(Sorry if it comes across overly pedantic and twisted: non-native speaker, not enough sleep, words hard.)
There's no way to arrive "logically" at value judgements.
You can just use logic as a klutch to support your pre-determined positions (and, of course, which is totally rational as a practice, to spread, support and enforce them).
"Things are what they are. There is only one reality, namely the way things are."
That's only true for the least interesting things: objects and their arrangements in space-time.
On that, the huge majority (besides maybe crazy people) agrees anyway, when they see them, or when they're given evidence of them (e.g. a photo of a laptop on a desk. 99.999% of the people will agree there's a laptop on a desk there).
For anything else, politics, values, claims and the veracity of claims, morality, motives, aesthetics, goals, etc., there is no single way things are, there are ways people perceive them, and there are different interets, worldviews, and ways of interpreting them.
What is the "reality" or "non-reality" of "I'm willing to die for my country"? Or of "I find it OK to make money stealing"? Or "You should treat people well even if you are not forced to|?
Ayn Rand begins with axioms, and logically derives her position from there. (Well, maybe. I suspect that at least to some degree, she already had her position, and derived her axioms from there, then argued for her position from her axioms.) So I attack her position by saying that in her third axiom, she mis-defines consciousness, and the rest of her errors follow from her flawed starting position. That's rational. "It leaves me cold" is not a rational response. (It may be an indication that you feel there's something wrong with the position, even if you can't define it or prove it, and that's fine. But it's not a rational response.)