Quoted:
A=A is ayn's way of saying that things must be exactly as her objectivist mind thinks they is. a very primitive view.
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Actually, I think she was speaking of the collective denial that goes on. A lot of people will talk about how great socialism is, and how bad capitalism is, and stand in denial of both the positive features of capitalism, and the negative results of socialism. They refuse to see that developed capitalist nations generally have a higher technology level than developed communist nations. They refuse to acknowledge that socialist policies run directly counter to the continued functioning of a healthy economy. They divorce direct cause (socialist policies) and effect (a crashing economy). Ad Infinitum.
Another application of 'A=A' is simply to name the goal of the enemy, something the enemy will not do. People who are trying to be subtle and nonoffensive about their advocation of socialism will appeal to you about your social responsibility, the brotherhood of man, etc. Their success - how effectively they can convince people that the society should be the focus - depends on how effective they are in convincing people they are NOT advocating socialism. In other words, A cannot be seen as A, if socialism is to be accepted.
If you weren't already aware of it, all the rhetoric of the Democrats is consistent with a disguised desire for full-up socialism.
Objectivism is not without its problems, but Ayn was extremely perceptive when it comes to the methods of the enemies of capitalism and free enterprise.