The basic tenet of anarchism is that hierarchical authority -- be it state, church, patriarchy or economic elite -- is not only unnecessary, but is inherently detrimental to the maximization of human potential. Anarchists generally believe that human beings are capable of managing their own affairs on the basis of creativity, cooperation, and mutual respect. It is believed that power is inherently corrupting, and that authorities are inevitably more concerned with self-perpetuation and increasing their own power than they are with doing what is best for their constituents.
Liz A. Highleyman, "An Introduction to Anarchism"
I am an Anarchist! Wherefore I will
Not rule, and also ruled I will not be!
John Henry Mackay, "Anarchy"
A common description of anarchism is that it has as its aim the abolition of the state. Now, while this is certainly correct -- it would indeed be hard to find an anarchist who is positively enamored of any government apparatus, be it located in Chicago, Washington, Moscow, or Baghdad -- it is not (to my mind) the best way of describing the anarchist goal.
Rather, anarchism should be understood as aiming at the abolition of all forms of domination. That is, anarchism is resolutely opposed to any relations between humans in which one decides for another, without the other's consent, how that other is to live and coerces that other into living that way. So anarchism is opposed not only to government, to the police and military and legislature and judiciary. It is also opposed to capitalism, in which a few possessing the means of production compel the rest, on pain of starvation, to produce for the profit of those few in return for a wage; and to racism of any form; and to any sort of oppression on the basis of one's sexuality. In place of all this, which is inherently reprehensible (and if you want a justification of this claim, try living in an explicit state of being dominated and see what you think of it!), anarchists seek to bring about a situation in which everybody determines for oneself as much as possible, as free and cooperative as can be devised, how one is to live one's life.
Ron Carrier, "Anarchism and Power"
[To illustrate anarchy] J. A. Andrews used the example of a group of friends going on a camping trip. They plan their trip, and each person brings useful skills and tools to share. They work together to set up tents, fish, cook, clean up, with no one in a position of authority over anyone else. The group organizes itself, chores are done, and everyone passes the time as they please, alone or in groups with others. People discuss their concerns and possible solutions are proposed. No one is bound to go along with the group, but choosing to spend time together implies a willingness to at least try to work out constructive solutions to the problems and frictions that will inevitably arise. If no resolution is possible, the dissenting individuals can form another grouping or leave without fear of persecution by the rest of the group.
Affinity Group of Evolutionary Anarchists, "Consent or Coercion"
Anarchism (from the Greek, contrary to authority), the name given to a principle or theory of life and conduct under which society is conceived without government -- harmony in such a society being obtained, not by submission to law, or by obedience to any authority, but by free agreements concluded between the various groups, territorial and professional, freely constituted for the sake of production and consumption, as also for the satisfaction of the infinite variety of needs and aspirations of a civilized being.
Peter Kropotkin, "Anarchism," The Encyclopaedia Britannica, 1910
In the evolution of political ideas, anarchism can be seen as an ultimate projection of both liberalism and socialism, and the differing strands of anarchist thought can be related to their emphasis on one or the other of these aims. Historically, anarchism was a radical answer to the question "What went wrong?" that followed the outcome of the French Revolution. Conservatives like Edmund Burke, liberals like Alexis de Tocqueville, had their own responses. Anarchist thinkers were unique on the political left in affirming that workers and peasants, grasping the chance to overturn the result of centuries of exploitation and tyranny, were betrayed by the seizure of centralised state power by a new class of politicians who had no hesitation in applying violence and terror, a secret police and a professional army to maintain themselves in power. The institution of the state was itself the enemy. They applied the same criticism to every revolution of the nineteenth and twentieth centuries.
Colin Ward, "Anarchism," in Paul A. B. Clarke and Andrew Linzey, Dictionary of Theology and Society
Note: For a longer definition of anarchism and a debunking of some common myths about it, read "Defining Anarchism" by Jason Justice.
One can debate the meaning of the term "socialism," but if it means anything, it means control of production by the workers themselves, not owners and managers who rule them and control all decisions, whether in capitalist enterprises or an absolutist state.
To refer to the Soviet Union as socialist is an interesting case of doctrinal doublespeak. The Bolshevik coup of October 1917 placed state power in the hands of Lenin and Trotsky, who moved quickly to dismantle the incipient socialist institutions that had grown up during the popular revolution of the preceding months -- the factory councils, the Soviets, in fact any organ of popular control -- and to convert the workforce into what they called a "labor army" under the command of the leader. In any meaningful sense of the term "socialism," the Bolsheviks moved at once to destroy its existing elements. No socialist deviation has been permitted since.
Noam Chomsky, "Socialism, Real and Fake," What Uncle Sam Really Wants
The world's two major propaganda systems did not agree on much, but they did agree on using the term socialism to refer to the immediate destruction of every element of socialism by the Bolsheviks. That's not too surprising. The Bolsheviks called their system socialist so as to exploit the moral prestige of socialism.
The West adopted the same usage for the opposite reason: to defame the feared libertarian* ideals by associating them with the Bolshevik dungeon, to undermine the popular belief that there really might be progress towards a more just society with democratic control over its basic institutions and concern for human needs and rights.
If socialism is the tyranny of Lenin and Stalin, then sane people will say: not for me. And if that's the only alternative to corporate state capitalism, then many will submit to its authoritarian structures as the only reasonable choice.
Noam Chomsky, "Socialism, Real and Fake," What Uncle Sam Really Wants
* Note: The word "libertarian" is used in two different ways throughout this Web site. Here Chomsky refers to an anti-capitalist and anti-authoritarian conception of freedom. In other quotes, some authors use the meaning most common in the U.S. -- "libertarian" meaning a mix of laissez faire capitalism and personal freedom. You should be able to tell from the context which meaning is being invoked.