I'm not really interested in left anarchist propaganda
I am not going to deny the existence of left-anarchist propaganda which exaggerates or makes mistakes. But I think that left-anarchism and right-anarchism both have some valid points which need more critical interpretation and qualification than they usually give. This is, however, more a problem of the people promoting the ideas online than the originators of these ideas. I would say that Carson is a serious scholar who has raised very interesting questions, although I disagree with him on practically every point of economic reasoning the ideas he and several Austrians have developed have, I think, raised our understanding of the present economic conditions. Everyone know that mercantalism/fascism is not the free market, but few pro-market scholars will examine just what the exact economic effects institutions of this nature have. If Carson were correct that abnormal concentration of economic control and the promotion of certain forms of economic organization which allow the state to effect abnormal power on people's lives this would be an important 'utilitarian' argument; indeed it seems a natural outgrowth of hard-core libertarian and Austrian claims that Corporatism sucks; why do we put so much emphasis on how the government rules screws over consumers and businessmen for power but ignore the way it screws people over as employees and limits their options. Indeed, work by Stromberg and others along the same lines indicate that this is perhaps the natural direction of private-property 'capitalism' under a State regime. It fascinates me in that, although complicity of some interests in business is obvious, the business community might actually be 'roped in' to this sort of organization even if they would prefer others and even if they personally and politically object to the measures which promote it.
If capitalism is the opposite of socialism, then it is the private ownership of the means of production
I agree with this, and I don't agree with Carson's views on land. But remember that 'private' simply means owned and disposed of by somebody in particular, libertarians promote a certain type of private property. Thus even the view of capitalism by your defintion is open to statist misinterpretation.
All of these elaborate explanations, when we have a perfectly good one,
As I expressed, I do not agree with Carson's economic theorems but find some of his ideas interesting - epsecially when further developed by Austrians. It is important to realise that Carson's theory of the firm in the present is very Austrian and thus fits with our 'perfectly good' explanation.
If you refer to what an anarchist society might be like, we have a lot of interesting and plausible ones but I think it is incumbent upon us to realise that we don't really know what a free market society would look like. But, from an economic standpoint, potential merits or flaws in our imaginary organizations have no bearing on the fact that the market does work, and it's really the only organization we can say objective 'works' in the sense of mutual gain. So while it is important to recognize holes or guesses within our 'Future-World' for intellectual clarity and precision I am not saying that 'an-caps' or others need to abandon their ideas of what society would be like, or what they'd like it to be like. Because the market works to solve these problems, even if - especially if - a handful of guys with immense amounts of knowledge and free time can still find things to argue over. All these things that depend on our subjective evaluation and preferences will get worked out by people's actual choices, and these will work as well as anything we can expect.
Anarcho-syndicalism in its classic formulation is not anarchistic in our sense. It is decentralized fascism. And though errors are present on the left, the more 'vulgar' the more common, dismissing such a broad grouping really doesn't seem justified considering that Proudhoun and Josiah Warren could easily consider themselves in the same tradition. Thus many individualist anarchists and right anarchists came at certain observations and conclusions through the development of what would be called 'leftist' ideas. Indeed, it is important never to forget that what is generally recognized as a culturally left radicalism did grow out of classical liberalism, just like egoism and 'natural' elitism. I prefer an argument with a good radical statist to an argument with a welfare statist, who doesn't even understand what he's for much less opposed to. Radicalism in intellect may be intellectually converted communists tend to have more in common with libertarians than with modern liberals.
Mises knew what capitalism was, and he used the term correctly.
I agree Mises was fairly justified in using 'capitalism' for the free market on several grounds, but I think it is historically and strategically problematic. Capital is important, yes, but capital doesn't control, make up or define the market economy. The market does. Taking on a term of approbation because others spite you with it is certainly something I appreciate. But Marx did confuse State-mercantalism with laissez-faire, or at least thought there was no difference. What he describes as 'capitalism' is not laissez-faire, and just as Marxist criticism certainly don't apply to the free market I can not see why we would call the free market 'capitalism' except that Rand and a handful of others tended to do so. I do think it is stupid that people get so hung up on labels without even exploring core ideas, but even ignoring this 'capitalism' is a misleading label.
He also knew that socialism was not only not viable, like fascism, it was a form of statism.
No disagreement here. But don't forget that socialists, past and present, aren't always statists. Some of them really do believe in a libertarian society of individual freedom and simply think it would take a different form. And, like all free-market transactions, a voluntary commune is productive and can make economic calculation just like a firm or individual agent.
Let's dot our Is and cross our Ts. This redefinition nonsense is bunk.
But you don't need to argue this fact with me. Almost everyone in favor of something they call 'capitalism' mean a free or more-free market. But because of the negative press of the word, mostly directed against mercantalism, why not simply stick with the word 'market' or 'free market'? I am not trying to waste time in semantics, I presume you do mean a laissez-faire economy and if anything I think Mises' defense of it wasn't thorough going enough. But the language we're using depends at least partially on the rest of the human race who sees the as 'capitalist' the present system and resents the very real defects. To tell him this isn't 'really' capitalism, and that the capitalism you envision will have none of this is simply confusing and implausible. Imagine if we called market defense agencies 'Government', but went around talking to anarchists telling them that our 'government' won't involve any of the problems of the old one. You run a serious risk of justified disinterest, just as I am unlikely to spend my time listening to people talk about 'communism'. They might very well mean 'individual liberty and freedom with social interaction predominated by voluntary pooling of assets'. This communist-corporation idea might be very fascinating and appealing to me, but I might never hear it because I hear 'communism' and my brain scoffs. Recognizing this reaction to 'capitalism' should at least give us pause before tossing the world around willy-nilly without qualification.
To Brainpolice: I agree with the views you presented, have probably duplicated some of them here. But, as I am sure you know, many who consider themselves right-anarchists or who behave as vulgar-libertarians are philosophically libertarian and simply have not been exposed to rational and libertarian critiques of their views as regards existing-business.