Objectivism sees the virtuous man as one who follows reason at all costs. In this way, its main virtue is rationality, whose corollary is objectivity — adherence to reality through the rational recognition of facts. The rational man moves from the perceptual field of his moment-to-moment experiences to the conceptual field of abstract knowledge through the use of logic. The virtues show him in the form of principles the values he should pursue, and how to apply his rationality to the daily concrete choices he faces. Leonard Peikoff expounds the Objectivism’s main virtues in the same order they appear in John Galt’s speech in Atlas Shrugged; I follow a slightly different order which I consider a bit more logical.
To be rational is to adhere to reality (rationality) and to obtain your means of survival through your own thinking (independence). To think means also to act according to your convictions in a consistent manner (integrity) and to shape the world (productivity) and your own character (pride) according to your rational values. And you do so by never falsifying reality (honesty), nor your assessment of the character and conduct of men (justice).
Independence is “the acceptance of the responsibility to form one’s own judgments and to live by the work of one’s own mind.” It basically means orienting yourself to reality, not to other men. Others may, no doubt, offer you many values; they can not, however, become your means of survival or your basic frame of reference. You may like to receive the approval of others, but others can not be your source of self-esteem. You must estimate yourself by evaluating your own character, and only then appreciate (or not) the approval of only those whom you approve independently.
In fundamental terms, if you are independent you do not need others; you act among men in exactly the same way as you would away from them. In principle, you are as alone in society as on a desert island, a “self-sufficient ego.”
If you are independent you capture the distinction between the metaphysically given and the man-made. You understand that conformity with the metaphysically given is essential for successful action; the man-made can only be accepted if and when it reaches or flows from such conformity. Otherwise, you must oppose and fight the man-made in order to effect the changes you deem necessary.
Intellectual independence is thus the recognition of the fact that the mind is an attribute of the individual and that no one can think for another. If you are intellectually independent you process perceptual material by the use of your own rational faculty. In dealing with any question, wether of fact or value, end or means, philosophy or science, you follow the method of objectivity.
So you must accept the responsibility of implementing your conclusions in practice, that is, you must build your own path. You must be self-sufficient in the mental world and in the physical world. You must rely on your own creative power to survive. You count on the value of your work being recognized by rational men, not on receiving favors from any person or group. You are existentially independent, according to Objectivist ethics, if you support yourself in a rational field of enterprise, using your own intellect and creativity.
In short, you are independent if you live by the work of your own mind.