trick you into thinking they're here for your own good. The institution of these Imposed Authorities is called the State.
In free-marketeer terms, we would describe this phenomenon as division of labour, with some people specializing in the production of some services (taking the right decision about a specific issue is the prototypical service). A natural authority is a provider chosen by the consumer on a free market, whereas an imposed authority is a provider imposed by force (as usually instituted into the State).
To us, the question is not whether there "is a market" or not — as soon as there is potential interaction between humans, the resolution of these potentialities we call "market". The question is whether this market will be free or not. Whether each consumer may pick the providers of his choice, or whether they will be imposed upon him by force.
As you may see, the fundamental idea is exactly the same, and up to here, we are in perfect agreement. It's only the vocabulary that changes, though in ways that may seem bizarre to you. At least, up to this point, it's really the very same principle as Bakunin's anarchism. If there is disagreement, it comes much later on. So please accept that for the moment, we may be anarchists with just a different tradition as far as terminology goes.
The Word "Market"
When we Free-Marketeers speak about "market", we really mean "any way by which the interaction between people are resolved". That's what all libertarians and anarcho-capitalists mean by "market". We use the term in a very consistent way. We never silently imply any of the dreadful things that you may suspect us to imply, and that other people might indeed imply. In particular, we do not imply any such thing as a State to make laws, "regulate" the market, and enforce property; we don't imply money, banking, central banking, or any kind of intermediates; we don't imply companies, Stock Exchange, employers and employees. No. When we say "the market", we really mean "whichever way by which the interaction between people are resolved".
Of course, many people make a whole lot of assumptions about markets and what they include in that concept. Indeed, neo-classical economists, keynesians, marxists, often restrict "the market" to only things that are done exchanged against money; or only to things that are officially exchanged against money. To most politicians, agents of the State, employees of the IRS, economists in public administrations and fiscal accountants, this is indeed the one concept of "market" that matters: all the things on which taxes are collected. But once again, this is not the point of view taken by we free-marketeers.
Using our free-marketeer terminology, the notion that the market be replaced with "something else" is non-sensical. Whatever replaces "the market" becomes ipso facto "the market". The market exists by definition, unless there is no more social interaction. People who advocate to replace the market are just using the word with a completely different meaning from ours; as such, they are not in "disagreement" with us by stating such thing; they are just being oblivious to what we say. Some may be actually responding to one notion of "market" as advanced by proponents of the State. Some do that because they fail to understand there is a gap in terminology. Some may be oblivious to the very notion of gap in terminology, and think that words have a one sacred god-given and academy-enforced meaning that everyone knows about (or ought to know about before entering debate). Some may think that the debate is not worth it, or that it is foolish to ever try to meet the enemy on his grounds. But we are not enemies, and we are not trying to fool anyone, and if you should propose another term for the concept we're discussing, we'll gladly accept it.
But in the meantime, we Free-Marketeers will continue to use the term "Market" among us, with this well-understood traditional meaning, and we really don't imply anything else when we use it. And when we will speak of "Free Market", we really won't be meaning anything else but Bakunin's anarchist principle: each individual choosing which natural authorities to delegate activities to, and not being imposed authorities by anyone else.
"Free-Market" vs "Market"
Obviously, when conservative, socialists, or whomever accuse "the market" of some vice, of course, they make some presupposition about what "the market" is, and they really mean "the market as organized in such or such way". They don't usually propose the end of civilization and all human interactions (though I imagine a few rare proponents of human extinction might).
And certainly, when one speaks of "the market organized in such or such way", there is no reason why free-marketeers should approve of this particular way. We're not "marketeers" who approve of "the market", whatever it be — which would mean that anything goes, since the market always is. No, we're "free-marketeers", which means we approve of the market when it is free (when it follows Bakunin's anarchist principle above), and we disapprove of it when it isn't.
This whole matter of terminology is a frequent source of needless misunderstanding between free-marketeers and socialists. Needless, since someone like Benjamin Tucker could without contradiction say both that he was a socialist and a free-marketeer (and an anarchist, too, of course), having overcome the terminology barrier.
Please do not think that we suppose anything when we speak of "markets". And please do not think that when we speak of "free market" we're speaking of anything but the liberty of people to interact in voluntary ways, whereas coercive and deceptive interactions are recognized as illegitimate. — If we resolve this terminology problem, we can see that all free-marketeers are anarchists who ignore it, and all anarchists are free-marketeers who ignore it!
Studying the Market
Since we use the term "market" in a very general meaning, and see no implicit condition in it, we will always use a longer description than "the market" when we discuss a particular point of a particular instance of market. We may restrict our consideration of the market to the production exchange and consumption of a particular product or service; or we may implicitly talk about the current state of the market. But in any case, before we may emit judgments on "the market", we will have to examine its details, and not just what can be known from its definition as "anything that happens".
The science that studies what happens in the market is called Economics. Actually, since to us Free-Marketeers, "the market" is everything that humans do, we call this science "Praxeology", the science of Human Action.
Note how this is a point of view completely different from from the point of view of neo-classical, keynesians or marxist economists, who have a much narrower view of what they mean by market. Their view of Economics is filled with Statistics, with Econometrics, with equations, with exchange rates, stock quotes, and the whole lot of inhumane figures that scare people out of economics.
But our view of Economics is completely different; though we know how to use the tools of mathematics (that we use mostly to debunk the theories of Statist economists) what we insist upon are the interactions between individuals, based on their preferences, on the opportunities that are open to them, on the the conflicts that may arise, and on the principles of Law by which these conflicts are solved.
And indeed, Libertarianism, Classical Liberalism, Free-Marketism, Anarcho-Capitalism, or whatever you call it, is ultimately a theory of Law: we study the rules of human interactions. Typically, we search for elements of coercion in some rules of behaviour; we trace how the coercion that may be introduced in the human interactions make these interactions unfair, inefficient, evil, iniquitous, stupid, etc., and we conclude that coercion is illegitimate, and that those rules are valid that avoid coercion. In a way, Free-Marketeers are anarchist legists.
If there is any real disagreement between socialist anarchists and anarcho-capitalists, it must reside in the particular evaluation of what is or isn't coercion according to the anarchist principle: that all voluntary interactions are legitimate, and all coercive interactions are illegitimate.
That is why disagreements will come from different theories of human psychology (what is voluntary), epistemology (how do we know anything at all), metaphysics (what are basic concepts that we may rely upon).
As for difference in ethics (what goals are worth pursuing), they remain in the sphere of individual preference (or group preference, for collectivists), which are the things that people are free to choose about: this doesn't forcibly mean that all choices are equivalent — only that by definition imposing a different choice is coercion and goes against anarchist law. However, many anarchists who are not so strong about the basic anarchist principle, and see cases where it must be sacrificed on ethical grounds. So disagreements about ethics may sometimes be sources of opposition between anarchists, and it is sometimes necessary to resolve such issues.
Now, since indeed there are no a priori widely established common ground to discuss details about the principles of human interaction, or the key notions of metaphysics, epistemology, human psychology and ethics, it will often be necessary to dig deep into such matters so as to identify and possibly resolve disagreements. And that's a whole lot of things to discuss, that can leave place for a lot of disagreements — but not necessarily between Free-Marketeers and Socialist Anarchists more than inside each group or between random people.
References vs Arguments of Authority
Now, in discussing all these issues, we Free-Marketeers will invoke many past authors, such as Frederic Bastiat, Gustave de Molinari, Ludwig von Mises, Ayn Rand, Murray Rothbard, David Friedman, Anthony de Jasay, etc. We know that these authors are not well-known outside from Free-Marketeer circles — and we even have theories about why they aren't. And it's precisely because they are not well-known that we have to promote reading them, to begin with.
Are we being sectarian about some authors having a superior authority? Are we trying to make you waste your time rather than explain our case? No. We're just promoting authors we think make our point best. Is that good or bad? Well, please let me come back to Bakunin's notions of Natural Authorities vs Imposed Authorities.
There are authors that you read, and such that you decide, after rational examination, that they are right. You thus find an agreement a posteriori with these authors. Then among the authors you agree with, some make their points better, make less mistakes, are clearer, etc. So when you try to explain an idea you have, you find that these authors have best expressed the idea. Just like you cannot be specialists in everything, you cannot be specialists in explanation of all ideas — and even when you are, explaining well takes time, and time is expensive. So you delegate the expressing your ideas to those who you think do it best — and since you agree to them voluntarily, they are perfectly legitimate Natural Authorities.
Now, if you were saying to other people saying that they should agree with your favorite authors a priori — that would be trying to make them Imposed Authorities. That is the essence of the fallacious appeal to authority". But that's not necessarily what making a reference means.
Making a reference to your own Natural Authorities, just like giving the address of your favorite shoemaker, is but a tip — "here's the best I found, decide for yourself if you like it, but in as much as I could compare to other authors that I know, this one does the best job." So if there are some concepts you're currently discussing, and there lacks common convention as to what is being meant by the concept, or common knowledge as to how this concept relates to other concepts, then it is perfectly legitimate to point out an author you think explains these concepts better than you could explain yourself.
Of course when a reference is given, it is of no value if the other party doesn't read it (or asks one of her Natural Authority to read it for her) so she can decide whether to agree to it or not. And of course she may lack time to read (and her Natural Authority if any can be lazy or incompetent). But then, if she has no time to get enough in the depth of the debate, then indeed the debate is grossly limited, anyway. The reference isn't at fault: with the same limitations in time and efforts, your explaining things yourself instead of referring to someone who already explained them best would only slow down the discussion.
So a good reference is a way to quicken up the discussion, and if the two parties are really interested in exploring and possibly settling their divergences (instead of say fighting with baseball bats), then they will take time to read enough of the given referenced works so as to continue with the debate.
Notice that my referencing Bakunin is not an appeal to authority, either — you'll have to read it so that you know whether you, like me, agree with this particular point he makes.
But my citing an author I expect you to appreciate is also a sign that we (might) have common "Natural Authorities" and that communication is thus possible, starting from there.
One advantage of well-known authors who are natural authorities of many people is that you can share knowledge faster based on ideas and terminology you share with these people. To use a computer science analogy, it's really like reuse and sharing of software libraries: you can code as much without, but it takes more effort. Or to use a geographic analogy, it's easier to tell someone where you are if you can name mutually known places from which to give directions.
PS: See also Stigmergic Socialism by Brad Spangler.