Interpretation of "A is A" from Atlas Shrugged - For all Purists

Many of my friends have found the concept of "A is A", which was presented in "Atlas Shrugged" by Ayn Rand, to be hazy, while some have thought of it as an idiom which was used throughout the book to represent, or, in a sense, to symbolize/embody John Galt (the protagonist). To those, I want to clarify that "A is A" is not an idiom. The concept of "A is A" was put forth in Aristotle’s Law of Identity, where he held that everything that exists has a specific nature and a single identity. 'A' can only be 'A'; it cannot also be 'B' at the same time just because someones "believes" it to be so. This means that things exist: they are what they are regardless of the nature of the observer. Even if a person wants 'A' to be something else or believes that it should be something else, it will still be 'A'.

According to Ayn Rand "The work of a person’s consciousness is to perceive reality in its objective sense, to identify and recognize it as what it is, not to invent an alternate reality".