Independence

Independence is the virtue of accepting the responsibility of forming one's own judgments and of living by the work of one's own mind. Objectivism treats it as a cognitive virtue before a social one: the issue is not whether a person works alone, but whether his conclusions are reached by looking at reality or at other people.

“Independence is the recognition of the fact that yours is the responsibility of judgment and nothing can help you escape it.”
~ Ayn Rand, Atlas Shrugged

The first-hander and the second-hander

Rand's term for the alternative is second-handedness, developed at length in The Fountainhead. A second-hander does not hold false convictions so much as hold no convictions at all: his standard of truth is what others accept, and his standard of value is what others admire.

The argument that this cannot work is epistemological rather than moral:

Consciousness has no proxy. Perceiving, integrating and judging are performed by an individual mind or not at all. A person can learn from others, take testimony as evidence and defer to expertise, but the act of deciding that a source is credible is itself a first-handed judgment he cannot delegate.
"Everyone knows" is not a reason. A consensus is a set of people who each did or did not do the work. Treating agreement as evidence for a claim is arbitrary unless one can say what the agreement is based on.
The dependence is unstable. If A defers to B and B defers to A, nobody has looked. Rand's charge against second-handedness is that it is parasitic on the independent judgment of someone, somewhere, and generates none of its own.

The same structure applies materially. A man who lives by the production of others depends on their thinking as well as their goods; see Productiveness and Exploitation.

What independence does not mean

Not isolation. Trading, collaborating, teaching, being persuaded by a better argument and loving other people are all compatible with the virtue. See Trader Principle.
Not originality for its own sake. Reaching the same conclusion as everyone else, by one's own reasoning, is fully independent. Disagreeing in order to be different is second-handedness with the sign reversed.
Not the rejection of expertise. Accepting a physicist's account of a matter one cannot check personally is rational, provided one has grounds for treating physics as a discipline that checks itself. See Certainty and Context.
Not self-sufficiency. Nobody grows his own food or builds his own tools. The division of labour multiplies what an independent mind can accomplish; it does not substitute for one.

Common misunderstandings

That it means never asking for help. Asking is how a person gets information. What the virtue forbids is asking someone else to do the judging.
That caring what others think is a violation. The judgment of people one has reason to respect is evidence worth weighing. Making their approval the goal, rather than the truth, is what fails.
That it conflicts with love or friendship. Objectivism treats other people as among the highest values available to a person. What it excludes is deriving one's sense of self from them; see Self-esteem.
That it implies contempt for tradition. A practice that has survived may encode a great deal of accumulated knowledge. The virtue asks what that knowledge is, rather than accepting or rejecting the practice on the strength of its age.

Discussion

References

Rand, Ayn. "The Objectivist Ethics", The Virtue of Selfishness. New American Library, 1964.
Rand, Ayn. The Fountainhead — Roark's courtroom speech, on the creator and the second-hander.
Rand, Ayn. Atlas Shrugged — Galt's speech, on the responsibility of judgment.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 8.

External links

Independence at the Ayn Rand Lexicon