>>It seems more intuitive to say that whatever feels real is real, and the fundamental entities that aren't directly observed may as well be considered non-existent.
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>Then, how real is the dark side of the moon to you? You haven't ever seen it. Some people did, but you haven' seen them either - are they real?

You asked this question in a most excellent manner. Instead of saying "Is it real" you said "How real is it"

Let me tell you. The dark side of the moon is not observed by me, so its image is not in my conscious experience and thus not real.

However, the dark side of the moon still exerts a gravitational force on me. The mass of all the moon is present in my observations (though ridiculously small and subtle, it is still present), even the parts that aren't observed visually must still be real in that respect.

>How real is mathematics? It could be construed as our collective imaginative work, that we for some reason treat as proof, but is it real? Could be the real mathematics (or physics, for that matter) of the current universe is something completely different from our toy.

Mathematics is a human language like English or dBase. In that respsect it is very real.

>Since any proof of this (either way - proving or disproving) can be only constructed using what we _think_ is logical and sound, we can only conclude that there's no logical flaw in solipsism. Any further conclusion is the personal choice of one who concludes.

There is no logical flaw is solipsism. But my critique of objectivism has not much to do with logical flaws as practicality. Can it be used to solve problems? If no, then it isn't much use as a philosophy.

Another important question is are there other philosophies that are better at solving problems? If yes, then there is something more useful as a philosophy.

This has been my critique of objectivism. I think it accurately describes Rand's version of Utopia, but to solve problems I've adopted Critical Rationalism (the method of Popper, Descartes, ect.) over objectivism.

>>It is this realization that causes us to look a statement like "reality is an objective absolute, facts are facts" and say that this could be true if we agreed on the required assumptions and definitions. Thus in the process of making the statement true, we are really proving it false.
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>We aren't proving it either way. The meaning of it, as I take it, is that facts are facts, but we may interpret them, misread them, be unable to find them, evaluate them based on flawed theories, and generally get them wrong in all imaginable ways. The facts would remain the same - unless, of course, these are facts about ourselves, which can change - i.e. unperturbed by our meddling.

What then is a "fact"?

I've been assuming it is a statement in language. If it is something other than a statement of language then you may be right. But then what is fact?

>Therefore, I'm really tempted to find out how can this rigmarole be used to prove that capitalism is good - and prove that using just a couple of axioms and pure logic. Ummm... 45 proof logic, maybe?

There is one more premise that Rand assumes and it is that man shall not be sacraficed for another man. Lazze fair capitalism is best political-economic match for the premises.